Transcript CHAPTER 5 Risk and Rates of Return

CHAPTER 5
Risk and Rates of Return

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
Stand-alone risk
Portfolio risk
Risk & return: CAPM / SML
5-1
Return & Risk
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Return is the annual income received plus any
change in market price of an asset or
investment.
Risk is the variability of actual return from the
expected return associated with a given asset.
5-2
Rate of Return

The rate of return on an investment for a
period (which is usually a period of one
year) is defined as follows,
Annual Income + (Ending price – Beginning price)
Beginning price
5-3
Rate of Return
Price at the beginning of the year = Tk. 60.00
Dividend paid toward the end to the year = Tk.
2.40
Price at the end of the year = Tk. 66.00
2.40 + (66.00 – 60.00)
60.00
= 0.14 or 14%.
5-4
Rate of Return
Current Yield & Capital gains/Losses
Current Yield
Capital gains/Losses Yield
5-5
Current Yield & Capital gains/Losses
Annual Income
Beginning Price
(Current Yield)
Ending – Beginning Price
+
Beginning Price
(Capital Gain/Losses)
5-6
Current Yield & Capital gains/Losses
2.40
(66.00 – 60.00)
+
60.00
=
4%
Current Yield
60.00
+
10%
Capital gains/Losses
5-7
Current Yield & Capital gains/Losses
If the price of a share on April 1 is TK. 25, the
annual dividend received at the end of the
year is TK. 1 and the year end price on
March 31 is TK 30.
Find the Rate of Return
Find the Current Yield
Find the Capital gains/Losses Yield.
5-8
1 + (30.00 – 25.00)
Rate of return
=
25.00
= 0.24 or 24%.
Current & Capital gain/Losses
1
(30.00 – 25.00)
+
25
=
4%
Current Yield
25.00
+
20%
Capital gains/Losses
5-9
What is investment risk?

Two types of investment risk
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Stand-alone risk
Portfolio risk
Investment risk is related to the probability
of earning a low or negative actual return.
The greater the chance of lower than
expected or negative returns, the riskier the
investment.
5-10
Measurement of Risk: Single Asset

The risk associated with single asset is
assessed from both,
Behavioral point of view
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Sensitivity Analysis
Probability Distribution
Statistical point of view
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
Standard Deviation
Coefficient of Variation
5-11
Measurement of Risk: Single Asset
Behavioral Point of View
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This approach is to estimate the worst (pessimistic),
the expected (most likely) and the best (optimistic)
return associated with the asset.
The level of outcome may be related to the
economic conditions namely, recession, growth and
Boom.
The difference between pessimistic and optimistic
outcome is the RANGE which is the measurement
of RISK.
The greater the RANGE, the more RISKY the Asset.
5-12
Sensitivity Analysis
Particular
Initial Outlay
Annual Return (%)

Pessimistic

Most Likely

Optimistic
Asset X
Asset Y
50
50
14
16
18
8
16
24
RANGE =
4
(optimistic – Pessimistic)
16
5-13
Measurement of Risk: Single Asset
Behavioral Point of View
Probability Distribution


The probability of an event represent the %
chance of its occurrence.
Probability Distribution is model that relates
probabilities to the associated outcome.
5-14
Probability Distribution : Asset X
Possible
Outcome
(1)
Pessimistic
Most Likely
Optimistic
Probability
(2)
Returns
(3)
Expected
Returns
(2)X(3)=4
0.20
0.60
0.20
1.00
14
16
18
2.8
9.6
3.6
16.00
5-15
Probability Distribution : Asset Y
Possible
Outcome
(1)
Pessimistic
Most Likely
Optimistic
Probability
(2)
Returns
(3)
Expected
Returns
(2)X(3)=4
0.20
0.60
0.20
1.00
8
16
24
1.6
9.6
4.8
16.00
5-16
Measurement of Risk: Single Asset
Statistical Point of View
Standard Deviation
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Risk refers to the dispersion of returns
around an expected value.
The most common statistical measure of risk
of an asset is the standard deviation from the
mean/expected value of return.
2
 = (R-R) X pr
5-17
Standard Deviation
Asset X
i
R
R
1
14
%
2
3
R-R
2
(R – R)
Pr
16% -2%
4%
.20 .80
16
%
16% 0%
0%
.60 0
18
%
16% 2%
4%
.20 .80
1.6
2
(R – R) x Pr
5-18
Standard Deviation
2
 = (R-R) X pr
= 1.6
= 1.26%
5-19
Standard Deviation
Asset Y
i
R
R
1
8%
2
3
R-R
2
(R – R)
Pr
16% -8%
64%
.20 12.80
16
%
16% 0%
0%
.60 0
24
%
16% 8%
64%
.20 12.80
25.6
2
(R – R) x Pr
5-20
Standard Deviation
2
 = (R-R) X pr
= 25.6
= 5.06%
The greater the Standard Deviation of
Returns, the greater the risk.
5-21
Measurement of Risk: Single Asset
Statistical Point of View
Coefficient of Variation
it is the measure of relative dispersion used
in comparing the risk of assets with differing
expected returns.

