Glossary term
Carhart Four-Factor Model
The Carhart four-factor model extends the Fama-French three-factor model by adding a momentum factor to market, size, and value exposures.
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What Is the Carhart Four-Factor Model?
The Carhart four-factor model is an asset-pricing and performance-attribution model that extends the Fama-French three-factor model by adding a momentum factor. It explains stock or fund returns using market, size, value, and momentum exposures.
The model is especially useful in fund analysis because momentum can be an important source of historical return. A manager who appears to outperform may simply have owned stocks with strong recent performance.
Key Takeaways
- The model adds momentum to the Fama-French market, size, and value factors.
- It is commonly used to analyze mutual fund and portfolio performance.
- The momentum factor captures the tendency for recent winners and losers to continue moving for a period.
- The model can reduce apparent alpha by explaining more return through factor exposure.
- It is useful, but it remains a simplified model of market behavior.
The Core Formula
A common version of the four-factor model is:
In this expression, Ri - Rf is the asset's excess return, Rm - Rf is market excess return, SMB is the size factor, HML is the value factor, MOM is the momentum factor, and αi is return not explained by the factors.
For example, if a fund beats its benchmark during a period when momentum stocks are leading the market, the four-factor model can test whether the outperformance came from momentum exposure rather than security-selection skill.
What the Fourth Factor Adds
Factor | What it captures |
|---|---|
Market | Broad equity-market exposure. |
Size | Small-company versus large-company exposure. |
Value | Value-stock versus growth-stock exposure. |
Momentum | Recent winners versus recent losers. |
How the Model Is Used
The Carhart model gives analysts a more demanding test of manager performance than a market-only benchmark. If a fund's returns are explained by market beta, size, value, and momentum, the remaining alpha may be smaller than it first appeared.
That is useful for fee evaluation. An investor may be willing to pay for genuine skill, but less willing to pay active fees for factor exposures that can be obtained more cheaply elsewhere.
Where It Can Mislead
The model depends on the factor definitions, sample period, data quality, and investment universe. Momentum can reverse sharply, transaction costs can matter, and real portfolios may have exposures that the four-factor model does not capture.
It also should not be treated as proof that a manager has no skill. A model can explain much of the return while still missing process quality, risk control, tax management, liquidity decisions, or other forms of value.
The Bottom Line
The Carhart four-factor model explains returns using market, size, value, and momentum factors. It is a useful performance-attribution tool, especially for fund analysis, but it should be read as a model-based diagnosis rather than a final verdict.