In: Finance
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) E.R. 15 % S.D. 32 %
Bond fund (B) E.R. 9 % S.D. 23 %
The correlation between the fund returns is 0.15. Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio. (Do not round intermediate calculations and round your final answers to 2 decimal places.)
Portfolio invested in the stock | not attempted | % |
Portfolio invested in the bond | not attempted | % |
Expected return | 10.89selected answer incorrect | % |
Standard deviation | 19.94selected answer incorrect | % |
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 |
Where | ||
Stock fund | E[R(d)]= | 15.00% |
Bond fund | E[R(e)]= | 9.00% |
Stock fund | Stdev[R(d)]= | 32.00% |
Bond fund | Stdev[R(e)]= | 23.00% |
Var[R(d)]= | 0.10240 | |
Var[R(e)]= | 0.05290 | |
T bill | Rf= | 5.50% |
Correl | Corr(Re,Rd)= | 0.15 |
Covar | Cov(Re,Rd)= | 0.0110 |
Stock fund | Therefore W(*d)= | 0.6466 = 64.66% |
Bond fund | W(*e)=(1-W(*d))= | 0.3534 = 35.34% |
Expected return of risky portfolio= | 12.88% | |
Risky portfolio std dev= | 23.34% |
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 |