Question

In: Finance

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 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.

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

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

Related Solutions

A pension fund manager is considering three mutual funds. The first is a stock fund,...
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 5.5%. The stock fund has an expected return of 15% and a standard deviation of 23%. The bond fund has an expected return of 9% and a standard deviation of 23%. The correlation between the fund returns is.15. a) What...
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 sure rate of 5.5%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 16% 45% Bond fund (B) 7% 39% The correlation between the fund returns is 0.0385. What is the expected return and standard deviation for...
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 sure rate of 5.5%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 16% 45% Bond fund (B) 7% 39% The correlation between the fund returns is 0.0385. What is the expected return and standard deviation for...
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 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...
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) 17 % 30 % Bond fund (B) 11 22 The correlation between the fund returns is 0.10. a-1. What are the investment proportions...
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 sure rate of 5.8%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 19% 48% Bond fund (B) 9% 42% The correlation between the fund returns is 0.0762. What is the Sharpe ratio of the best feasible...
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 sure rate of 5.5%. The probability distributions of the risky funds are:Expected ReturnStandard DeviationStock fund (S)15%32%Bond fund (B)9%23%The correlation between the fund returns is .15 What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds? (Do not...
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 sure rate of 4.1%. The probability distributions of the risky funds are:    Expected Return Standard Deviation Stock fund (S) 11 % 33 % Bond fund (B) 8 % 25 % The correlation between the fund returns is .1560. Suppose now that your portfolio...
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 sure rate of 5.9%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 20% 49% Bond fund (B) 9% 43% The correlation between the fund returns is 0.0721. What is the expected return and standard deviation for...
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 sure rate of 5.0%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 11% 40% Bond fund (B) 6% 20% The correlation between the fund returns is 0.0500. What is the Sharpe ratio of the best feasible...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT