Question

2. Suppose that the index model for stocks A and B is estimated from excess returns with the following results: R. 396 + 0.7 Rmte, Rs:-2% + 1.2 Rm+eb Ơn® 20%; R-SQRas 0.20;R-SQRb 0.12 What is the standard deviation for each stock? Break down the variance of each stock to the systematic and firm-specific components. What are the covariance and correlation coefficient between the two stocks? What is the covariance between each stock and the market index? Are the intercepts of the two regressions consistent with the CAPM? Interpret their values a. b. c. d. e.

Answer 1

a)Standard deviation=Explained variance/total variance
Variance=(beta^2*std of market^2)/R square

Variance of A=(0.7*0.2)^2/0.2
=9.8%
std of A=9.8%^0.5=31.3%
std of B=((1.2*0.2)^2)/0.12)^0.5
=69.28%

b)Systematic risk of A=beta square A*variance of Market=(0.7*0.2)^2=1.96%
Firm specific risk=total risk-sysytematic risk
=9.8%-1.96%=7.84%
systematic risk of B=(1.2*0.2)^2=5.76%
Firm specific risk B=48%-5.76%=42.24%

c)Covariance=beta A*beta B*variance market
=0.7*1.2*0.2^2
=0.0336
Correlation coefficent=covariance/(std A*std B)
=0.0336/(31.3%*69.28%)
=0.155

d)Cov(a,market)=coreelation coefficent A*std A*std Market
=(0.2^0.5)*31.3%*20%=02.80
Cov(B,market)=(0.12^0.5)*69.28%*20%=4.8%