Question

SHOW YOUR WORK, DO NOT USE EXCEL

Consider a portfolio consisting of the following two assets:  Stock A has E[RA] = 10% and ?? = 20%  Stock B has E[RB] = 20% and ?? = 40% Calculate the expected return and standard deviation of the portfolio under the four following sets of assumptions:

(a) wA = 1/2 and wB = 1/2 and ???= 0

(b) wA = 1/2 and wB = 1/2 and ???= -1 (c) wA = 2/3 and wB = 1/3 and ??? = 0

(d) wA = 2/3 and wB = 1/3 and ??? = -1

Answer 1

a

Expected return%=	Wt Asset A*Return Asset A+Wt Asset B*Return Asset B
Expected return%=	0.5*0.1+0.5*0.2
Expected return%=	15
Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
Variance	=0.5^2*0.2^2+0.5^2*0.4^2+2*0.5*0.5*0.2*0.4*0
Variance	0.05
Standard deviation=	(variance)^0.5
Standard deviation=	22.36%

b

Expected return%=	Wt Asset A*Return Asset A+Wt Asset B*Return Asset B
Expected return%=	0.5*0.1+0.5*0.2
Expected return%=	15
Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
Variance	=0.5^2*0.2^2+0.5^2*0.4^2+2*0.5*0.5*0.2*0.4*-1
Variance	0.01
Standard deviation=	(variance)^0.5
Standard deviation=	10.00%

c

Expected return%=	Wt Asset A*Return Asset A+Wt Asset B*Return Asset B
Expected return%=	0.6666*0.1+0.3333*0.2
Expected return%=	13.33
Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
Variance	=0.6666^2*0.2^2+0.3333^2*0.4^2+2*0.6666*0.3333*0.2*0.4*0
Variance	0.03555
Standard deviation=	(variance)^0.5
Standard deviation=	18.85%

d

Expected return%=	Wt Asset A*Return Asset A+Wt Asset B*Return Asset B
Expected return%=	0.6666*0.1+0.3333*0.2
Expected return%=	13.33
Variance	=( w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cor(RA, RB)*σ(RA)*σ(RB))
Variance	=0.6666^2*0.2^2+0.3333^2*0.4^2+2*0.6666*0.3333*0.2*0.4*-1
Variance	0
Standard deviation=	(variance)^0.5
Standard deviation=	0.00%