Question

Problem 11-14 Minimum Variance Portfolio (LO4, CFA4)

Refer to the table below:

		3 Doors, Inc.			Down Co.
Expected return, E(R)		10	%		11	%
Standard deviation, σ		25			22
Correlation				0.20

Using the information provided on the two stocks in the table above, find the expected return and standard deviation on 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 3 Doors that will result in the risky portfolio with minimum variance the following formula to determine the weight of 3 Doors in risky portfolio should be used

	Where
3 Doors	E[R(d)]=	10.00%
Down co	E[R(e)]=	11.00%
3 Doors	Stdev[R(d)]=	25.00%
Down co	Stdev[R(e)]=	22.00%
	Var[R(d)]=	0.06250
	Var[R(e)]=	0.04840
T bill	Rf=	8.00%
Correl	Corr(Re,Rd)=	0.2
Covar	Cov(Re,Rd)=	0.0110
3 Doors	Therefore W(*d) (answer a-1)=	0.4207
Down co	W(*e)=(1-W(*d)) (answer a-1)=	0.5793
	Expected return of risky portfolio (answer a-2)=	10.58%
	Risky portfolio std dev (answer a-2)=	18.07%

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