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 sure rate of 4.0%. The probability distributions of the risky funds are:   

Expected Return STD DEV.

Stock Fund (S)            10%                 32%

Bond Fund (B)            7%                  24%

The correlation between the fund returns is .1250.

Suppose now that your portfolio must yield an expected return of 8% and be efficient, that is, on the best feasible CAL.

a. What is the standard deviation of your portfolio? %

b-1. What is the proportion invested in the T-bill fund? %

b-2. What is the proportion invested in each of the two risky funds?

Proportion Invested

Stocks                                     %

Bonds                                     %

Answer 1

stock fund bond fund 0.1 0.07 0.32 0.24 0.1024 0.0576 0.125 0.0096 0.04 portfolio stock fund 2 expected return 3 standard deviation 4 variance 5 correlation 6 covariance 7 T-bill rate 8 9 a) 10 expected return 11 12 weights in portfolio 13 variance of portfolio 14 expected return of portfolio 15 standard deviation of portfolio 16 17 18 optimal risky portfolio 19 excess return 20 21 Portfolio weights 22 expected return 23 variance 24 standard deviation 0.08 bond fund 0.3333 0.6667 0.041244444 0.0800 20.31% stock fund stock fund Bond fund 0.06 0.03 Bond fund 0.5593 0.4407 0.0868 0.0480 0.2190 25 26 optimal risky portfolio 0.855072464 T-bill 0.144927536 27 % invested 28 b-1 29 % invested in T-bill 30 b-2 14.49% 31 stock fund Bond fund 37.68% 32 % invested 47.83%

stock fund bond fund 0.1 0.07 0.24 =C3*C3 2 expected return 3 standard deviation 4 variance 5 correlation 6 covariance 7 T-bill rate 0.32 =B3*B3 0.125 =B5*B3*C3 0.04 9 a) 10 expected return 11 12 weights in portfolio 13 variance of portfolio 14 expected return of portfolio 15 standard deviation of portfolio 16 17 18 optimal risky portfolio 19 excess return portfolio 0.08 stock fund =(B10-C2)/(B2-C2) =(B12*B12*B4)+(C12*C12*C4)+(2*B12*C12*B6) =(B12*B2)+(C12*C2) =SQRT(B13) bond fund =1-B12 20 21 Portfolio weights 22 expected return 23 variance 24 standard deviation stock fund Bond fund =B2-$B$7 =C2-$B$7 stock fund Bond fund =((B19*C4)-(C19*B6))/((B19*C4)+(C19*B4)-((B19+C19)*B6)) =1-B21 =(B21*B2)+(C21*C2) =(B21*B21*B4)+(C21*C21*C4)+(2*B21*C21* B6) =SQRT(B23) 25 optimal risky portfolio =(B10-B7)/(B22-B7) T-bill =1-B27 26 27 % invested 28 b-1 29 % invested in T-bill 30 b-2 =C27 stock fund =$B$27*B21 Bond fund =$B$27*021 32 % invested