Question

Problem 7-4 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 17% Standard Deviation 35% 18 Stock fund (S) Bond fund (5) The correlation between the fund returns is 0.09 0-1. 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 a-2. What is the expected value and standard deviation of its rate of return? (Do not round Intermediate calculations. Enter your answers as decimals rounded to 4 places.) Rate of Return Expected return Standard deviation

Answer 1

Covariance(S,B) = Correlation * $\sigma _{S}$ * $\sigma _{B}$

= 0.09*35*18 = 56.7

Portfolio weights providing a minimum variance portfolio can be calculated as follows

W_Min(B) =

os - Cours - TB)/03 +03 - 2* CouT's,7B)

= 1225-56.7/1225+324-2*56.7

= 0.8138

W_Min(S) = 1-W_Min(B) = 0.1862

Therefore, portfolio invested in S = 18.62%

Portfolio invested in Bond = 81.38%

Expected return of portfolio = W_S*E(r_S) +W_B*E(r_B)

=0.1862*17 + 0.8138*14 = 14.5586

Variance of portfolio,

o = w* 03 + w *03 +2* Ws* WB * Cour's,B)

= 0.1862² * 35² + 0.8138² * 18² + 2*.1862*.8138*56.7

= 274.227

Standard deviation $\sigma _{P}$ = = 16.55

V274.227