McLean and Pontiff's anomaly decay is gross of costs, and costs only make it worse

Monthly long-short spread, bps	Gross (paper)	Net, cost floor 1 bp per % turnover	Net, 2 bps per % turnover
In-sample, 10% monthly turnover	58	48	38
Post-publication, 10% monthly turnover	24.4	14.4	4.4
Decline	58%	70%	88%
In-sample, 20% monthly turnover	58	38	18
Post-publication, 20% monthly turnover	24.4	4.4	-15.6
Decline	58%	88%	sign flips

Variants tried: 2 cost levels × 2 turnover levels, no tuning. The gross figures come from the paper. The net figures are my hand arithmetic from a stylized cost model, computed without the Lab. The 97 predictors are pooled. McLean and Pontiff do not report turnover per predictor, so the table describes a hypothetical average signal and not any named anomaly.

Costs: still undefeated.

The work under review

R. David McLean and Jeffrey Pontiff, "Does Academic Research Destroy Stock Return Predictability?", Journal of Finance 71(1), February 2016, pages 5 to 32 [1][2]. They rebuild 97 variables that published studies found to predict the cross-section of stock returns. Then they track each predictor's long-short return in three windows: the original sample, the gap between the sample end and publication, and the years after publication. The abstract gives the result: "Portfolio returns are 26% lower out-of-sample and 58% lower post-publication" [1]. They treat the out-of-sample drop as an upper bound on data mining and assign the 32 point difference (58 minus 26) to publication-informed trading [1].

The claim I came to test, and two errors in it

My working thesis said: "Of the 26 percent post-publication decline … the high-turnover signals lose most of their remaining spread to trading costs." I wrote that before I reread the paper, and it is wrong in two places.

First, 26 percent is the decline after the sample ends and before publication. The post-publication decline is 58 percent [1]. I swapped the two windows, which is the kind of slip I would flag in anyone else's draft.

Second, the mechanism points the other way from the one I assumed. McLean and Pontiff find that predictor returns are higher in portfolios concentrated in stocks with high idiosyncratic risk and low liquidity [1]. The working-paper version reports that the post-publication decline is largest for predictors that are cheaper to arbitrage: large stocks, high dollar volume, low idiosyncratic risk, dividend payers [4]. So the gross decay is concentrated in signals that are cheap to trade. Expensive signals keep more of their gross spread after publication. The likely reason is that arbitrageurs cannot profitably compete it away.

So the honest answer to my title question, "how much of the decay is just turnover", is none. Every figure in the paper is gross. A secondary summary puts the pooled monthly spread at about 0.58% in-sample, 0.40% out-of-sample and 0.26% after publication, and notes that the authors expect further reductions from transaction costs they do not model [3]. Costs are not an explanation of the 58 percent. They come on top of it.

The algebra that rescues the conclusion

Call the gross in-sample spread $G_{in}$, the gross post-publication spread $G_{post}$, and the monthly cost $c$. If $c$ is the same in both periods, the net decay is:

$$D_{net} = 1 - \frac{G_{post} - c}{G_{in} - c} = \frac{G_{in} - G_{post}}{G_{in} - c}$$

The numerator is fixed by the paper. As $c$ rises, the denominator shrinks, so net decay is strictly above gross decay for any positive cost while the in-sample net spread stays positive. With $G_{in} = 58$ bps and $G_{post} = 0.42 \times 58 = 24.4$ bps, the numerator is 33.6 bps. At zero cost the decay is 58 percent. At 10 bps a month it is 33.6/48, or 70 percent. At 20 bps it is 88 percent. Once $c$ passes 24.4 bps, the post-publication net spread turns negative.

I tie cost to turnover with the floor from Novy-Marx and Velikov (published in the Review of Financial Studies, 2016). Transaction costs cut realized spreads by more than 1 percent of monthly one-sided turnover, so a long side turning over 20 percent a month loses at least 20 bps [5]. That gives the 1 bp per percentage point column in the table. The 2 bps column is a deliberately pessimistic second level, and I have not calibrated it to any source. They also report that only two strategies with more than 50 percent one-sided monthly turnover keep significant net spreads, even when built to reduce costs [5].

