Question

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A pension fund manager is considering three mutual funds. The first is a stock fund, 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 rate of 8%. The probability distribution of the risky funds is as follows:

Expected Return Standard Deviation
Stock fund (S) 23 % 28 %
Bond fund (B) 15 17

The correlation between the fund returns is 0.12.

a-1. What are the investment proportions in the minimum-variance portfolio of the two risky funds. (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

a-2. What is the expected value and standard deviation of its rate of return? (Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.)

Solutions

Expert Solution

To find the fraction of wealth to invest in Stock fund that will result in the risky portfolio with minimum variance the following formula to determine the weight of Stock fund in risky portfolio should be used

Where
Stock fund E[R(d)]= 23.00%
bond fund E[R(e)]= 15.00%
Stock fund Stdev[R(d)]= 28.00%
bond fund Stdev[R(e)]= 17.00%
Var[R(d)]= 0.07840
Var[R(e)]= 0.02890
T bill Rf= 8.00%
Correl Corr(Re,Rd)= 0.12
Covar Cov(Re,Rd)= 0.0057
Stock fund Therefore W(*d) (answer a-1)= 0.2419
bond fund W(*e)=(1-W(*d)) (answer a-1)= 0.7581
Expected return of risky portfolio (answer a-2)= 16.93%=0.1693
Risky portfolio std dev (answer a-2)= 15.26%=0.1526
Where
Var = std dev^2
Covariance = Correlation* Std dev (r)*Std dev (d)
Expected return of the risky portfolio = E[R(d)]*W(*d)+E[R(e)]*W(*e)
Risky portfolio standard deviation =( w2A*σ2(RA)+w2B*σ2(RB)+2*(wA)*(wB)*Cor(RA,RB)*σ(RA)*σ(RB))^0.5

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