The Reference Factor Models: What a Strategy Is Measured Against
Which common factors explain the returns of a proposed investment strategy?
Regress dated strategy returns on a declared set of market, size, value and momentum factor returns, with the same frequency and investable universe. Examine the residual and its uncertainty after costs; a homemade proxy is not an official factor series.
Simple proxies are not official academic factors; regression or construction inside Stochastly needs a tested runnable graph.
Evidence map
| Aspect | Finding |
|---|---|
| What it is | The models that define what counts as an ordinary return. |
| Key result / formula | Fama and French's three-factor model adds size and value to the market factor, on the evidence that portfolios sorted on market capitalisation and on book-to-market produce return spreads the market factor does not explain. |
| Why it matters for backtesting | The transferable part is the regression procedure; the specific factors are mostly defined for equity cross-sections and may not apply to a user's instruments. |
What it is
A strategy's claim is that it earns something beyond the known compensations for risk, so the models that enumerate those compensations determine what the claim means.
Key result / formula
Carhart adds momentum as a fourth factor, motivated by the observation that mutual fund performance persistence was largely explained by funds holding recent winners rather than by skill, which is the canonical demonstration of an apparent alpha dissolving into a known exposure. The five-factor model adds profitability and investment, derived from the dividend discount identity without appeal to a behavioural story, and its introduction came with the finding that the value factor becomes redundant in the presence of the new pair for the samples examined, which is contested. Each model is a claim about what is ordinary, and the evolution shows that what counts as alpha shrinks as the set of documented exposures grows.
Why it matters for backtesting
A strategy's returns should be regressed on whatever set of common exposures is available and plausible, and the question is what remains. The Carhart case is the cautionary one: a strategy can appear to have skill and turn out to be an ordinary exposure held in a different container, and the regression is what reveals it. In Stochastly the practical version is to construct simple proxies from the user's own instruments, a market average, a trend exposure, a volatility exposure, and check the strategy's loading on each (see [The Factor Exposure Map: Low Cross-Correlation Does Not Mean No Common Exposure]). A strategy whose return vanishes against such proxies may still have practical value; its return is explained by existing exposures.
Source
Fama & French, "Common risk factors in the returns on stocks and bonds", Journal of Financial Economics 33(1), 1993, 3-56; Fama & French, "A five-factor asset pricing model", Journal of Financial Economics 116(1), 2015, 1-22; Carhart, "On Persistence in Mutual Fund Performance", Journal of Finance 52(1), 1997, 57-82. Primary source