# What Is CAPM?

The Capital Asset Pricing Model, commonly known as CAPM, is a financial model 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.

## The CAPM Formula

The CAPM formula is given by:

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

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.

## Implementing CAPM in MATLAB

MATLAB® offers specialized functions in its Statistics and Machine Learning Toolbox™ to estimate the parameters of CAPM through regression analysis. However, one common issue that arises is the use of incomplete or missing data when estimating beta. To mitigate this, Financial Toolbox™ provides functions for missing data estimation, reducing your estimation risk when utilizing CAPMs derived from data sets containing missing data.