Carhart four-factor model

Carhart four-factor model
Name	Carhart four-factor model
Developer	Mark M. Carhart
Introduced	1997
Related	Fama–French three-factor model, Capital Asset Pricing Model, momentum

Carhart four-factor model The Carhart four-factor model is an asset pricing extension that augments the Fama–French three-factor model with a momentum factor, designed to explain cross-sectional variation in stock returns. Developed by Mark M. Carhart in 1997, it builds on prior work by Eugene F. Fama and Kenneth R. French and has been applied by practitioners at institutions such as Goldman Sachs, J.P. Morgan, and BlackRock for performance attribution. The model is frequently cited in empirical research appearing in journals like the Journal of Finance and referenced in textbooks used at universities such as Harvard University and University of Chicago.

Introduction

The model extends the Capital Asset Pricing Model (CAPM) introduced by William F. Sharpe and John L. Williams by incorporating size and value factors from Fama–French three-factor model and a momentum factor inspired by studies by Narendra Jegadeesh and Sridharan (coauthors often cited include J. F. Carhart). It addresses anomalies documented in empirical studies at institutions like the National Bureau of Economic Research and appears in asset management practices at firms including Vanguard and State Street. The Carhart model is used in contexts ranging from mutual fund evaluation at Morningstar to hedge fund performance analysis at Moody's.

Model Components

The four factors are: market, size, value, and momentum. The market factor is proxied by excess return on a broad market index such as the S&P 500 or CRSP value-weighted return and relates to the CAPM market premium associated with figures like Eugene F. Fama and concepts taught at Massachusetts Institute of Technology. The size factor (SMB, small minus big) contrasts portfolios of small-cap firms with large-cap firms, using breakpoints influenced by datasets from Center for Research in Security Prices. The value factor (HML, high minus low) contrasts high book-to-market firms and low book-to-market firms, building on research by Kenneth R. French. The momentum factor (WML or UMD, winners minus losers) captures return continuation documented by Narendra Jegadeesh and Sheldon Natenberg and implemented in trading strategies used by hedge funds like Renaissance Technologies.

Each factor is typically constructed from long-short portfolios formed via market cap and accounting measures drawn from databases maintained by CRSP and Compustat, and momentum portfolios formed on past returns over 3–12 month formation periods used by researchers at Columbia University and Stanford University.

Empirical Performance and Applications

Empirical studies show the Carhart model improves explanatory power over CAPM and often outperforms the Fama–French three-factor model in mutual fund performance attribution studies published in the Review of Financial Studies and the Journal of Financial Economics. It is used by analysts at Morningstar and portfolio managers at BlackRock for alpha decomposition, risk budgeting, and performance fees analysis. Applications span mutual funds, exchange-traded funds issued by iShares, and smart-beta strategies marketed by State Street Global Advisors.

Academic work at institutions such as University of Pennsylvania and London School of Economics has tested the model across international markets including London Stock Exchange, Tokyo Stock Exchange, and Deutsche Börse, often incorporating extensions like liquidity factors proposed by Amihud or profitability and investment factors from Fama and French (2015). The model also appears in regulatory and consulting reports by PwC and EY when evaluating manager performance and fee structures.

Estimation and Implementation

Estimation proceeds via time-series regressions of portfolio or asset excess returns on the four factor returns, typically using ordinary least squares as in empirical finance courses at New York University and University of California, Berkeley. Factor return series can be sourced from academia (Kenneth R. French Data Library) or constructed from raw data in CRSP/Compustat with cleaning protocols found in methodological papers by Campbell R. Harvey and others. Practitioners implement rolling-window regressions, constrained optimization for exposure estimation at firms like Goldman Sachs, and Bayesian shrinkage techniques developed in literature influenced by scholars at Princeton University.

Standard diagnostics include R-squared, t-statistics for factor loadings, and tests for autocorrelation and heteroskedasticity using procedures associated with White test and Newey–West standard errors. Portfolio managers in quantitative trading groups at Two Sigma and Citadel integrate factor exposures into risk models alongside value-at-risk systems used in Deutsche Bank.

Criticisms and Limitations

Critics argue that the Carhart model, like the Fama–French three-factor model, is an empirical description rather than a structural theory, echoing debates involving Eugene F. Fama and proponents of behavioral finance such as Richard H. Thaler. Momentum's persistence has been questioned after episodes like the 2008 financial crisis and increased transaction costs highlighted by market microstructure researchers at Columbia Business School and MIT. Other limitations include data-snooping concerns raised by authors affiliated with National Bureau of Economic Research, factor instability across time and regions noted by scholars at University of Oxford, and difficulties capturing tail risk relevant to regulators such as Securities and Exchange Commission.

Extensions and alternatives incorporate additional factors proposed by Fama and French (2015), liquidity measures by Yakovenko and others, and macroeconomic factors explored by researchers at Federal Reserve Bank of New York. Despite limitations, the Carhart four-factor specification remains a standard tool in asset-pricing, portfolio management, and mutual fund evaluation at academic centers and financial institutions worldwide.

Category:Asset pricing models