May · Trading · 84 pages
Machines trading money at speed — who really has the edge, and what it means for an ordinary portfolio.
Trading - Market structure
The plumbing a retail order passes through was built by one rule in 2005 and measured by a rule with a hole in the middle of it. The hole was closed this autumn, and the Commission now proposes to repeal the rule itself.
An order to buy five hundred shares feels like an instruction. It is closer to a request for routing. The rulebook it enters was written in June 2005, when the Securities and Exchange Commission adopted Regulation NMS in Release No. 34-51808, effective that August, and it did four things. The Order Protection Rule, Rule 611, addressed trade-throughs. The Access Rule, Rule 610, capped what an exchange could charge for taking its displayed liquidity. The Sub-Penny Rule, Rule 612, barred quoting below a cent for anything above a dollar. And a set of amendments to the market data rules changed how quotations are consolidated into the single figure everyone cites, the national best bid and offer. Twenty-one years on, that figure is still the most widely misunderstood number in American finance.
Rule 611 is where the misunderstanding starts. It does not promise anybody the best price. What it says, in paragraph (a)(1), is that a trading venue must establish, maintain and enforce written policies and procedures "reasonably designed to prevent trade-throughs" of protected quotations. A protected quotation is the best displayed bid or offer at an automated venue and nothing beyond it. The Commission put the consequence in its own words this June: with seventeen exchanges quoting NMS stocks and no active participants in the alternative display facility, "practically, Rule 611 only applies to the best round-lot prices on an exchange," and it "does not cover any additional depth-of-book prices." The obligation runs to the venue's written procedures, not to your fill, and a round lot can now be as few as ten shares in a stock above a thousand dollars.
So where does the order actually go? The Commission's own count, in its 2024 disclosure release, describes a first quarter of 2023 in which NMS stocks traded on sixteen national securities exchanges and off-exchange at thirty-three alternative trading systems and more than 220 other FINRA members. About fifty-six per cent of share volume went through the exchanges. Most of the remainder was executed by wholesalers, who handled 26.9 per cent of all share volume and roughly sixty-one per cent of the off-exchange total. For orders from individual accounts the concentration is far higher. A Commission analysis of routing reports found that in the first quarter of 2022 a sample of forty-six retail broker-dealers sent 87.3 per cent of their orders in S&P 500 stocks to wholesalers and 9.1 per cent to exchanges.
The reason is payment for order flow, and the thing most readers do not know is that it is already disclosed, in detail, for free. Rule 606 requires every broker to publish a quarterly report on its non-directed orders, split between S&P 500 stocks and everything else, naming the top ten venues it used and any venue that took five per cent or more of its flow. For each of those venues the broker must state the net aggregate amount of payment for order flow received, any payment from a profit-sharing relationship, transaction fees paid and rebates received. The report must appear within a month of the quarter's end and stay up for three years. A customer may also demand, for any individual order placed in the previous six months, which venue filled it and at what time.
Execution quality is the other half of the picture, and until this autumn the measurement had a hole in the middle of it. Rule 605 required market venues to publish monthly execution-quality statistics, but it did not require reporting of orders smaller than a hundred shares, which excluded odd lots and fractional shares entirely, and by exemptive relief it also left out orders of ten thousand shares or more. The Commission's own analysis of consolidated audit trail data for August 2023 found that orders containing a fractional-share component made up about four per cent of all executed orders and twenty-two per cent of those originating in individual accounts. The regime built to measure retail execution quality was structurally blind to a great deal of what retail investors were actually doing.
On 6 March 2024 the Commission adopted amendments closing it, in Release No. 34-99679. Reporting now reaches beyond market venues to any broker-dealer introducing or carrying at least a hundred thousand customer accounts: about eighty-five firms, which between them handle over ninety-eight per cent of all customer accounts. The reports must cover fractional shares, odd lots, larger orders, orders outside regular hours, stop prices and certain short sales, with new statistics including effective spread divided by quoted spread and a size-improvement measure taken when the order is received rather than when it is filled. The compliance date, originally December 2025, was pushed to 1 August 2026. Collection began that day; the first reports were due public by the end of September; the last tranche of price-improvement statistics falls due this month.
