Question

Assume Stocks A and B have the following characteristics: Stock Expected Return Standard Deviation A 8.3% 32.3% B 14.3% 61.3% The covariance between the returns on the two stocks is .0027. a. Suppose an investor holds a portfolio consisting of only Stock A and Stock B. Find the portfolio weights, XA and XB, such that the variance of her portfolio is minimized. (Hint: Remember that the sum of the two weights must equal 1.) (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.) b. What is the expected return on the minimum variance portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) c. If the covariance between the returns on the two stocks is −.05, what are the minimum variance weights? (Do not round intermediate calculations and round your answers to 4 decimal places, e.g., .1616.) d. What is the variance of the portfolio in part (c)? (Do not round intermediate calculations and round your answer to 4 decimal places, e.g., .1616)

Answer 1

a. Weight of A = ((Standard Deviation of B)^2 -Covariance)/((Standard Deviation of A)^2 + (Standard Deviation of B)^2 - 2 * Covariance)
= ((61.3%^2)-0.0027)/((32.3%^2)+(61.3%^2)-2*0.0027)=78.59% or 0.7859
Weight of B =1-78.59%=21.41% or 0.2141

b. Expected return =78.59%*8.3%+21.41%*14.3% =9.58%

c. If covariance =-0.05
Weight of A = ((Standard Deviation of B)^2 -Covariance)/((Standard Deviation of A)^2 + (Standard Deviation of B)^2 - 2 * Covariance)
= ((61.3%^2)+0.05)/((32.3%^2)+(61.3%^2)+2*0.05)=0.7340
Weight of B =1-0.7340=0.2660

d. Variance= (Weight of A * Standard Deviation of A)^2 + (weight of B * standard Deviation of B)^2 + 2* Weight of A * Standard Deviation of A * weight of B * standard Deviation of B * correlation =((0.7859*32.3%)^2+(0.2141*62.3%)^2+2*0.7859*0.2141*0.0027) =0.0826