Question

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

R_A = 4.5% + 1.40R_M + e_A

R_B = –2.2% + 1.7R_M + e_B

σ_M = 24%; R-square_A = 0.30; R-square_B = 0.20

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.)

	Risk A	Risk B
Systematic
Firm-specific

Answer 1

Variance of A=Beta A^2*Standard Deviation of M^2/Ra^2 =1.4^2*24%^2/0.30 =0.37362
Variance of of B=Beta B^2*Standard Deviation of M^2/Rb^2 =1.7^2*24%^2/0.20 =0.83232

Systematic Risk of A=Beta A^2*Standard Deviation of M^2=1.40^2*24%^2=0.1129
Firm Specific risk of A =Variance of Risk A-Systematic Risk=0.37362-0.1129 =0.2634

Systematic Risk of B=Beta A^2*Standard Deviation of M^2=1.7^2*24%^2=0.1665
Firm Specific risk of B=Variance of Risk B-Systematic Risk=0.83232-0.1665 =0.6658