 # Rates of Return Questions

## Question

1. Expected return

A stock’s returns have the following distribution:

Demand for the Probability of This Rate of Return
Weak 0.1 (50%)
Below average 0.2 (5)
Average 0.4 16
Above Average 0.2 25
Strong 0.1 60

Calculate the stock’s expected return, standard deviation, and coefficient of variation.

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?

2. Beta and required rate of return

A stock has a required return of 11 percent; the riskfree rate is 7 percent; and the market risk premium is 4 percent.
What is the stock’s beta?

If the market risk premium is creased to 6 percent, what would happen to the stock’s required rate of return? Assume the risk-free rate and the beta remain unchanged.

3. 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 4 percent and the risk-free rate is 6 percent, what is the fund’s required rate of return?

4. Burner Aeronautics has perpetual preferred stock outstanding with a par value of \$100. The stock pays a quarterly dividend of \$2, and its current price is \$80.

a. What is its nominal annual rate of return?
b. What is its effective annual rate of return?

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