1. Mark Harrywitz proposes to invest in two shares, X and Y. He expects a return of 12 percent from X and 8 percent from Y. The standard deviation of returns is 8 percent for X and 5 percent for Y. The correlation coefficient between the returns is .2.

a. Compute the expected return and standard deviation of the following portfolios:

Portfolio Percentage in X Percentage in Y
1 50 50
2 25 75
3 75 25

2. The Treasury bill rate is 4 percent, and the expected return on the market portfolio is 12 percent. Using the capital asset pricing model:

a. Draw a graph similar showing how the expected return varies with beta.

b. Illustrate what is the risk premium on the market?

c. Illustrate what is the required return on an investment with a beta of 1.5?

d. If an investment with a beta of .8 offers an expected return of 9.8 percent, does it have a positive NPV?

e. If the market expects a return of 11.2 percent from stock X, what is its beta?

3. Percival Hygiene has $10 million invested in long-term corporate bonds. This bond portfolio's expected annual rate of return is 9 percent, and the annual standard deviation is 10 percent.

Amanda Reckonwith, Percival's financial adviser, recommends that Percival consider investing in an index fund which closely tracks the Standard and Poor's 500 index. The index has an expected return of 14 percent, and its standard deviation is 16 percent.

a. Suppose Percival puts all his money in a combination of the index fund and Treasury bills. Can he thereby improve his expected rate of return without changing the risk of his portfolio? The Treasury bill yield is 6 percent.

b. Could Percival do even better by investing equal amounts in the corporate bond portfolio and the index fund? The correlation between the bond portfolio and the index fund is _.1.