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 8%. The probability distribution of the risky funds is as follows:

	Expected Return	Standard Deviation
Stock fund (S)	17%	38%
Bond fund (B)	12	17

The correlation between the fund returns is 0.13.

a-1.	What are the investment proportions in the minimum-variance portfolio of the two risky funds. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Portfolio invested in the stock
Portfolio invested in the bond

a-2.	What is the expected value and standard deviation of its rate of return? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Rate of Return

Expected return

Standard deviation

Assume that you manage a risky portfolio with an expected rate of return of 22% and a standard deviation of 34%. The T-bill rate is 6%. Your client chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund.

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

Your reward-to-volatility ratio
Client's reward-to-volatility ratio

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 6%. The probability distribution of the risky funds is as follows:

	Expected Return	Standard Deviation
Stock fund (S)	16%	35%
Bond fund (B)	12	15

The correlation between the fund returns is 0.13.

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.)

Portfolio invested in the stock
Portfolio invested in the bond
Expected return
Standard deviation

Suppose that there are many stocks in the security market and that the characteristics of stocks A and Bare given as follows:

Stock	Expected Return				Standard Deviation
A		14	%			6	%
B		16				9
	Correlation = 1

Suppose that it is possible to borrow at the risk-free rate, r_f . What must be the value of the risk-free rate? (Hint: Think about constructing a risk-free portfolio from stocks A and B.) (Do not round intermediate calculations. Round your answer to 3 decimal places. Omit the "%" sign in your response.)

Risk-free rate

%

Assume that you manage a risky portfolio with an expected rate of return of 20% and a standard deviation of 37%. The T-bill rate is 7%. Your clients degree of risk aversion is A = 2.5, assuming a utility function U= E(r) - A.

a.	What proportion, y, of the total investment should be invested in your fund? (Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Investment proportion y

%

b.	What is the expected value and standard deviation of the rate of return on your clients optimized portfolio? (Do not round intermediate calculations. Round your answers to 2 decimal places. Omit the "%" sign in your response.)

Expected return		%
Standard deviation		%