Question

2. Two stocks A and B have return and risk information: E(rA) = 8%, E(rB) = 10%; aA = 12%, aB = 15%; pAB = 0.6. The two stocks are used to construct a minimum variance portfolio. Answer the following questions:

2.1. What is the weight of stock A of the minimum variance portfolio?

2.2. What is the expected return of the minimum variance portfolio?

2.3. What is the standard deviation of the minimum variance portfolio?

Answer 1

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

	Where
Stock A	E[R(d)]=	8.00%
Stock B	E[R(e)]=	10.00%
Stock A	Stdev[R(d)]=	12.00%
Stock B	Stdev[R(e)]=	15.00%
	Var[R(d)]=	0.01440
	Var[R(e)]=	0.02250
T bill	Rf=	5.50%
Correl	Corr(Re,Rd)=	0.6
Covar	Cov(Re,Rd)=	0.0108
Stock A	Therefore W(*d) (answer 2.1)=	0.7647
Stock B	W(*e)=(1-W(*d))=	0.2353
	Expected return of risky portfolio (answer 2.2)=	8.47%
	Risky portfolio std dev (answer 2.3)=	11.64% 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