Slide 1

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 2

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 3

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 4

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 5

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 6

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 7

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 8

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 9

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 10

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 11

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 12

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 13

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 14

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 15

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 16

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 17

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 18

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 19

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 20

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 21

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 22

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 23

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 24

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 25

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 26

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 27

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 28

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 29

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 30

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 31

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 32

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 33

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 34

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 35

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 36

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 37

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38


Slide 38

MBA & MBA – Banking and Finance
(Term-IV)
Course : Security Analysis and Portfolio
Management

Unit III: Asset Pricing Theories

Asset Pricing Theories:

•
•
•

Asset pricing theories describe how
assets should be priced in the capital
market. Following are the important
theories:
Capital Market Theory - CMT
Capital Asset Pricing Model - CAPM
Arbitrage Pricing Theory - APT
2

1) Capital Market Theory
• It is a major extension of the portfolio
theory of Markowitz. CMT tells us how
assets should be priced in the capital
markets if, indeed, everyone behaved in
the way portfolio theory suggests.
• It is based on the following 8 assumptions:

3

Assumptions:
1. Investors make decisions based solely upon risk
and return assessments which takes the form of
expected return and standard deviation measures.
2. The purchase or sale of a security can be
undertaken in infinitely divisible units.
3. Investors can short sell any amount of shares
without limit.
4. Purchases and sales by a single investor cannot
affect prices. This means that there is perfect
competition where investors in total determine
prices by their actions.
4

5. There are no transaction costs.
6. There is absence of personal income taxes. So
one is indifferent to the form in which the return is
received (dividends or capital gains)
7. The investor can borrow or lend any amount of
funds desired at an identical risk less rate.
8. Investors share identical expectations with regard
to the relevant decision period, the necessary
decision inputs, their form and size. Otherwise there
would be a family of efficient frontiers because of
differences in expectations.
5

RP

Expected
Return
B
RF

Risk

σP
6

Rp = XRM + (1-X)RF
Where:
Rp = expected return on portfolio
X = percentage of funds invested in risky portfolio
(1-X) = percentage of funds invested in risk less asset
RM = expected return on risky portfolio
RF = expected return on risk less asset

7

And:

σP = X σM
Where:
σP = expected standard deviation of the portfolio
X = percentage of funds invested in risky portfolio
σM = expected standard deviation on risky portfolio

8

• Let point B is the optimum portfolio for an
investor where RM = 0.10 and σP = .06. If he
placed one half of the available funds in the risk
less asset and one half in the risky portfolio B,
the combined risk-return measures for the mixed
portfolio , O, can be found using above
equations as :

9

RP= (1/2)(.10) + (1/2)(.05) = .075

σP = (1/2)(.06) + (1/2)(00) = .03

10

Situations:
• There can be three cases based on the percentage
of investment wealth or equity placed in the risky
portfolio:
• Case 1: X=1, investment wealth is totally committed
to the risky portfolio.
• Case 2: X<1, only a fraction of X is placed in the
risky portfolio and remainder is lent at the rate RF.
• Case3: X>1, Investor is borrowing rather than
lending.

11

Expected
Return

RP

Borrowing
Lending
M

Risk

σP
12

Lending is an investment in a risk less security
like T-bills or a savings account or a high grade
commercial paper.
Borrowing can be thought of as the use of
margin.
Borrowing and lending options transform the
efficient frontier into a straight line.
13

Point M now represents the optimal combination of risky
securities. The existence of this combination simplifies the
problem of portfolio selection. The investors need to only
decide how much to borrow or lend. No other combination
is as efficient as point M. The decision to purchase M is the
investment decision and the decision to buy some risk less
asset (lend) or to borrow is the financing decision. This
condition gives rise to the separation theorem which
implies that all investors, conservative or aggressive should
hold the same mix of stocks from the efficient set. In other
words all types of investors should hold identically risky
portfolios. Desired risk levels are achieved through
combining portfolio M with borrowing and lending.
14

If all investors hold the same risky portfolio, then in
equilibrium it must be the market portfolio. The
market portfolio is a portfolio comprised of all risky
assets. Each asset will be held in the proportion
that the market value of the asset represents to the
total market value of all risky assets.

15

Capital Market Line:
• The line formed by the action of all investors
mixing the market portfolio with the risk free
asset is known as the capital market line.
• All efficient portfolios of all investors would lie
along this CML.

16

 Rm  R f
Re  R f  
 m


 e


Where
Re= expected return on efficient portfolio
The subscript ‘e’ denotes an efficient portfolio
The above equation can also be written as:
(Expected return) = (price of time)
+ (Price of risk) (amount of risk)

17

2) Capital Asset Pricing Model
( CAPM)
• Portfolio theory implied that each investor faced
an efficient frontier. But differences in
expectations leads to different frontiers for
different investors.
• CAPM provides a framework for assessing
whether a security is overpriced, under priced or
correctly priced.

