Risk and Rates Return
Expected return
A 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
0.2
-44%
Below average
0.2
-5
Average
0.3
15
Above average
0.1
30
Strong
0.2
75
1.0
Calculate the stock’s expected return. Round your answer to two decimal places.
%
Calculate the stock’s standard deviation. Do not round intermediate calculations. Round your answer to two decimal places.
%
Calculate the stock’s coefficient of variation. Round your answer to two decimal places.
Portfolio beta
An individual has $15,000 invested in a stock with a beta of 0.4 and another $35,000 invested in a stock with a beta of 2.0. If these are the only two investments in
her portfolio, what is her portfolio’s beta? Round your answer to two decimal places.
Required rate of return
Assume that the risk-free rate is 6.5% and the required return on the market is 12%. What is the required rate of return on a stock with a beta of 1.5? Round your
answer to two decimal places.
%
Expected and required rates of return
Assume that the risk-free rate is 3% and the market risk premium is 8%.
a. What is the required return for the overall stock market? Round your answer to two decimal places.
%
b. What is the required rate of return on a stock with a beta of 0.5? Round your answer to two decimal places.
%
Beta and required rate of return
A stock has a required return of 9%; the risk-free rate is 2.5%; and the market risk premium is 3%.
What is the stock’s beta? Round your answer to two decimal places.
If the market risk premium increased to 9%, what would happen to the stock’s required rate of return? Assume that the risk-free rate and the beta remain unchanged.
If the stock’s beta is greater than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
If the stock’s beta is less than 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
If the stock’s beta is greater than 1.0, then the change in required rate of return will be less than the change in the market risk premium.
If the stock’s beta is equal to 1.0, then the change in required rate of return will be greater than the change in the market risk premium.
If the stock’s beta is equal to 1.0, then the change in required rate of return will be less than the change in the market risk premium.
New stock’s required rate of return will be
%. Round your answer to two decimal places.
Expected returns
Stocks A and B have the following probability distributions of expected future returns:
Probability
A
B
0.2
-6%
-40%
0.2
6
0
0.3
15
24
0.2
23
27
0.1
34
47
Calculate the expected rate of return, rB, for Stock B (rA = 12.50%.) Do not round intermediate calculations. Round your answer to two decimal places.
%
Calculate the standard deviation of expected returns, ?A, for Stock A (?B = 27.80%.) Do not round intermediate calculations. Round your answer to two decimal places.
%
Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.
Portfolio required return
Suppose you are the money manager of a $4.99 million investment fund. The fund consists of four stocks with the following investments and betas:
Stock
Investment
Beta
A
$ 440,000
1.50
B
760,000
– 0.50
C
1,340,000
1.25
D
2,450,000
0.75
If the market’s required rate of return is 13% and the risk-free rate is 7%, what is the fund’s required rate of return? Do not round intermediate calculations. Round
your answer to two decimal places.
%
