Beyond Fama-French: q-Factors, AQR's Factors, and Why Your Alpha Depends on the Model

For thirty years the Fama-French models have been the default way to ask whether a fund’s returns came from skill or from exposure to known factors. They are not the only models. Hou, Xue and Zhang built a rival from corporate investment theory, the q-factor model. AQR publishes its own versions of value, momentum, quality and low beta. Behavioral researchers built factors out of mispricing, and statisticians let the data choose the factors.¹

These models ask the same question and give different answers, and the differences land on real funds. We regressed seven funds on seven models over the same 144 months. Vanguard’s small-cap value ETF trailed the CAPM by 4.7% a year, the Fama-French models by about 1.5%, and the q5 model by 0.1%. Which number counts as its alpha depends on which model you believe.²

Four things that get called a “factor”

Much of the confusion about factor models comes from using one word for four different objects:

• A characteristic is a number about a company: its book-to-market ratio, return on equity, or asset growth.
• An asset-pricing factor is the return of a long-short portfolio sorted on a characteristic, such as HML (cheap minus expensive stocks). It is a research construct, rebalanced without costs, and nobody holds it.
• An investable strategy is an attempt to capture the factor after trading costs, taxes, and limits on shorting and leverage.
• A fund is one implementation of a strategy, with its own fee, index rules and capacity.

A regression can tell you a fund behaves as if it held 0.4 units of HML. It cannot tell you the fund will earn HML’s historical premium, because the fund holds only the long side and pays costs the research portfolio does not.

“AQR factors” is a case of the same confusion. AQR’s data library posts monthly returns for factors from individual papers: Quality Minus Junk, Betting Against Beta, HML Devil, and value and momentum across asset classes. They are hypothetical research portfolios, not returns of AQR funds.³ Portfolio Visualizer lets users add QMJ and BAB to a Fama-French regression, and many investors call the result “the AQR model.” AQR has never proposed it as an asset-pricing model. Below, the “AQR set” means AQR’s own US market, size, HML Devil, momentum, QMJ and BAB series, which is our grouping.

The models side by side

Why profitability and investment keep reappearing

Fama and French reached profitability and investment by rearranging the dividend discount model. If two stocks have the same price, the one expected to produce more earnings must have a higher expected return. If two firms have the same profits, the one reinvesting more of them leaves less for shareholders and must have a lower expected return. Adding RMW and CMA to their three-factor model made HML redundant in their 1963–2013 US sample: its average return was fully explained by the other four factors.⁴

Hou, Xue and Zhang started from the firm’s side. A company keeps investing until the expected return on one more unit of capital equals its cost of capital. A firm with a low cost of capital finds more projects worth doing and invests more, so high investment signals low expected returns. A firm that earns high profits without investing heavily must be discounting those profits at a high rate, so high profitability signals high expected returns. The model reaches the Fama-French conclusions without calling them anomalies.¹

The two constructions differ in the details. The q-factor ROE factor uses the latest quarterly earnings and is rebalanced monthly, while RMW uses annual operating profitability updated once a year. The q-factor model has no value factor at all. Here is how the factors correlate:

Spanning regressions test the overlap directly: regress one model’s factor on the other model and see whether any average return is left over. Over the same 708 months, the q5 model left no significant alpha in RMW, CMA, HML or momentum. The Fama-French six-factor model left large alphas in three factors: q’s ROE factor (2.8% a year, t = 3.9), its expected-growth factor (8.4%, t = 10.1) and AQR’s QMJ (3.6%, t = 5.2). BAB kept an alpha of about 4% a year against both models, with t-statistics near 2.²

That asymmetry favors q5 on this test, and it matches a Bayesian comparison by Barillas and Shanken. Their highest-probability model combined q’s ROE and investment factors with size, momentum and a value factor updated monthly, and it beat both FF5 and the original q-factor model. In their words, both FF5 and the q-factor model are “dominated by a variety of models that include a momentum factor, along with value and profitability factors that are updated monthly.”¹⁰

Which model wins the horse races

Every model’s authors report that it beats its rivals, which is why these results need reading with care.

