Suppose that the index model for stocks A and B is estimated from excess returns

Question

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

RA = 2.8% + 1.00RM + eA RB = –1.0% + 1.30RM + eB M = 18%; R-squareA = 0.27; R-squareB = 0.13 Assume you create a portfolio Q, with investment proportions of 0.40 in a risky portfolio P, 0.35 in the market index, and 0.25 in T-bill. Portfolio P is composed of 70% Stock A and 30% Stock B.

1. What is the standard deviation of portfolio Q? (Calculate using numbers in decimal form, not percentages. Do not round intermediate calculations. Round your answer to 2 decimal places. Omit the "%" sign in your response.)

Explanation / Answer

corr(A, M) = sqrt(0.27)
cov(A,M) = corr(A, M) * M*A = sqrt(0.27)*0.18* A
beta = cov(A, M)/M^2 = sqrt(0.27)*0.18* A/0.18^2 = sqrt(0.27)* A/0.18
and you know from your regression equation above that beta = 1.0 so

Solve 1.0 = sqrt(0.27)* A/0.18

0.3464 =A

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