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Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns: Market Return Aggressive Stock Defensive Stock 6% 2
Consider the following table, which gives a security analyst's expected return on two stocks for two particular market returns:
Market Return Aggressive Stock Defensive Stock
6% 2.0% 5.0%
20 32 15
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 6% 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 6% 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.)
Expert Solution
a) Computation of the beta of each stock:-
Beta A = (2.0% - 32%) / (6% - 20%)
= -30% / -14%
= 2.14
Beta D = (5.0% - 15%) / (6% - 20%)
= -10% / -14%
= 0.71
b) Computation of the expected rate of return on each stock:-
Rate of return A = (0.5 * 2.0%) + (0.5 * 32%)
= 1.00% + 16.00%
= 17.00%
Rate of return D = (0.5 * 5.0%) + (0.5 * 15%)
= 2.50% + 7.50%
= 10.00%
c) Computation of the alphas of two stocks:-
Market expected return = 0.5 * (6% + 20%)
= 0.5 * 26%
= 13%
Required return on aggressive stock = Risk free rate + Beta * (Market expected return - Risk free rate)
= 7% + 2.14 * (13% - 7%)
= 7% + (2.74 * 6%)
= 7% + 12.86%
= 19.86%
Alpha A = 17.00% - 19.86%
= -2.86%
Required return on defensive stock = Risk free rate + Beta * (Market expected return - Risk free rate)
= 7% + 0.71 * (13% - 7%)
= 7% + (0.71 * 6%)
= 7% + 4.29%
= 11.29%
Alpha D = 10.00% - 11.29%
= -1.29%
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