Question

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) 17% 30%

Bond Funds 11 22

The correlation between the fund returns is 0.10. 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.)

Answer 1

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)]=	17.00%
bond fund	E[R(e)]=	11.00%
Stock fund	Stdev[R(d)]=	30.00%
bond fund	Stdev[R(e)]=	22.00%
	Var[R(d)]=	0.09000
	Var[R(e)]=	0.04840
T bill	Rf=	8.00%
Correl	Corr(Re,Rd)=	0.13
Covar	Cov(Re,Rd)=	0.0086
Stock fund	Therefore W(*d) (answer a-1)=	0.3284
bond fund	W(*e)=(1-W(*d)) (answer a-1)=	0.6716
	Expected return of risky portfolio (answer a-2)=	12.97%
	Risky portfolio std dev (answer a-2)=	18.79%
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