Question

The index model has been estimated for stocks A and B with the following results: RA 0.12 +0.610 RM+eA RB 0.04 1.416 RM+ eB OM-0.270 O(eA) 0.20 O(eB) 0.10 What is the correlation coefficient between the two stocks? (Round your answer to 4 decimal places.) Correlation coefficient

Answer 1

Variance of A^2=Beta A^2*Standard Deviation of M^2/Rx^2 =0.610^2*0.27^2/0.20 =0.13563
Standard Deviation of A =0.13563^0.5
Standard Deviation of B^2=Beta B^2*Standard Deviation of M^2/Ry^2 =1.416^2*0.27^2/0.1=146.1686%
Standard Deviation=146.1686%^0.5

Covariance =Beta of A*Beta of B*Standard Deviation of M^2=0.610*1.416*0.27^2 =0.06297
Correlation=Covariance/(Standard Deviation of A*Standard Deviation of B)
=0.06297/(0.13563^0.5 *146.1686%^0.5) =0.1414