Question

Suppose the expected returns and standard deviations of Stocks A and B are E(RA) = .094, E(RB) = .154, σA = .364, and σB = .624.

a-1. Calculate the expected return of a portfolio that is composed of 39 percent Stock A and 61 percent Stock B when the correlation between the returns on A and B is .54. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

a-2. Calculate the standard deviation of a portfolio that is composed of 39 percent Stock A and 61 percent Stock B when the correlation between the returns on A and B is .54. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b. Calculate the standard deviation of a portfolio with the same portfolio weights as in part (a) when the correlation coefficient between the returns on Stocks A and B is −.54. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

a-1. Expected Return =Weight of Stock A*E(RA)+Weight of Stock B*E(RB) =0.39*0.094+0.61*0.154 =13.06%

a-2 )Standard Deviation =((Weight of A*E(σA))^2+(Weight of B*E(σB))^2+2*Weight of A*Weight of B*E(σA)*E(σB)*correlation)^0.5
=((0.39*0.364)^2+(0.61*0.624)^2+2*0.39*0.61*0.364*0.624*0.54)^0.5=47.265% or 47.27%

b Standard Deviation =((Weight of A*E(σA))^2+(Weight of B*E(σB))^2+2*Weight of A*Weight of B*E(σA)*E(σB)*correlation)^0.5
=((0.39*0.364)^2+(0.61*0.624)^2+2*0.39*0.61*0.364*0.624*-0.54)^0.5=32.66%