The index model has been estimated for stock A with the following results:
R_A = 0.01 + 0.8R_M + e_A
Σ_M = 0.20 σ(e_A) = 0.10
The standard deviation of the return for stock A is __________.

Question

Quizplus · Accepted Answer

The formula for the standard deviation of a stock's return in the context of the index model is:

σA = √[βA^2σM^2 + σe^2]

where βA is the beta of stock A, σM is the standard deviation of the market return, and σe is the standard deviation of the error term in the index model equation.

Using the values given in the question:

βA = 0.8
σM = 0.20
σe = 0.10

Therefore:

σA = √[0.8^2 x 0.20^2 + 0.10^2] = 0.1886

So the answer is (B).

The Index Model Has Been Estimated for Stock a with the Following