CV =
R
5-22
Measurement of Risk: Single Asset
Statistical Point of View
Coefficient of Variation
The coefficient of variation of assets X & Y
are respectively,
Asset X = ( 1.26% / 16%) = 0.079
Asset Y = (5.06 / 16% ) = 0.316
The larger the CV, the larger the relative risk
of the asset.
5-23
Risk & Return of PORTFOLIO
Portfolio means a combination of two or more Assets.
Each portfolio has risk return characteristics of its
own.
Portfolio theory developed by Harry Markowitz,
shows that portfolio risk, unlike portfolio return, is
more than simple aggregation of the risks of
individual assets. This depends on the interplay
between the returns on assets comprising the
portfolio.
5-24
Portfolio Expected return
E (rp) = wi E(ri)
E (rp) = Expected return from portfolio
Wi = Proportion invested in asset i
E(ri) = Expected return for asset i
n = number of assets in portfolio
5-25
Portfolio Expected return
The expected return on two assets L and H
are 12% & 16% respectively. If the
corresponding weights are 0.65 & 0.35.
Calculate Portfolio Expected return
E (rp) = wi E(ri)
= [0.65 x 0.12 + 0.35 x 0.16]
= 0.134
= 13.4%.
5-26
Portfolio Risk:Two Asset portfolio
2p = w2121 + w2222 + 2 w1 w2 (12)
Alternatively,
2p = (w11)2 + (w22 )2 + 2 w1 w2 (P 12 1  2)
W1 = fraction of total portfolio invested in Asset 1
W2 = fraction of total portfolio invested in Asset 2
21 = Variance of asset 1
1 = Standard deviation of Asset 1
22 = Variance of asset 2
2 = Standard deviation of Asset 2
12 = Covariance between returns of two assets (P 12 1  2)
P 12 = Coefficient of correlation between the returns of two
asset.
5-27
Portfolio Risk:Two Asset portfolio
The expected return on two assets L and H
are 12% & 16% respectively. The standard
deviations of assets L & H are 16% and 20%
respectively. If the coefficient of correlation
between their returns is 0.6 and the two
assets are combined in the ratio of 3:1.
(1) Calculate expected rate of return
(2) variance of Portfolio
(3) Standard Deviation
5-28
Portfolio Expected return
E (rp) = wL E(rL) + wH E(rH)
= (0.75 x 0.12) + (0.25 x 0.16)
= 9%+4%
= 13%.
5-29
The Variance of the Portfolio
[2] 2p = (w11)2 + (w22 )2 + 2 w1 w2 (P 12 1  2)
= (0.75 x 16)2 + (0.25 x 20) 2 + 2 (0.75) (0.25) [(0.06) (16 x 20)
= 144 + 25+ (0.375)(192)
= 144 + 25+72
= 241
[3] p = 241
= 15.52
5-30
Portfolio Risk
The above discussion shows that the
portfolio risk depends on 3 factors
[1] Variance or Standard deviation of each
asset in portfolio.
[2] Relative importance or weight of each
asset in the portfolio
[3] Interplay between returns on two assets
Among these only weights can be controlled
by the portfolio managers. Therefore his/her
primary task is to decide the proportion of
each security in the portfolio.
5-31
Investor attitude towards risk
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Risk aversion – assumes investors
dislike risk and require higher rates
of return to encourage them to hold
riskier securities.
Risk premium – the difference
between the return on a risky asset
and less risky asset, which serves as
compensation for investors to hold
riskier securities.
5-32
Breaking down sources of risk
Stand-alone risk = Market risk + Firm-specific risk
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Market risk – portion of a security’s stand-alone
risk that cannot be eliminated through
diversification. Measured by beta.
Firm-specific risk – portion of a security’s
stand-alone risk that can be eliminated through
proper diversification.
5-33
Capital Asset Pricing Model
(CAPM)
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Model based upon concept that a stock’s
required rate of return is equal to the riskfree rate of return plus a risk premium that
reflects the riskiness of the stock after
diversification.
It is the logical & major extension of the
portfolio theory of Markowitz by william
Sharpe (1964), John Linter ( 1965) & Jan
Mossin (1967).
5-34
Capital Asset Pricing Model
(CAPM)
CAPM is a theory that explains how asset
prices are formed in the market place.
CAPM provides the framework for
determining the equilibrium expected return
for risky return. It uses the results of capital
market theory to derive the relationship
between expected return and systematic risk
of individual assets/securities and portfolio.
5-35
Capital Asset Pricing Model
(CAPM)
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The CAPM has implication for
Risk-Return relationship for an efficient
Portfolio
Risk-Return relationship for an individual asset
Identification of over valued or under valued
assets traded in in the market
Pricing of assets not yet traded in the market
