Loading
An asset pricing model that adds a momentum factor to the Fama-French three-factor model.
An asset pricing model that adds a momentum factor to the Fama-French three-factor model.
Proposed by Mark Carhart (1997), the four-factor model augments Fama-French with a momentum factor (UMD, Up Minus Down: long recent winners, short recent losers over 12 months). The model captures the momentum anomaly documented by Jegadeesh and Titman (1993) and is the standard benchmark for evaluating active equity strategies that may have momentum exposure.
UMD is the 12-month return skip-month (11 months) long-short momentum portfolio.
Alpha with respect to all four factors is the cleanest measure of active equity skill.
Momentum is the most persistent post-publication anomaly in equity returns.
Portfolio optimization is the construction of an asset allocation that maximises risk-adjusted return subject to investor constraints. The classical framework is mean-variance optimisation (Markowitz, 1952); the modern framework is factor-based, with the portfolio constructed to express a target set of factor exposures and to harvest the corresponding risk premia.
Quantitative research is the disciplined process of turning a financial hypothesis into a validated, deployable trading model. It spans data engineering, signal design, backtesting with proper out-of-sample validation, and ongoing production monitoring. The discipline's central problem is overfitting: most strategies that pass backtests fail in production.