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 5.5%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 15 % 32 % Bond fund (B) 9 % 23 % The correlation between the fund returns is 0.15. a. What would be the investment proportions of your portfolio if you were limited to only the stock and bond funds and the portfolio has to yield an expected return of 12%

Explanation:

From the information given we  first calculate the co-variance matrix

Stock = 32%*32%=1024

Bond = 23%*23%= 529

stocks/bonds = 32%*34*1.5 =110.4

Min weight for proportion to be invested in stocks can be calculated using the formula

Mws =B^2 - CV(S,B)/B^2+S^2-2CV(S,,B)

        529 -110.4/1024+529-2(110.4)

        =0.3142

The minimum to be invested in bonds can be calculated as

Mwb = 1 -0.3142

           0.6858

since the investment horizon is between stocks and bonds only.

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answer; coefficient of correlation;