A pension fund manager is considering three mutual funds. The first is a stock f

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 4.3%. The probability distribution of the risky funds is as follows: The correlation between the fund returns is 0.12. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places. Omit the 94 sign in your response.)

Explanation / Answer

Answer: The parameters of the opportunity set:

E(rs)=13%, E(rb)=6%, standard deviation of stock =34%, standard deviation of bond =27, p=0.12

From the standard deviation and the correlation coefficient we generte the covariance matrix.

cov (rs,rb)=p* standard deviation of stock*standard deviation of bond

The minimum variance portfolio is found by applying the formula:

W min (S) =729+110.16/(1156+729-2(110.16))

=839.16/1664.68=0.5041

W min (B) =0.4960

The minimum variance portfolio of mean and standard deviation are:

E( r min)=05041*13%+0.4960*6=6.5533+2.976=9.5293%

STANDARD DEVIATION = square root of [(0.5041)2*1156+(0.4960)2 *729+2*0.5041*0.4960*110.16

=square root of [(293.76+179.35+55.09]

=22.98%

Bonds Stock Bonds 729 110.16 Stock 110.16 1156

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