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Question
NARRBEGIN: SA_89_92Suppose that Mrs. Smart invested 25% of her portfolio in four different stocks. The mean and standard deviation of the annual return on each stock are shown in the first table below. The correlations between the annual returns on the four stocks are shown in the second table below.
| Distributions of returns | ||||
| Mean | Stdev | |||
| Stock 1 | 16% | 21% | ||
| Stock 2 | 12% | 13% | ||
| Stock 3 | 25% | 38% | ||
| Stock 4 | 18% | 20% | ||
| Correlation matrix | ||||
| Stock 1 | Stock 2 | Stock 3 | Stock 4 | |
| Stock 1 | 1 | 0.75 | 0.7 | 0.6 |
| Stock 2 | 0.75 | 1 | 0.8 | 0.5 |
| Stock 3 | 0.7 | 0.8 | 1 | 0.65 |
| Stock 4 | 0.6 | 0.5 | 0.65 | 1 |
(A) Use @Risk with 100 replications, provide a summary statistics of portfolio return; namely, minimum, maximum, mean, and standard deviation.
(B) Use your answers to (A) to estimate the probability that Mrs. Smart's portfolio's annual return will exceed 20%.
(C) Use your answers to (A) to estimate the probability that Mrs. Smart's portfolio will lose money during the course of a year.
(D) Suppose that the current price of each stock is as follows: stock 1: $16; stock 2: $18; stock 3: $20; and stock 4: $22. Mrs. Smart has just bought an option involving these four stocks. If the price of stock 1, six months from now are is $18 or more, the option enables Mrs. Smart to buy, if she desires, one share of each stock for $20 six months from now. Otherwise the option is worthless. For example, if the stock prices six months from now are: stock 1: $18; stock 2: $20; stock 3: $21; and stock 4: $24, then Mrs. Smart would exercise her option to buy stocks 3 and 4 and receive (21- 20) + (24-20) = $5 in each cash flow. How much is this option worth if the risk-free rate is 8%?
Answer
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