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 5.2%. The probability distributions of
the risky funds are:

Expected Return | Standard Deviation | |

Stock fund (S) |
13% | 42% |

Bond fund (B) |
6% | 36% |

The correlation between the fund returns is 0.0222.

What is the expected return and standard deviation for the
minimum-variance portfolio of the two risky funds? **(Do not
round intermediate calculations. Round your answers to 2 decimal
places.)**

Answer #1

For minimum Variance portfolio

Weight of (S) = ((Standard Deviation of B)^{2} -correlation
* Standard Deviation of S * Standard

Deviation of B)/((Standard Deviation of S)^{2} + (Standard
Deviation of B)^{2} - 2 * correlation * Standard Deviation
of S * Standard Deviation of B) = ( 36%^{2}
-0.0222*42%*36%)/(42%^{2} + 26%^{2} -2 *
0.0222*42%*36%) = 42.18%

Weight of S = 42.18%

Weight of B =1-42.18% =57.82%

Expected Return =Weight of S* Expected Return of S+Weight of B*
Expected Return of B =42.18%*13%+57.82%*6% **=8.95%**

Standard Deviation = ((Weight of S * Standard Deviation of
S)^{2} + (weight of B * standard Deviation of
B)^{2} + 2* Weight of S * Standard Deviation of S* weight
of B * standard Deviation of B * correlation)^{0.5}

= ((42.18*42%) + (57.82%*36%) + 2* 42.18*42% * 57.82*36% *
0.022)^{0.5} = **27.63%**

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Standard Deviation
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