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Chapter 8 OAES Assignment

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Chapter 8 OAES Assignment
Problem 8-1
Expected returnA stock’s returns have the following distribution:
Demand for the Company’s
Products
Probability of This Demand
Occurring
Rate of Return If This
Demand Occurs
Weak 0.1 (50%)
Below average 0.2 (5)
Average 0.4 16
Above average 0.2 25
Strong 0.1 60
1.0
Calculate the stock’s expected return, standard deviation, and coefficient of variation.
Expected return= 0.1(-50) + 0.2(-5) + 0.4(16) + 0.2(25) + 0.1(60)
=11.4%
P )D- (D = )( Deviation Standard
×
2
σ
Root of; 0.1(-50-11.4)
2
+ 0.2(-5-11.4)
2
+ 0.4(16-11.4)
2
+ 0.2(25-11.4)
2
+0.1(60-11.4)
2
=28.09%
Coefficient of Variation = SD/Er
= 28.09/11.4
=2.46

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Problem 8-3
Required rate of return. Assume that the risk-free rate is 6 percent and the expected
return on the market is 13 percent. What is the required rate of return on a stock with a
beta of 0.7?
r
i
= r
RF
+ (r
M
+ r
RF
)b
i
=6% + (13%-6%)(0.7)
=10.9%
Problem 8-5
Beta and required rate of return. A stock has a required return of 11 percent; the risk-free
rate is 7 percent; and the market risk premium is 4 percent.
a. What is the stock’s beta?
Beta= (r
i
– r
rf
)/RP
M
=(11-7)/4
= 1
b. If the market risk premium increased to 6 percent, what would happen to the
stock’s required rate of return? Assume the risk-free rate and the beta remain
unchanged.
r
i
= r
RF
+ (r
M
+ r
RF
)b
i
=7 + (6)1
=13%
The required rate of return will increase to 13% from the initial 11%
Problem 8-7

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Portfolio required return. Suppose you are the money manager of a $4 million investment
fund. The fund consists of 4 stocks with the following investments and betas:
Stock Investment Beta
A $ 400,000 1.50
B 600,000 (0.50)
C 1,000,000 1.25
D 2,000,000 0.75
If the market’s required rate of return is 14 percent and the risk-free rate is 6 percent,
what is the fund’s required rate of return?
B
p
= 0.1*1.5 + 0.15*-0.5 + 0.25*1.25 + 0.5*0.75
=0.7625
r
i
= r
RF
+ (r
M
+ r
RF
)b
i
=6 + (14 – 6)0.7625
=12.1%

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