Question

The following data applies to Questions 4 to 9. A pension fund manager is considering three investment options. The first is a stock fund, the second is a corporate bond fund, and the third is a T-bill money market fund (the risk-free asset) that yields a sure rate of 5.5%. The probability distributions of the risky funds are: Expected return (%) Standard Deviation (%) Stock fund (S) 15 32 Bond fund (B) 23 The correlation between the fund returns is 0.15. What is the portfolio weight for the stock fund in the minimum-variance portfolio which doesn't include the risk-free asset? Your answer should be in decimal values and accurate to the hundredth (NOT in percentage points, so 0.24 if the weight is 0.2410).

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Answer 1

a) 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 = (0.23² -0.23*0.32 *0.15) / ( 0.32²+0.23² -2*0.23*0.32 *0.15)

= 0.3142 = 31.42%

and W_B = 1-   W_S = 1-0.3142 =0.6858=68.58%

So, portfolio weight for stock fund is 0.31

b) The standard deviation of a portfolio is given by

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

=sqrt (0.3142^2*0.32^2+0.6858^2*0.23^2+2 *0.23*0.32*0.3142*0.6858*0.14)

= sqrt (0.03943)

=0.198569

=19.86%