Carhart Four-Factor Model

Mark Carhart introduced the four-factor model in his 1997 study of mutual fund performance persistence. Building on the Fama-French framework, he added a momentum factor — labeled UMD for Up Minus Down, or sometimes WML for Winners Minus Losers — to capture the cross-sectional momentum anomaly documented by Jegadeesh and Titman in 1993.

The momentum factor is constructed by ranking stocks on their past 12-month return (excluding the most recent month to avoid short-term reversal effects), buying the top-performing decile, and shorting the bottom-performing decile. This factor has been one of the most robust and widely replicated findings in empirical finance, showing positive average returns across dozens of markets and time periods.

Carhart's motivation was practical: he wanted to determine whether actively managed mutual funds that appeared to generate persistent alpha were actually doing so through skill, or whether they were simply maintaining persistent tilts toward momentum stocks. His finding was largely the latter — much of what appeared to be fund manager skill evaporated after controlling for momentum exposure.

The four-factor model became a standard benchmark for academic studies of fund performance and trading strategies throughout the 2000s. It was later extended by Fama and French in their 2015 Five-Factor Model, which added profitability and investment factors, and by the AQR six-factor model, which preserved momentum alongside the Fama-French five factors.

For practitioners, the Carhart model's importance lies in distinguishing between genuine stock-selection skill and returns that can be explained by systematic factor tilts — particularly the momentum tilt that naturally accrues to strategies that hold winning positions too long.