Risk and return
Note
1. Risk defined
2. Probability distribution
3. Expected rate of return
4. The standard deviation
5. Coefficient of variation
6. Types of risk
7. Portfolio risk and CAPM
Question 1
Assuming the following probability distribution of the possible return. Calculate the (a) expected return (b) standard deviation of the return
| Probability | Return |
| 0.1 | (20%) |
| 0.2 | 5% |
| 0.3 | 10% |
| 0.4 | 25% |
Question 2
Stocks A and stocks B have the following probability distributions of possible future returns:
| Probability | Stock A | Stock B |
| 0.1 | -15% | 12% |
| 0.2 | 0 | 10 |
| 0.4 | 5 | 20 |
| 0.2 | 10 | 30 |
| 0.1 | 25 | 50 |
a. Calculate the expected rate of return for each stock
b. Calculate the standard deviation of returns for each stock
c. Calculate the coefficient of variation
d. Which stock is less risky? Explain.
Question 3
You have observed the following returns over time:
| Year | Stock X | Stock Y | Market |
| 1997 | 14% | 13% | 12% |
| 1998 | 19 | 7 | 10 |
| 1999 | -16 | -5 | -12 |
| 2000 | 3 | 1 | 1 |
| 2001 | 20 | 11 | 15 |
Assume that the risk free rate is 6 percent and the market risk premium is 5 percent.
(a) What are the betas of Stocks X and Y?
(b) What are the required rates of return for Stocks X and Y?
(c) What is the required rate of return for a portfolio consisting of 80 percent of Stock X and 20 percent of Stock Y?
(d) If Stock X’s expected return is 22 percent, is Stock X under or overvalued?
Question 4
An individual has $35,000 invested in a stock which has a beta of 0.8 and $40,000 invested in a stock with a beta of 1.4. If these are the only two investments in her portfolio, what is her portfolio beta? (b=1.12)
Question 5
Assume that the risk free rate is 5 percent and the market risk premium is 6%. What is the expected return for the overall stock market? What is the required rate of return on a stock that has a beta of 1.2? (answer: rm = 11%, r = 12.2%)
Question 6
The market and stock J have the following probability distributions.
| Probability | rm | rj |
| 0.3 | 15% | 20% |
| 0.4 | 9 | 5 |
| 0.3 | 18 | 12 |
a. Calculate the expected rates of return for the market and Stock J.
b. Calculate the standard deviation for the market and Stock J.
c. Calculate the coefficients of variation for the market and Stock J.
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