Question

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

R_A = 3.6% + 1.20R_M + e_A

R_B = -1.6% + 1.50R_M + e_B

σ_M = 16%; R-square_A = 0.25; R-square_B = 0.15

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

Given,

Two stocks A and B

Return of stock A (RA) = 3.6% + 1.20RM + eA

I.e., Rf = 3.6% , β of stock A = 1.20

Return of stock B (RB) = - 1.6% + 1.5RM + eB

I.e., Rf = - 1.6%, β of stock B = 1.5

Coefficient of determination of stock A ( R - square) = 0.25 and for stock B ( R - square ) = 0.15

σM = 16%

Required: Covariance of each stock with Market index

Stock A:

β = Covariance ÷ σM^2

1.20 = Covariance ÷ (0.16)^2

1.20 = Covariance ÷ 0.0256

Covariance = 1.20 × 0.0256

Covariance = 0.031

Therefore Covariance of stock A with Market index = 0.031

Stock B:

β = Covariance ÷ σM^2

1.5 = Covariance ÷ (0.16)^2

1.5 = Covariance ÷ 0.0256

Covariance = 1.5 × 0.0256

Covariance = 0.038

Therefore Covariance of stock B with Market index = 0.038