Key takeaways
- On the 32 test portfolios sorted by profitability and investment, adding the two new factors cut the average pricing error from 18.2 to 10.3 basis points a month.
- On the 25 portfolios sorted by size and book-to-market, the same two factors were worth 0.8 of a basis point a month, from 10.2 down to 9.4.
- Across the 757 months from July 1963 to July 2026, the profitability factor averaged 0.26% a month and the investment factor 0.25%, against 0.19% for size.
- Since the paper's sample ended in December 2013, the investment factor has averaged minus 0.07% a month across 151 months, on a t-statistic of minus 0.35.
- In Japan the profitability premium has averaged 0.02% a month over the 433 months from July 1990, a t-statistic of 0.23.
What the five-factor model bought, in basis points a month
Does adding profitability and investment to the Fama-French three-factor model explain anything the three factors missed? It does. But the size of the gain runs from almost nothing to nearly a tenth of a percentage point a month, and which one you get depends entirely on what you point the model at.
Fama and French made the case in A five-factor asset pricing model, published in the Journal of Financial Economics in 2015. They ran six sets of test portfolios through three-, four- and five-factor versions, over the 606 months from July 1963 to December 2013. Each set gets two numbers. One is a GRS statistic, which tests whether a model's pricing errors are jointly zero. The other is the average absolute pricing error itself, in percent a month.
Here's the spread. On 32 portfolios sorted by size, profitability and investment, the three-factor model left an average absolute error of 18.2 basis points a month, with a GRS statistic of 4.38. Adding the two new factors cut that to 10.3 basis points and 2.92. On 25 portfolios sorted by size and book-to-market, the same addition moved the error from 10.2 basis points to 9.4, and the statistic from 3.62 to 2.84.
The paper says it in words too. On the size and book-to-market portfolios the improvement is "less than a basis point, in the average absolute intercept". On the profitability and investment portfolios, the gain of 6.9 to 8.2 basis points a month is "the biggest" anywhere in the study. The chart above plots that gain across all six sets of test portfolios. It doesn't show how good the model is. It shows how much the two additions were worth on top of what was already there, and the tallest bar is 7.9 against 0.8 for the shortest.
The paper is blunt about the ceiling. "In short, the GRS test says all our models are incomplete descriptions of expected returns." The best p-value across the six sets was under 0.04, so every model is rejected. Less wrong is the claim being made. Right isn't.
Profitability and investment fall out of the same equation that motivates value
The two additions aren't bolted on. They come out of the same dividend discount arithmetic that motivates book-to-market in the first place.
Start with the idea that a share is worth the discounted value of what it eventually pays out. Hold price and book value fixed, then raise expected earnings. The return implied by that price has to rise, because the same price now buys more expected profit. Now hold price and expected earnings fixed, and raise expected investment, meaning earnings retained rather than paid out. The implied return has to fall, because the same expected profit now supports a bigger book. Higher expected profitability points to higher expected returns. Higher expected investment points to lower ones.
Kenneth French's data library turns that into two portfolios anyone can measure. The profitability factor, RMW, is "the average return on the two robust operating profitability portfolios minus the average return on the two weak operating profitability portfolios". The investment factor, CMA, is "the average return on the two conservative investment portfolios minus the average return on the two aggressive investment portfolios". Investment here means asset growth, not capital spending: total assets in one year set against total assets in the year before.
Robert Novy-Marx had already shown the profitability half was worth measuring. His 2010 working paper reported that gross profits-to-assets "has roughly the same power as book-to-market predicting the cross-section of average returns". The NBER issued that paper in April 2010, five years before the five-factor model appeared.
The two premiums by decade, and how little the decades agree
Below is every decade of the US series, from the library's own monthly file. Each cell is the mean monthly return of that factor over the period, multiplied by 12. These are long-short paper portfolios with no trading costs in them, so read them as the raw premium and nothing closer to an outcome.
| Period | Profitability, RMW | Investment, CMA | Value, HML | Market |
|---|---|---|---|---|
| July 1963 to 1969 | 1.41% | -0.96% | 2.30% | 4.51% |
| 1970 to 1979 | -0.60% | 6.23% | 7.84% | 1.17% |
| 1980 to 1989 | 4.93% | 5.58% | 5.91% | 8.54% |
| 1990 to 1999 | 2.31% | 0.16% | 0.05% | 12.80% |
| 2000 to 2009 | 8.31% | 6.64% | 7.95% | -1.71% |
| 2010 to 2019 | 1.35% | 0.19% | -2.35% | 13.14% |
| 2020 to July 2026 | 3.40% | 0.73% | 2.64% | 12.88% |
Read down the profitability column and the pattern isn't decay. It's dispersion. The factor ran at 8.31% a year in the 2000s and lost money outright in the 1970s. The investment column is worse behaved still: two strong decades, one negative, and three that round to nothing much.
