A pension fund manager is considering three mutual funds. The first is a stock fund, thesecond is a long-term government and corporate bond fund, and the third is a T-billmoney market fund that yieldstwo risky funds are:a sure rate of 5.8%. The probability distributions of theExpectedReturn19%StandardDeviationStock fund (S)Bond fund (B)48%42%9%The correlation between the two fund returns is .0762What is the expected return and standard deviation for the minimum-variance portfolioof the two risky funds? (Do not round intermediate calculations. Enter your answer asa percentage rounded to two decimal places.)Expected returnStandard deviation

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Asked Oct 7, 2019
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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 corporate bond fund, and the third is a T-bill
money market fund that yields
two risky funds are:
a sure rate of 5.8%. The probability distributions of the
Expected
Return
19%
Standard
Deviation
Stock fund (S)
Bond fund (B)
48%
42%
9%
The correlation between the two fund returns is .0762
What is the expected return and standard deviation for the minimum-variance portfolio
of the two risky funds? (Do not round intermediate calculations. Enter your answer as
a percentage rounded to two decimal places.)
Expected return
Standard deviation
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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 corporate bond fund, and the third is a T-bill money market fund that yields two risky funds are: a sure rate of 5.8%. The probability distributions of the Expected Return 19% Standard Deviation Stock fund (S) Bond fund (B) 48% 42% 9% The correlation between the two fund returns is .0762 What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places.) Expected return Standard deviation

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Expert Answer

Step 1

Cov (S,B) is calculated as follows:

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Cov(S.B) SD of Sx SD of B x Corelation =48x 42x 0.0762 =153.62%

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Step 2

The weight of stock fund (S) and stock fund (B) at optimal portfolio can be ascertained as follows:

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Weight of stock fund (S) at optimal portfolio E(t)-J[E(,)-1;]0 E ()-o7,-[E(1,)-E(5)Cov(B.S) [E()Cov(BS) I O _ B Ws 11 [E(T)-Jo+ 19-5.8x 4229-5.8x153.62 19-5.8]x 422 +[9-5.8]x 482 - [19-5.8+9-5.8]x153.62 X X -0.81 Weight of bond fund (B) at optimal portfolio( Wg) = 1- 0.81 =0.19

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Step 3

Expected return of portfolio can be ascertained as follows:

Therefore, the expected retur...

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E(b)= W,x E ()+W3 x E(I) (0.81x 19)+(0.19x9) -15.391.71 17.1%

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