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 probability distributions of
the risky funds are:

Expected Return | Standard Deviation | |

Stock fund (S) |
16% | 45% |

Bond fund (B) |
7% | 39% |

The correlation between the fund returns is 0.0385.

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

Given about funds

expected return on stock fund E(S) = 16%

standard devidation on stock fund SD(S) = 45%

expected return on Bond fund E(B) = 7%

standard devidation on Bond fund SD(B) = 39%

The return correlation between Stock fund and Bond fund Corr(S,B) = 0.0385

Weight of stock find WS in Minimum variance portfolio is given by

WS = (SD(B)^2 - SD(S)*SD(B)*Corr(S,B))/(SD(S)^2 + SD(B)^2 - 2*SD(S)*SD(B)*Corr(S,B))

So, WS = (39^2 - 45*39*0.0385)/(45^2 + 39^2 + 2*45*39*0.0385) = 0.3948 or 39.48%

So, weight of security B in the portfolio = 1-0.3948 = 0.6052 or 60.52%

Expected return of this minimum variance portfolio is

WS*E(S) + WB*E(B) = 0.3948*16 + 0.6052*7 = 10.55%

Standard deviation of this minimum variance portfolio is

SD(p) = ((WS*SD(S))^2 + (WB*SD(B))^2 - 2*WS*WB*SD(S)*SD(B)*Corr(A,B))

SD(p) = SQRT((0.3948*45)^2 + (0.6052*39)^2 + 2*0.3948*0.6052*45*39*0.0385) = 29.81%

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) 16% 45%
Bond fund (B) 7% 39%
The correlation between the fund returns is 0.0385. What is the
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A pension fund manager is considering three mutual funds. The
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A pension fund manager is considering three mutual funds. The
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Expected Return
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A pension fund manager is considering three mutual funds. The
first is a stock fund, the second is a long-term government and
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the risky funds are:
Expected Return
Standard Deviation
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Bond fund (B)
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39%
The correlation between the fund returns is .0385.
What is the expected return and standard deviation for...

A pension fund manager is considering three mutual funds. The
first is a stock fund, the second is a long-term government and
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that yields a sure rate of 5.5%. The probability distributions of
the risky funds are:
Expected Return
Standard Deviation
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The correlation between the fund returns is .15.
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