• The original q-factor paper screened nearly 80 anomalies and tested the models on the 35 that were significant. The q-factor model left 5 of them with significant high-minus-low alphas, against 19 for Carhart and 27 for FF3. Its weak spots were operating accruals and R&D-to-market.¹
• q5 added an expected-growth factor that averaged 0.84% a month (t = 10.27) from 1967 to 2018, and its authors report it outperforms FF6.⁵
• Fama and French evaluated their six-factor model by the maximum Sharpe ratio the factors can produce together, and compared versions of profitability and spread factors.¹¹

Two results limit how much weight any winner deserves. Kozak, Nagel and Santosh found that models built from a handful of characteristics cannot summarize the cross-section of returns, while a few principal components of many characteristics can.⁹ On that evidence, the final five-factor model is unlikely to exist. And a factor that prices other factors has not thereby shown why it earns a premium. Qi Lin tested whether q5’s expected-growth factor behaves like a hedge against changing investment opportunities, which the model’s intertemporal interpretation requires. It predicted those opportunities with the wrong sign, while the investment factor passed.¹²

Risk, mispricing or frictions

The models also disagree about why factors pay. There are three broad explanations, and each model leans on a different one:

• Risk. The premium compensates for losses at bad times. Pástor and Stambaugh found that stocks most sensitive to market-wide liquidity shocks earned 7.5% a year more than the least sensitive, after adjusting for market, size, value and momentum.¹³ Fama-French and q-theory are usually read as risk models.
• Mispricing. Investors make correlated errors that take time to correct. Stambaugh and Yuan built their two factors by averaging rankings across 11 anomalies, on the argument that the anomalies share one source of mispricing.⁶ Daniel, Hirshleifer and Sun used share issuance and buybacks for long-horizon mispricing (managers issue stock when it is expensive) and post-earnings drift for short-horizon underreaction.⁷
• Frictions. Rules and constraints move prices. Betting Against Beta rests on leverage constraints: investors who cannot borrow buy high-beta stocks to get more market exposure, which bids them up and leaves low-beta stocks cheap.¹⁴

The data have not settled the question. Daniel and Titman found that a stock’s characteristics predicted its returns better than its loadings on the Fama-French factors, which pointed away from a risk story.¹⁵ Kelly, Pruitt and Su later showed that letting factor loadings depend on characteristics reconciles much of that result: five latent factors with characteristic-driven loadings priced anomaly portfolios better than the standard models.⁸ A premium can persist without an agreed explanation. Still, the less anyone can say about why it exists, the less confidence it deserves out of sample.

The factor zoo in brief

John Cochrane popularized the term in his 2011 presidential address: “Now we have a zoo of new factors.”¹⁶ Harvey, Liu and Zhu catalogued 316 factors and argued a new one should clear a t-statistic of 3.0.¹⁷ Whether most published anomalies replicate depends on the method. Hou, Xue and Zhang found 65% of 452 failed a standard test once microcaps were controlled, while Jensen, Kelly and Pedersen found most of 153 factors, grouped into 13 themes, replicated in the US and across 93 countries.¹⁸¹⁹ Published returns shrank 26% out of sample and 58% after publication in McLean and Pontiff’s study of 97 predictors.²⁰ We cover that evidence in Is Factor Investing Dead? and The ABCs of Systematic and Factor Investing.

For model choice, the zoo matters in one way. Each competing model is a claim that a few factors summarize hundreds of anomalies. Jensen, Kelly and Pedersen’s 13 themes suggest that is roughly right: many named anomalies are different measurements of value, profitability, investment, momentum and low risk. The models argue over which measurement of each theme works best.

Your alpha depends on the model

To see how much the choice matters, we regressed monthly excess returns of seven funds on seven models over one window, January 2014 to December 2025. That is 144 months, and the end date is set by the latest q-factor data. The funds cover the total market, small-cap value (an index fund and a screened one), minimum volatility, quality, momentum and one AQR fund. Each cell is the annualized alpha, with its Newey-West t-statistic in parentheses. An absolute t-statistic above about 2 is the usual bar for significance.²

What the table shows:

