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 standard deviation 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%

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 = ((89.62%*36)² + (10.38%* 30%)² + 2* 89.62% *36% *10.38% * 30% * 0.16)^0.5 = 32.90% or 0.3290