Question

# A pension fund manager is considering three mutual funds. The first is a stock fund, the...

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 4.8%. The probability distributions of the risky funds are:
expected return standard deviation
Stock Fund ( S )---------18%-------------38%
Bond Fund ( B )----------9----------------32
the correlation between the fund returns is .13

Standard deviation of optimal risky portfolio is 30.92%. If you were to use only the two risky funds and still require an expected return of 15% , what would be the investment proportions of your portfolio? Compare its standard deviation to that of the optimal portfolio in the previous problem. What do you conclude?

 We know that 15.00 `= 18xs `+ 9xb 30.66 `= 38xs `+ 32xb or, 5.00 `= 6s `+ 3b 15.33 `= 19s `+ 16b or, 95.00 `= 114s `+ 57b 91.98 `= 114s `+ 96b or, 3.02 `= -39.00 b b `= -0.08 s `= 1.08 hence, the pension fund manager should sell Bond Fund by 8% and on the same hand buy Stock Fund by 108% so as to get the optimal return of 15%