What does the evidence establish meanwhile? That quoted spreads in liquid US equities are a fraction of their pre-electronic levels, and that retail marketable orders routinely execute inside the displayed quote, is not seriously disputed. That high-frequency trading systematically harms small retail orders is a different proposition and remains contested, and the honest distinction is between order types rather than between villains: a five-hundred-share marketable order is filled in one go, against a dealer who wants that flow because it is uninformed, while an institutional order of two hundred thousand shares must be worked over hours, and it is during the working that a faster participant can infer what is coming. The enforcement record holds one case squarely on the retail point. On 13 January 2017 Citadel Securities paid $22.6 million, of which $16 million was a civil penalty, to settle findings that its retail order handling unit told broker-dealer clients it would internalise orders at the best observed price or seek that price in the market, while two algorithms, FastFill and SmartProvide, instead exploited discrepancies between market data feeds from 2007 to 2010.
The one well-measured number in the field comes from Matteo Aquilina of the Financial Conduct Authority, Eric Budish of Chicago and Peter O'Neill, who used exchange message data rather than public trade prints, letting them see the losing orders as well as the winning ones. They found latency-arbitrage races occurring roughly once a minute per symbol in FTSE 100 stocks, the modal race lasting five to ten millionths of a second, accounting for about a fifth of trading volume, with six firms taking around eighty per cent of both wins and losses. Races accounted for about a third of price impact and of the effective spread, which the authors convert into a tax on trading of half a basis point and an estimate near five billion dollars a year across global equity markets.
Five billion dollars is a large number and half a basis point is a small one, and both are the same finding. On a ten-thousand-dollar order, half a basis point is fifty cents. The authors say so themselves: the tax "does seem small enough that ordinary households need not worry about it" in the context of their retirement decisions. Whether the mechanism can be engineered away has been tried. The Investors Exchange routes every incoming message through a coil of fibre equivalent to 350 microseconds of delay, and in June 2016 the Commission approved it as a national securities exchange, while expressly declining to adopt the bright line it had proposed, saying "establishing a bright line de minimis threshold is not appropriate at this time." The published evidence on what the speed bump actually achieved remains thin.
The sequel is the part almost nobody reports. In January 2023 the Commission proposed two rules that would have changed retail order handling directly: an Order Competition Rule, exposing most retail marketable orders to an auction before a wholesaler could internalise them, and Regulation Best Execution, a Commission best-execution standard. On 12 June 2025 both were withdrawn among fourteen proposals, the Commission saying it did not intend to issue final rules. Then, in June 2026, it proposed to rescind Rule 611 altogether, on grounds that read like an indictment: the rule "has contributed to an environment where speed has become the primary competitive advantage," fragmenting displayed liquidity, which "in turn creates latency arbitrage opportunities." The answer to the headline, then, is that the disclosure arrived first and the rule may not outlast it.
26.9% Share of all US equity share volume executed by wholesale market makers in the first quarter of 2023, by the Commission's own count — SEC, Disclosure of Order Execution Information, Release No. 34-99679
Regulation NMS protects the quotation. It does not protect your order. The difference is the entire subject.
Trading - Returns
The arithmetic against active management is airtight, and almost always misquoted. The evidence for the factors that replaced it is contested by the people who built them. Both stories are more interesting than the version in the brochure.
In January 1991 the Financial Analysts Journal published a three-page note by William Sharpe called The Arithmetic of Active Management. It contains no data at all. It asserts that, with the terms sensibly defined, "before costs, the return on the average actively managed dollar will equal the return on the average passively managed dollar", and that after costs it must be less. This is not an empirical finding waiting to be overturned by a better dataset. It is accounting. Every share is held by somebody. If passively held shares track the market in aggregate, then the actively held ones must also track it in aggregate, because together they are the market. What remains is the cost of the activity, and the cost is subtracted from one side only.
