Chapter13
•Return, Risk, and the
Security Market Line
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter 13 – Index of Sample
Problems
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Slide # 02 - 03
Slide # 04 - 05
Slide # 06 - 07
Slide # 08 - 18
Slide # 19 - 22
Slide # 23 - 26
Slide # 27 - 32
Slide # 33 - 35
Expected return of individual stock
Standard deviation of individual stock
Portfolio weights
Portfolio expected return
Portfolio standard deviation
Portfolio beta
Capital asset pricing model
Reward-to-risk ratio
2: Expected return of individual stock
You own 500 shares of ABC, Inc. This stock has the following
expected returns given the various possible states of the economy.
State of
Economy
Boom
Normal
Recession
Probability of
State of Economy
.20
.70
.10
What is your expected return on this stock?
Rate of Return
if State Occurs
28%
12%
-40%
3: Expected return of individual stock
E r  (.20  .28)  (.70  .12)  (.10  .40)
 .056  .084  .04
 .10
 10%
4: Standard deviation of individual
stock
A stock has returns of 6.8%, 9.2%, -4.3% and 18.7% over the last
four years, respectively.
What is the standard deviation of this stock assuming the returns
are normally distributed?
5: Standard deviation of individual
stock
(.068  .076) 2  (.092  .076) 2  (.043  .076) 2  (.187  .076) 2

