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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 Funds (S) 24% 30%

Bonds Funds (B) 12 19

The correlation between the fund returns is 0.13. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio.

Portfolio invested in stocks?

Portfolio invested in bonds?

Expected return?

Standard Deviation?

(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 maximum Sharpe ratio
the following formula to determine the weight of Stock fund in risky portfolio should be used
w(*d)= ((E[Rd]-Rf)*Var(Re)-(E[Re]-Rf)*Cov(Re,Rd))/((E[Rd]-Rf)*Var(Re)+(E[Re]-Rf)*Var(Rd)-(E[Rd]+E[Re]-2*Rf)*Cov(Re,Rd)
Where
Stock fund E[R(d)]= 24.00%
bond fund E[R(e)]= 12.00%
Stock fund Stdev[R(d)]= 30.00%
bond fund Stdev[R(e)]= 19.00%
Var[R(d)]= 0.09000
Var[R(e)]= 0.03610
T bill Rf= 8.00%
Correl Corr(Re,Rd)= 0.13
Covar Cov(Re,Rd)= 0.0074
Stock fund Therefore W(*d) (answer a)= 0.6941
bond fund W(*e)=(1-W(*d)) (answer b)= 0.3059
Expected return of risky portfolio (answer c)= 20.33%
Risky portfolio std dev (answer Risky portfolio std dev)= 22.34%
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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