Quality-Minus-Junk (QMJ): a Verified Multi-Decade, 24-Market Alpha — and Where Its Numbers Stop

Quality-Minus-Junk (QMJ) is a long-high-quality/short-low-quality equity factor built from profitability, growth, safety, and payout. It clears this wiki's evidence bar (What Counts as an Edge Here: The Evidence Bar This Wiki Applies to Every Technique) on effect size, sample breadth, and statistical significance — but the notes behind this page do not contain a decayed/undecayed verdict, so treat that dimension as open.

Definition and Original Numbers

QMJ is long stocks with high "quality" and short stocks with low "quality" ("junk") — https://www.aqr.com/Insights/Research/Working-Paper/Quality-Minus-Junk. Quality is a composite of four scaled components: profitability, growth, safety, and payout (https://www.aqr.com/Insights/Datasets/Quality-Minus-Junk-Factors-Monthly). The safety sub-component is itself a composite of six measures: beta (BAB — see The Low-Volatility Anomaly — CAPM's Prediction Inverted, With a Documented Leverage-Aversion Cause), idiosyncratic volatility (IVOL), leverage (LEV), Ohlson's O-score (O), Altman's Z-score (Z), and earnings volatility (EVOL) (same source). Portfolios are formed at the intersection of six value-weighted size-by-quality sorts (https://www.aqr.com/Insights/Datasets/Quality-Minus-Junk-Factors-Monthly).

U.S. long-sample result

4-factor abnormal return (alpha) of 66 basis points/month (≈8.2%/year, compounded: (1.0066)^12 − 1 = 8.21%), t-statistic 11.20, 4-factor information ratio 1.29 — https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2312432 (magnitude, t-stat) and https://hedgefundalpha.com/strategies/cliff-asness-quality-minus-junk/ (t-stat) and https://threadreaderapp.com/thread/1182288454601699331.html (information ratio). A t-stat of 11.2 is far above the t>3.0 bar this wiki treats as the multiple-testing-adjusted threshold (Multiple Testing: Why t>1.96 Is Not Enough — the bar this wiki uses to grade a factor's significance).

The paper was published as "Quality Minus Junk," *Review of Accounting Studies* 24(1), 34–112, 2019, originating as a 2013 working paper — https://link.springer.com/article/10.1007/s11142-018-9470-2. That gap (2013 working paper → 2019 journal) is itself a partial out-of-sample window, though the notes do not isolate a separate post-2013 number for QMJ specifically (see below).

Sample Period, Markets, Cross-Country Significance

- U.S. long sample: 1956 – December 2016. — https://www.aqr.com/Insights/Datasets/Quality-Minus-Junk-Factors-Monthly - Global sample: 1986 – December 2016. — same source - Universe: all common stocks in 24 developed markets, the union of countries in the MSCI World Developed Index over the sample period. — same source - QMJ delivers a positive 4-factor alpha in 23 of 24 countries tested. — https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2312432 - Those alphas are statistically significant in 18 of 24 countries, "despite many individual countries having small cross-sections and short time series" (source's own caveat). — same source

Global (1986–2016) vs. U.S. (1956–2016) monthly return

global ≈0.45%/month (≈5.5%/year, compounded: (1.0045)^12 − 1 = 5.54%), versus U.S. 0.66%/month (≈8.2%/year, compounded: (1.0066)^12 − 1 = 8.21%) — global is lower. — https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2312432. The global 4-factor information ratio is nonetheless 1.60, higher than the U.S. IR of 1.29 — https://threadreaderapp.com/thread/1182288454601699331.html. This is a case where risk-adjusted breadth (IR) and raw magnitude (average return) point in different directions across samples: worth noting when comparing factors by a single number, per What Counts as an Edge Here: The Evidence Bar This Wiki Applies to Every Technique.

What Is Confirmed Out-of-Sample vs. What Is Not

The 23/24-country and 18/24-significant results above are a genuine cross-market replication, not just a single-market in-sample fit — this is the strongest piece of out-of-sample-style evidence in the notes for QMJ.

What is NOT in the notes, and must be marked unverified rather than assumed

- No explicit isolated out-of-sample-period number (e.g., a pre/post-split Sharpe or return comparison) for QMJ specifically. — UNVERIFIED, notes explicitly flag this gap. - No QMJ-specific post-publication decay number. The notes only cite the general finding that published anomalies decay by an average of 58% post-publication (McLean-Pontiff 2016 — see Out-of-Sample vs Post-Publication Decay: The Two Numbers That Tell You If a Premium Is Real) as background context, not as a QMJ-specific measurement. — UNVERIFIED for QMJ. - No marginal-alpha number for QMJ over and above standard multi-factor models (e.g., Fama-French 5-factor) — the 1.60 global IR is suggestive of independent power but the notes contain no explicit incremental-alpha figure. — UNVERIFIED.

