Question

The index model is estimated for the following two stocks. Stock Expected Return Beta Firm-specific Standard Deviation A 13% 0.8 30% B 18% 1.2 40% The market index has a standard deviation of 22% and the risk-free rate is 8%. What is the standard deviation of stock B

Answer 1

Standard Deviation of Stock B = 47.93

Step-by-step explanation:

Stock - Expected Return - Beta - Firm-specific standard deviation

A - 13% - 0.8 - 30%

B - 18% - 1.2 - 40%

Standard Deviation of stock B = [βB²σ²M + σ²(eB)]

Where βB = Beta of Stock B= 1.2

σ(eB ) = Firm specific standard deviation = 40%,

and

σM=Standard Deviation of market index= 22%

Calculating standard deviation of stock B

σB= (1.2² * 22²+ 40²)^½

σB= (1.44 * 484 + 1600)^½

σB= (696.96 + 1600)^½

σB= (2296.96)^½

σB= 47.92661056240050

σB= 47.93 --------- Approximated