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 5.5%. The probability distribution of the risky funds is as follows:

	Expected Return		Standard Deviation
Stock fund (S)	15	%	32	%
Bond fund (B)	9	%	23	%

The correlation between the fund returns is 0.15.

Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio.

Portfolio invested in stock? %

Portfolio invested in bond? %

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 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)]=	15.00%
Bond fund	E[R(e)]=	9.00%
Stock fund	Stdev[R(d)]=	32.00%
Bond fund	Stdev[R(e)]=	23.00%
	Var[R(d)]=	0.10240
	Var[R(e)]=	0.05290
T bill	Rf=	5.50%
Correl	Corr(Re,Rd)=	0.15
Covar	Cov(Re,Rd)=	0.0110
Stock fund	Therefore W(*d)=	64.66%
Bond fund	W(*e)=(1-W(*d))=	35.34%
	Expected return of risky portfolio=	12.88%
	Risky portfolio std dev=	23.34%

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