# The Carhart Four-Factor Model: Why Mutual Fund Persistence Is Not Skill

Cite as: Gorak, R. (2026). The Carhart Four-Factor Model: Why Mutual Fund Persistence Is Not Skill. Tradicted. https://www.tradicted.com/research/carhart-four-factor-1997/
Paper: Mark M. Carhart — *On Persistence in Mutual Fund Performance*
Published in: Journal of Finance (1997)
Original: https://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1997.tb03808.x
DOI: 10.1111/j.1540-6261.1997.tb03808.x

Key finding: Buying last year's top-decile mutual funds and selling last year's bottom-decile funds yields 8 percent per year; 4.6 percent is explained by size, book-to-market, and one-year momentum factor exposures, 0.7 percent by expense ratios, and 1 percent by transaction costs.

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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 size, book-to-market, and one-year momentum 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.

## FAQ

### What is the Carhart four-factor model?

Four factors — market (RMRF), size (SMB), book-to-market (HML), and one-year momentum (PR1YR) — compose the Carhart model. PR1YR is the equal-weighted spread between the top and bottom 30% of stocks by eleven-month return, re-formed monthly. The model is: r = α + b·RMRF + s·SMB + h·HML + p·PR1YR + ε.

### How much of the mutual fund "hot hands" effect is explained by momentum?

31 basis points of the 67-basis-point monthly spread between decile 1 and decile 10 comes from the PR1YR momentum factor — almost half. Hot-hands funds do not actively follow momentum strategies. They hold last year's winning stocks by chance. The elevated returns fade after one year.

### What did Carhart find about expense ratios and fund performance?

A 100-basis-point increase in expense ratios reduces annual abnormal return by about 154 basis points — more than one-for-one. A 100-basis-point increase in turnover reduces returns by about 95 basis points, implying round-trip transaction costs of 95 basis points. Load funds underperform no-load funds by approximately 79 basis points per year, holding expense ratios constant.

### Do top-performing mutual funds continue to outperform?

More than 80% of top-decile fund composition turns over each year. Performance persistence is mostly eliminated after one year. Top-decile PR1YR loadings fall from 0.29 in the formation year to 0.14 one year later. Only bottom-decile funds show significant persistence — they continue to underperform and are more likely to disappear.

## Source

Carhart, M. M. (1997). On Persistence in Mutual Fund Performance. *Journal of Finance*, 52(1), 57–82.

[Read the full paper →](https://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1997.tb03808.x)