Problem 1. Stocks X and Y have the following probability distributions of expected future returns:
| PROBABILITY |
X |
Y |
Rate of return Y |
Rate of return X |
| 10% |
-10% |
-35% |
-4% |
-1% |
| 20% |
20% |
0% |
0% |
4% |
| 40% |
12% |
20% |
8% |
5% |
| 20% |
20% |
25% |
5% |
4% |
| 10% |
38% |
45% |
5% |
4% |
a. Calculate the expected rate of return, khat, for Stock Y (expected return for Stock X, Kx hat, equals 12%).
b. Calculate the standard deviation of expected returns for Stock X. (that for Stock Y is 20.35%). Now Calculate the coefficient of variation for Stock Y. Is it possible that most investors might regard Stock Y as being less risky than Stock X? Explain.
Problem 2. Shalit Corporation's 2002 sales were $12 million. Sales were $6 million 5 years earlier (in 1997).
a. To the nearest percentage point, at what rate have sales been growing?
b. Suppose someone calculated the sales growth for Shalit Corporation in part a as follows:
"Sales doubled in 5 years. This represents a growth of 100 percent in 5 years, so dividing 100 percent by 5, we find the growth rate to be 20 percent per year". Explain what is wrong with this calculation.