Question

You have asset ABC. Its covariance with the market portfolio is 0.01. The expected price of the market portfolio is $120. Its current price is $100. The standard deviation of the market portfolio returns is 20%. The risk free rate is 5%.
(a) What is the expected return of company ABC? (b) What is the expected return of company XYZ if the covariance of its returns with the market is 0.05?

Answer 1

(a) Expected Price of Market Portfolio = $ 120 and Current Price of Market Portfolio = $ 100

Expected Return on Market = Rm = (120-100) / 100 = 20 % and Risk-Free Rate = Rf = 5 %

Standard Deviation of Market Portfolio Return = Sm = 20 % and Covariance with Market Portfolio = 0.01

Therefore, Beta of ABC = Covariance / (Standard Deviation of Market Portfolio Return)^(2) = 0.01 / (0.2)^(2) = 0.25

Expected Return = Rf + Beta of ABC x (Rm - Rf) = 5 + 0.25 x (20 - 5) = 8.75 %

(b) Covariance of XYZ with Market = 0.05

Beta of XYZ = 0.05 / (0.2)^(2) = 1.25

Expected Return = Rf + Beta of XYZ x (Rm - Rf) = 5 + 1.25 x (20 - 5) = 23.75 %