Question

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

b. What is the risk premium on the market?
c. 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 expect a return of 11.2 percent from Stock X, what is its beta?

2. Percival Hygiene has $10 million invested in long-term corporate bonds. This bonds portfolios expected annual rate of return is 9 percent and annual standard deviation is 10 percent.
Amanda Reckcon with, Percival's financial adviser recommends that Percival consider investing in an index fund which closely tracks the Standard and Poor's 500 index.

a.Suppose Percival put all his money in a combination of index fund and treasury bills. Can he thereby improve his expected rate of return without changing the risk of portfolio . The treasury bill yield is 6 percent.
b.Could Percival do even better by investing equal amount in the corporate bond portfolio and the index fund? The correlation between the bond portfolio and the index fund is + 1.

Answer 1

The risk premium is the market return minus the risk free return (treasury bill rate)
12%-4%= 8%.

The Capital Asset pricing model says the expected return on a stock is equal to the risk free rate plus beta times the difference between the expected market return and the risk free return. Beta is a measure of the risk of the individual stock you get by running a linear regression on the returns of the individual stock versus the returns of the market.

So here we have R= 4 + 1.5(12-4)= 4+12=16% expected return on the stock.

If the expected return on the stock is 9.8 we have

9.8= 4 +.8(x-4)
9.8= 4+ .8x- 3.2
.8x=9
x=11.25 since this is less than the market return of 12% we would expect the stock to have a negative NPV.

If the stock has an expected return of 11.2 we have
11.2= 4 +B(12-4)
8B= 7.2
B= 0.9

The investor could do better by, say, putting 40% of his portfolio in T-bills and 60% in an index fund. This would have an expected return of .4(6) +.6(12)= 9.6, which would be better than the bonds, but have less risk due to the T-bills which are risk free.

You wouldn't want to put your money in two investments that are perfectly correlated (+1). This increases rather than decreases the risk. You want negative correlation which will reduce the volatility of the portfolio and thus the risk.