The load-bearing word in that sentence is dollar. Sharpe's identity says nothing whatever about what proportion of managers underperform, and he was careful about the difference. His paper allows explicitly that some active managers can beat their passive counterparts even after costs, noting only that such managers must between them run a minority of the actively managed dollars in the market concerned. It also contains, three decades before the point became fashionable, a warning that excluding managers who went out of business during a period produces a survivorship bias flattering to the survivors. The identity is strong because it is narrow. Almost every popular restatement of it swaps the dollar for the fund, which is a different claim with a different answer.
Start with the part nobody disputes. The Commission's investor bulletin on fees sets out an illustration: a hundred thousand dollars, a four per cent annual return, twenty years, and an ongoing fee of 0.25, 0.50 or one per cent. The bulletin does not print the three ending values, and any publication quoting them is not quoting the bulletin. What it prints is the gap. A 0.50 per cent fee reduces the portfolio by ten thousand dollars against a 0.25 per cent fee. A one per cent fee reduces it by nearly thirty thousand. And in a second illustration it adds the part people forget: the one per cent fee itself totals almost twenty-eight thousand dollars over the twenty years, and had that money been invested instead it would have earned about twelve thousand more. No forecast is involved anywhere in the exercise.
Now the statistic everybody cites, which is that eighty per cent of active managers underperform. It is worth saying plainly that this figure cannot be traced to any single primary document, because none exists. What does exist is a recurring measurement, the SPIVA scorecard published twice yearly by S&P Dow Jones Indices, and the reason the folk number is sticky is that it lands near real rows. In the mid-year 2026 edition, with data to 30 June, 78.69 per cent of American large-cap funds underperformed the S&P 500 over one year and 92.61 per cent over twenty. The round number is the short horizon and the ninety-plus figure is the long one; they are the same statistic read at different distances. Note also that the widely reported sixty-seven per cent is the year-to-date column, not the one-year.
The companion document is more damaging than the headline one. S&P's Persistence Scorecard for year-end 2025 takes the funds that were in the top quartile of their category in December 2021 and follows them. Of 164 large-cap funds in that cohort, 20.12 per cent were still top quartile a year later and none at all, 0.00 per cent, by December 2023. Across all domestic equity categories, only small-cap funds produced any survivors by the end of 2025. The same report notes that just 4.5 per cent of above-median large-cap funds stayed persistently above median, against the 6.25 per cent that pure chance would deliver. Separately, SPIVA's survivorship table records that 36.52 per cent of large-cap funds were still in existence twenty years on.
Here the received wisdom deserves the same scepticism as the sales pitch. In May 2026 Martijn Cremers, Jon Fulkerson and Timothy Riley circulated a paper arguing that the scorecard systematically understates active funds, and the mechanism is the one Sharpe identified. SPIVA counts funds, weights them equally, treats any fund that closes as an underperformer whatever its record, and compares them with index figures rather than with investable passive funds. Reweight by assets, and twenty-year underperformance in American equities falls from ninety-two per cent of funds to about fifty-five per cent of dollars. In fixed income the ten-year figure drops from seventy-one to thirty-seven, reversing the conclusion. The paper was funded by the Investment Adviser Association's Active Managers Council, a conflict worth weighing; it also independently reproduces SPIVA's thirty-six per cent survivorship.
So the industry moved its claim. The modern pitch is not a manager with judgement but a rule with a name, harvesting a premium documented in a journal, and that is a better argument because it can be audited. In 2016 the Review of Financial Studies published a paper by Campbell Harvey, Yan Liu and Heqing Zhu which did what nobody had bothered to do and counted: across 313 articles, 250 of them published, they catalogued 316 distinct factors advanced to explain the cross-section of stock returns, and argued that with that many candidates tested on the same few decades of data a t-statistic above two is meaningless. A new factor should clear three. Their famous line, that most such findings are likely false, is an argument rather than a computed result; their own tables classify between eighty and 158 of the 296 published significant factors as false discoveries, which is to say between twenty-seven and fifty-three per cent, depending on which adjustment you accept.
