Question

Stock A has an expected return of 15% and a standard deviation of 26%. Stock B has an expected return of 15% and a standard deviation of 12%. The risk-free rate is 4% and the correlation between Stock A and Stock B is 0.5. Build the optimal risky portfolio of Stock A and Stock B. What is the standard deviation of this 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
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]-2*Rf)*Cov(Re,Rd)
	Where
Stock A	E[R(d)]=	15.00%
Stock B	E[R(e)]=	15.00%
Stock A	Stdev[R(d)]=	26.00%
Stock B	Stdev[R(e)]=	12.00%
	Var[R(d)]=	0.06760
	Var[R(e)]=	0.01440
T bill	Rf=	4.00%
Correl	Corr(Re,Rd)=	0.5
Covar	Cov(Re,Rd)=	0.0156
Stock A	Therefore W(*d)=	-0.0236
Stock B	W(*e)=(1-W(*d))=	1.0236
	Expected return of risky portfolio=	15.00%
	Risky portfolio std dev (answer Risky portfolio std dev)=	11.99%
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