Question

Suppose that the index model for stocks A and B is estimated from excess returns with the following results:

R_A = 4.0% + 0.50R_M + e_A

R_B = –1.2% + 0.70R_M + e_B

σ_M = 17%; R-square_A = 0.26; R-square_B = 0.18

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.)

Covariance:

Correlation coefficient:

Answer 1

Variance of A=Beta A^2*Standard Deviation of M^2/Rx^2 =0.50^2*17%^2/0.26 =0.027788462
Standard Deviation of A =0.027788462^0.5 =0.166698715
Variance of B=Beta B^2*Standard Deviation of M^2/Ry^2 =0.70^2*17%^2/0.18 =0.0786722
Standard Deviation of B =0.0786722^0.5 =0.280485690

Covariance =Beta of A*Beta of B*Standard Deviation of M^2=0.50*0.70*17%^2 =0.010115 or 0.0101

Correlation=Covariance/(Standard Deviation of A*Standard Deviation of B)
=0.010115/(0.166698715*0.280485690) =0.2163