Transcript Document

Corporate Finance
Lecture 3
Risk and Return
Selcuk Caner
Bilkent University
7/7/2015
1
Chapter 6 Outline
Risk return relationship
 Stand-alone risk
 Portfolio risk
 Risk & return: CAPM/SML

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What is investment risk?
Investment risk is the probability
of actually earning a low or
negative return.
The greater the chance of low or
negative returns, the riskier the
investment.
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Probability Distribution of Returns
Firm X
Firm Y
-70
0
15
100
Rate of
return (%)
Expected Rate of Return
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Annual Total Returns,1926-1998
Average
Return
Small-company
stocks
17.4%
Standard
Deviation
Distribution
33.8%
0
Large-company
stocks
13.2
20.3
0
Long-term
corporate bonds 6.1
17.4%
13.2%
8.6
0 6.1%
Long-term
government
5.7
9.2
0 5.7%
Intermediate-term
government
5.5
5.7
0 5.5%
U.S. Treasury
bills
3.8
3.2
0 3.8%
Inflation
3.2
4.5
0 3.2%
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Daily Rates of Returns of the Istanbul Stock
Exchange Index 1990-2001 (Mean Annualized
Return 62.85%)
600
Series: ISE
Sample 1 3075
Observations 3075
500
400
300
200
100
0
-0.20 -0.15 -0.10 -0.05 0.00
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0.05
0.10
Mean
Median
Maximum
Minimum
Std. Dev.
Skewness
Kurtosis
0.001937
0.000000
0.177736
-0.199785
0.032131
-0.085282
6.057701
Jarque-Bera
Probability
1201.637
0.000000
0.15
6
Daily Rates of Returns of the Bank Index
1000
1990-2001 (Mean Annualized Return 63.59%)
Series : BANKINDEX
Sample 1 3075
Obs erv ations 3075
800
Mean
Median
Max imum
Minimum
Std. Dev .
Sk ewnes s
Kurtos is
600
400
0.001955
0.000000
0.174317
-0.325123
0.035720
-0.178774
7.656613
200
J arque-Bera 2794.648
Probability 0.000000
0
-0.3
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-0.2
-0.1
0.0
0.1
7
Daily Rates of Returns of Akbank 1990-2001
1200
Series : AKBANK
Sample 1 2775
Obs erv ations 2775
1000
800
Mean
Median
Max imum
Minimum
Std. Dev .
Sk ewnes s
Kurtos is
600
400
200
0.001947
0.000000
0.287033
-0.226315
0.043825
0.273380
5.691547
J arque-Bera 872.2024
Probability 0.000000
0
-0.2
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-0.1
0.0
0.1
0.2
0.3
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Investment Alternatives
(Given in problem 6-19)
Economy Prob. T-Bill
Recession 0.1
Below avg. 0.2
Average
0.4
Above avg. 0.2
Boom
0.1
1.0
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High
Tech
Collec
tions
US
Rubber
8.0% -22.0% 28.0% 10.0%
8.0
-2.0 14.7 -10.0
8.0 20.0
0.0
7.0
8.0 35.0 -10.0 45.0
8.0 50.0 -20.0 30.0
Market
Port.
-13.0%
1.0
15.0
29.0
43.0
9
Why is the T-bill return
independent of the economy?
Return the promised 8%
regardless of the economy.
This is the coupon rate of
the bond.
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Do T-bills promise a completely
risk-free return?
No, T-bills are still exposed to the
risk of inflation.
However, not much unexpected
inflation is likely to occur over a
relatively short period.
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Do the returns of HT and Coll. move
with or counter to the economy?
HT: Moves with the economy, and
has a positive correlation. This is
typical.
 Coll: Is countercyclical of the
economy, and has a negative
correlation. This is unusual.

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Calculate the expected rate of
return on each alternative:
^
k = expected rate of return.
kˆ =
k P.
n
i i
i =1
^
kHT = (-22%)0.1 + (-2%)0.20
+ (20%)0.40 + (35%)0.20
+ (50%)0.1 = 17.4%.
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^
k
HT
17.4%
Market
15.0
USR
13.8
T-bill
8.0
Coll.
1.7
HT appears to be the best, but is it
really?
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What’s the standard deviation
of returns for each alternative?
 = Standard deviation.
=
=
Variance =  2
n
ˆ) 2 P .
(
k

k
 i
i
i 1
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 
n

2
ˆ
( k i  k ) Pi .
i1
 T-bills
 (8.0 – 8.0)20.1 + (8.0 – 8.0)20.2  1/2


=  + (8.0 – 8.0)20.4 + (8.0 – 8.0)20.2 


2
 + (8.0 – 8.0) 0.1

T-bills = 0.0%.
HT = 20.0%.
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Coll = 13.4%.
USR = 18.8%.
M = 15.3%.
16
Prob.
T-bill
USR
HT
0
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13.8
17.4
Rate of Return (%)
17
Standard deviation (i) measures
total, or stand-alone, risk.
 The larger the i , the lower the
probability that actual returns will
be close to the expected return.

