Consider the following table, which gives a security analyst\'s expected return
ID: 2772845 • Letter: C
Question
Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns:
What are the betas of the two stocks? (Round your answers to 2 decimal places.)
What is the expected rate of return on each stock if the market return is equally likely to be 7% or 20%? (Round your answers to 2 decimal places.)
If the T-bill rate is 8%, and the market return is equally likely to be 7% or 20%, what are the alphas of the two stocks? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.)
Explanation / Answer
The beta is the sensitivity of the stock return to the market return movements. Let A be the aggressive stock and D be the defensive one. Then beta is the change in the stock return per change in the market return. Therefore, we compute each stock’s beta by calculating the difference in its return across the two scenarios divided by the difference in the market return.
A = (3.7 - 30)/(7 - 20) = 2.023
D = (5.5 - 14)/(7 - 20) = 0.607
(b) With equal likelihood of either scenarios, the expected return is an average of the two possible outcomes.
E(RA) = 0.5 (3.7 + 30) = 16.85%
E(RD) = 0.5 (5.5 + 14) = 9.75%
(d) The SML is determined by the market expected return of 0.5 x (7 + 20) = 13.5%, with a beta of 1, and the T-bill return of 8% with a beta of zero. The equation for the security market line is:
E(R) = 8% + (12.5% - 8%)
The aggressive stock has a fair expected return of: E(RA) = 8% + 2.023(13.5% - 8%) = 19.162%,
and the expected return by the analyst also is 16.85%.
Alpha = Actual expect return - required rate of return = 16.85 - 19.162 = -2.276%
Similarly, the required return on the defensive stock is: E(RD) = 8% + 0.607(13.5% - 8%) = 11.338%,
but the expected return on Stock D is only 9.75%,
and hence, D = actual expected return - required return given risk) = 9.75% - 11.338% = -1.5885%.