Question

Asset K has an expected return of 21 percent and a standard deviation of 36 percent. Asset L has an expected return of 9 percent and a standard deviation of 20 percent. The correlation between the assets is 0.45. What are the expected return and standard deviation of the minimum variance portfolio? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

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

	Where
Asset K	E[R(d)]=	21.00%
Asset L	E[R(e)]=	9.00%
Asset K	Stdev[R(d)]=	36.00%
Asset L	Stdev[R(e)]=	20.00%
	Var[R(d)]=	0.12960
	Var[R(e)]=	0.04000
T bill	Rf=	8.00%
Correl	Corr(Re,Rd)=	0.45
Covar	Cov(Re,Rd)=	0.0324
Asset K	Therefore W(*d) (answer a-1)=	0.0725
Asset L	W(*e)=(1-W(*d)) (answer a-1)=	0.9275
	Expected return of risky portfolio (answer a-2)=	9.87%
	Risky portfolio std dev (answer a-2)=	19.86%

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