Part -1:
Problem 1. You are considering three stocks with the following expected dividend yields and capital gains:
|
|
Dividend Yield
|
Capital Gain
|
|
A
|
14%
|
0%
|
|
B
|
8
|
6 |
|
C
|
0 |
14 |
a) What is the expected return on each stock?
b) How may transactions costs and capital gains taxes affect your choices among the three securities?
Problem 2. A portfolio consists of assets with the following expected returns:
|
|
Expected Return
|
Weight in Portfolio
|
|
Real estate
|
16% |
20%
|
|
Low-quality bonds
|
15 |
10
|
|
AT&T stock
|
12 |
30
|
|
Savings account
|
5 |
40
|
a) What is the expected return on the portfolio?
b) What will be the expected return if the individual reduces the holdings of the AT&T stock to 15 percent and puts the funds into real estate investments?
Problem 3. You are given the following information concerning two stocks:
|
A |
|
B |
| Expected return |
10% |
|
14% |
| Standard deviation of the expected return |
3 |
|
5 |
| Correlation coefficient of the returns |
|
-1 |
|
a) What is the expected return on a portfolio consisting of 40 percent in stock A and 60 percent in stock B?
b) What is the standard deviation of this portfolio?
c) Discuss the risk and return associated with investing (a) all your funds in stock A, (b) all your funds in stock B, and (c) 40 percent in A and 60 percent in B. (This answer must use the numerical information in your answers derived above.)
Problem 4. You are given the following information:
|
Expected return on stock A
|
12%
|
|
Expected return on stock B
|
20%
|
|
Standard deviation of returns:
|
|
|
stock A
|
1.0
|
|
stock B
|
6.0
|
|
Correlation coefficient of the returns on stocks A and B
|
+.2
|
a) What are the expected returns and standard deviations of a portfolio consisting of:
1. 100 percent in stock A?
2. 100 percent in stock B?
3. 50 percent in each stock?
4. 25 percent in stock A and 75 percent in stock B?
5. 75 percent in stock A and 25 percent in stock B?
b) Compare the above returns and the risk associated with each portfolio.
c) Redo the calculations assuming that the correlation coefficient of the returns on the two stocks is -0.6. What is the impact of this difference in the correlation coefficient?
Problem 5. What is the beta of a portfolio consisting of one share of each of the following stocks, given their respective prices and beta coefficients?
| Stock |
Price |
Beta |
| A |
$10 |
L4 |
|
24 |
0.8 |
|
41 |
1.3 |
|
19 |
1.8 |
How would the portfolio beta differ if (a) the investor purchased 200 shares of stocks B and C for every 100 shares of A and D and (b) equal dollar amounts were invested in each stock?
Problem 6. What is the return on a stock according to the security market line if the risk-free rate is 6 percent, the return on the market is 10 percent, and the stock's beta is 1.5? If the beta had been 2.0, what would be the return? Is this higher return consistent with the portfolio theory explained in this chapter? Why?
Problem 7. You are considering purchasing two stocks with the following possible returns and probabilities of occurrence:
| Investment A |
Return |
Probability of Occurrence |
|
-10% |
20% |
|
5 |
40 |
|
15 |
30 |
|
25 |
10 |
| Investment B |
Return |
Probability of Occurrence |
|
-5% |
20% |
|
5 |
40 |
|
7 |
30 |
|
39 |
10 |
Compare the expected returns and risk (as measured by the standard deviations) of each investment. Which investment offers the higher expected return? Which investment is riskier? Compare their relative risks by computing the coefficient of variation.
For explanations and illustrations of the required calculations, see the appendix to this chapter.
Problem 8. Using the material on the standard deviation and the coefficient of variation presented in the appendix to this chapter, rank the following investments with regard to risk.
|
a) Investment Returns b)
|
Investment Returns
|
|
Stock A
|
Stock B
|
Stock A
|
Stock B
|
|
2.50%
|
7.50%
|
1.70%
|
7.40%
|
|
2.75
|
8.25
|
1.85
|
7.70
|
|
3.00
|
9.00
|
2.00
|
8.00
|
|
3.25
|
9.75
|
2.15
|
8.30
|
|
3.50
|
10.50
|
2.30
|
8.60
|
Part -2:
Although investing requires the individual to bear risk, the risk can be controlled through the construction of diversified portfolios and by excluding any portfolio that offers an inferior return for a given amount of risk. While this concept seems obvious, one of your clients, Laura Spegele, is considering purchasing a stock that you believe will offer an inferior return for the risk she will bear. To convince her that the acquisition is not desirable, you want to demonstrate the trade-off between risk and return.
While it is impractical to show the trade-off for all possible combinations, you believe that illustrating several combinations of risk and return and applying the same analysis to the specific investment should be persuasive in discouraging the purchase.
Currently, U.S. Treasury bills offer 7 percent. Three possible stocks and their betas are as follows:
| Security |
Expected return |
Beta |
| Stock A |
9% |
0.6 |
| Stock B |
11 |
1.3 |
| Stock C |
14 |
1.5 |
1. What will be the expected return and beta for each of the following portfolios?
a) Portfolios 1 through 4: All of the funds are invested solely in one asset (the corre¬sponding three stocks or the Treasury bill).
b) Portfolio 5: One-quarter of the funds are invested in each alternative.
c) Portfolio 6: One-half of the funds are in¬vested in stock A and one-half in stock C.
d) Portfolio 7: One-third of the funds are in¬vested in each stock.
2. Are any of the portfolios inefficient?
3. Is there any combination of the Treasury bill and stock C that is superior to portfolio 6 (i.e., half the funds in stock A and half in stock C)? Since your client's suggested stock has an an-ticipated return of 12 percent and a beta of 1.4, does that information argue for or against the purchase of the stock?
Why is it important to consider purchasing an asset as part of a portfolio and not as an inde-pendent act?