Carhart Four Factor ModelEdit
The Carhart four-factor model is an asset-pricing framework that extends the earlier Fama-French multi-factor approach by adding a momentum factor. Introduced by Mark Carhart in 1997, the model was designed to explain a substantial portion of mutual fund returns that the three-factor framework could not account for, specifically the tendency of recent winners to continue performing for a period. In practical terms, the model is used to decompose portfolio and fund returns into common risk exposures and an idiosyncratic performance term that would be labeled “alpha” in simpler analyses.
The core idea is straightforward: returns can be broken down into exposures to four systematic sources of risk, plus an unexplained residual. For a given asset or portfolio i, the excess return over the risk-free rate is typically written as: R_i − R_f = α_i + β_i,MKT × (R_MKT − R_f) + β_i,SMB × SMB + β_i,HML × HML + β_i,MOM × MOM + ε_i where: - R_i is the asset’s return, R_f is the risk-free rate, and R_MKT − R_f is the market risk premium. - SMB is the size factor, capturing the historical tendency for smaller firms to outperform larger ones. - HML is the value factor, capturing the tendency for value stocks with high book-to-market ratios to outperform growth stocks. - MOM is the momentum factor, capturing the persistence of returns for stocks that have outperformed recently (and, conversely, underperformers that have fallen behind). - α_i is the abnormal return, or “alpha,” after accounting for these exposures, and ε_i is an error term.
Model and factors
- The market factor (MKT) represents broad market risk and is proxied by the excess return of the broad market portfolio.
- The size factor (SMB) reflects the historical premium associated with smaller firms.
- The value factor (HML) captures the premium associated with value versus growth characteristics.
- The momentum factor (MOM) embodies the tendency of recent winners to persist for some time.
For readers who want to trace the origins, Carhart’s formulation built on the empirical findings of the Fama-French program and the observed momentum phenomenon across a wide set of funds. See Fama-French three-factor model for the predecessor framework, and Momentum (finance) for a deeper treatment of the momentum concept that underpins MOM. The introduction of momentum helps address a well-documented regularity in cross-sectional returns that the original three-factor model did not fully capture. For a historical account of Carhart’s contribution, see On Persistence in Mutual Fund Performance.
Practical use and interpretation
The Carhart model is widely used by fund managers, analysts, and researchers to: - attribute fund performance to known risk exposures rather than to “skill,” by isolating α after controlling for MKT, SMB, HML, and MOM. - compare different funds on a like-for-like basis, adjusting for how much of their returns come from broad market shifts, size and value biases, or momentum bets. - inform portfolio construction, particularly when evaluating whether a manager’s track record is robust to a variety of market conditions.
In practice, momentum is often the most economically important addition in equilibrium periods because it captures the repeatable pattern that recent performance tends to continue for several months. However, momentum strategies can incur substantial turnover costs and may suffer during regime shifts when asset prices reverse abruptly. The model’s explanatory power is thus contingent on the persistence of momentum and the stability of factor premia across time.
Controversies and debates
Like many asset-pricing frameworks, the Carhart model has its share of debates. Proponents argue that the momentum premium reflects real, economically meaningful risk and behavioral regularities, and that a four-factor specification provides a more faithful account of fund performance than models with fewer factors. Critics, however, point to concerns such as: - Data-snooping and overfitting: Some argue momentum might be partially a statistical artifact of depending on the sample or the look-back/formation period used to construct the MOM factor. - Stability across regimes and markets: The magnitude and even the sign of factor premia can shift across time and geography, limiting the model’s universality. - Practicality and costs: Implementing momentum-based strategies raises turnover and trading costs, which can erode the apparent advantage suggested by the factor in raw, before-cost analyses. - Risk mispricing versus true skill: A debate persists over how much of a fund’s alpha is truly skill, and how much is compensation for bearing the factor risks the model identifies.
From a market-centric perspective, the momentum element is appealing because it aligns with the idea that investors’ behavior and price movements generate systematic patterns. Critics who emphasize ideological agendas often frame momentum as a puzzle that needs grand re-interpretation or derive suspicion about “active management” in favor of purely passive approaches. Proponents respond that adjusting for known risk exposures provides a clearer view of performance and aligns incentives with prudence and discipline, rather than with fashion or overconfidence.
Limitations and extensions
The Carhart model, while influential, has limitations. Its effectiveness depends on stable factor premia, which can vary over time and across markets. Momentum, in particular, tends to reverse over longer horizons (a few years) and can be fragile during crises or structural shifts. Researchers have built on Carhart by adding further factors (for example, the five-factor model or other multi-factor specifications) to capture additional pricing anomalies or risk dimensions. See Fama-French five-factor model for a widely cited extension. Researchers also explore cross-market applicability and the sensitivity of factor loadings to data sets, formation windows, and transaction costs. For broader context on how factor models fit into the field of asset pricing, see Asset pricing.