Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is 0.4. The risk-free rate of return is 5%.

What is the REWARD to VARIABILITY Ratio of the Optimal Portfolio?

Answer 1

To find the fraction of wealth to invest in Stock A that will result in the risky portfolio with maximum Sharpe ratio the following formula to determine the weight of Stock A in risky portfolio should be used

	Where
Stock A	E[R(d)]=	21.00%
Stock B	E[R(e)]=	14.00%
Stock A	Stdev[R(d)]=	39.00%
Stock B	Stdev[R(e)]=	20.00%
	Var[R(d)]=	0.15210
	Var[R(e)]=	0.04000
T bill	Rf=	5.00%
Correl	Corr(Re,Rd)=	0.4
Covar	Cov(Re,Rd)=	0.0312
Stock A	Therefore W(*d)=	0.2923
Stock B	W(*e)=(1-W(*d))=	0.7077
	Expected return of risky portfolio=	16.05%
	Risky portfolio std dev=	21.43%
Sharpe ratio=	(Port. Exp. Return-Risk free rate)/(Port. Std. Dev)		=(0.1605-0.05)/0.2143	=0.5156
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