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.

I calculated the a) and b)

a) correlation between stock A and B = Covariance/(SD of stock A*SD of stock B)

= 0.012/(0.2*0.15)

= 0.4

b)

Expected return for portfolio S = 80%*0.14 + 20%*0.08

= 12.8%

Variance of portfolio S = 80%*80%*0.04 + 20%*20%*0.0225 + 2*80%*20%*0.4*0.2*0.15

= 0.0303 = 3.03%

SD of portfolio S = Square root of variance = 0.1742 = 17.42%

But I have questions for c) d) the way that calculate

first method of calculation

Portfolio V consists of Portfolio S and risk free asset with 4% return.

SD of portfolio V = 27.9%

Expected return for V = Risk free return + [(Expected return for Portfolio S - risk free return)/SD of portfolio S]*SD of portfolio V

= 4% + [(12.8% - 4%)/17.42%]*27.9%

= 18.09%

Second method of calculation

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%

and Ws would be 1.6025

Can you tell me which way is correct?