• Small-cap value moves the most. VBR’s alpha goes from −4.69% under the CAPM to about −1.5% under the Fama-French models and −0.06% under q5. DFSVX follows the same pattern. Under the CAPM, both funds look like poor performers. Under Fama-French, most of the shortfall is explained by their size and value loadings in a period when both factors lost money (Fama-French SMB averaged −2.9% a year and HML −1.4%). Under q5, the rest is explained by negative loadings on expected growth (−0.35 for VBR, −0.29 for DFSVX): small value stocks are the opposite of the fast-growing firms that factor buys, and that factor returned about 5% a year over the window.
• The momentum fund needs a momentum factor. MTUM shows +1.79% under the CAPM and +0.70% under FF3, then −0.92% once Carhart adds momentum. The q5 model has no momentum factor, and it explains less of MTUM’s monthly movement (adjusted R² 0.79 against 0.90 for FF6), even though q5 prices momentum’s average return over the long sample.
• Minimum volatility looks worst under the AQR set. USMV’s alpha is near zero under most models and −2.23% (t = −1.87) under the AQR set, because it loads on BAB (0.25) and QMJ (0.18), and both factors did well over the window. Measured against the low-beta factor it resembles, USMV fell short, though not by a statistically significant margin. See our USMV guide for why a long-only fund cannot capture BAB.
• The only significant result is an artifact. VTI, a total market index fund, shows +0.49% a year (t = 2.57) under the AQR set. AQR’s US market series averaged about 1 percentage point a year less than French’s over the window, with a 0.998 correlation. Swap French’s market factor into the AQR set and VTI’s alpha flips to −0.41% (t = −2.45). An index fund that costs 0.03% cannot have a real alpha of either sign at that size. The number comes from the factor data.

Two cautions apply to the whole table. First, 144 months is short. Standard errors on these alphas run from about 0.2 percentage points a year for VTI to more than 3 for the small-value funds under the CAPM, so differences of a point or two between funds are mostly noise. Second, alpha here is measured against each model’s factor returns, which carry no costs. A fund that captures a factor exactly but charges a fee and pays trading costs will show a negative alpha roughly equal to those costs, which is part of why most cells are negative. It is not a direct estimate of the fund’s costs or its manager’s skill. AVUV, which started in 2019, is not in the table. Over its 74 months to December 2025, its alpha ranged from −3.2% under the CAPM to +1.4% under q5, and none was significant.

Which model to use

For checking your own portfolio or a fund, we recommend:

1. Start with Fama-French five factors plus momentum. The data are free, updated monthly, and match the language fund companies use. Most long-only factor funds are built on these characteristics, and a Fama-French model had the highest or near-highest adjusted R² for six of the seven funds here. The exception was USMV, which the AQR set fit better (0.86 against 0.80) because of its BAB loading.
2. Check the result against q5 and the AQR factors. If a fund’s alpha survives all three, it is worth attention. If it appears under one model and vanishes under the others, the model produced it.
3. Compare loadings more than alphas. Loadings are estimated far more precisely. VBR’s size loading had a t-statistic above 18 while its alpha never cleared 1.7 in absolute value. Knowing what a fund holds is more reliable than knowing whether it beat a model.
4. Hold the window fixed. Compare funds and models over the same months, and state the window every time you quote a number.

We would not switch to q5 as the default because it won particular tests. Its expected-growth factor comes from a forecast of each firm’s investment growth, which is harder to audit than a sort on a reported accounting number, and no fund targets it. Its test record is strong and its economic interpretation is still disputed.¹²

When AQR’s factors justify an allocation

A factor model never justifies an allocation on its own. It measures what a portfolio did. AQR’s research does support a few specific decisions:

• Combining value and momentum. Asness, Moskowitz and Pedersen found value and momentum premia across eight markets and asset classes, with value and momentum negatively correlated both within and across them.²¹ The −0.64 correlation between HML Devil and momentum above is the same effect. A long-only investor can hold both tilts, and a multi-style fund holds them together.
• Screening small value for quality. QMJ’s clearest practical use is keeping junk out of small caps. Screened funds such as AVUV and DFSV already do this through profitability; see our QMJ guide.
• Treating low-volatility funds as something other than BAB. BAB is leveraged low-beta minus high-beta. Novy-Marx and Velikov found its published returns depend on construction choices that effectively equal-weight stocks, committing on average $1.05 per dollar invested to the smallest 1% of stocks by market cap; after costs it still earns positive returns, but through tilts toward profitability and investment.²² A long-only minimum-volatility ETF gets the defensive part and none of the leverage.
• A market-neutral style-premia sleeve. AQR’s own case for capturing value, momentum, carry and defensive premia across asset classes requires what it calls the three dirty words of finance: leverage, short-selling and derivatives.²³ Over a century of data, AQR researchers found these premia about 30% smaller out of sample, which they attribute mostly to overfitting, and found that timing them did not pay after data lags and trading costs.²⁴ This can fit an investor who wants a return source with little equity beta and will hold through long losing stretches. It is a poor fit for someone who wants a better version of a total market fund. We cover the funds and their costs in AQR Funds for Bogleheads.

