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.

Compute the proportions of bond fund of the optimal risky portfolio. Assume that short sales of mutual funds are allowed. Enter as a decimal number rounded to 4 decimal places

Answer 1

For optimally risky portfolio we should using following formula
Weight of S = ((Return of S - Risk Free Rate) * (Standard Deviation B)² - (Return of B - Risk Free Rate)*(Standard Deviation S* Standard Deviation B*Correlation Coefficient))/((Return of S - Risk Free Rate) * (Standard Deviation B)² +(Return of B - Risk Free Rate) * (Standard Deviation S)² - ((Return of S - Risk Free Rate) +(Return of B - Risk Free Rate))*(Standard Deviation S* Standard Deviation B*Correlation Coefficient)))

Weight of Stock =((16%-4.6%)*30%^2-(7%-4.6%)*36%*30%*0.16)/((16%-4.6%)*30%^2+(7%-4.6%)*36%^2-(((16%-4.6%)+(7%-4.6%)) *36%*30%*0.16) =89.62%

Weight of Bond = 1- 89.62% =10.38% or 0.1038