Suppose that the index model for stocks A and B is estimated from excess returns with the following results:
?A = 3% + 0.7 RM+ ?A
?B = −2% + 1.2RM + ?A
?A-square= 0.20 ; ?B-square= 0.12, varianceM = 20% ;
a. What is the standard deviation of each stock?
b. Break down the variance of each stock to the systematic and firm-specific components.
c. What are the covariance and correlation coefficient between the two stocks?
d. What is the covariance between each stock and the market index?
e. For portfolio P with investment proportions of 0.60 in A and 0.40 in B, rework parts (a), (b) and (d). f. Rework part (e) for portfolio Q with investment proportions of 0.50 in P, 0.30 in the market index, and 0.20 in T-bills.
a) Standard deviation
stock A = 0.2^0.5 = 44.72%
stock B = 0.12^0.5 = 34.64%
b) Variance
Stock A
Systematic = (0.7*20%)^2 = 0.0196
Firm specific = 0.2-0.0196 = 0.1804
Stock B
Systematic = (1.2*20%)^2 = 0.0576
Firm specific = 0.12-0.0576 = 0.0624
c) Covariance = 0.7*1.2*(20%^2) = 0.0336
Correlation = 0.0336/(44.72%*34.64%) = 0.2169
d)
Stock A
covariance with market = systematic risk = 0.0196
correlation with market = 0.0196/(44.72%*20%) = 0.2191
Stock B
covariance with market = systematic risk = 0.0576
correlation with market = 0.0576/(34.64%*20%) = 0.8314
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