The order we suggest is the market portfolio first, then modest long-only tilts, then a diversified multifactor fund, and only then a long-short alternative. Each step adds fees, turnover, tax drag and model risk, so each needs a larger expected benefit to be worth it. Before sizing any tilt, cut the historical premium in half and check whether the tilt is still worth its fee; the factor tilt reality check does that arithmetic.

How Summitward helps

The Portfolio page runs CAPM, Fama-French three- and five-factor, and Carhart regressions on your holdings. Switch between them and watch how the alpha and loadings change: if a fund’s alpha disappears when you move from CAPM to five factors, its outperformance was factor exposure you could buy more cheaply.

Key Takeaways

• The models converge on a few themes. Fama-French and the q-factor model reach profitability and investment from different theories; CMA and the q investment factor correlated 0.92 over 1967–2025.
• “AQR factors” are a research library. QMJ, BAB and HML Devil come from separate papers, and grouping them into one regression is the user’s choice.
• Alpha is model-dependent. Over 2014–2025, VBR’s alpha was −4.7% a year under the CAPM, about −1.5% under Fama-French and −0.1% under q5. None was statistically significant.
• Factor data construction matters. Differences between AQR’s and French’s market series produced a “significant” alpha for a total market index fund, of either sign depending on the series.
• Use FF5 plus momentum, then check. Trust an alpha only if it survives q5 and the AQR factors, and rely on loadings more than alphas.

Frequently Asked Questions

What is the q-factor model?

A four-factor model from Hou, Xue and Zhang (2015) with market, size, investment and return-on-equity factors, derived from the theory of how firms decide to invest. The 2021 q5 version adds an expected-growth factor. Factor returns are free at global-q.org.

Is there an AQR factor model?

No. AQR publishes factor returns tied to individual research papers, such as Quality Minus Junk and Betting Against Beta. Tools like Portfolio Visualizer let you add them to a Fama-French regression, but AQR has not proposed that combination as an asset-pricing model.

Which factor model is best?

No model wins every test. The q-factor models do well in their authors’ tests and in a Bayesian comparison by Barillas and Shanken, and statistical models built from many characteristics beat all sparse models. For checking funds, Fama-French five factors plus momentum is a practical default, checked against q5 and AQR’s factors.

Why did HML become redundant in the five-factor model?

In Fama and French’s 1963–2013 US sample, value stocks’ average return was explained by their exposure to the profitability and investment factors. Value firms tend to invest conservatively, and HML and CMA correlated 0.68 in our 1967–2025 data.

What is the factor zoo?

The hundreds of return predictors published since the 1990s. Many overlap, and many shrink after publication. Studies disagree on how many replicate; grouping them into themes, as Jensen, Kelly and Pedersen did, finds most themes hold up.

Can I invest in the q-factors or AQR’s factors directly?

Not as researched. The factors are long-short portfolios without costs. Long-only funds capture part of the long side: profitability and investment screens in funds from Avantis and Dimensional, quality and minimum-volatility ETFs, and AQR’s own multi-style funds. Full long-short exposure requires market-neutral funds with higher fees and shorting costs.

Related Guides

• Fama-French Factor Analysis: What Your Portfolio Is Really Doing How to read loadings, t-statistics and alpha.
• Is Factor Investing Dead? Replication, decay and costs, with a tilt calculator.
• Quality Minus Junk (QMJ) AQR’s quality factor since 2016 and which funds hold it.
• Minimum Volatility and Betting Against Beta What 15 years of USMV show about the low-beta anomaly.
• RMW Explained The Fama-French profitability factor.
• AQR Funds for Bogleheads When AQR’s long-short funds can be worth their cost.