Over the whole 757 months the two averaged 0.26% and 0.25% a month, on t-statistics of 3.10 and 3.27. The size factor, over exactly the same months, averaged 0.19% on a t-statistic of 1.71. On that measure the two newer factors rest on firmer statistical ground than the size factor that was already in the model, which is worth holding next to the fact that the size premium is the better known of the three.
Persistence tells a similar story. Across the 638 overlapping 120-month windows in the sample, the mean monthly profitability return was positive in 90% of them, against 67% for size. Calendar years are noisier: RMW was positive in 42 of the 62 years from 1964 to 2025, CMA in 36.
None of that makes either factor smooth. The compounded profitability series fell 41.79% from its August 1998 peak to its February 2000 trough, as loss-making firms outran profitable ones into the top of the dot-com market. Its worst calendar year, 1999, was -28.93%; its best, 2021, was +26.72%. The investment series fell 27.63% between December 2022 and October 2025. A tilt sized so that a 41.79% fall in the long-short leg is survivable is a different tilt from one sized on the headline premium.
Adding the two factors made the value factor redundant
This is the result the paper itself flags as "so striking we caution the reader that it may be specific to this sample". Once profitability and investment are in the model, the value factor stops adding anything.
The test is a spanning regression: regress each factor on the other four and look at the intercept, which is the part of its average return the others can't explain. In the paper, the HML intercept is -0.04% a month, with a t-statistic of -0.47. In plain terms, the value premium is fully accounted for by exposure to the other four. Fama and French put it directly: the value factor "is redundant for describing average returns", in US data from 1963 to 2013.
Running the same regression over the library's current file, all 757 months to July 2026, the intercept comes out at -0.02% a month with a t-statistic of -0.25, and the slope on CMA is 1.00. Twelve and a half further years haven't rescued it. The mechanism is visible in one correlation: HML and CMA move together at 0.68 over the full sample, and at 0.70 in the paper's window. The paper puts the reason plainly: "high B/M value firms tend to do little investment", so the two portfolios keep buying the same names.
Run the regression the other way and the picture inverts. The profitability factor's intercept against the other four is 0.35% a month, on a t-statistic of 4.41. The investment factor's is 0.21% on 3.86. Both survive the company they keep; value doesn't. That doesn't make the value premium fictional. Its average return over those 757 months is 0.30% a month, higher than either newcomer. What the regression says is that you could reproduce it out of the other four factors and not miss it.
Since the paper's sample ended, one of the two has paid and one has not
The paper's sample stops in December 2013. Everything after that is out of sample, and it's the cleanest test available.
Across the 151 months from January 2014 to July 2026, the profitability factor averaged 0.21% a month, on a t-statistic of 1.08. The investment factor averaged minus 0.07%, on minus 0.35. Value managed minus 0.03%, size minus 0.18%. Only the market delivered: 0.99% a month, or 11.92% a year annualised, on a t-statistic of 2.80.
Take those numbers at face value and the honest summary is narrow. Profitability kept roughly four-fifths of its in-sample average and lost its statistical significance on a shorter window, which is what a 151-month sample does to a premium of that size. Investment stopped working. Neither of those is a forecast, and a t-statistic of 1.08 over twelve and a half years is not evidence that the factor has died either. It is an interval that contains both answers.
There's one thing this doesn't test. These are the same portfolios, rebuilt monthly, sorted the same way. A real position in the same idea carries turnover, spreads and a fund fee, and factor ETF returns have generally landed below the index records they were built from.
The strongest objection is that a rival model prices both new factors
The serious criticism doesn't say profitability and investment are fake. It says Fama and French built worse versions of two factors that already existed.
Kewei Hou, Haitao Mo, Chen Xue and Lu Zhang set this out in Which Factors?, an NBER working paper first circulated in November 2014 and revised in July 2018. Their q-factor model uses a market factor, a size factor, an investment factor and a return-on-equity factor. Over the 600 months from January 1967 to December 2016 they ran the spanning tests in both directions.
