Question

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 7%. The characteristics of the risky funds are as follows:

	Expected Return				Standard Deviation
Stock fund (S)		19	%			31	%
Bond fund (B)		14				23

The correlation between the fund returns is 0.10.

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.

	Portfolio invested in the stock Portfolio invested in the bond Expected return Standard deviation

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)
=(19%-7%)*23%^2-(14%-7%)*31%*23%*0.10)/((19%-7%)*23%^2+(14%-7%)*31%^2-(19%-7%+14%-7%)*31%*23%*0.10))
= 0.4990
Weight of Bond =1-0.4516 = 0.5010

Expected Return =Weight of Stock*Return of Stock+Weight of Bond*Return of Bond =0.4990*19%+0.5010*14% =16.50% or 0.1650
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
=((0.4990*31%)^2+(0.5010*23%)^2+2*0.4990*0.5010*31%*23%*0.1)^0.5 =20.19% or 2019