Sources

1. Kewei Hou, Chen Xue and Lu Zhang, “Digesting Anomalies: An Investment Approach,” Review of Financial Studies 28(3), 2015, 650–705. doi.org
2. Summitward calculations: factor correlations and spanning regressions 1967-01 to 2025-12; fund regressions 2014-01 to 2025-12 (AVUV 2019-11 to 2025-12), numpy OLS with Newey-West t-statistics (6 lags; 12-lag results in the repository). Data: Ken French data library, global-q.org, AQR data library (through 2026-07, not redistributed), Yahoo Finance. Script and output: summitward-research
3. AQR Capital Management, Datasets. aqr.com
4. Eugene F. Fama and Kenneth R. French, “A Five-Factor Asset Pricing Model,” Journal of Financial Economics 116(1), 2015, 1–22. doi.org
5. Kewei Hou, Haitao Mo, Chen Xue and Lu Zhang, “An Augmented q-Factor Model with Expected Growth,” Review of Finance 25(1), 2021, 1–41. doi.org
6. Robert F. Stambaugh and Yu Yuan, “Mispricing Factors,” Review of Financial Studies 30(4), 2017, 1270–1315. doi.org
7. Kent Daniel, David Hirshleifer and Lin Sun, “Short- and Long-Horizon Behavioral Factors,” Review of Financial Studies 33(4), 2020, 1673–1736. doi.org
8. Bryan T. Kelly, Seth Pruitt and Yinan Su, “Characteristics Are Covariances: A Unified Model of Risk and Return,” Journal of Financial Economics 134(3), 2019, 501–524. doi.org
9. Serhiy Kozak, Stefan Nagel and Shrihari Santosh, “Shrinking the Cross-Section,” Journal of Financial Economics 135(2), 2020, 271–292. doi.org
10. Francisco Barillas and Jay Shanken, “Comparing Asset Pricing Models,” Journal of Finance 73(2), 2018, 715–754. doi.org
11. Eugene F. Fama and Kenneth R. French, “Choosing Factors,” Journal of Financial Economics 128(2), 2018, 234–252. doi.org
12. Qi Lin, “The q5 Model and Its Consistency with the Intertemporal CAPM,” Journal of Banking & Finance 127, 2021, 106096. doi.org
13. Ľuboš Pástor and Robert F. Stambaugh, “Liquidity Risk and Expected Stock Returns,” Journal of Political Economy 111(3), 2003, 642–685. doi.org
14. Andrea Frazzini and Lasse Heje Pedersen, “Betting Against Beta,” Journal of Financial Economics 111(1), 2014, 1–25. doi.org
15. Kent Daniel and Sheridan Titman, “Evidence on the Characteristics of Cross Sectional Variation in Stock Returns,” Journal of Finance 52(1), 1997, 1–33. doi.org
16. John H. Cochrane, “Presidential Address: Discount Rates,” Journal of Finance 66(4), 2011, 1047–1108. doi.org
17. Campbell R. Harvey, Yan Liu and Heqing Zhu, “…and the Cross-Section of Expected Returns,” Review of Financial Studies 29(1), 2016, 5–68. doi.org
18. Kewei Hou, Chen Xue and Lu Zhang, “Replicating Anomalies,” Review of Financial Studies 33(5), 2020, 2019–2133. doi.org
19. Theis Ingerslev Jensen, Bryan Kelly and Lasse Heje Pedersen, “Is There a Replication Crisis in Finance?” Journal of Finance 78(5), 2023, 2465–2518. doi.org
20. R. David McLean and Jeffrey Pontiff, “Does Academic Research Destroy Stock Return Predictability?” Journal of Finance 71(1), 2016, 5–32. doi.org
21. Clifford S. Asness, Tobias J. Moskowitz and Lasse Heje Pedersen, “Value and Momentum Everywhere,” Journal of Finance 68(3), 2013, 929–985. doi.org
22. Robert Novy-Marx and Mihail Velikov, “Betting Against Betting Against Beta,” Journal of Financial Economics 143(1), 2022, 80–106. doi.org
23. Clifford Asness, Antti Ilmanen, Ronen Israel and Tobias Moskowitz, “Investing With Style,” Journal of Investment Management, 2015. aqr.com
24. Antti Ilmanen, Ronen Israel, Rachel Lee, Tobias J. Moskowitz and Ashwin Thapar, “How Do Factor Premia Vary Over Time? A Century of Evidence,” Journal of Investment Management 19(4), 2021. joim.com

Author disclosure

Summitward has no business relationship with AQR, Vanguard, Dimensional, Avantis, BlackRock or any firm mentioned here and receives no compensation from them. Figures labeled as Summitward calculations are historical measurements over the stated window, not forecasts. Nothing here is investment advice.