You have a portfolio worth $50,000 consisting of two stocks, A and B. You invest

ID: 2629765 • Letter: Y

Question

You have a portfolio worth $50,000 consisting of two stocks, A and B. You invested $20,000 in stock A. Consider the following information:

a) What is the expected return for A? for B?

b) What is the standard deviation for A? for B?

c) What is the expected return and standard deviation for the portfolio?

d) What is the correlation between A and B? are there benefits to forming a portfolio of these two securities?

State of economy Probability Return on A Return on B Growth .30 10% 20% Normal .5 15% 4% Recession .2 -12% 0%

a.) E(r) for A = 0.3*0.1 + 0.5*0.15 - 0.2*0.12 = 0.081 = 8.1%

E(r) for B = 0.3*0.2 + 0.5*0.04 = 0.08 = 8.0%

b.) Variance for A = 0.3*(0.1-0.081)^2 + 0.5*(0.15-0.081)^2 + 0.2*(-0.12-0.081)^2 = 0.010569

s.d for A = sqrt(Var) = 0.1028 = 10.28%

Variance for B = 0.3*(0.2-0.08)^2 + 0.5*(0.04-0.08)^2 + 0.2*(0-0.08)^2 = 0.0064

s.d for B = sqrt(Var) = 0.08 = 8.0%

c.) weight of A = 20,000/50,000 = 2/5

weight of B = 3/5

E(r) of portfolio = (2/5)*0.081 + (3/5)*0.08 = 0.0804 = 8.04%

s.d of portfolio = sqrt[wA^2*s.dA^2 + wB^2*s.dB^2 + 2*wA*wB*Cov(A,B)]

Cov(A,B) = 0.3(0.1-0.081)(0.2-0.08) + 0.2(0.15-0.081)(0.04-0.08) + 0.2(-0.12-0.081)(0-0.08) = 0.003348

So s.d of portfolio = sqrt[ 0.4^2*0.1028^2 + 0.6^2*0.08^2 + 2*0.4*0.6*0.009504 ] = 0.07485 = 7.485%

d.) Correlation between A and B = Cov(A,B)/(s.dA*s.dB) = 0.003348/(0.1028*0.08) = 0.407

Since correlation coefficient is 0.4, there are benefits to forming a portfolio between A nd B

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