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Expected Returns vs. Risk
Security
HT
Market
USR
T-bills
Coll.
Expected
return
17.4%
15.0
13.8*
8.0
1.7*
Risk, 
20.0%
15.3
18.8*
0.0
13.4*
*Seems misplaced, why?
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Risk return relationship of the above securities
return-risk relationship
20
15
10
5
0
-5
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0
5
10
risk
15
20
25
20
Figure 1 - Means and Standard Deviations of National Market Returns.
5
Turkey
4
Me an (%)
3
Hungary
2
Malaysia
1
U.S.A
World
0
0
5
Mexico Brazil
Philippines
Singapore
TaiwanArgentina
Korea
Chili
Hong Kong
Czech Republic10
Japan
Russia
15
Indonesia
20
25
Poland
-1
Thailand
Standard Deviation (%)
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B
A
0
A = B , but A is riskier because larger
probability of losses.

= CVA > CVB.
^
k
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Portfolio Risk and Return
Assume a two-stock portfolio with
$50,000 in HT and $50,000 in
Collections.
^
Calculate kp and p.
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Portfolio Return, kp
^
^
kp is a weighted average:
n
^ = S w^
k
p
iki.
i=1
^
kp = 0.5(17.4%) + 0.5(1.7%) = 9.6%.
^
kp is between ^kHT and ^kCOLL.
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Alternative Method
Economy
Prob.
Recession
0.10
Below avg. 0.20
Average
0.40
Above avg. 0.20
Boom
0.10
Estimated Return
HT
Coll.
Port.
-22.0% 28.0%
3.0%
-2.0
14.7
6.4
20.0
0.0
10.0
35.0
-10.0
12.5
50.0
-20.0
15.0
^
kp = (3.0%)0.10 + (6.4%)0.20 + (10.0%)0.40
+ (12.5%)0.20 + (15.0%)0.10 = 9.6%.
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




p = 





1/ 2


(3.0 – 9.6)20.10

+ (6.4 – 9.6)20.20 

+ (10.0 – 9.6)20.40  = 3.3%.

+ (12.5 – 9.6)20.20 

2
+ (15.0 – 9.6) 0.10 

CVp = 3.3% = 0.34.
9.6%
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
p = 3.3% is much lower than that of
either stock (20% and 13.4%).

p = 3.3% is lower than average of
HT and Coll = 16.7%.
^
\ Portfolio provides average k but
lower risk.
 Reason: negative correlation.

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General statements about risk
Most stocks are positively
correlated. rk,m  0.65.
 35% for an average stock.
 Combining stocks generally lowers
risk.

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Returns Distribution for Two Perfectly
Negatively Correlated Stocks (r = -1.0)
and for Portfolio WM
Stock W
.
25 .
.
0
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.
.
.
25
15
-10
Stock M
.
25
. 15 . . . . .
15
0
0
-10
Portfolio WM
.
.
-10
29
Returns Distributions for Two Perfectly
Positively Correlated Stocks (r = +1.0)
and for Portfolio MM’
Stock M’
Stock M
Portfolio MM’
25
25
25
15
15
15
0
0
0
-10
-10
-10
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What would happen to the
riskiness of an average 1-stock
portfolio as more randomly
selected stocks were added?
 p would decrease because the
added stocks would not be
^
perfectly correlated but kp would
remain relatively constant.
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Prob.
Large
2
1
0
15
Even with large N, p 20%
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p (%)
35
Company Specific Risk
Stand-Alone Risk, p
20
Market Risk
0
10
20
30
40
2,000+
# Stocks in Portfolio
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As more stocks are added, each
new stock has a smaller riskreducing impact.
 p falls very slowly after about 10
stocks are included, and after 40
stocks, there is little, if any, effect.
The lower limit for p is about 20%
= M .

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Stand-alone Market
specific risk = risk +
Firmrisk
Market risk is that part of a security’s
stand-alone risk that cannot be
eliminated by diversification, and is
measured by beta.
Firm-specific risk is that part of a
security’s stand-alone risk that can be
eliminated by proper diversification.
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
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By forming portfolios, we can
eliminate about half the riskiness
of individual stocks (35% vs. 20%).
36
If you chose to hold a one-stock
portfolio and thus are exposed to
more risk than diversified investors,
would you be compensated for all
the risk you bear?
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NO!
 Stand-alone risk as measured by a
stock’s  or CV is not important to a
well-diversified investor.
 Rational, risk averse investors are
concerned with p , which is based
on market risk.

