Question

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

RA = 3.6% + 1.20RM + eA RB = –1.6% + 1.5RM + eB σM = 16%;

R-squareA = 0.25; R-squareB = 0.15

Break down the variance of each stock to the systematic and firm-specific components. (Do not round intermediate calculations. Calculate using numbers in decimal form, not percentages. Round your answers to 4 decimal places.)

Answer 1

Variance of A^2=Beta A^2*Standard Deviation of M^2/Rx^2 =1.20^2*16%^2/0.25 =0.147456
Standard Deviation of B^2=Beta B^2*Standard Deviation of M^2/Ry^2 =1.5^2*16%^2/0.15 =0.384

ii. Systematic Risk of A=Beta A^2*Standard Deviation of M^2=1.20^2*16%^2=0.0369
Firm Specific risk of A =Variance of Risk A-Systematic Risk=0.147456-0.0369=0.1106

Systematic Risk of B=Beta A^2*Standard Deviation of M^2=1.15^2*16%^2=0.0339
Firm Specific risk of B=Variance of Risk B-Systematic Risk=0.384-0.039 =0.3501