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 22% 12 Standard Deviation 38% 16 Stock fund (S) Bond fund (B) The correlation between the fund returns is 0.10. 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
Please show excel calculations, no handwritten answer.

Answer 1

The formula for minimum risk weights in a two stock portfolio is

Ws = [06-09 *OB* PBS]/[0+o's – 2* 09*0B * PBS

So, W_S = (0.16²-0.38*0.16 *0.10) / ( 0.16²+0.38² -2*0.16*0.38 *0.1)

= 0.01952/0.15784 =0.1237 =12.37%

and W_B = 1-   W_S = 1-0.1237 =0.8763=87.63%

So, portfolio invested in stock is 0.1237 and portfolio invested in Bond is 0.8763

b) The Expected value of rate of return of the portfolio is the weighted average return of its constituents

R_p = W_S *R_S +W_B *R_B  = 0.1237* 0.22 + 0.8763 *0.12 = 0.13237 or 13.24%

The standard deviation of a portfolio is given by

Op = W;*W, *0; * 0;* Pij

=sqrt (0.1237^2*0.38^2+0.8763^2*0.16^2+2 *0.38*0.16*0.1237*0.8763*0.1)

= sqrt (0.023186)

=0.152269=15.23%

=0.1523

The Expected Return is 0.1324 and the standard deviation is 0.1523