Consider the following two scenarios for the economy and the

Consider the following two scenarios for the economy and the returns in each scenario for the market portfolio, an aggressive stock A, and a defensive stock D. Scernario Market Agressive Stock A Defensive Stock D Bust -8% -10% -6% Boom 27 41 20

If the T-bill rate is 5%, what does the CAPM say about the fair expected rate of return on the two stocks?

Solution

Beta of a stock is the sensitivity of the stock return to the market return. It is the change in the stock return per change in the market return.

Therefore,

Beta of Stock A = (-10-41)/(-8-27) = 1.46

Beta of Stock D = (-6-20)/(-8-27) = 0.74

Now using CAPM, the fair expected return of the stocks would be:

Stock A = 5 + 1.46(9.5 - 5) = 11.57%

Stock D = 5 + 0.74(9.5 - 5) = 8.33%

Note: The expected market return is taken as 9.5%, assuming that the probability for Bust & Boom is equal    = 0.5*-8 + 0.5*27 = 9.5%.