Question

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 5.5%. The probability distributions of the risky funds are:

   

	Expected Return		Standard Deviation
Stock fund (S)	15	%	32	%
Bond fund (B)	9	%	23	%

   

The correlation between the fund returns is 0.15.

   

a.

What is the standard deviation of the Optimal Risky Portfolio using the Stock and Bond funds? (Hint: use the long "weight in the optimal risky portfolio" equation to figure out how much to invest in each fund. Then use the risky portfolio equations to find the expected return and standard deviation of the ORP.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)

   

Standard deviation

%

    

b-1.

Suppose that your portfolio must yield an expected return of 12% and be efficient, that is, on the best feasible CAL.What is the proportion invested in the T-bill fund? (Hint: Combine the ORP with the risk free T-bill so that the complete portfolio's expected return is 12%.) (Do not round intermediate calculations. Round your answer to 2 decimal places.)

   

Proportion invested in the T-bill fund

%

   

b-2.	What is the proportion invested in each of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

	Proportion Invested
Stocks	%
Bonds	%

Answer 1

Using excel solver or mathematical formulas, we need to find weight of S and B such that we get the highest Sharpe Ratio.

	S	B	ORP
E(R)	15%	9%	12.88%
SD	32%	23%	23.34%
Weight	64.66%	35.34%

Standard Deviation = 23.34%

b1) Assume you invest y in ORP and 1 - y in T-bill such that you get 12%

=> y x 12.88% + (1 - y) x 5.5% = 12%

=> y = 88.08% in ORP and

1-y = 11.92% in T-bill fund.

b2) Weight of Stock Fund = 88.08% x 64.66% = 56.95% and

Weight of Bond Fund = 88.08% x 35.34% = 31.12%