Framework
From CAPM to multi-factor models
The question it answers
When assessing a stock portfolio, which factors beyond market risk (size, value, momentum, profitability, investment) should an investor or fund manager use to explain returns?
- Origin
- Ross (1976); Fama and French (1992; 1993; 2015); Carhart (1997)
- Diagram type
- Comparison table
- Level of analysis
- Industry
- Topics
- Corporate finance

Diagram
From CAPM to multi-factor models
| Criterion | Factors | Added beyond CAPM |
|---|---|---|
| CAPM | Market | None |
| Arbitrage pricing | Several unspecified factors | Multiple risk sources |
| Three-factor | Market, size, value | Size and value |
| Four-factor | Market, size, value, momentum | Momentum |
| Five-factor | Adds profitability and investment | Profitability and investment |
Sources
References
Listed A–Z by author surname, Harvard style. A source with a DOI links to https://doi.org/…; one without links to its page or says plainly that it has no DOI.
- Carhart, M.M. (1997) ‘On persistence in mutual fund performance’, Journal of Finance, 52(1), pp. 57–82.doi:10.1111/j.1540-6261.1997.tb03808.xSource page
- Fama, E.F. and French, K.R. (1992) ‘The cross-section of expected stock returns’, Journal of Finance, 47(2), pp. 427–465.doi:10.2307/2329112Source page
- Fama, E.F. and French, K.R. (1993) ‘Common risk factors in the returns on stocks and bonds’, Journal of Financial Economics, 33(1), pp. 3–56.doi:10.1016/0304-405x(93)90023-5Source page
- Fama, E.F. and French, K.R. (2015) ‘A five-factor asset pricing model’, Journal of Financial Economics, 116(1), pp. 1–22.doi:10.1016/j.jfineco.2014.10.010Source page
- Ross, S.A. (1976) ‘The arbitrage theory of capital asset pricing’, Journal of Economic Theory, 13(3), pp. 341–360.doi:10.1016/0022-0531(76)90046-6Source page