What is the expected return and standard deviation of a port

What is the expected return and standard deviation of a portfolio which is comprised of $4,500 invested in stock S and $3,000 in stock T? Assume the correlation coefficient between the two securities = -.80. ?

State of Economy Probability of State of Economy. Return if State Occurs Stock S. Return if State Occurs Stock T

Boom 10% 12% 4%

Normal 65% 9% 6%

Recession 25% 2% 9%

Solution

1) The first step is to find the standard deviation of the two securities: Stock S: State of Economy Probability [p] Return [r] p*r Deviation from Expected return [d] d^2 p*d^2 Boom 0.10 12 1.20 4.45 19.8025 1.980250 Normal 0.65 9 5.85 1.45 2.1025 1.366625 Recession 0.25 2 0.50 -5.55 30.8025 7.700625 7.55 11.047500 Expected return = 7.55% Standard deviation = (11.0475)^0.5 = 3.32% Stock T: State of Economy Probability [p] Return [r] p*r Deviation from Expected return [d] d^2 p*d^2 Boom 0.10 4 0.40 -2.55 6.5025 0.650250 Normal 0.65 6 3.90 -0.55 0.3025 0.196625 Recession 0.25 9 2.25 2.45 6.0025 1.500625 6.55 2.347500 Expected return = 6.55% Standard deviation = (2.3475)^0.5 = 1.53% 2) Expected return of the portfolio = 7.55*4500/7500+6.55*3000/7500 = 7.15% 3) Standard deviation of the portfolio: Formula for finding out the SD of a two asset portfolio = [(SD1^2*W1^2+SD^2*+W2^2+2*SD1*SD2*W1*W2*COR(1,2)]^0.5 Where SD1 and SD2 are the standard deviations of the two assets W1 and W2 their weights in the portfolio and COR(1,2) their correlation. Substituting values in the above equation, portolio SD = (0.6^2*3.32^2+0.4^2*1.53^2+2*0.6*0.4*3.32*1.53*-0.80)^0.5 = 1.55%