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 5.5%. The stock fund has an expected return of 15% and a standard deviation of 23%. The bond fund has an expected return of 9% and a standard deviation of 23%. The correlation between the fund returns is.15.

 a) What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds?

Answer 1

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

C D Expected return Std. Deviation of return Correlation Stock Fund (S) Bond fund (B) 15.00% 9.00% 23.00% 23.00% 0.15 Minimum variance Portfolio (S+B) Portfolio invested in the stock Portfolio invested in the bond 0.5000 0.5000 Expected return Standard deviation 12.00% 17.44%

Cell reference -

D Stock Fund (s) Bond fund (B) 0.15 Expected return Std. Deviation of return Correlation 0.09 0.23 0.23 0.15 NMODE Minimum variance Portfolio (S+B) Portfolio invested in the stock =(D42-C5*C4*D4)/(C4^2+D4^2-2*C5*C4*D4) Portfolio invested in the bond =1-C8 a) Expected return Standard deviation =C8*C3+C9*D3 |=SQRT{(C8*C4)^2+(C9*D4)^2+2*C8*C9*C4*D4*C5) 13

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