# Fama–French Factor Model Lab: Size, Value, Momentum

Decompose a fund into market, size, value and momentum exposures with real Kenneth French factor data, and watch a CAPM alpha disappear.

## About this tool

The Fama–French model explains returns with more than the market. Besides market beta, it adds size (small stocks versus big), value (cheap stocks versus expensive), profitability, investment style and, in the Carhart extension, momentum. This lab uses the real monthly factor returns from the Kenneth French Data Library. You can decompose a mystery fund by dragging its loadings, watch a CAPM alpha shrink as factors are added, build the factors yourself from a sort, and test which model prices the 25 size and value portfolios.

## Frequently asked questions

### What are the Fama–French factors?

The three-factor model uses the market excess return (Mkt-RF), size (SMB, small minus big) and value (HML, high book-to-market minus low). The five-factor model adds profitability (RMW, robust minus weak) and investment (CMA, conservative minus aggressive). Each factor is the return of a long-short portfolio, so it is a return you could in principle earn by trading, not a statistic. Momentum (winners minus losers) is a separate factor added in the Carhart four-factor model.

### How do I read a factor loading?

A loading is a regression coefficient, the same idea as beta. A size loading of 0.7 means the fund moves like 0.7 units of the small-minus-big portfolio on top of its market exposure. A positive value loading marks a value tilt, a negative one a growth tilt. The standard error and t-statistic tell you whether the estimate is distinguishable from zero, because a noisy fund can show a large loading that is only chance.

### Why does a CAPM alpha shrink when factors are added?

CAPM alpha is whatever the market cannot explain. A fund that holds small value stocks earns the size and value premia, and a single-factor regression books that as alpha. Once the size and value factors enter the regression, their returns are credited to exposures instead. What remains is the part no listed factor explains, which for most funds is small and statistically hard to tell from zero.

### Where does the data come from?

The factor returns and the 25 size and book-to-market portfolios come from the Kenneth R. French Data Library, used with attribution. The page ships a snapshot of the monthly value-weighted series from July 1963, so no download is needed while you explore, and the retrieval date is shown at the bottom of the lab. The mystery funds are simulated on top of the real factors with hidden loadings, so your answer can be checked exactly.

## Learn the theory

- [Factor models and systematic risk](https://quantsandbox.dev/guide/portfolio/factor-models): The single-index model, splitting systematic from specific variance, and multi-factor models.
- [CAPM, beta and the security market line](https://quantsandbox.dev/guide/portfolio/capm): Systematic versus idiosyncratic risk, beta as market sensitivity, expected return and alpha.
- [The Fama–French factor models](https://quantsandbox.dev/guide/portfolio/fama-french-factors): Size, value, profitability, investment and momentum: multi-factor regressions, factor loadings, what alpha means and why CAPM alpha shrinks once the factors are added.

Open the interactive tool: https://quantsandbox.dev/fama-french