An extension of the Fama-French three-factor model includes a fourth factor to measure

Question

BlackTom AI · Accepted Answer

The question asks about an extension of the Fama-French three-factor model and what the added fourth factor measures.

First, note that the classic Fama-French three-factor model includes: (1) the market excess return, (2) the size factor (small minus big, SMB), and (3) the value factor (high book-to-market minus low, HML).

In traditional asset pricing literature, a common extension includes a momentum factor. This momentum factor captures the tendency of assets that have performed well recently to continue performing well in the short term, and those that have performed poorly to continue underperforming. In practical terms, it measures the persistence of stock returns over the prior 3 to 12 months and adds an asset-pricing risk/return dimension tied to those return patterns.

Because momentum is the widely recognized fourth factor in many extended models (notably Carhart’s four-factor model, which adds momentum to the Fama-French framework), the correct interpretation is that the fourth factor measures momentum.

If other options had been present, we would assess each based on whether it aligns with momentum concepts (persistence of past winners vs. losers, continuation of recent performance) or whether it describes entirely different attributes (e.g., profitability, investment, liquidity, or a mischaracterization of risk factors).

In sum, the extension introduces a factor that represents momentum in stock returns, i.e., the tendency for assets with strong recent performance to continue performing well in the near term, and for weak performers to continue underperforming.

FINS5513-Investments & Portfolio Sel. T1 2025

An extension of the Fama-French three-factor model includes a fourth factor to measure

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