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 4.8%. 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?

Answer #1

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% |

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