Question

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? Please show work.

Answer 1

Ans:

According to Capital asset pricing model,

E(r) = Rf + Beta*MP

E(r) = Expected rate of return =

Rf = Risk free return =

Beta =

MP = Market premium.

Insert above data in the formula, E(r) = Rf + Beta*(M(r) –Rf)

E(r) = Rf+ Beta* MP

As per above model, MP should be always same. Let us put data for each stock in above formula

For stock A, 8% = Rf + 0.5 MP

For stock B , 12% = Rf + 1MP

For stock C, 17% = Rf + 1.5 MP

Step1. Subtract equation for stock A and stock B

8%- 12% = Rf+0.5MP -Rf - 1MP

-4% = -0.5MP

MP = 8%

Step 2, Subtract equation for stock b and stock C

12%-17% = Rf+1MP-Rf-1.5MP

-5% = -0.5MP

MP = 10%

Step 3, Subtract equation for stock C and stock A

17% -8% = Rf +1.5MP -Rf-0.5MP

9% = 1MP

MP = 9%

By solving all equation in step 1,2 and 3 MP are different from each other. If CAPM holds correct , it would result in same MP that is same Market premium. Therefore they violated CAPM model