26. Portfolio risk and return (S7.4) Here are returns and standard deviations for four investments.

Chapter 7 Introduction to Risk, Diversification, and Portfolio Selection 219 7.1 The historic risk premium is 10.5% – 2% = 8.5%. With a current risk-free rate of 3%, the hurdle rate should be 3% + 8.5% = 11.5%.

7.2 The mean is (1 + 2 + 3 + 4 + 5 + 6) / 6 = 3.5.

The variance is [(1-3.5)2 + (2-3.5)2 + (3-3.5)2 + (4-3.5)2 + (5-3.5)2 + (6-3.5)2] /6 = 2.92, which corresponds to a standard deviation of √2.92 = 1.71.

7.3

a. If Applebaum and Banana were perfectly correlated, there would be no diversification benefit, so the portfolio standard deviation would be a (weighted) average of the individual standard deviations—that is, 15%. Since Applebaum and Banana are less than perfectly correlated, there is a diversification benefit, which reduces the portfolio standard deviation to lower than 15%.

b. –1: perfect negative correlation.

7.4

a. Systematic;

b. systematic;

c. specific;

d. specific.

7.5 Both investors will invest in both stocks in the same proportion. They will instead satisfy their preferences for risk through borrowing and lending.

7.6 $100 million. The whole is worth the sum of its parts, no more. While there is a diversification benefit, because the cash flows are less than perfectly positively correlated, shareholders can diversify themselves; there is no need for the companies to do so.

● ● ● ● ●

SOLUTIONS TO SELF-TEST QUESTIONS