Question

1. There are three stocks in the market: A, B, and C. The market betas for the three stocks are Beta(A) = 0.5, Beta(B) = 1.0, Beta(C) =1.5. The expected returns of the three stocks are E[R(A)] = 8%, E[R(B)] = 12%, and E[R(C)] = 17%. Based on these values, is there any violation of CAPM (i.e., are the betas and expected returns consistent with CAPM?)

Answer 1

If CAPM holds, we have following formula to calculate the required return on stocks

Required rate of Return of the stock = risk free rate + β* the market risk premium

Where,                

Required rate of Return of the stock A = 8%

Risk free rate = x (assumed)

The market risk premium = y (assumed)

And β of stock A = 0.50

Putting all the values in the equation we can get

8% = x + 0.50* y …………………….. (1)          

Similarly for stock B

12% = x + 1 * y ……………………. (2)

And for stock C

17% = x + 1.5 * y ………………….. (3)

Let’s calculate equation (1) & equation (2) to get the value of x & y

Equation (1) & equation (2) can be satisfied with x = 4% and y = 8%; but if we are putting that values in equation (3), we get 16% not 17%

4% + 1.5 * 8% = 16% ≠ 17%              

Based on these values, it is a violation of CAPM model because the betas and expected returns are not consistent with CAPM.