# CAPM

## Capital Asset Pricing Model (CAPM)

CAPM (Capital Asset Pricing Model) is used to evaluate investment risk and rates of returns 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.

In MATLAB, you can estimate the parameters of CAPM using regression functions from Statistics Toolbox. A common pitfall in estimating beta from historical data sets can arise when the data set is incomplete, or contains missing data. Financial Toolbox provides missing data estimation functions that reduce your estimation risk when using CAPM derived from data sets containing missing data.