The replication work splits the same way, and the split is about method rather than data. Kewei Hou, Chen Xue and Lu Zhang rebuilt 452 published anomalies on common foundations and found that sixty-five per cent could not clear a t-statistic of 1.96, rising to eighty-two per cent under a multiple-testing hurdle; their explanation is one word, microcaps, which are 3.2 per cent of American market value and 60.7 per cent of the listings. Andrew Chen and Tom Zimmermann rebuilt 319 characteristics and found that of the 161 clearly significant in the original papers, ninety-eight per cent reproduced above 1.96. The two findings do not contradict each other. One reproduces, using the original samples and methods; the other reanalyses, imposing value weighting and NYSE breakpoints, and its own failure rate falls from 65.3 per cent to 43.1 when those choices are relaxed.
What cuts through the argument is out-of-sample evidence. R. David McLean and Jeffrey Pontiff tracked 97 published predictors of stock returns and found portfolio returns 26 per cent lower out of sample and 58 per cent lower after publication, the gap between those two being their estimate of what publication-informed trading does to an edge once everybody knows about it. And the two premia that launched the entire industry can be measured on Kenneth French's own public monthly series, which anyone may download without charge. From July 1926 to December 1992, before the paper that made them household terms, the size premium compounded at about 2.2 per cent a year and the value premium at about 4.6. From January 1993 to September 2026 the size premium ran at about minus 0.2 per cent a year and value at about 1.5.
Fama and French examined the value figure themselves and were more careful than their reputation: realised premiums were much lower in the later period, but monthly volatility is high enough that they could not reject the hypothesis that the expected premium was unchanged. Which leaves the question in the headline. Hendrik Bessembinder found that the best-performing four per cent of listed American companies account for the entire net dollar gain of the US stock market since 1926, the rest collectively matching Treasury bills. Philippe Jorion and William Goetzmann assembled 39 markets back to the 1920s and found American equities the best performer of all of them from 1921 to 1996, at 4.3 per cent real against a median of 0.8 for everywhere else. The canonical long-run equity premium is itself drawn from the most successful sample available. None of which tells any reader what to own.
0.00% Share of the 164 top-quartile US large-cap funds of December 2021 still in the top quartile by December 2023 — S&P Dow Jones Indices, US Persistence Scorecard, year-end 2025
We argue that most claimed research findings in financial economics are likely false.Campbell Harvey, Yan Liu and Heqing Zhu, Review of Financial Studies, 2016
Trading - Automated advice
They are registered investment advisers carrying a genuine fiduciary duty, and when the Commission went to look at them, nearly every firm it examined came away with a deficiency letter. Here is what the record says, product by product.
Begin with the classification, because almost everything follows from it. A robo-adviser is not a fund and not a brokerage product. It is an investment adviser registered under the Investment Advisers Act of 1940, and the software is merely the means by which the advice is delivered. That status carries a fiduciary duty, and the Commission adopted an interpretation of it on 5 June 2019, Release No. IA-5248, effective that July: an adviser owes its clients a duty established by and enforceable through the Advisers Act, comprising a duty of care and a duty of loyalty, which cannot be waived. The standard applied to an algorithm is therefore the standard applied to a person in an office. The interesting question is what happened when the Commission went to check.
It went in 2021. On 9 November the Division of Examinations published a risk alert titled Observations from Examinations of Advisers that Provide Electronic Investment Advice, and the headline sentence is one line long: "Nearly all of the examined advisers received a deficiency letter". The observations clustered in three areas: compliance programmes, including whether written policies had actually been implemented and tested; portfolio management, including the fiduciary obligation to give advice in each client's best interest; and marketing, where more than half of the advisers had advertisement-related deficiencies. The Division does not say how many firms it examined, which is a limitation worth stating rather than glossing, and it names none of them.
The portfolio management findings go to the heart of the product. Examiners found that while advisers commonly used questionnaires to gather client information, some firms relied on just a few data points to formulate investment advice, raising the concern that the questions did not elicit enough information to conclude that the advice was suitable for that client. This is not a new worry. FINRA, reviewing digital advice tools in 2016, found they asked between four and twelve questions, and warned that averaging contradictory answers was a poor practice because it could place a client in a portfolio exceeding their risk tolerance. The British regulator went further in 2011: of eleven risk-profiling tools it reviewed, nine had weaknesses that could produce flawed outputs.
