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 sure rate of 5.5%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	16%	45%
Bond fund (B)	7%	39%

The correlation between the fund returns is 0.0385.

What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Answer 1

Given about funds

expected return on stock fund E(S) = 16%

standard devidation on stock fund SD(S) = 45%

expected return on Bond fund E(B) = 7%

standard devidation on Bond fund SD(B) = 39%

The return correlation between Stock fund and Bond fund Corr(S,B) = 0.0385

Weight of stock find WS in Minimum variance portfolio is given by

WS = (SD(B)^2 - SD(S)*SD(B)*Corr(S,B))/(SD(S)^2 + SD(B)^2 - 2*SD(S)*SD(B)*Corr(S,B))

So, WS = (39^2 - 45*39*0.0385)/(45^2 + 39^2 + 2*45*39*0.0385) = 0.3948 or 39.48%

So, weight of security B in the portfolio = 1-0.3948 = 0.6052 or 60.52%

Expected return of this minimum variance portfolio is

WS*E(S) + WB*E(B) = 0.3948*16 + 0.6052*7 = 10.55%

Standard deviation of this minimum variance portfolio is

SD(p) = ((WS*SD(S))^2 + (WB*SD(B))^2 - 2*WS*WB*SD(S)*SD(B)*Corr(A,B))

SD(p) = SQRT((0.3948*45)^2 + (0.6052*39)^2 + 2*0.3948*0.6052*45*39*0.0385) = 29.81%