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) |
15 | % | 32 | % |

Bond fund (B) |
9 | % | 23 | % |

The correlation between the fund returns is 0.15.

**a.** What would be the investment proportions of
your portfolio if you were limited to only the stock and bond funds
and the portfolio has to yield an expected return of 12%?

**b.** Calculate the standard deviation of the
portfolio which yields an expected return of 12%. **(Do not
round intermediate calculations. Round your answer to 2 decimal
places.)**

Answer #1

**Answer (a):**

Let us assume investment proportion of Stock fund is Ws.

Hence:

Investment proportion of Bond fund will be = 100% - Ws

Expected return of portfolio = 12%

As such:

=> Ws*15% + (100% - Ws) * 9% = 12%

=> 15% Ws + 9% - 9% Ws =12%

=> 6% Ws = 12% -9% = 3%

=> Ws = 3% / 6% = 50%

Investment proportion of Bond fund will be = 100% - Ws = 100% - 50% = 50%

Hence:

**Investment proportions of your portfolio in the stock
fund = 50%**

**Investment proportions of your portfolio in the bond
fund = 50%**

**Answer (b):**

The correlation between the fund returns is 0.15.

Formula for Standard deviation of portfolio (of Asset A and B) is:

Standard deviation of portfolio

= SQRT (50% ^{2} * 32% ^{2} + 50% ^{2} *
23% ^{2} + 2 * 50% * 50% * 0.15 * 32% * 23%)

= 21.06%

**Standard deviation of the portfolio which yields an
expected return of 12% = 21.06%**

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 0.15.
1. What would be the investment proportions...

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 rate of 5.5%. The probability distribution of the
risky funds is as follows:
Expected Return
Standard Deviation
Stock fund (S)
15%
32%
Bond fund (B)
9
23
The correlation between the fund returns is 0.15.
Solve numerically for the proportions of each...

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 0.15. Suppose now that your portfolio...

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 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 vields a sure rate of 5.5%, The correlation between the stock
and bond fund returns is 0.25.The probability distributions of the
risky funds are:
Expected
Return Standard Deviation
Stock Fund
(S)
15%
32%
Bond Fund (B)
9%
23%
What is the standard deviation of...

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 .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 .0385.
What is the...

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