What happens in a drawdown is usually discussed through anecdote, which is unnecessary, because the regulator wrote it down. Several advisers, the alert records, lacked written policies covering the operation and supervision of their own automated platforms, increasing the risk of algorithms producing unintended and inconsistent results through coding errors or code insufficient for unforeseen conditions; the examples given are geopolitical events, oil price movements and interest rate changes. Examiners then observed, in plain terms, rebalancing errors and other trade errors at firms lacking adequate oversight of those platforms. There is also a structural gap worth knowing: Regulation SCI, which imposes system capacity and resiliency obligations, applies to exchanges and clearing agencies, not to advisers or retail brokers.
The enforcement record is small, specific and worth reading closely. On 21 December 2018 the Commission settled with two firms. Wealthfront Advisers had told clients it monitored their accounts for wash sales as part of tax-loss harvesting; from October 2012 to mid-May 2016 the Commission found wash sales in at least 31 per cent of enrolled accounts. The honest denominator belongs beside it: the order also records that those wash sales amounted to roughly 2.3 per cent of the losses harvested. Wealthfront paid $250,000, the order also covering retweeted client testimonials and some $97,000 paid to bloggers for referrals. Hedgeable, far smaller, had published performance comparisons drawn from fewer than four per cent of its accounts, chosen because their returns were above average. It paid $80,000.
The case that matters most for anyone weighing the headline feature came later. On 18 April 2023 the Commission settled with Betterment over its tax-loss harvesting service, finding three defects: an undisclosed change in how often portfolios were scanned for losses, an undisclosed constraint affecting clients who held more than one portfolio, and two coding errors running from 2016 that stopped losses being harvested at all for some accounts. In the order's own arithmetic, these "adversely impacted the value of TLH for over 25,000 client accounts, and as a result, clients lost approximately $4 million dollars in potential tax benefits." Betterment paid a $9 million penalty, placed in a Fair Fund for distribution to the clients affected.
The largest action in the sector was not about algorithms at all. On 13 June 2022 three Charles Schwab entities settled for $186,536,861, comprising $45.9 million in disgorgement, $5.6 million in interest and a $135 million civil penalty, over Schwab Intelligent Portfolios. Between March 2015 and November 2018 the firms marketed a robo-adviser with no advisory fee while holding a fixed allocation to cash, sweeping it to an affiliated bank and keeping the interest spread. The order records that the allocations ran from 6 per cent to 29.4 per cent, that management set them partly by reference to what the bank would earn, and that internal models showed the cash would reduce returns by roughly as much as an advisory fee would have.
Which brings us to what these services cost all in. The advertised figure is 0.25 per cent a year at Wealthfront, and 0.25 per cent at Betterment above a threshold. Beneath it sit the expense ratios of the underlying funds, charged in addition, and here is a finding rather than a figure: no major robo-adviser publishes the weighted expense ratio of the portfolio it builds for you, so the all-in cost cannot be read off any public page. The flat fees deserve care too. Betterment's base price is five dollars a month, which equals 0.25 per cent only near a balance of $24,000, where the percentage schedule takes over; on five thousand dollars the same sixty dollars a year is 1.2 per cent.
Tax-loss harvesting is the feature most often used to justify the fee. Shomesh Chaudhuri, Terence Burnham and Andrew Lo, in the Financial Analysts Journal in 2020, applied a harvesting strategy to the 500 largest American listings from 1926 to 2018, assuming capital gains rates of 15 per cent long-term and 35 per cent short-term, and found a before-cost tax alpha of 1.08 per cent a year, falling to 0.82 per cent once the wash sale rule bound. That rule is the constraint the marketing skips. Under section 1091 of the Internal Revenue Code, as set out in IRS Publication 550, buying substantially identical securities within thirty days either side of a loss sale disallows the loss, which is then added to the basis of the replacement: a deferral, not a cancellation. With one exception that is no deferral at all. Buy the replacement inside an IRA and there is no basis adjustment, so the loss is simply gone.
