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 8%. The probability distribution of the risky funds is as follows: Expected Return Standard Deviation Stock fund (S) 16 % 35 % Bond fund (B) 12 15 The correlation between the fund returns is 0.13. 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.)
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 | |||||
w(*d)= ((Stdev[R(e)])^2-Stdev[R(e)]*Stdev[R(d)]*Corr(Re,Rd))/((Stdev[R(e)])^2+(Stdev[R(d)])^2-Stdev[R(e)]*Stdev[R(d)]*Corr(Re,Rd)) | |||||
Where | |||||
Stock fund | E[R(d)]= | 16.00% | |||
bond fund | E[R(e)]= | 12.00% | |||
Stock fund | Stdev[R(d)]= | 35.00% | |||
bond fund | Stdev[R(e)]= | 15.00% | |||
Var[R(d)]= | 0.12250 | ||||
Var[R(e)]= | 0.02250 | ||||
T bill | Rf= | 8.00% | |||
Correl | Corr(Re,Rd)= | 0.13 | |||
Covar | Cov(Re,Rd)= | 0.0068 | |||
Stock fund | Therefore W(*d) (answer a-1)= | 0.1193 | |||
bond fund | W(*e)=(1-W(*d)) (answer a-1)= | 0.8807 | |||
Expected return of risky portfolio (answer a-2)= | 12.48% = 0.1248 | ||||
Risky portfolio std dev (answer a-2)= | 14.36% = 0.1436 | ||||
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 |