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 .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.)**

Expected return | % |

Standard deviation | % |

Answer #1

From the standard deviations and the correlation coefficient we can generate the “covariance matrix” | |||||

Bonds | Stock | ||||

Bonds | ?^2 B | COV(B,S)= ?SBx ?S X ?B | |||

Stock | COV(B,S) | ?^2A | |||

Bonds | Stock | ||||

Bonds | 1521 | 67.5675 | 0.00675675 | covariance % | |

Stock | 67.5675 | 2025 | |||

minimum variance weight | |||||

WSMin
= ?^2 B - COV(B,S)/?^2 B + ?^2 S - 2Cov(B,S) |
|||||

WSMin = (1521-67.5675)/(1521+2025 - 2 x 67.5675) | 42.6118% | Weight Stock | |||

WB min = 1- 42.61% | 57.3882% | Weight Bond | |||

Expected Return = 16% x 42.61% +7% x 57.38% | 10.84% | ||||

Standard Deviation = [(0.4261)^2(0.45)^2+ (0.5738)^2(0.39)^2+ 2(0.4261)(0.5738)(.006757)]^1/2 | 30.03% | ||||

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 .0385.
What is 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 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 .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
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...

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...

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)
15
%
32
%
Bond fund (B)
9
%
23
%
The correlation between the fund returns is .15.
What is the expected return...

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) 15 % 32 % Bond fund (B) 9 % 23 % The correlation between the
fund returns is .15. What is the expected return...

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)
15%
32%
Bond fund (B)
9%
23%
The correlation between the fund returns is .15.
What is the expected return and standard deviation...

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 (Left) Standard Deviation (Right)
Stock fund (S) 16% 45%
Bond fund (B) 7% 39%
The correlation between the fund returns is 0.0385. What is the
Sharpe ratio of 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 5.8%. The probability distributions of
the risky funds are: Expected Return Standard Deviation Stock fund
(S) 19% 48% Bond fund (B) 9% 42% The correlation between the fund
returns is .0762. 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
corporate bond fund, and the third is a T-bill money market fund
that yields a sure rate of 5.3%. The probability distributions of
the risky funds are:
Expected Return
Standard Deviation
Stock fund (S)
14%
43%
Bond fund (B)
7%
37%
The correlation between the fund returns is 0.0459.
What is the expected return and standard deviation for...

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