You manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 29%. The T-bill rate is 8%. Your client chooses to invest 65% of a portfolio in your fund and 35% in a T-bill money market fund.

What is the reward-to-volatility (Sharpe) ratio (S) of your risky portfolio? Your clients? (Do not round intermediate calculations. Round your answers to 4 decimal places.)

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 rate of 9%. The probability distribution of the risky funds is as follows:

	Expected Return			Standard Deviation
Stock fund (S)		17	%		30	%
Bond fund (B)		11			22

The correlation between the fund returns is 0.10.

Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Data: S₀ = 105; X = 114; 1 + r = 1.1. The two possibilities for S_T are 133 and 95.

a. The range of S is 38 while that of P is 19 across the two states. What is the hedge ratio of the put? (Round your answer to 2 decimal places. Negative value should be indicated by a minus sign.)

b. Form a portfolio of one share of stock and two puts. What is the (nonrandom) payoff to this portfolio?

c. What is the present value of the portfolio? (Round your answer to 2 decimal places.)

d. Given that the stock currently is selling at 105, calculate the put value. (Do not round intermediate calculations. Round your answer to 2 decimal places.)