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A pension fund manager is considering three mutual funds. The first is a stock fund, thelong-term government and corporate bond fund, and the third is a T-billrate of 4.6%. The probability distribution of the twosecond is amoney market fund that yields arisky funds is as follows:ExpectedReturnStandard DeviationStock fund (SBond fund (B36%30%16%7%The correlation between the two fund returns is 0.16.Compute the proportions of stock fund and bond fund of the optimal risky portfolio, andcalculate the expected return and standard deviation of the optimal risky portfolio.Assume that short sales of mutual funds are allowed. (Do not round intermediatecalculations. Enter your answer as a percentage rounded to two decimal places.)Proportion invested in the stockfund%Proportion invested in the bondfund%Expected returnStandard deviation

Question
A pension fund manager is considering three mutual funds. The first is a stock fund, the
long-term government and corporate bond fund, and the third is a T-bill
rate of 4.6%. The probability distribution of the two
second is a
money market fund that yields a
risky funds is as follows:
Expected
Return
Standard Deviation
Stock fund (S
Bond fund (B
36%
30%
16%
7%
The correlation between the two fund returns is 0.16.
Compute the proportions of stock fund and bond fund of the optimal risky portfolio, and
calculate the expected return and standard deviation of the optimal risky portfolio.
Assume that short sales of mutual funds are allowed. (Do not round intermediate
calculations. Enter your answer as a percentage rounded to two decimal places.)
Proportion invested in the stock
fund
%
Proportion invested in the bond
fund
%
Expected return
Standard deviation
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A pension fund manager is considering three mutual funds. The first is a stock fund, the long-term government and corporate bond fund, and the third is a T-bill rate of 4.6%. The probability distribution of the two second is a money market fund that yields a risky funds is as follows: Expected Return Standard Deviation Stock fund (S Bond fund (B 36% 30% 16% 7% The correlation between the two fund returns is 0.16. Compute the proportions of stock fund and bond fund of the optimal risky portfolio, and calculate the expected return and standard deviation of the optimal risky portfolio. Assume that short sales of mutual funds are allowed. (Do not round intermediate calculations. Enter your answer as a percentage rounded to two decimal places.) Proportion invested in the stock fund % Proportion invested in the bond fund % Expected return Standard deviation

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Step 1

Let the Stock Fund be Security A and Bond Fund be security B

Calculation of Covariance of security A,B:

Correlation (A B)=Covariance (A,B)
σΑχ σΒ
O.16=Covariance (A,B)
0.36x0.30
0.16x0.36x0.30 =Covariance (AB)
0.01728 Covariance (A,B
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Correlation (A B)=Covariance (A,B) σΑχ σΒ O.16=Covariance (A,B) 0.36x0.30 0.16x0.36x0.30 =Covariance (AB) 0.01728 Covariance (A,B

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Step 2

Calculation of Expected Return of the portfolio(A,B):

Covariance(A.B) = Expected Return (A,B) -Expected Return ( A ) x Expected Retun (B)
0.01728=Expected returm (A,B)-0.16x 0.07
0.01728+0.16x0.07 = Expected return ( A,B)
0.02848= Expected Return (A,B)
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Covariance(A.B) = Expected Return (A,B) -Expected Return ( A ) x Expected Retun (B) 0.01728=Expected returm (A,B)-0.16x 0.07 0.01728+0.16x0.07 = Expected return ( A,B) 0.02848= Expected Return (A,B)

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Step 3

Calculation of Weights of Stock Fund and bond fund:

Therefore the weight of security B be (1-x)i.e (1-(-0...

Expected Return(A B) = Return(A)x Weight(A)+Return(B) x Weight(B)
0.02848 =0.16xx+0.07 x (1 - x)
0.02848= 0.16x+ 0.07 - 0.07x
0.02848-0.07=0.09x
-0.04152 0.09x
-0.46 x
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Expected Return(A B) = Return(A)x Weight(A)+Return(B) x Weight(B) 0.02848 =0.16xx+0.07 x (1 - x) 0.02848= 0.16x+ 0.07 - 0.07x 0.02848-0.07=0.09x -0.04152 0.09x -0.46 x

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