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 rate of 4.6%. The probability distribution of the two risky funds is as follows:

	Expected Return	Standard Deviation
Stock fund (S)	16%	36%
Bond fund (B)	7%	30%

The correlation between the two fund returns is 0.16.

1A) Compute the proportions of stock fund of the optimal risky portfolio. Assume that short sales of mutual funds are allowed. (Do not round intermediate calculations. Enter your answer as a decimal number rounded to 4 decimal places.)

1B) Compute the proportions of bond fund of the optimal risky portfolio. Assume that short sales of mutual funds are allowed. (Do not round intermediate calculations. Enter your answer as a decimal number rounded to 4 decimal places.)

1C) Calculate the expected return of the optimal risky portfolio. Assume that short sales of mutual funds are allowed. (Do not round intermediate calculations. Enter your answer as a decimal number rounded to 4 decimal places.)

1D) Calculate the standard deviation of the optimal risky portfolio. Assume that short sales of mutual funds are allowed. (Do not round intermediate calculations. Enter your answer as a decimal number rounded to 4 decimal places.)

Answer 1

1 A)Weight of (S) = ((Standard Deviation of B)^2 -correlation * Standard Deviation of S * Standard Deviation of B)/((Standard Deviation of S)^2 + (Standard Deviation of B)^2 - 2 * correlation * Standard Deviation of S * Standard Deviation of B)
=((30%^2)-0.16*36%*30%)/((36%^2)+(30%^2)-2*0.16*36%*30%)=39.2996% or 0.3930

B) Weight of B =1-39.2996%=60.7004% or 0.6070

C) Expected Return of min variance portfolio =39.2996%*16%+60.7004%*7%=0.1054

D) Standard Deviation = ((Weight of S * Standard Deviation of S)^2 + (weight of B * standard Deviation of B)^2 + 2* Weight of S * Standard Deviation of S * weight of B * standard Deviation of B * correlation)^0.5
=((39.2996%*36%)^2+(60.7004%*30%)^2+2*39.2996%*60.7004%*36%*30%*0.16)^0.5=0.2478