Consider the following table, which gives a security analyst\'s expected return
ID: 2783447 • Letter: C
Question
Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns:
a. What are the betas of the two stocks? (Round your answers to 2 decimal places.)
b. 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.)
c. 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
a) When Market Return = 7%, A's expected return = 3.1%
When Market Return = 20%, A's expected return = 30%
Hence, a 13% change in Market Return leads to a 26.9% change in A's expected return.
Thus, A's Beta = 26.9/13 = 2.07
When Market Return = 7%, D's expected return = 4.9%
When Market Return = 20%, D's expected return = 15%
Hence, a 13% change in Market Return leads to a 10.1% change in D's expected return.
Thus, D's Beta = 10.1/13 = 0.78
b) Since both scenarios are equally probable, there is an equal chance of A's expected return being 3.1% and 30%
Thus, A's expected return = 0.5 * 3.1 + 0.5 * 30 = 16.55 %
Similarly, since both scenarios are equally probable, there is an equal chance of D's expected return being 4.9% and 15%
Thus, D's expected return = 0.5 * 4.9 + 0.5 * 15 = 9.95%
c) The SML is determined by the market expected return of 0.5 x (20 + 7) = 13.5%. T bill rate is 8%. Therefore-
E(R) = 8% + (13.5% - 8%)
The aggressive stock has a fair expected return of: E(RA) = 8% + 2.07 (13.5% - 8%) = 19.385%, and the expected return by the analyst also 16.55 %. Thus, its alpha is -
D = actual expected return - required return given risk = 16.55%-19.385% = -2.835%
Similarly, the required return on the defensive stock is: 8% + 0.78 (13.5% - 8%) = 12.29% and the expected return by the analyst is 9.95 %.Thus, its alpha is -
D = actual expected return - required return given risk = 9.95%-12.29% = -2.34%