Fundamentals of coroprate finance 7th ross westerfield CH13

Chapter13
•Return, Risk, and the
Security Market Line

McGraw-Hill/Irwin

Copyright ©

by The McGraw-Hill Companies, Inc. All rights


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
σ=
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

Portfolio Weight
40%
60%
100%

E r = (.40 × .11) + (.60 × .07)
= .044 + .042
= .086
= 8.6%


10: Portfolio expected return
Your portfolio consists of the following stocks:
Stock
A
B
C

Expected Return
9%
14%
7%

640
250
700

Number of Shares
$25
$40
$20

What is the expected return on your portfolio?

Stock Price


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
14%
Normal
9%
Recession
-5%

Probability of
Rate of Return if State Occurs
State of Economy Stock A Stock B Stock C
.10
24%
5%
.70

11%

6%

.20

-30%

7%

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

σ 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
β portfolio = (.20 × .76) + (.30 ×1.89) + (.40 ×1.05) + (.10 × .34)
= .152 + .567 + .42 + .034
= 1.173
= 1.17 (rounded)