Question

Suppose that the index model for stocks A and B is estimated from excess returns with the following results: RA = 3.0% + 1.05RM + eA RB = –1.2% + 1.20RM + eB σM = 29%; R-squareA = 0.29; R-squareB = 0.14 What are the covariance and correlation coefficient between the two stocks? (Do not round intermediate calculations. Calculate using numbers in decimal form, not percentages. Round your answers to 4 decimal places.)

Answer 1

Variance of A^2=Beta A^2*Standard Deviation of M^2/Rx^2 =1.05^2*29%^2/0.29 =31.9725%
Standard Deviation of A =31.9725%^0.5 =56.5422%
Standard Deviation of B^2=Beta B^2*Standard Deviation of M^2/Ry^2 =1.20^2*29%^2/0.14 =86.5029%
Standard Deviation=86.5029%^0.5 =93.0069%

Covariance =Beta of A*Beta of B*Standard Deviation of M^2=1.05*1.20*29%^2 =10.5966%
Correlation=Covariance/(Standard Deviation of A*Standard Deviation of B) =10.5966%/(56.5422%*93.0069%) =0.2015