Effect of leverage on cost of equity.
5-36
Capital Asset Pricing Model
(CAPM)
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Capital budgeting decision & cost of capital
Risk of the firm through diversification of the
project portfolio.
5-37
Capital Asset Pricing Model
(CAPM) : Assumption
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All investors are price takers. There number
is so large that no single investor can affect
prices
Assets/securities are perfectly divisible
All investors plan for one identical holding
period
Investors can lend or borrow at an identical
risk-free rate.
There is no transaction costs & income Tax
5-38
Capital Asset Pricing Model
(CAPM)
The elements of the model:
K = K RF + (KM - K RF) β
Where,
K RF = Risk Free Return
KM = required rate of return of market
β = Beta (systematic risk of the asset)
5-39
Beta
It measure the risk of an individual asset relative to
the market portfolio. Beta shows how the price of
securities responds to market force. In practice, the
more responsive the price of security is to changes
in the market, the higher will be its beta. The beta
for the overall market is equal to 1.00 Beta can be
positive or negative. Investors will find beta helpful
in assessing systematic risk and understanding the
impact the market movement can have on the
return expected from a share or stocks.
5-40
Calculating betas
The ABC Company is considering a new capital
investment proposal. The project’s risk structure is
very similar to that of the company’s existing
business. Return for this company’s stocks for the
past ten years are given in the following table
together with returns for a country’s stock market
index. The Govt. Treasury Bill return (Risk Free
Return) was around 5.6% per annum.
5-41
Calculating betas
Year
Company’s Stock
Return
Stock Market Index
Return
1992
0.09
0.07
1993
0.10
0.09
1994
0.10
0.10
1995
0.11
0.12
1996
0.10
0.11
1997
0.11
0.10
1998
0.11
0.10
1999
0.10
0.09
2000
0.09
0.08
2001
0.07
0.07
5-42
Calculating betas
Required
Calculate the
[1] Beta
[2] Required Return according to CAPM
model
5-43
5-44
Comments on beta
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If beta = 1.0, the security is just as risky as
the average stock.
If beta > 1.0, the security is riskier than
average.
If beta < 1.0, the security is less risky than
average.
Most stocks have betas in the range of 0.5 to
1.5.
5-45
Problem:
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Assume a security with beta of 1.2 being
considered at a time when the risk free rate
is 4% and the market return is expected to
be 12%. Substitute those data by using
CAPM equation.
Calculate Expected Return according to CAPM
model
5-46
Problem:
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There are three assets- X, Y & Z with
beta value of 0.5, 1.0 & 1.5
respectively. The risk free rate is
assumed to be 5% and the market
return is expected to be 15%.
calculate the expected return
5-47
Illustrating the calculation of beta
_
ki
20
.
15
.
10
Year
1
2
3
kM
15%
-5
12
ki
18%
-10
16
5
-5
.
0
-5
-10
5
10
15
_
20
kM
Regression line:
^
k = -2.59 + 1.44 ^
k
i
M
5-48
The Security Market Line (SML):
Calculating required rates of return
SML: ki = kRF + (kM – kRF) βi
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Assume kRF = 8% and kM = 15%.
The market (or equity) risk premium is
RPM = kM – kRF = 15% – 8% = 7%.
5-49
Illustrating the
Security Market Line
SML: ki = 8% + (15% – 8%) βi
ki (%)
SML
.
..
HT
kM = 15
kRF = 8
-1
.
Coll.
. T-bills
0
USR
1
2
Risk, βi
5-50
Factors that change the SML

What if investors raise inflation expectations
by 3%, what would happen to the SML?
ki (%)
D I = 3%
SML2
SML1
18
15
11
8
Risk, βi
0
0.5
1.0
1.5
5-51
Factors that change the SML

What if investors’ risk aversion increased,
causing the market risk premium to increase
by 3%, what would happen to the SML?
ki (%)
D RPM = 3%
SML2
SML1
18
15
11
8
Risk, βi
0
0.5
1.0
1.5
5-52
Verifying the CAPM empirically
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The CAPM has not been verified
completely.
Statistical tests have problems that
make verification almost impossible.
Some argue that there are additional
risk factors, other than the market risk
premium, that must be considered.
5-53
More thoughts on the CAPM

Investors seem to be concerned with both
market risk and total risk. Therefore, the
SML may not produce a correct estimate of ki.
ki = kRF + (kM – kRF) βi + ???

CAPM/SML concepts are based upon
expectations, but betas are calculated using
historical data. A company’s historical data
may not reflect investors’ expectations about
future riskiness.
5-54