Capital Asset Pricing Model (CAPM)¶

The capital asset pricing model is one of the most foundational models in finance. The idea of this model is to capture the expected returns of stocks based on three pieces of information: the stock beta, the market return and the risk-free rate. It has two main ideas behind it: Higher risk (higher beta) stocks should provide proportionally more return, and the only risk that should be captured is the market risk because all other risk can be diversified away.

Let’s consider two end points, a stock with a beta of 0 and one with beta of 1. The stock with a beta of 0 should provide just the risk-free rate because there is hypothetically no (market) risk. The stock with a beta of 1 should return the same as the market because it has the same (market) risk. All other expected returns can be found through fitting a line between these two points. Fitting a line between these two points yields the following equation:

$$ E(R_i) = r_f + \beta_i (r_m – r_f) $$

where

$ E(R_i) = \text{The expected return of stock i} $$

$ r_f = \text{The risk-free rate} $

$ r_m = \text{The return of the market} $

$ \beta_i = \text{The beta of stock i} $

Also, the term $r_m – r_f$ is often called the market risk premium. It is the return that we expect from the market in excess of the risk-free rate.