Question

Suppose you observe the following situation:

Security	Beta	Expected Return
Peat Co.	1.40	12.4
Re-Peat Co.	0.60	10.2

Assume these securities are correctly priced. Based on the CAPM, what is the expected return on the market? What is the risk-free rate? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places.)

Answer 1

Let the market return be Rm and Risk-Free Rate be Rf

Peat Co: Beta = B1 = 1.4 and Expected Return = R1 = 12.4 %

Using CAPM, R1 = Rf + B1 x (Rm - Rf)

12.4 = Rf + 1.4 x (Rm - Rf)

12.4 = 1.4Rm - 0.4 Rf (A)

Re-Peat Co: Beta = B2 = 0.6 and Expected Return = R2 = 10.2 %

Using CAPM, R2 = Rf + B2 x (Rm - Rf) = Rf + 1.4 x (Rm - Rf)

10.2 = Rf + 0.6 x (Rm - Rf) - (B)

10.2 = 0.4Rf + 0.6Rm - (B)

Adding Equation (A) and (B), we get:

22.6 = 2 Rm

Rm = 22.6 / 2 = 11.3 %

Rf = (10.2 - 0.6Rm) / 0.4 = (10.2-11.3 x 0.6) / 0.4 = 8.55 %