# CAPM

## Capital Asset Pricing Model

CAPM (capital asset pricing model) is used to evaluate investment risk and rates of return compared to the overall market. You can use CAPM to price an individual asset, or a portfolio of assets, using a linear model defined as:

$E(r_i)=r_f + \beta_f \left(E( r_m) - r_f \right)$

Where:
$$E( r_i )$$ is the expected return of the asset or portfolio denoted with $$i$$.
$$r_f$$ is the risk-free rate of return.
$$\beta_i$$ (beta) is the sensitivity of returns of asset $$i$$ to the returns from the market, and is defined as the covariance of returns between the asset $$i$$ and the market to the market variance.
$$E( r_m)$$ is the expected return of the market.

Using CAPM, you can calculate the expected return for a given asset by estimating its beta from past performance, the current risk-free (or low-risk) interest rate, and an estimate of the average market return.

A common pitfall in estimating beta from historical data sets can arise when the data set is incomplete, or contains missing data, so it is important to have missing data estimation functions to reduce this type of estimation risk for CAPM.

For more information, see Statistics and Machine Learning Toolbox and Financial Toolbox.