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.

Calculate the expected return 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 B = 1- 89.62% =10.38%

Expected Return of optimally risky portfolio =89.62%*16%+10.38%*7% = 15.07% or 0.1507