Factor Models

A factor model explains the returns of stocks, funds or strategies with a small number of common drivers, called factors. Instead of treating each of thousands of stocks as unique, it says most of their movement comes from shared influences: the overall market, company size, valuation, momentum, industry, interest rates and so on. Factor models are used to measure true alpha, understand where risk comes from, build portfolios and hedge unwanted exposures. They sit at the heart of modern quantitative investing and risk management.

The general form#

Excess return = Alpha + Beta1 × Factor1 + Beta2 × Factor2 + ... + Error

• Betas (factor loadings): how sensitive the asset is to each factor.
• Factors: the returns of the common drivers.
• Alpha: the return left unexplained.
• Error: the asset specific part, which diversifies away in large portfolios.

Well known factor models#

SMB stands for small minus big and HML for high minus low book to market. Factor return data for these models is published free on Kenneth French's website at Dartmouth. See Size Factor and Value Factor.

Types of factor models#

Running a factor regression#

Uses of factor models#

Factor covariance matrices#

Estimating correlations directly between 3,000 stocks requires about 4.5 million pairwise values, far more than the data can support reliably. A factor model with, say, 20 factors only needs the factor covariances, each stock's loadings and its specific risk. This produces more stable risk estimates. See Covariance and Correlation.

Limitations#

• Factor zoo: hundreds of published factors, many likely due to data mining. See P-Hacking and Multiple Testing.
• Unstable loadings: exposures drift over time.
• Crowding: popular factors can suffer sharp drawdowns. See Factor Timing, Crowding and Crashes.
• Model choice: alpha depends on which factors are included.

Frequently asked questions#

What is a factor model?#

A model that explains asset returns using a few common drivers, such as the market, size, value and momentum, plus an asset specific remainder.

What is the Fama French three factor model?#

A model explaining stock returns with the market, a size factor (small minus big) and a value factor (high minus low book to market).

Why do factor models matter for investors?#

They show whether returns come from skill or from known exposures that can be obtained cheaply, and they help measure and control risk.

Next, learn how to keep a portfolio on target in Rebalancing.