What is the reward to volatility ratio of the best feasible

Question

1. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long- term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 4.8%. The probability distributions of the risky funds are:

Expected Return Standard Deviation

Stock fund (S)                      18%                          38%

Bond fund (B)                         9%                          32%

The correlation between the fund returns is 1313.

What is the Reward to volatility Ratio of the best feasible CAL?

2. A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long- term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.9%. The probability distributions of the risky funds are:

Expected Return         Standard Deviation

Stock fund (S)                   20%                              49%

Bond fund (B)                     9%                              43%

The correlation between the fund returns is 0721.

Suppose now that your portfolio must yield an expected return of 18% and be efficient, that is, on the best feasible CAL.

a. What is the standard deviation of your portfolio?

b-1 What is the proportion invested in the T-bill fund?

b-2 What is the proportion invested in each of the two risky funds?

3. Suppose that many stocks are traded in the market and that it is possible to borrow at the risk-free rate, r_f. The characteristics of two of the stocks are as follows:

Stock                     Expected Return   Standard Deviation

A                              5%                         45%

B                            10%                         55%

Correlation = -1

a. Calculate the expected rate of return on this risk-free portfolio? (Hint: Can a particular stock portfolio be substituted for the risk-free asset?)

b. Could the equilibrium rf be greater than 7.25%?
a. Yes
b. No

4. A project has a 0.64 chance of doubling your investment in a year and a 0.36 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment?

5. Investors expect the market rate of return this year to be 12.50%. The expected rate of return on a stock with a beta of 0.9 is currently 11.25%. If the market return this year turns out to be 9.70%, how would you revise your expectation of the rate of return on the stock?