Question

The index model for stock A has been estimated with the following result:

| Rₐ = 0.01 + 0.9Rₘ + eA.
If Oₘ = 0.25 and R²ₐ= 0.25, the standard deviation of return of stock A is
Multiple Choice
a) 0.2025.
b) 0.2500.
c) 0.2500.
d) 0.4500.

Answer 1

Using the index model for stock A, standard deviation is derived using the formula involving market standard deviation and coefficient of determination. The correct standard deviation does not match any of the options given, indicating a potential error in the question.

Step-by-step explanation:

The question relates to the index model for stock A which has been estimated as Rᵢ = 0.01 + 0.9Rₘ + eA. To find the standard deviation of return of stock A, we leverage the information provided: the standard deviation of the market (Oₘ) is 0.25, and the coefficient of determination (R²ᵢ) is 0.25. The coefficient of determination indicates the proportion of the variance of stock A that is predictable from the market index. The standard deviation of stock A can be calculated using the formula: standard deviation of stock A = sqrt((1 - R²ᵢ) * (Oₘ2)).

Substituting the given values, we get standard deviation of stock A = sqrt((1 - 0.25) * (0.252)) = sqrt(0.1875 * 0.0625) = sqrt(0.01171875), which yields an approximate value of 0.1083. Since this number isn't listed in the multiple choice options provided, there appears to be a mistake either in the question or the calculation provided in the question.

However, from the choices given, none of them match the correct calculation, suggesting a typo or error in the question.