Over the years, academic community have tried to come up with various models trying to explain asset returns. These models, or asset pricing models as they are usually called, describe expected returns of financial assets, such as stocks, bonds, etc. using various characteristics or factors.

Simply put, factor can be considered as a quantitative representation of a qualitative theme that can be used to explain asset returns.

A simple example is Capital Asset Pricing Model or CAPM, which says, expected return of an asset is Risk Free Rate, plus a constant times market risk premium (expected market returns minus risk free rate)

Ri = Rf +βi(Rm – Rf)

Ri is the expected return on asset i; Rf is the risk-free rate; βi is the beta of the investment; and Rm is the expected return of the market.

Despite its popularity, CAPM is simplistic and is often criticized for its inability of explain asset returns based on empirical data. In particular, multiple studies indicated that value stocks and small cap stocks tends to outperform growth and large cap stocks respectively. This led Kenneth French and Eugene Fama to come up with a 3 Factor model that had value and size as two additional factors. Mark Carhart subsequently added a fourth factor, which was the momentum factor.

Ri – Rf =αi +βi,m(Rm – Rf) + βi,SMB(SMB) + βi,HML(HML) + βi,WML(WML) + εi

α is the intercept of the regression line; (SMB) is the return of the size factor, Small Minus Big; (HML) is the return of the value factor, High Minus Low, (WML) is the return of the momentum factor, Winner Minus Looser; ε is the residual of the regression model

Subsequently, many more factors have been identified to explain asset returns and newer factors are getting discovered by academia and industry alike. These factors can be used to develop models for systematic, rule-based trading, using software programs.