21. Here are some historical data on the risk characteristics of Dell and McDonald’s:

Dell McDonald’s

␤ (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.)