Consider the following table, which gives a security analyst\'s expected return
ID: 2780164 • 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 8% or 20%? (Round your answers to 2 decimal places.)
c. If the T-bill rate is 7%, and the market return is equally likely to be 8% 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) Beta of the stock =
change in stock return ÷ change in market return
Change in market return = 20 - 8 = 12%
Change in return of stock A = 31 - 3 = 28%
Change in return of stock B = 14 - 4.8 = 9.2%
Therefore
Beta A = 28 / 12 = 2.33
Beta B = 9.2 / 12 = 0.77
b) Expected return on the stock E(R) = weighted average of return
Expeted Return on Stock A = 0.5 * 3 + 0.5 * 31 = 17%
Expeted Return on stock = 0.5* 4.8 + 0.5 * 14 = 9.4%
c) Alpha of the Stock = E(R) - R(E)
Alpha of stock A
E(R) = 17 %
R(E) = Rf + ( Rm - Rf) * beta
Rf = 7%
Rm = 8 * 0.5 + 20 * 0.5 = 14%
Beta = 2.33
R(E) = 7 + ( 14-7) 2.33 = 23.33 %
Therefore Alpha A = 17 - 23.33 = - 6.33%
Alpha of Stock B
E(R) = 9.4 %
Rf = 7%,
Rm = 14%
Beta B =. 77
R(E) = 7 + (14-7) *. 77 = 12.37%
Alpha B = 9.4 - 12.37 = - 2.97%