Capital Asset Pricing Model (CAPM)

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:

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

\(E( r_i )\) 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.

See also: portfolio optimization, Black-Litterman, financial engineering