Question

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

R_A = 3.60% + 1.20R_M + e_A

R_B = -1.60% + 1.50R_M + e_B

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

Assume you create portfolio P with investment proportions of 0.70 in A and 0.30 in B.
a. What is the standard deviation of the portfolio? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

b. What is the beta of your portfolio? (Do not round your intermediate calculations. Round your answer to 2 decimal places.)

c. What is the firm-specific variance of your portfolio? (Do not round your intermediate calculations. Round your answer to 4 decimal places.)

d. What is the covariance between the portfolio and the market index? (Do not round your intermediate calculations. Round your answer to 3 decimal places.)

Answer 1

Data for stocks A and B:

Formula					(b*SDm)^2/Rs	(Var)^2	(b*SDm)^2	Var - SR	(betaA*betaB*SDm^2)	Covariance(A,B)/(StdevA*StDevB)	(Rs)^0.5*SDm*SD
Stock	Weight (w)	Beta (b)	R-square (Rs)	Stdevmarket (SDm)	Variance (Var)	StDev (SD)	Systematic risk (SR)	Firm-specific risk (FSR)	Covariance (A,B)	Correlation coefficient	Covariance (Stock, mkt index)
A	0.7	1.2	0.25	16%	0.147	38.40%	0.0369	0.1106	-	-	0.0307
B	0.3	1.5	0.15	16%	0.384	61.97%	0.0576	0.3264	-	-	0.0384
									0.0461	0.1936

a). Portfolio standard deviation = [(wA*SDA)^2 + (wB*SDB)^2 + (2*w1*w2*Covariance(A,B)]^0.5

= (0.7*38.40%)^2 + (0.3*61.97%)^2 + (2*0.7*0.3*0.0461)]^0.5 = 35.52% or 0.36

b). Portfolio beta = (wA*betaA) + (wB*betaB) = (0.7*1.2)+(0.3*1.5) = 1.29

c). Firm-specific variance = portfolio variance - (beta*market standard deviation)^2

= (35.52%)^2 - (1.29*16%)^2 = 0.0836

d). Covariance (portfolio, market index) = beta*market variance = 1.29*(16%^2) = 0.033