4 1

.000064  .000256  .014161  .012321
3

.026802
3
 . 008934
 .0945
 9.45%
.068  .092  .043  .187
4
.304

4
 .076
Er 
6: Portfolio weights
You own 50 shares of Stock A and 200 shares of stock B. Stock A
sells for $30 a share and stock B sells for $22 a share.
What are the portfolio weights for each stock?
7: Portfolio weights
Stock
A
B
Number of
Shares
50
200
Price per
Share
$30
$22
Totals
Total
Value
$1,500
$4,400
$5,900
Portfolio
Weight
25.4%
74.6%
100.0%
8: Portfolio expected return
You have $3,600 invested in stock A and $5,400 invested in stock
B. Stock A has an expected return of 11% and stock B has an
expected return of 7%.
What is the expected return of your portfolio?
9: Portfolio expected return
Stock Expected Return Amount Invested
A
11%
$3,600
B
7%
$5,400
Totals
$9,000
E r  (.40  .11)  (.60  .07)
 .044  .042
 .086
 8.6%
Portfolio Weight
40%
60%
100%
10: Portfolio expected return
Your portfolio consists of the following stocks:
Stock
Expected Return
A
B
C
9%
14%
7%
Number of Shares
640
250
700
What is the expected return on your portfolio?
Stock Price
$25
$40
$20
11: Portfolio expected return
Stock
A
B
C
Expected
Return
9%
14%
7%
Number
of Shares
640
250
700
Price
per Share
$25
$40
$20
Totals
Stock
Value
$16,000
$10,000
$14,000
$40,000
E r  (.40  .09)  (.25  .14)  (.35  .07)
 .036  .035  .0245
 .0955
 9.55%
Portfolio
Weight
40%
25%
35%
100%
12: Portfolio expected return
You have a portfolio with an expected return of 12.94%. Your
portfolio consists of stock A and stock B only. Stock A has an
expected return of 18% and stock B has an expected return of 7%.
What are the portfolio weights?
13: Portfolio expected return
Er
portfolio ( w A
 E r A )  (w B  E r B )
.1294  [ w A  .18]  [(1  w A )  .07]
.1294  .18w A  .07  .07 w A
.0594  .11w A
w A  .54
w A  54%
.1294  [.54  .18]  [(1  .54)  .07]
.1294  .0972  .0322
.1294  .1294
14: Portfolio expected return
State of
Economy
Boom
Normal
Recession
Probability of
State of Economy
.15
.60
.25
What is the expected return on this portfolio?
Rate of Return
if State Occurs
18%
11%
2%
15: Portfolio expected return
E r  (.15  .18)  (.60  .11)  (.25  .02)
 .027  .066  .005
 .098
 9.8%
16: Portfolio expected return
State of
Economy
Boom
Normal
Recession
Probability of
Rate of Return if State Occurs
State of Economy Stock A Stock B Stock C
.20
17%
13%
40%
.50
8%
6%
13%
.30
-12%
-5%
-50%
Your portfolio consists of 50% stock A, 40% stock B and
10% stock C.
What is the expected return on your portfolio?
17: Portfolio expected return
E r boom  (.50  .17)  (.40  .13)  (.10  .40)
 .085  .052  .04
 .177
E r normal  (.50  .08)  (.40  .06)  (.10  .13)
 .04  .024  .013
 .077
E r recession  (.50  .12)  (.40  .05)  (.10  .50)
 -.06  .02  .05
 -.130
18: Portfolio expected return
State of
Economy
Boom
Normal
Recession
Probability of
State of Economy
.20
.50
.30
Expected Return
if State Occurs
. 177
.077
-.130
E r portfolio  (.20  .177)  (.50  .077)  (.30  .130)
 .0354  .0385  .039
 .0349
 3.49%
19: Portfolio standard deviation
State of
Economy
Boom
Normal
Recession
Probability of
Rate of Return if State Occurs
State of Economy Stock A Stock B Stock C
.10
24%
5%
14%
.70
11%
6%
9%
.20
-30%
7%
-5%
Your portfolio consists of 30% stock A, 50% stock B and
20% stock C.
What is the standard deviation of your portfolio?
20: Portfolio standard deviation
E r boom  (.30  .24)  (.50  .05)  (.20  .14)
 .072  .025  .028
 .125
E r normal  (.30  .11)  (.50  .06)  (.20  .09)
 .033  .03  .018
 .081
E r recession  (.30  .30)  (.50  .07)  (.20  .05)
 -.09  .035  .01
 -.065
21: Portfolio standard deviation
State of
Economy
Boom
Normal
Recession
Probability of
State of Economy
.10
.70
.20
Expected Return
if State Occurs
. 125
.081
-.065
E r portfolio  (.10  .125)  (.70  .081)  (.20  .065)
 .0125  .0567  .013
 .0562
22: Portfolio standard deviation
State of
Probability of
Economy
State of Economy
Boom
.10
Normal
.70
Recession
.20
Portfolio expected return = .0562
Expected Return
if State Occurs
. 125
.081
-.065
 portfolio  .10  (.125  .0562) 2  .70  (.081  .0562) 2  .20  (.065  .0562) 2
 .10  .004733  .70  .000615  .20  .014689
 .000473  .000431  .002938
 .003842
 .061984
 6.20%
23: Portfolio beta
Your portfolio consists of the following stocks:
Stock
A
B
C
D
Portfolio Weight
20%
30%
40%
10%
What is the beta of your portfolio?
Beta
.76
1.89
1.05
.34
24: Portfolio beta
 portfolio  (.20  .76)  (.30 1.89)  (.40 1.05)  (.10  .34)
 .152  .567  .42  .034
 1.173
 1.17 (rounded)
25: Portfolio beta
You want to create a portfolio that has a risk level equal to the
overall market. Your portfolio will consist of the following
securities:
Security
Stock A
Treasury bills
Portfolio Weight
?
?
What do the portfolio weights need to be?
Beta
1.4
?
26: Portfolio beta
 portfolio  ( w A   A )  ( w B   B )
1.0  [ w A 1.4]  [(1  w A )  0]
1.0  1.4w A  0
w A  .7143
w A  71.43%
Weight of Stock A
Weight of Treasury bills = 100% - 71.43%
= 71.43%
= 28.57%
27: Capital asset pricing model
You own shares of Big Burgers, Inc. This stock has a beta of 1.24.
U.S. Treasury bills are returning 3.4%. The return on the market is
11.4%.
What is the expected return on Big Burgers, Inc.?
28: Capital asset pricing model
E r  rf    (rm  rf )
 .034  [1.24  (.114  .034)]
 .034  [1.24  .08]
 .034  .0992
 .1332
 13.32%
29: Capital asset pricing model
You own shares of International Coffees. The expected return on
this stock is 16%. The risk-free rate is 3% and the market risk
premium is 7%.
What is the beta of the International Coffees stock?
30: Capital asset pricing model
E r  rf    (rm  rf )
.16  .03  (   .07)
.13  .07 
  1.857
31: Capital asset pricing model
A stock has a beta of .86 and an expected return of 13.5%. The riskfree rate is 4%.
What is the expected return on the market?
32: Capital asset pricing model
E r  rf    (rm  rf )
.135  .04  .86  (rm  .04)
.135  .04  .86rm  .0344
.1294  .86rm
rm  .1505
rm  15.05%
33: Reward-to-risk ratio
Stock
A
B
C
Beta
.42
1.23
.89
Expected Return
6.6%
11.8%
9.8%
Are these stocks correctly priced if the risk-free rate is 3% and
the market risk premium is 8%?
34: Reward-to-risk ratio
E r  r f    (rm  rf )
E r A  .03  (.42  .08)  .0636
E r B  .03  (1.23  .08)  .1284
E r C  .03  (.89  .08)  .1012
35: Reward-to-risk ratio
Expected
CAPM
Stock
Stock
Return
Return
Pricing
A
B
C
6.6%
11.8%
9.8%
6.36%
12.84%
10.12%
underpriced
overpriced
overpriced
Chapter13
•End of Chapter 13
McGraw-Hill/Irwin
Copyright © 2006 by The McGraw-Hill Companies, Inc. All rights reserved.