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 6%. The probability distribution of the risky funds is as follows: Expected Return Standard Deviation Stock fund (S) 21 % 36 % Bond fund (B) 13 22 The correlation between the fund returns is 0.13. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Answer 1

Optimally Risky Portfolio

Weight of Stock =(E(r)of Stock-Rf)* b^2-(E(r) of Bond -Rf)* s* b*Correlation)/((Er of Stock-Rf)* b^2+(Er of Bond-Rf)* s^2-(E(R) of Stock -Rf)* b^2+(E(R) of bond -Rf)* s^2-(E(R) of Stock -Rf+E(R) of bond -Rf)* s* b*Correlation)
=(21%-6%)*22%^2-(13%-6%)*36%*22%*0.13)/((21%-6%)*22%^2+(13%-6%)*36%^2-(21%-6%+13%-6%)*36%*22%*0.13))
=0.4649
Weight of Bond =1-0.4649 =0.5351

Expected Return =Weight of Stock*Return of Stock+Weight of Bond*Return of Bond =0.4649*21%+0.5351*13% =16.72% or 0.1672
Standard Deviation =((Weight of Stock*Standard Deviation of Stock)^2+(Weight of Bond*Standard Deviation of Bond)^2+2*Weight of Stock*Weight of Bond*Standard Deviation of Stock*Standard Deviation of Bond*Correlation)^0.5
=((0.4649*36%)^2+(0.5351*22%)^2+2*0.4649*0.5351*36%*22%*0.13)^0.5 =21.68% or 0.2168