The honest marking, then. The legal wrapper is sound, the published fees are genuinely low by the standards of what preceded them, and the documented failures were not failures of automation: every one was a disclosure failure, which is a category error people make in both directions. The algorithm did what it was built to do; what was wrong was the account given of it. On the tax benefit, the most useful paper is the least quoted. Kevin Khang, Thomas Paradise and Joel Dickson showed in 2021 that the familiar hundred-basis-point figure assumes an investor with an unlimited supply of offsetting capital gains, and that investor characteristics drive roughly sixty per cent of the variation in what harvesting is actually worth. Set that against Wealthfront's public claim that harvesting "can typically cover our annual fee more than 4.2x over", which implies about 1.05 per cent a year, essentially the unconstrained academic figure, by a method the page does not show. The sharpest thing the examiners said remains the one a prospective client can check in four minutes: count the questions it asks before it decides what to do with your money.
31% Minimum share of enrolled Wealthfront accounts in which wash sales occurred from October 2012 to mid-May 2016, while clients were told the accounts were monitored for them — SEC, press release 2018-300, 21 December 2018
Nearly all of the examined advisers received a deficiency letter.SEC Division of Examinations, risk alert of 9 November 2021
Trading - Methodology
A backtest is a claim about a world that did not happen, and its credibility rests on a number that is almost never printed. American law now regulates how such claims are presented. It still does not require the number.
Every backtest makes a specific claim: had this rule been followed over this period, these would have been the returns. Whether the claim means anything depends almost entirely on a figure that is virtually never published, which is how many other rules were tried before this one was selected. In May 2014 the Notices of the American Mathematical Society, not an obvious venue for investment journalism, carried a paper by David Bailey, Jonathan Borwein, Marcos Lopez de Prado and Qiji Jim Zhu which made the point with a proof rather than an anecdote. Their argument is that an impressive backtest can be manufactured out of nothing whatever, that the manufacture requires no bad faith, and that the ease of it is precisely quantifiable.
The mechanism is extreme-value statistics applied to noise. Suppose a researcher evaluates several variants of a strategy, all of which are genuinely worthless in the sense that their true expected excess return is zero. The best of those variants, identified after the fact, will still show a flattering record, because the maximum of a set of random draws sits above the average draw. The authors compute how flattering. Try ten alternative configurations of a strategy whose true Sharpe ratio is zero, and the expected Sharpe ratio of the best of them, measured in sample, is 1.57. Not 0.1, not 0.3. A figure that in any marketing document would be presented as evidence of a durable edge, produced from data containing no edge at all.
From that they derive what they call the minimum backtest length: how long a sample must be, given the number of variants tried, before a given in-sample Sharpe ratio carries information. The worked case is blunt. If only five years of data are available, no more than forty-five independent model configurations should be tried, or, in their words, "we are almost guaranteed" to produce a strategy showing an annualised in-sample Sharpe ratio of one and an expected out-of-sample Sharpe ratio of zero. Forty-five is a trivial number. A spreadsheet with three parameters at four settings apiece exceeds it. And the trials need not be deliberate: every discarded variant counts, including those abandoned before anybody wrote them down.
Bailey and Lopez de Prado then proposed a correction, the deflated Sharpe ratio, in the Journal of Portfolio Management the same year. The deflated ratio adjusts a reported figure for what they describe as the two leading sources of performance inflation: selection bias under multiple testing, and returns that are not normally distributed. Computing it requires five things about the research that produced the number. The length of the sample, the skewness and the kurtosis of the selected strategy's returns, and the variance of the Sharpe ratios the trials produced, are all in principle recoverable. The fifth, the count of independent trials, is not. It exists only in the researcher's memory, and nothing obliges anybody to publish it.
This is not a problem confined to commercial backtests. The same arithmetic has been turned on the academic literature that supplies their ideas. Campbell Harvey, Yan Liu and Heqing Zhu counted 316 distinct factors across 313 articles and argued that a newly discovered one should clear a t-statistic of three rather than two. Kewei Hou, Chen Xue and Lu Zhang then rebuilt 452 published anomalies on common foundations and found sixty-five per cent unable to clear a t-statistic of 1.96, and eighty-two per cent failing under a multiple-testing hurdle. Any strategy sold on the authority of that literature inherits its multiple-testing problem, whether or not the person selling it has read the papers.
