Question

2. Two stocks A and B have expected returns, and a variance-covariance matrix of returns given in Table 1.

Table 1 Stock A		Stock B
E(R)	0.14		0.08
Variance-covariance matrix:
Stock A		Stock B
Stock A	0.04		0.012
Stock B	0.012		0.0225

a) What is the correlation coefficient between the returns on stock A and stock B?

b) What is the expected return and standard deviation of portfolio S which is invested 80% in stock A and 20% in stock B?

c) If you combine portfolio S with a risk free asset paying a return of 4%, what would be the expected return on a new portfolio V if you desire a standard deviation of 27.9%?

d) Plot in mean-standard deviation space the efficiency frontier between Stock A and Stock B, and identify portfolios S and V.

Answer 1

Part A

Correlation coefficient i.e. r = CoV(A,B)/(SD(A) * SD(B))

Where

COV(A,B) = covariance between A and B= .012

Var(A) = variance of A=.04

Var(B) = variance of B =.0225

SD(A) =(.04)^.5 =.2

SD(B) = (.0225)^.5 = .15

r = .012/(.2 * .15) = .40

Part b

Expected return in portfolio S = ERs = Weighted average of returns = .80 * .14 + .20 * .08 = .128 or 12.8%

SD of this portfolio s is given by

SDs =((Wa*SD(A))^2 +( Wb*SD(B))^2+ 2 * Wa*Wb*COV(A,B))^.50

Where

Wa= wieght of A = .80

Wb= weight of B= .20

Therefore

SDs = ((.80*.2)^2 +(.20*.15)^2 +2*.80*.20*.012)^.50

=.1741 =17.41%

Part c

Since SD of a risk free asset=0

The SD of portfolio V is

SDv= Ws* SDs

Where

Ws = weight of portfolio S (risky portfolio) in portfolio V(balanced portfolio)

Our Desired SDv= 27.9%

Therefore

27.9% =Ws*17.41%

Ws= .6243

So the weight of risk free asset =Wf= 1-Ws= 1-.6243 =.3757

Expected return of portfolio V=ERv= Ws*ERs +Wf*Rf

Rf= risk free return =4%

ERv= .6243 * 12.8% + .3757 *4% = 9.5%

Part d