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 8%. The probability distribution of the risky funds is as follows: Expected Return 203 Standard Deviation 356 15 Stock fund (S) Bond fund (B) The correlation between the fund returns is 0.09. ces a-1. What are the investment proportions in the minimum-variance portfolio of the two risky funds. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.) Portfolio invested in the stock Portfolio invested in the bond

Answer 1

Given for stock fund

E(Rs) = 20%

SD(Rs) = 35%

For bond funs

E(Rb) = 11%

SD(Rb) = 15%

CORR(s,b) = 0.09

a). For minimum variance portfolio of two risky assets, weight is calculated using following formula

W- WÁS CAP Of-Cov. AB 40+2 Cov.AB

where CovAB = Corr(A,B)*SD(A)*SD(B)

So, Ws = (0.15^2 - 0.09*0.15*0.35)/(0.15^2 + 0.35^2 - 2*0.09*0.15*0.35) = 0.131132

& Wb = 1-0.13 = 0.868868

So portfolio invested in stock = 13.1132%

And Portfolio invested in bond = 86.8868%

b). Expected return of portfolio is weighted average return = 0.868868*11 + 0.131132*20 = 12.1802%

Standard deviation = Sqrt(SD(Rs)^2*Ws^2 + SD(Rb)^2*Wb^2 + 2*SD(Rs)*SD(Rb)*Ws*Wb*CORR(s,b))

SD(P) = Sqrt((0.35^2)*(0.131132^2) + (0.15^2)*(0.868868^2) + 2*0.35*0.15*0.131132*0.868868*0.09) = 14.2018%