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Homework answers / question archive / Consider the following two scenarios for the economy and the expected returns in each scenario for the market portfolio
Consider the following two scenarios for the economy and the expected returns in each scenario for the market portfolio. an aggressive stock A, and a defensive stock D.
Rate of Return Aggressive Defensive Scenario Market Stock A Stock D Bust -5% -7% -3% Boom 25 33 17
Required: a. Find the beta of each stock.
b. If each scenario is equally likely, find the expected rate of return on the market portfolio and on each stock.
c. If the T-bill rate is 3%, what does the CAPM say about the fair expected rate of return on the two stocks?
d. Which stock seems to be a better buy on the basis of your answers to (a) through (c)?
1-a). Computation of the beta of each stock:-
Beta of stock A = (change in expected return of stock A) / (change in market return)
= (33% - (-7%)) / (25% - (-5%))
= 40% / 30%
= 1.33
Beta of stock D = (17% - (-3%)) / (25% - (-5%))
= 20% / 30%
= 0.67
b). Computation of the expected return on market portfolio:-
Expected return on market portfolio = (0.5 * 25%) + (0.5 * -5%)
= 12.5% + (-2.5%)
= 10%
Computation of the expected return on stock A:-
Expected return = (0.5 * 33%) + (0.5 * -7%)
= 16.5% + (-3.5%
= 13%
Computation of the expected return on stock D:-
Expected return = (0.5 * 17%) + (0.5 * -3%)
= 8.5% + (-1.5%)
= 7%
c). Computation of the expected rate of return on stock A:-
Expected rate of return on stock A = Risk free rate + Beta * (Expected market return - Risk free rate)
= 3% + 1.33 * (10% - 3%)
= 3% + (1.33 * 7%)
= 3% + 9.33%
= 12.33%
Computation of the expected rate of return on stock D:-
Expected rate of return on stock D = Risk free rate + Beta * (Expected market return - Risk free rate)
= 3% + 0.67 * (10% - 3%)
= 3% + (0.67 * 7%)
= 3% + 4.67%
= 7.67%
d). Stock A is better because expected Return is greater than fair rate of return.
