Question

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

R_A = 2.0% + 0.40R_M + e_A

R_B = -1.8% + 0.9R_M + e_B

σ_M = 15%; R-square_A = 0.30; R-square_B = 0.22

What is the covariance between each stock and the market index? (Calculate using numbers in decimal form, not percentages. Do not round your intermediate calculations. Round your answers to 3 decimal places.)

	Covariance
Stock A
Stock B

Answer 1

Variance of A^2=Beta A^2*Standard Deviation of M^2/Rx^2 =0.40^2*15%^2/0.30 =1.2%
Standard Deviation of A =1.2%^0.5 =10.9545%
Standard Deviation of B^2=Beta B^2*Standard Deviation of M^2/Ry^2 =0.90^2*15%^2/0.22 =8.2841%
Standard Deviation=8.2841%^0.5 =28.7821%

Covariance of Stock A with Market =R*Standard deviation of A *Standard Deviation of M =0.30^0.5*10.9545%*15% =0.009
Covariance of Stock B with Market =R*Standard deviation of B *Standard Deviation of M =0.22^0.5*28.7821%*15%=
0.020