What is the standard deviation of each stock?
Suppose that the index model for stocks A and B is estimated from excess returns with the following results:
RA = 2.2% + 0.80RM + eA
RB = –2.2% + 1.2RM + eB
σM = 24%; R-squareA = 0.16; R-squareB = 0.12
What is the standard deviation of each stock? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
| Standard Deviation | |
| Stock A | % |
| Stock B | % |
Solution :-
RA = 2.2% + 0.80 RM + e A
RB = –2.2% + 1.2 RM + e B
σM = 24%; R-square A = 0.16; R-square B = 0.12
Now from the equation
Beta of Stock A = 0.80
And Beta of Stock B = 1.2
R-square A = Beta A * Beta B * σM * σM / (σA * σA) =
0.16 = 0.80 * 1.2 * 0.24 * 0.24 / (σA * σA)
(σA * σA) = 0.3456
σA = Standard Deviation of A = 58.79%
R-square B = Beta A * Beta B * σM * σM / (σB * σB) =
0.12 = 0.80 * 1.2 * 0.24 * 0.24 / (σB * σB)
(σB * σB) = 0.4608
σB = Standard Deviation of B = 67.88%
If there is any doubt please ask in comments
What is the standard deviation of each stock? Suppose that the index model for stocks A...