Question

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

RA = 5.0% + 1.30RM + eA

RB = –2.0% + 1.6RM + eB

σM = 20%; R-squareA = 0.20; R-squareB = 0.12

What is the standard deviation of each stock? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Stock A:

Stock B:

Answer 1

From an index model, standard deviation of stock is calculated using formula

Standard deviation = Square root of ((βA*σM)^2 + σ[eA]^2)

R-squareA = (βA*σM)^2/Standard deviation^2

=> Standard deviation of the stock = Square root of((βA*σM)^2/R-squareA)

So, for stock A, βA = 1.3

So, standard deviation of stock A = Square root of((1.3*0.2)^2/0.2) = 0.5814 or 58.14%

Similarly, for stock B, βB = 1.6

standard deviation of stock B = Square root of((1.6*0.2)^2/0.12) = 0.9238 or 92.38%