Here are some historical data on the risk characteristics of Dell and McDonald’s:
| Dell | McDonald’s |
β (beta) | 1.41 | .77 |
Yearly standard deviation of return (%) | 30.9 | 17.2 |
Assume the standard deviation of the return on the market was 15%.
a. The correlation coefficient of Dell’s return versus McDonald’s is .31. What is the standard deviation of a portfolio invested half in Dell and half in McDonald’s?
b. What is the standard deviation of a portfolio invested one-third in Dell, one-third in McDonald’s, and one-third in risk-free Treasury bills?
c. What is the standard deviation if the portfolio is split evenly between Dell and McDonald’s and is financed at 50% margin, i.e., the investor puts up only 50% of the total amount and borrows the balance from the broker?
d. What is the approximate standard deviation of a portfolio composed of 100 stocks with betas of 1.41 like Dell? How about 100 stocks like McDonald's? (Hint: Part (d) should not require anything but the simplest arithmetic to answer.)
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