A pension fund manager is considering three mutual funds. The first is a stock fund, the...

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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
w(d)= ((E[Rd]-Rf)Var(Re)-(E[Re]-Rf)Cov(Re,Rd))/((E[Rd]-Rf)Var(Re)+(E[Re]-Rf)Var(Rd)-(E[Rd]+E[Re]-2Rf)*Cov(Re,Rd)

						Where
					Stock fund	E[R(d)]=	17.00%
bond fund	E[R(e)]=	13.00%
Stock fund	Stdev[R(d)]=	38.00%
bond fund	Stdev[R(e)]=	18.00%
	Var[R(d)]=	0.14440
	Var[R(e)]=	0.03240
T bill	Rf=	5.00%
Correl	Corr(Re,Rd)=	0.12
Covar	Cov(Re,Rd)=	0.0082
Stock fund	Therefore W(*d) =	0.2342
bond fund	W(e)=(1-W(d))=	0.7658
	Expected return of risky portfolio =	13.94%
	Risky portfolio std dev =	17.28%
Sharpe ratio=	(Port. Exp. Return-Risk free rate)/(Port. Std. Dev)		=(0.1394-0.05)/0.1728	=0.5174


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?2(RA)+w2B?2(RB)+2(wA)(wB)Cor(RA,RB)?(RA)*?(RB))^0.5

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