The index model for stock A has been estimated with the following result: R_A = 0.01 + 0.9R_M + e_A.
If $\sigma$ _M = 0.25 andR²_A = 0.25, the standard deviation of return of stock A is

Question

The index model for stock A has been estimated with the following result: R_A = 0.01 + 0.9R_M + e_A.
If

\sigma

_M = 0.25 andR²_A = 0.25, the standard deviation of return of stock A is

Quizplus · Accepted Answer

Using the index model, the standard deviation of return for stock A can be calculated as:
σAS1U1B0 = (βAS1U1B1MS1U1B0)σMS1U1B0
Since βAS1U1B1MS1U1B0 = 0.9 and σMS1U1B0 = F1F1F1S1F1F1F10S1U1B1MS1U1B0, we can substitute the given value for F1F1F1S1F1F1F10S1U1B1MS1U1B0 into the above equation:

σAS1U1B0 = (0.9)(0.25) = 0.225

However, this is the standard deviation of the excess return of stock A, not the total return. To find the standard deviation of the total return, we must add the standard deviation of the market return (σMS1U1B0) to the standard deviation of the excess return:

σAS1U1B0 + σMS1U1B0 = 0.225 + F1F1F1S1F1F1F10S1U1B1MS1U1B0 = 0.25

Therefore, the standard deviation of return of stock A is 0.25, which corresponds to choice C.

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