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
There can only be one price, hence
market return, for a given security.
Therefore, no compensation can be
earned for the additional risk of a
one-stock portfolio.
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Beta measures a stock’s market
risk. It shows a stock’s volatility
relative to the market.
Beta shows how risky a stock is if
the stock is held in a well-diversified
portfolio.
 Beta is the measure of systematic
risk. Measures the sensitivity of
stock’s return to changes in returns
on the market portfolio.
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
How are betas calculated?
Run a regression of past returns
on Stock i versus returns on the
market. Returns = D/P + g.
 The slope of the regression line is
defined as the beta coefficient.

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Illustration of beta calculation:
_
ki
20
.
15
.
Year kM
1
15%
2
-5
3
12
10
5
-5
0
5
10
Regression line:
^
^
ki = -2.59 + 1.44 k
M
15
20
ki
18%
-10
16
_
kM
-5
.
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-10
42
Estimation of beta for the Turkish
Banking Industry
Dependent Variable: BANKINDEX
Variable
Coefficient
Std. Error
t-Statistic
C
0.000279
0.000405
0.687
ISE
0.865051
0.012596
68.677
Prob.
0.491
0.000
R-squared 0.605
Mean dependent var
0.001955
Adjusted R-squared
0.6053
0.035
S.D. dependent var
Log likelihood 7313.344
F-statistic
Durbin-Watson stat
1.928040
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4716.560
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If beta = 1.0, average stock.
 If beta > 1.0, stock riskier than
average.
 If beta < 1.0, stock less risky than
average.
 Most stocks have betas in the range
of 0.5 to 1.5.

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List of Beta Coefficients
Stock
Merrill Lynch
America Online
General Electric
Microsoft Corp.
Coca-Cola
IBM
Procter & Gamble
Heinz
Energen Corp.
Empire District Electric
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Beta
2.00
1.70
1.20
1.10
1.05
1.05
0.85
0.80
0.80
0.45
45
Can a beta be negative?
Answer: Yes, if ri, m is negative. Then
in a “beta graph” the regression line
will slope downward. Though, a
negative beta is highly unlikely.
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_
ki
HT
b = 1.29
40
b=0
20
T-Bills
-20
0
-20
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_
kM
40
b = -0.86
Coll.
47
Security
HT
Market
USR
T-bills
Coll.
Expected
Return
Risk
(Beta)
17.4%
15.0
13.8
8.0
1.7
1.29
1.00
0.68
0.00
-0.86
Riskier securities have higher returns,
so the rank order is OK.
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Use the SML to calculate the
required returns.
SML: ki = kRF + (kM – kRF)bi .
Assume kRF = 8%.
 Note that kM = ^
kM is 15%. (Equil.)
 RPM = kM – kRF = 15% – 8% = 7%.

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Required Rates of Return
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kHT
= 8.0% + (15.0% – 8.0%)(1.29)
= 8.0% + (7%)(1.29)
= 8.0% + 9.0%
= 17.0%.
kM
kUSR
kT-bill
kColl
=
=
=
=
8.0% + (7%)(1.00)
8.0% + (7%)(0.68)
8.0% + (7%)(0.00)
8.0% + (7%)(-0.86)
= 15.0%.
= 12.8%.
= 8.0%.
= 2.0%.
50
Expected vs. Required Returns
^
HT
k
17.4%
k
17.0%
Market
USR
15.0
13.8
15.0
12.8
T-bills
Coll.
8.0
1.7
8.0
2.0
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Undervalued:
^>k
k
Fairly valued
Undervalued:
^
k>k
Fairly valued
Overvalued:
^
k<k
51
SML: ki = 8% + (15% – 8%) bi .
ki (%)
SML
.
HT
kM = 15
kRF = 8
.
. .
. T-bills
USR
Coll.
-1
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0
1
2
Risk, bi
52
The required return on the
HT/Coll. portfolio is:
kp = Weighted average k
= 0.5(17%) + 0.5(2%) = 9.5%.
Or use SML:
kp= kRF + (kM – kRF) bp
= 8.0% + (15.0% – 8.0%)(0.22)
= 8.0% + 7%(0.22) = 9.5%.
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If investors raise inflation
expectations by 3%, what would
happen to the SML?
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Required Rate
of Return k (%)
D I = 3%
New SML
SML2
SML1
18
15
11
8
Original situation
0
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0.5
1.0
1.5
Risk, bi
55
If inflation did not change
but risk aversion increased
enough to cause the market
risk premium to increase by
3 percentage points, what
would happen to the SML?
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Required
Rate of
Return (%)
After increase
in risk aversion
SML2
kM = 18%
kM = 15%
SML1
18
15
D RPM = 3%
8
Original situation
1.0
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Risk, bi
57
Has the CAPM been verified
through empirical tests?

Not completely. Those statistical
tests have problems that make
verification almost impossible.
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
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)b + ?
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
Also, CAPM/SML concepts are
based on expectations, yet betas
are calculated using historical data.
A company’s historical data may
not reflect investors’ expectations
about future riskiness.
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