# Beta

The expected rate of return is twice the 12% expected rate of return on the market. What is the beta if the risk free rate is 6% My initial wrong answer was 2. Because I thought that if beta were 2 that means that every market movement is supposed to double the movement of the individual stock. But of course the right answer is to plug this all into the capital asset pricing model and get 3. Which I understand, but I don’t see where my initial thought is wrong. Why is my initial thought wrong?

CAPM = Rate of return on stock = Rf + Beta[R(m) - Rf] Assumptions: Rate of return on stock - 2 * 12% = 24% R(m) = 12% Rf = 6% Thus, 24 = 6 + X[12-6] X = 3 = beta.

Yea, I know that’s right, but I’m just trying to figure out whats wrong with saying that the beta shows how a stock moves in relation to the market. Which in this case if you took that statement, would mean a beta of 2 because the stock moved 2x the 12% of the market. Kind of hard to explain my problem but thanks anyways.

Sorry didn’t read the rest of your post. The rate of return on the stock would only be beta * rate of return on market if the risk free rate were zero.

It’s a common intuitive error. Think of the expected return on an investment as being the sum of the RF rate AND the investment’s risk premium. In the CAPM model, Beta x the Market Risk premium yields the investment’s risk premium. So, in the above example, the MRP is 6% (i.e. 12% - 5%). In contrast, your investment’s risk premium is 18% (24% - 6%). So, if your Risk premium is 3x the MRP, your beta must be 3x the market beta, or 3.0 (the market beta is always 1).

“common intuitive error” - perfect that’s what I was getting at.