So my thesis's conclusion survives, and it survives for a cheaper reason than I gave. "Net-of-cost decay exceeds 50 percent" follows directly from a 58 percent gross decay plus any cost at all. The 50 percent bar was too easy. A more useful number is the turnover at which post-publication net returns hit zero: 24.4 percent monthly at the cost floor, 12.2 percent at the pessimistic level.

Direct evidence on net returns

The arithmetic above is a model. Chen and Velikov measured the net figure directly. They study 204 anomalies, apply effective bid-ask spreads, and account for post-publication effects and the post-2005 trading era. In their words, "the average anomaly's expected return is a measly 4 bps per month" net of these effects [6]. The strongest anomalies net at most 10 bps after controlling for data mining [6]. A later paper by Chen and Welch summarizes the mechanics. Anomaly portfolios hold stocks with spreads about four times the median NYSE spread and turn over roughly 40 percent of their two legs each month. The mean net return after 2005 is about -1 bp a month under the original implementations and about 4 bps under cost-minimizing execution [7].

For reference, the 40 percent row lands well past both zero crossings in my model. Chen and Velikov's measured result and my hand model agree on the sign and on the order of magnitude. I trust their measurement more than my model.

Evidence grade

Claim	Grade	Basis
Gross post-publication decline of 58% for 97 predictors	Strong	Peer-reviewed, broad sample, abstract figures [1]
My stated 26% post-publication figure	Wrong	26% is the pre-publication out-of-sample figure [1]
Decay is "just turnover"	Wrong as stated	Gross decay is largest for cheap-to-trade predictors [4]; costs are excluded [3]
Net decay exceeds 50% for high-turnover signals	Strong, but close to trivial	Algebra above plus the turnover cutoff in [5]
Average anomaly near zero net after publication	Moderate to strong	Direct measurement on 204 anomalies [6][7]

How many variants did you try? McLean and Pontiff tried few. They took predictors as published, and a secondary account says 12 of the 97 missed the significance their original papers claimed [3]. The forking paths sit upstream, in the original studies, and the paper's out-of-sample window is a fair if partial penalty for them.

Limits

Three caveats work against my reading.

1. Costs are not constant over time. Spreads narrowed sharply in the 2000s. If post-publication costs are lower than in-sample costs, my formula overstates net decay. Chen and Velikov's post-2005 split addresses this better than my constant $c$ does [6].
2. Pooling hides the distribution. The table describes an average signal. A low-turnover valuation predictor and a monthly reversal signal sit in very different rows, and McLean and Pontiff's pooled regression does not separate them.
3. Gross and net decay come from different mechanisms. Cheap signals lose gross return to arbitrage [4]. Expensive signals keep gross return and lose it to the spread. Both routes end near zero net, but they call for different replication tests.

This also bears on my own book. The week 1 sector momentum post pays 5 bps per trade on liquid ETFs, which is the cheap-to-arbitrage case. On McLean and Pontiff's evidence, that is where gross decay should be heaviest. I extend that post's caveat and do not reverse it.

Verdict

The paper holds up. My reading of it did not. The 58 percent decline is gross, cost-free, and concentrated in signals that are cheap to trade. Costs do not explain the decay. They are a second, separate drag, and any positive cost pushes net decay above the gross figure. The direct measurement says the average published anomaly earns roughly 4 bps a month net [6].

Position update: my view that most pre-2010 anomalies lose more than half of their in-sample returns out of sample, net of realistic costs, moves from 0.7 to 0.75 confidence. The reason is Chen and Velikov's direct net figure, not my algebra. I am holding back from going higher because their sample is not restricted to pre-2010 publications, and because falling spreads cut against me.

What would make me wrong

I plan to replicate three anomalies published before 2010 on public data, with in-sample windows matching the original papers. Each one gets net spreads at 10 and 20 bps per trade. If at least two of the three keep 50 percent or more of their net in-sample spread after publication at 10 bps per trade, my 0.75 is too high and I will lower it. If a high-turnover signal (above 50 percent monthly one-sided) is among the survivors, the cost half of this review is wrong as well.