The Carhart Four-Factor Model: Why Mutual Fund Persistence Is Not Skill
The Carhart four-factor model extends the Fama-French three-factor model by adding a one-year price momentum factor. In "On Persistence in Mutual Fund Performance," Carhart (1997) analyzed 1,892 diversified equity funds in the ICDI/Micropal database from January 1962 to December 1993. Buying last year's top-decile funds and selling the bottom decile yields 8 percent per year. Of that 8 percent, 4.6 percent reflects momentum and size factor exposures, 0.7 percent expense ratios, and 1 percent transaction costs.
What the Study Found
Of the 67-basis-point monthly return spread between decile 1 and decile 10, the momentum factor explains 31 basis points — almost half. Under the CAPM, top-decile funds earn about 22 basis points per month of alpha. Bottom-decile funds earn about -45 basis points per month under the same model. A 100-basis-point increase in expense ratios reduces annual abnormal return by about 154 basis points. Load funds underperform no-load funds by approximately 79 basis points per year, holding expense ratios constant.
Methodology
The study uses the ICDI/Micropal database of diversified U.S. equity mutual funds, free of survivor bias. The sample includes 1,892 funds and 16,109 fund years from January 1962 to December 1993. Funds are sorted annually into equal-weighted decile portfolios on lagged one-year returns. Key controls include expense ratios, modified turnover (Mturn), total net assets, load fees, and the four-factor model loadings (RMRF, SMB, HML, PR1YR).
Key Statistics
| Metric | Finding | Context |
|---|---|---|
| Annual return spread, decile 1 vs. decile 10 | ~8% per year | Funds sorted on lagged one-year return, 1963–1993 |
| Spread explained by momentum factor (PR1YR) | 31 of 67 bp/month | 4-factor model attribution, decile 1 vs. decile 10 |
| Expense ratio coefficient (Fama-MacBeth) | –1.54 | 100 bp increase in expense ratio → 154 bp drop in annual abnormal return |
| Round-trip transaction costs (implied) | 95 bp | Estimated from turnover coefficient in cross-sectional regression |
| Load fund underperformance vs. no-load | ~79 bp/year | Holding expense ratios constant |
| 4-factor model mean absolute pricing error | 0.14% per month | vs. 0.35% (CAPM) and 0.31% (3-factor) on 27 stock portfolios |
| Carhart 4-factor model | r_{it} = a_{iT} + b_{iT}RMRF_t + s_{iT}SMB_t + h_{iT}HML_t + p_{iT}PR1YR_t + e_{it} | Equation (3); primary performance measurement model |
| PR1YR factor construction | EW avg(top-30% eleven-month return stocks, lagged 1 month) − EW avg(bottom-30%) | Zero-investment momentum factor, re-formed monthly |
Why This Matters
The four-factor model became the standard benchmark for mutual fund performance attribution after 1997. Sorting funds on longer intervals of 2 to 5 years does not reveal more manager skill than sorting on one year. The only persistent anomaly that survives is concentrated in the strong underperformance of the worst-return funds. Investors seeking to outperform should prioritize minimizing expense ratios and avoiding the bottom decile of past performers.