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 sure rate of 4.7%. The probability distributions of
the risky funds are:
Expected Return | Standard Deviation | |
Stock fund (S) | 17% | 37% |
Bond fund (B) | 8% | 31% |
The correlation between the fund returns is 0.1065.
What is the Sharpe ratio of the best feasible CAL?
PLEASE DO NOT ROUND ANY NUMBERS UNTIL FINAL ANSWER OR ELSE IT WILL BE 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)]= | 17.00% | |||
Bond fund | E[R(e)]= | 8.00% | |||
Stock fund | Stdev[R(d)]= | 37.00% | |||
Bond fund | Stdev[R(e)]= | 31.00% | |||
Var[R(d)]= | 0.13690 | ||||
Var[R(e)]= | 0.09610 | ||||
T bill | Rf= | 4.70% | |||
Correl | Corr(Re,Rd)= | 0.1065 | |||
Covar | Cov(Re,Rd)= | 0.0122 | |||
Stock fund | Therefore W(*d)= | 0.7911 | |||
Bond fund | W(*e)=(1-W(*d))= | 0.2089 | |||
Expected return of risky portfolio= | 15.12% | ||||
Risky portfolio std dev= | 30.64% | ||||
Sharpe ratio= | (Port. Exp. Return-Risk free rate)/(Port. Std. Dev) | =(0.151197-0.047)/0.30644 | =0.340024 | ||
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 |