18

Security Market Line :
• For well diversified portfolios, non systematic
risk tends to go to zero, and the only relevant
risk is systematic risk measured by beta. So
a straight line that shows investors risk and
return in terms of expected return and beta is
called the SML. Thus SML provides the
relationship between the expected return and
beta of a security or portfolio.
19

Expected
Return
RM

SML

M

RF

1.0
Beta
20

Equation of SML is:
Ri = RF + (RM –RF)βi
where:
Ri = expected return on ith security.
RF = return on risk free asset
βi = beta of ith security
21

CAPM:
It was developed in mid 1960’s. It is referred to as
Sharpe, lintner and Mossin (SLM) capital asset
pricing model.
• The relationship between risk and return established
by the SML is known as the CAPITAL ASSET
PRICING MODEL. It is basically a simple linear
relationship. The higher the value of beta, higher
would be the risk of the security and therefore larger
would be the return expected by the investors. In
other words all securities are expected to yield return
commensurate with the riskiness as measured by
beta. This relationship is valid not only for individual
securities, but is also valid for all portfolios whether
22
efficient or inefficient.

SML & CML
• It is necessary to contrast SML and CML. Both
postulate a linear ( straight) line relationship
between risk and return. In CML the risk is
defined as total risk and is measured by
standard deviation, while in SML the risk is
defined as systematic risk and is measured by
beta. CML is valid only for efficient portfolios
while SML is valid for all portfolios and all
individual securities as well. CML is the basis of
the Capital market theory while SML is the basis
of the Capital asset pricing model.
23

Pricing of securities with CAPM:
• The CAPM can also be used for
evaluating the pricing of securities. The
expected return on security can be
calculated using the CAPM formula. This
return can be designated as the theoretical
return. The real rate of return estimated to
be realized from investing in a security can
be calculated by the following formula:
24

Ri 

 P1  P0   D1
P0

where:

Ri = Estimated return
P0 = current market price
P1 = estimated market price after one year
D1 = anticipated dividend for the year

25

Rp

Expected
return

T
S
R

C

B

A
U

SML

W
V

Beta
26

R, S and T lie above the SML and U, V and
W lie below the SML. The stocks above the
SML yield higher returns for the same level
of risk. They are thus under priced
compared to their beta value while the
stocks that lie below the SML are overpriced
as the return that they provide is not
commensurate to their beta value.

27

Problems
Q.1) Assume the assets below are correctly
priced according to the SML. Derive the
SML. What is the expected return on an
asset with a beta of 2?
R1 = 6%
R2 = 12%

B1 = 0.5
B2 = 1.5
28

Q 2) Assume the SML is given as:
Ri = 0.04 + 0.08B and the estimated betas
on two stocks are Bx = 0.5 and By = 2. What
must the expected return on each of the two
securities be in order for one to feel that they
are a good purchase?

29

Q.3) Calculate the expected return on the following
stocks if Rf = .05 and Rm = .11
Stock

beta

1

-.80

2

.03

3

.44

4

.76

5

1.10

6

1.75
30

3) Arbitrage Pricing Theory (APT)
• The theory was developed by: Stephen
Ross as an alternative to CAPM in 1976.

• The CAPM asserts that only a single
number- a security’s beta against the
market- is required to measure risk. At the
core of APT is the recognition that several
systematic factors affect security returns.
31

The APT asserts that asset prices are
determined through an arbitrage
relationship. It is based on the premise that
two or more securities or portfolios that
provide the same payoffs to their investors
are same and must therefore sell at the
same price. This is the ‘Law of One Price’.
The fundamental logic of APT is that
investors indulge in arbitrage whenever they
find differences in the returns of assets with
similar risk characteristics.
32

In other words if there are two securities that have
the same risk but different expected returns ,
investors will arbitrage, or eliminate, these
differences by buying the security with the higher
expected return (lower Price) and selling the one
with lower expected return (higher price). This
process of buying and selling the two securities by
investor will cause the price of the security of the
higher expected return to rise relatively to the one
with the lower expected return. This trading activity
will continue until the two securities have the same
expected returns.
33

Ross began with the idea that returns vary
from expected levels because of :
i) changes in the expected level of industrial
production.
ii) unanticipated inflation.
iii) unanticipated movement in the shape of
term structure of interest rates.
iv) unanticipated shifts in risk premiums
because of other economic forces.
34

Assumptions of APT
• Investors have homogeneous expectations
and are expected-utility-of-wealth
maximizers.
• There are no imperfections or frictions in
the market to impede investor buying and
selling. Specifically, there are no transaction
costs involved in security transactions. This
assumption makes possible the arbitraging
of mispriced securities thus forcing an
equilibrium price.
35

• One important assumption of this model of
equilibrium concerns the process of return
generation on securities. The APT model
assumes that various factors give rise to
returns on securities and that the relation
between security returns and that these
factors is linear.
•Return Generating Process
The APT assumes that the return on any
stock is linearly related to a set of factors also
referred to as systematic factors or risk factors
as given in the following equation:
36

R i  a i  bi1 I 1  bi 2 I 2  ......  bij I j  e i
Where:
Ri = return on stock i
ai = expected return on stock i if all factors
have a value of zero.
Ij = value of jth factor which influences the
return on stock i (j = 1,…..j)
bij = sensitivity of stock i’s return to jth factor.
ei = random error term which has a mean of
zero and variance of σ2ei

37

• The last assumption is about the error term
of above equation. The error term is
expected to have a mean value of zero that is
E(e) = 0.

38