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 sure rate of 5.2%. The probability distributions of the risky funds are:

	Expected Return	Standard Deviation
Stock fund (S)	13%	42%
Bond fund (B)	6%	36%

The correlation between the fund returns is 0.0222.

What is the expected return and standard deviation for the minimum-variance portfolio of the two risky funds?

Expected Return=?

Standard Deviation=?

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

	Where
Stock fund	E[R(d)]=	13.00%
Bond fund	E[R(e)]=	6.00%
Stock fund	Stdev[R(d)]=	42.00%
Bond fund	Stdev[R(e)]=	36.00%
	Var[R(d)]=	0.17640
	Var[R(e)]=	0.12960
T bill	Rf=	5.20%
Correl	Corr(Re,Rd)=	0.0222
Covar	Cov(Re,Rd)=	0.0034
Stock fund	Therefore W(*d)=	0.4218
Bond fund	W(*e)=(1-W(*d))=	0.5782
	Expected return of risky portfolio=	8.95%
	Risky portfolio std dev=	27.63%

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