Beneath the statistics sit five specific mechanisms, all mechanical rather than mysterious. Survivorship bias is the simplest: a database of the companies that exist today has quietly deleted the ones that went to zero, so a rule tested on it is tested on a population pre-selected for having survived. Look-ahead bias is subtler and far more common, because company fundamentals are restated after the fact, sometimes years later, and a backtest reading today's version of a 2008 balance sheet is using information no investor possessed in 2008; avoiding it requires point-in-time data, which is expensive, and its absence is rarely disclosed because the error does not announce itself. Third comes in-sample optimisation, the deliberate cousin of the trials problem: tuning thresholds, holding periods and position sizes until the curve is smooth, then reporting the tuned result as though it had been specified in advance. Fourth is the start date, the one mechanism a reader can audit unaided. Shift the beginning of a sample across a major turning point and a long-run average moves by a large multiple of its own standard error. A chart beginning in 1975, or in 2009, is making its argument through the axis rather than the line.
Juhani Linnainmaa and Michael Roberts tested that fourth mechanism directly, hand-collecting pre-1963 accounting data from Moody's manuals to extend 36 accounting-based anomalies across the whole twentieth century. Thirty of the thirty-six were significant in their original samples. Only eight were significant before discovery, and only two of thirty-four afterwards. The detail that settles the interpretation is a correlation: these anomalies move together at 0.62 inside their original samples and at 0.01 in the decades before anyone found them. Because the pattern vanishes going backwards in time, where no arbitrageur could possibly have traded it away, the likeliest explanation is not that the market learned. It is that the sample was searched.
The fifth mechanism is cost, in two parts. Robert Novy-Marx and Mihail Velikov tested 23 anomalies net of trading costs and found that the cost of running the high-turnover strategies always exceeded one per cent a month, exceeding the gross spread for all but two of the anomalies examined; short-run reversals went from a gross 0.37 per cent a month to minus 1.28 per cent net. Andrew Chen and Velikov later took 204 anomalies and, after effective bid-ask spreads, post-publication decay and a data-mining correction, put the average expected net return at four basis points a month. The second part is borrowing: a long-short result assumes the short leg can be borrowed cheaply, and the names that fall most reliably are often the dearest to borrow.
American law now has something exact to say about all this, and it is worth reporting exactly rather than loosely. On 22 December 2020 the Commission adopted a rewritten Rule 206(4)-1 under the Investment Advisers Act, replacing both the old advertising rule and the cash solicitation rule, effective 4 May 2021 with compliance required from 4 November 2022. The rule defines hypothetical performance as "performance results that were not actually achieved by any portfolio of the investment adviser", and states in terms that the category includes performance backtested by applying a strategy to data from periods when the strategy was not actually in use, along with model-portfolio results and targeted or projected returns. Seven general prohibitions apply to every advertisement, among them unsubstantiated material statements and discussing benefits without balanced treatment of the risks.
Crucially, the rule does not ban backtested performance. It conditions it, and the conditions are about method. An adviser may present hypothetical performance only if it has adopted and implemented policies and procedures reasonably designed to ensure the figures are relevant to the likely financial situation and objectives of the intended audience; only if it provides enough information for that audience to understand the criteria used and the assumptions made; and only if it provides enough information to understand the risks and limitations of relying on such performance in making investment decisions. The Commission has enforced this, and more than once. On 11 September 2023 it charged nine investment advisers over hypothetical performance displayed on their public websites without the required policies in place, two of which had also failed to keep copies of their advertisements; all nine settled, paying between $50,000 and $175,000 each, for $850,000 in total. On 12 April 2024 it charged five more on substantially the same ground, one of them also for model performance it could not substantiate, for a further $200,000. The useful question for a reader is therefore narrow. Ask how many configurations were tried. If nobody will say, the chart has no interpretation.
4bp Average expected net return a month across 204 anomalies, after effective spreads, post-publication decay and a data-mining correction — Chen and Velikov, Zeroing In on the Expected Returns of Anomalies, Journal of Financial and Quantitative Analysis, 2023
Four of the five inputs you need to deflate a Sharpe ratio sit in the track record. The fifth sits only in the researcher's memory.