One direction is decisive. RMW averaged 0.26% a month in their sample; against the q-factors its alpha is 0.01%, with a t-statistic of 0.08. CMA averaged 0.33% a month; its alpha against the q-factors is "virtually zero", carried by a loading of 0.96 on the q investment factor. Testing whether the alphas of HML, CMA and RMW are jointly zero under the q-factor model gives a GRS statistic of 0.2, with a p-value of 0.9. The q-factors price all three.
The other direction fails. Asking whether the q-factor model's investment and return-on-equity factors are priced by the five-factor model gives a GRS statistic of 22.72, with a p-value that rounds to zero. Their conclusion is that "the q-factor model largely subsumes the Fama-French (2015, 2018) 5- and 6-factor models".
The disagreement is about construction, and they say why. Their return-on-equity factor "is constructed from monthly sorts on the latest known quarterly earnings data, whereas RMW is from annual sorts on the more stale operating profitability from the last fiscal year end". Their investment factor sorts on size, investment and profitability together, while "the CMA construction does not control for return on equity". Fresher data and a joint sort, in other words, not a different idea about the world. Both camps agree on the economics: how profitable a firm is, and how fast it grows its assets, is priced. They are disputing the measurement.
Outside the United States the profitability premium travels and Japan is the exception
The library publishes the same five factors for regions outside the US, built from Bloomberg data rather than from CRSP, starting in July 1990.
Across the 433 months to July 2026, developed markets outside the United States produced a profitability premium of 0.27% a month on a t-statistic of 4.10. That is a firmer reading than the US series over its own much longer sample. The investment premium there is weaker: 0.17% a month on 2.02, which is the kind of number that moves a lot with the window you pick.
Japan is the outlier, and it's the one worth knowing about. The Japanese profitability premium over the same 433 months is 0.02% a month, on a t-statistic of 0.23. Call that zero. Japanese value, by contrast, ran at 0.41% a month on 2.75 over the same window. A premium that reads 4.10 standard errors from zero in developed markets outside the US, and 0.23 in one of the largest of them, is not the uniform mechanism the dividend discount argument implies. That regional split matters for anyone building on international factor investing, because the global average hides it.
What this evidence cannot tell you
Start with who built the data. The paper's own first footnote reads: "Fama and French are consultants to, board members of, and shareholders in Dimensional Fund Advisors." Dimensional runs funds that tilt to exactly these variables. That doesn't make the tables wrong, and they're reproducible from the public file, but it's why the adversarial paper above has a section of its own.
The series is not fixed. Recomputing the paper's own window, July 1963 to December 2013, from the July 2026 version of the library gives a profitability mean of 0.27% a month, against the 0.25% printed in the paper. The market factor matches at 0.50%. The two are built from different vintages of the same underlying database, and the sorted portfolios move when accounting data is restated. The limitation is small in this case and it is not zero, and it applies to every backtest that quotes this library.
These are long-short portfolios, re-sorted once a year at the end of June and value-weighted, with no transaction costs, no borrow fee and no tax. Nothing you can buy has those properties. The gap between a factor and a fund is the subject of its own literature, and the measured tilt inside real multi-factor funds is typically a fraction of the academic factor's.
And 757 months is one history, not a distribution of histories. The whole US sample contains one dot-com melt-up, one financial crisis and one long growth run. Fama and French name the model's own worst failure in the abstract: it fails "to capture the low average returns on small stocks whose returns behave like those of firms that invest a lot despite low profitability". Small unprofitable firms that keep expanding are the portfolio the model prices worst, and they are not a rare species.
What would change the conclusion
If the out-of-sample window keeps going the way it has. The profitability factor's t-statistic since January 2014 is 1.08 and the investment factor's is minus 0.35. Another decade at that pace would take the full-sample t-statistics down toward the level where the size factor already sits, and the size factor is the cautionary tale in this literature.
If the measurement dispute resolves against the two-by-three sorts. The q-factor result isn't a rival claim about the world, it's a claim that a different construction of the same two ideas prices more. If that holds up in the next decade of data, the five-factor model survives as a description while losing its claim to be the efficient one.
If Japan turns out to be the rule rather than the exception. One region with a 0.02% profitability premium across 433 months is an anomaly. Two or three would be a boundary condition on where the mechanism works at all, and the dividend discount argument gives you no reason to expect it to stop at a border.
The number to watch isn't the premium. It's the spread between what a factor earns on paper and what a fund tracking it earns after costs, which is where the argument stops being academic. LedgerTouch measures the second one. The first is free on Ken French's website, and this piece is built entirely on it.