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 21% 12 Standard Deviation 288 18 Stock fund (S) Bond fund (B) The correlation between the fund returns is 0.09. 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 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

a-1) Calculating the Investment portion in the minimum variance of portfolio by using following formula:

Weightof S = o +o's - 2pbs of - PBS

(18)2 – 45.36 Weightof S = a (18)2 + (28)2 – 2* (45.36)

324 - 45.36 WeightofS = 324 + 784 - 90.72

So, Portfolio instead in Stock (Weight of S) = 0.2739

Portfolio instead in Bond (Weight of Bond)= 1 -0.2739 = 0.7261

Note- Cov_BS (ρ_B,S) = Correlation*(S.D. of S)*(S.D. of S) = 0.09*18*28 = 45.3

a-2). Expected return using above weights:

Expected return on Portfolio = W_S*R_S + W_B*R_B

= (0.2739)(21) +(0.7261)(12)

= 5.7519 + 8.7132

= 14.4651%

Standard Deviation using above weights:

S.D. = V(W)*(0) + (W) * () + 2W8Ww RpRw PW B

S.D. = V(0.2739)2(28)2 + (0.7261)2(18)2 + 2*0.2739 * 0.7261 * 28 * 18 * 0,09

S.D. = 58.8166 + 170.8197 + 18.0423

S.D. 15.7378%