Consider the following table, which gives a security analyst\'s expected return
ID: 1170413 • Letter: C
Question
Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns: Market Return 6% 16 Aggressive Stock 2.3% 25 Defensive Stock 41% 14 a. What are the betas of the two stocks? (Round your answers to 2 decimal places.) Beta A Beta D b. What is the expected rate of return on each stock if the market return is equally likely to be 6% or 16%? (Round your answers to 2 decimal places.) Rate of return on A Rate of return on D c. If the T-bill rate is 8%, and the market return is equally likely to be 6% or 16%, what are the alphas ofthe two stocks? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 2 decimal places.) Alpha A Alpha DExplanation / Answer
a.
Beta is the change in stock return per change in market return.
Beta A = ( 2.3 - 25) / ( 6 - 16) = 2.27
Beta D = ( 4.1 - 14) / ( 6 - 16) = 0.99
b.
With equal possibility of either scenario, the expected return is the average of the two possible outcomes.
Rate of return on A = 0.5 x ( 2.3 + 25) = 13.65 %
Rate of return on D = 0.5 x ( 4.1 + 14) = 9.05 %
c.
The security market line is determined by the market expected return of 0.5 ( 6 + 16) = 11% with a beta of 1.
Aggressive stock has required expected return of : 8 + 2.27 ( 11 - 8 ) = 14.81 %.
Alpha A = 13.65 % - 14.81 % = - 1.16 %
Defensive stock has required expected return of : 8 + 0.99 ( 11 - 8) = 10.97 %
Alpha D = 9.05 % - 10.97 % = - 1.92 %
Beta A 2.27 Beta D 0.99