Fama-French Five Factor Model: Profitability and Investment

Key Takeaways

• The Fama-French five factor model adds RMW (robust minus weak profitability) and CMA (conservative minus aggressive investment) to the original market, size, and value factors.
• Fama and French's own 2015 paper found that HML becomes redundant once RMW and CMA are included, though practitioners still commonly use all five.
• Confusing factor exposure with manager skill is the key mistake; a quality-tilted fund with high RMW loading can look like a star without the regression to prove it.
• Momentum is deliberately excluded from the five-factor model; adding it requires a separate Carhart or six-factor extension.

What It Is

The three-factor model (market, size, value) left a systematic pattern in returns unexplained: firms with high operating profitability earned more than low-profitability firms, and firms that invested aggressively earned less than conservative investors. Work by Robert Novy-Marx in 2013 on the profitability premium made this hard to ignore.

Fama and French responded with two additional factors:

• RMW (Robust Minus Weak), the return of high operating-profitability stocks minus low operating-profitability stocks.
• CMA (Conservative Minus Aggressive), the return of firms with low asset growth minus firms with high asset growth.

Together with the market factor, SMB, and HML from the 1993 paper, these make up the five-factor model.

The Intuition

The easiest way to understand RMW and CMA is through a simple dividend-discount argument. A firm's value is the present value of expected future cash flows. Holding the current price fixed, a firm with higher expected profitability should have a higher expected return. A firm that plows cash into aggressive investment has fewer near-term dividends available to shareholders, which, again holding price fixed, implies a lower expected return.

That framing is exactly what Fama and French formalize. RMW captures the profitability premium. CMA captures the investment premium. Both are consistent with the same cash-flow logic that motivated value (HML) in the first place.

One striking finding: in the five-factor model's U.S. sample, HML becomes redundant. Its average return is well described by a combination of market, size, RMW, and CMA. Fama and French are explicit about this in the 2015 paper. HML is not dropped in practice, but it is no longer independently needed once profitability and investment are included.

How It Works

The model expresses expected excess return as a linear combination of five factor exposures:

E[R_i] - R_f = alpha_i
             + beta_i * (E[R_m] - R_f)
             + s_i    * SMB
             + h_i    * HML
             + r_i    * RMW
             + c_i    * CMA

Where:

R_m   = broad market return
SMB   = small minus big (size)
HML   = high minus low book-to-market (value)
RMW   = robust minus weak operating profitability
CMA   = conservative minus aggressive investment (asset growth)
beta, s, h, r, c = factor sensitivities

Kenneth French's Dartmouth data library publishes monthly RMW and CMA series alongside the older factors, with construction documented in the same methodology. RMW sorts firms by operating profitability. CMA sorts by the change in total assets.

You estimate loadings with a time-series regression of the portfolio's excess returns on the five factor returns. The signs and magnitudes tell you what kind of exposures you are running.

Note what the five-factor model does not include: momentum. A momentum factor (UMD, winners minus losers) is not in Fama and French's 2015 specification. To include momentum you add it separately, which produces the Carhart four-factor model (with momentum replacing the two new factors) or variants that combine all six.

Worked Example

Suppose you regress a quality-tilted U.S. equity fund on the five factors and get: beta = 0.95, s = -0.10, h = -0.05, r = 0.35, c = 0.20, alpha = 0.02 percent monthly.

The negative s loading says it leans large-cap. The slightly negative h says it tilts away from deep value. The positive r and c say it holds more profitable and less aggressively investing firms.

Over the estimation window, if average monthly factor returns were market premium 0.55 percent, SMB 0.15, HML 0.10, RMW 0.30, CMA 0.15, the model predicts monthly excess return of roughly:

0.95*0.55 + (-0.10)*0.15 + (-0.05)*0.10 + 0.35*0.30 + 0.20*0.15
= 0.523 - 0.015 - 0.005 + 0.105 + 0.030 = 0.638%

Plus a tiny alpha of 0.02 percent. Almost all of the fund's return is explained by RMW and CMA loadings rather than stock picking.

Common Mistakes

1. Treating five factors as definitive. Asset pricing is an open field. Low-volatility, momentum, quality, and betting-against-beta factors all have credible empirical support and are not in the five-factor model. Claiming five factors fully capture expected returns goes beyond what the evidence supports.

2. Overfitting factor combinations. It is easy to run backtests that mix RMW, CMA, momentum, and quality until the in-sample Sharpe ratio looks wonderful. Most of that number is curve fit. Use walk-forward validation and equal-weighted factor blends as sanity checks.

3. Exporting U.S. factors to emerging markets unchanged. Book-to-market, operating profitability, and asset growth are defined from specific accounting conventions. Emerging-market samples often need re-derived factors with local breakpoints before the model produces stable loadings.

4. Ignoring factor crowding. As more capital tracks the same factor definitions, the premium available to any single investor can compress. This is a slow effect but worth watching in expected-return assumptions.

5. Confusing factor exposure with skill. A fund that loads heavily on RMW and CMA in a friendly decade can look like a star manager. The five-factor regression is precisely the tool that strips that appearance away. Do the regression before paying for alpha.

Frequently Asked Questions

Q: What is the Fama-French five factor model in simple terms? It extends the three-factor model by adding two new systematic risk factors: RMW, which captures the tendency of highly profitable firms to earn more, and CMA, which captures the tendency of conservatively investing firms to earn more than aggressive investors.

Q: How does the Fama-French five factor model affect investment decisions? It provides a more complete lens for attribution. A quality-focused fund can now have its outperformance fully explained by RMW and CMA loadings, stripping away the illusion of skill. It also helps portfolio managers deliberately target specific factor tilts with better precision.

Q: What is a real-world example of the Fama-French five factor model? A quality-tilted US equity fund with r = 0.35 (RMW) and c = 0.20 (CMA) loadings can see nearly all its excess return explained by those two factors when the model is run over its history, leaving almost no unexplained alpha for the manager to claim.

Q: How can investors use the Fama-French five factor model? Before paying for any actively managed equity fund, run a five-factor regression on its return history. If the alpha disappears, switch to a low-cost factor ETF. Reserve active fees only for funds that show residual alpha unexplained by any of the five factors.

Q: How is the Fama-French five factor model different from the three-factor model? The five-factor model adds profitability and investment factors, which the three-factor model omits. The critical difference is that HML (value) becomes statistically redundant in the five-factor framework once RMW and CMA are included, even though it still carries explanatory power in the three-factor version.

Sources

1. Fama, E.F. and French, K.R. (2015). "A five-factor asset pricing model." Journal of Financial Economics, 116(1), 1-22. Working paper PDF: https://tevgeniou.github.io/EquityRiskFactors/bibliography/FiveFactor.pdf
2. Fama, E.F. and French, K.R. (2015). "A five-factor asset pricing model." ScienceDirect entry. https://www.sciencedirect.com/science/article/abs/pii/S0304405X14002323
3. French, K.R. "Description of Fama/French Factors." Data Library, Tuck School of Business, Dartmouth College. https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/Data_Library/f-f_factors.html
4. "Construction of the Fama-French-Carhart four factors." Swedish House of Finance methodology note. https://www.hhs.se/globalassets/swedish-house-of-finance/data-center/fama_french_methodology.pdf

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.