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% + 0.90R_M + e_B
σ_M = 15%; R-square_A = 0.30; R-square_B = 0.22

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 = .2570

Answer 1

Given that,

R_A = 2.0% + 0.40R_M + e_{A, here}
R_B = –1.8% + 0.90R_M + e_{B, here}

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

[ Explained variance/ total variance]

=>

Hence for stock A,

=> = 0.1095

For Stock B,

=> = 0.2878

Hence,

Covariance of stock A ,B (Cov(A,B)) = 0.40*0.90* (0.15)^2 = 0.0081

Also,

Here is the Correlation Coefficient of stock A & B

HENCE,

0.0081 = 0.1095* 0.2878 *

=> = 0.2570

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Covariance = 0.0081 Correlation Coefficient = 0.2570