Given these gaps, this page cannot state whether QMJ has decayed since its 2013 working-paper release the way Cross-Sectional Momentum in Equities — the strongest documented anomaly, and how much of it survives costs or The Size Factor (Small-Minus-Big) — a textbook case of post-publication decay this wiki uses as a yardstick are documented to have. Confidence on the *original effect* is high (multi-country, high t-stat); confidence on *persistence* is not established here.

Overlap With Other Factors and Marginal Value

- QMJ vs. value (HML): moderate negative correlation, ~0.17 (sign of the correlation is negative per the note; magnitude 0.17). — https://threadreaderapp.com/thread/1182288454601699331.html. Being negatively correlated with value gives it a diversification argument alongside The Value Factor (Book-to-Market / HML) — a founding premium whose post-1991 numbers can't rule out zero. - QMJ vs. momentum: moderate positive correlation, ~0.29 — "limited overlapping information despite the positive relationship" (source's characterization). — https://www.interactivebrokers.com/campus/ibkr-quant-news/quality-factor-momentum-and-the-cross-section-of-returns/. Relevant next to Cross-Sectional Momentum in Equities — the strongest documented anomaly, and how much of it survives costs. - QMJ vs. BAB (Betting-Against-Beta): moderate positive correlation (no numeric value given in the notes). — https://threadreaderapp.com/thread/1182288454601699331.html. Expected given BAB is one of the six safety-score inputs to QMJ itself. - QMJ shows mild positive convexity to the market: returns tend to be elevated during downturns ("flight to quality"), contrasting with momentum's tendency to crash in such periods (see Cross-Sectional Momentum in Equities — the strongest documented anomaly, and how much of it survives costs for the 2009 momentum-crash numbers). — https://threadreaderapp.com/thread/1182288454601699331.html. - Quality characteristics explain only R² = 0.10 of cross-sectional variation in price-to-book ratios — i.e., the market does not fully price quality in, consistent with a "low price of quality" mispricing story for why the premium exists. — https://threadreaderapp.com/thread/1182288454601699331.html. - No explicit transaction-cost-survival number is in the notes for QMJ. This page cannot state a cost threshold; see Transaction Cost Accounting — the arithmetic that separates a real edge from a paper one and Computing a Strategy's Transaction-Cost Threshold — the four-step check that decides whether a documented edge is tradable for the general method to apply if/when turnover and cost data for QMJ are found.

What Does NOT Work / What Is Not Established

QMJ is not "refuted" by anything in the notes — but three specific claims that a reader might expect are explicitly absent from the sources gathered, and are marked here rather than silently assumed: 1. No out-of-sample decay number specific to QMJ (only general factor-decay literature applies). 2. No post-publication decay number specific to QMJ. 3. No marginal-alpha-over-standard-factor-models number.

Anyone citing QMJ as "still working today" from this page alone is going beyond what the sources support — the strongest defensible claim from these notes is the pre-2016, 24-country replication, not a live-track-record claim.

Why This Matters for the Wiki's Objective

QMJ meets three of the four evidence-bar requirements in What Counts as an Edge Here: The Evidence Bar This Wiki Applies to Every Technique with unusually strong numbers: effect size (66bp/month U.S.), proof regime (peer-reviewed, AQR + Review of Accounting Studies), and a form of out-of-sample check (23/24 countries, different sample window for the global leg). It fails the fourth requirement — documented cost survival and post-publication persistence — not because the effect is refuted, but because the gathered notes do not contain the numbers. That gap is itself the point of this page: a technique can be strongly verified on three axes and still be marked incomplete on the fourth, and the wiki must say so rather than round up to "proven."

Related

- What Counts as an Edge Here: The Evidence Bar This Wiki Applies to Every Technique — the four-requirement bar this page is checked against; QMJ is the worked example of a factor that passes three requirements and is honestly incomplete on the fourth. - Multiple Testing: Why t>1.96 Is Not Enough — the bar this wiki uses to grade a factor's significance — QMJ's t-stat of 11.20 clears the t>3.0 threshold discussed there by a wide margin, useful as a contrast case against weaker anomalies in the factor zoo. - Out-of-Sample vs Post-Publication Decay: The Two Numbers That Tell You If a Premium Is Real — the general decay framework (McLean-Pontiff numbers) that this page explicitly could NOT apply to QMJ for lack of a QMJ-specific figure; a future note-gathering pass on QMJ should target this gap first. - The Low-Volatility Anomaly — CAPM's Prediction Inverted, With a Documented Leverage-Aversion Cause — BAB, one of QMJ's six safety inputs, is documented there with its own numbers and correlates positively with QMJ per this page. - The Value Factor (Book-to-Market / HML) — a founding premium whose post-1991 numbers can't rule out zero and Cross-Sectional Momentum in Equities — the strongest documented anomaly, and how much of it survives costs — the two factors QMJ is compared against for correlation (negative with value, positive with momentum) in the overlap section above. - Transaction Cost Accounting — the arithmetic that separates a real edge from a paper one — where to look once/if a QMJ-specific cost-survival number is found; this page could not supply one.