Introduction. This is Part III in my (7/.V) article series “In the Hands of a Few” (ITHOAF) with a touch of Tokyo Drift of the action movie series “The Fast and The Furious” (F&F). Too much drift can be deadly: Saleen Automotive Inc. – an American manufacturer of specialty high-performance sports cars with the slogan “Power in the Hands of a Few” – knows it. Public since 2013 on the OTC Bulletin Board (symbol: SLNN), SLLN’s problems began in earnest: in 2014, its U.S. Securities and Exchange Commission filing showed a loss of $5.3M. Saleen’s stock price spiraled down from 0.025 in Feb/2015, to 0.0003 in Feb/2016. It got crushed like its red 2003 Saleen S281-E Mustang got crushed between the two semi-trucks in “F&F II: 2 Fast 2 Furious.” High-Frequency Trading (HFT), too can get crushed if not driven properly. They have both “Need for Speed” and “Need for Agility.”

[1.] On May 11, 2015, I received an e-mail from [yet undisclosed] with a subject line “The Antidote to High-Frequency Trading.” If it had not been sent five days off mark, I would have thought it had been deliberately sent exactly five years after “The Flash Crash of May 6, 2010” – an event that still haunts many financial market regulators and politicians. The “E-Mail of May 11, 2015” describes nice investors poisoned by HFT – a venomous parasite running amok in an otherwise rock solid market. So bad it is that “markets are rigged,” as at least stated in the #1 New York Times Bestseller, “The Flash Boys: A Wall Street Revolt,” released in March 2014 – simultaneously with my less sensationalist, for sure less known, and miles more academic “Lit and Dark Liquidity with Lost Time Data: Interlinked Trading Venues around the Global Financial Crisis.” It is a cruel world, and it motivates this article.

[2.] High-frequency traders (HFTrs, European top listed) trade in the microsecond regime. Order-books may be recorded at a nanosecond accuracy. Speed has always been a central factor in trading, no matter the trigger. When and how (“beautiful” it is) matter, too. But by how much you win does not really matter if the costs and risks outweigh the rewards. In this respect, the E-mail of May 11, 2015, goes to repeat the most frequent misconceptions: financial markets are seen as casinos and the odds are set in favor of HFT (or the “house”). To be fair, there is some truth to the claims of unfair gaming: schemes in dark pool trading space (private trading platforms) have been recently discovered; in January, 2016, Barclays and Credit Suisse settled to pay $154M due to systematically favoring HFTrs. Likewise, HFT technology, as all state-of-the-art technology, can be used for illegal actions by bad guys.

[3.] To be clear: My aim here is not to do a review of  “The Good, the Bad, and the Ugly of Automated HFT” or HFT regulations. I have done that extensively enough (see the link). However, there does exist some negatively connoted aspects in today’s financial markets, such as “liquidity black-holes,” which are claimed, mostly unfairly, to be caused by HFT – or the lack of it – and misunderstandings should be cleared. Causality is not correlation. It is simply more complex: For example, I have co-authored a study of the Flash Crash of May 6, 2010, where we built an agent-based model in order to investigate more carefully what happened on May 6th, 2010. We managed to reproduce the main events of S&P500 E-Mini futures contracts as described by the CFTC-SEC report except that in our crash simulation HFT market-makers of E-mini do not vanish. Black-holes are hard objects to understand.

[4.] One recent industry side antidote to HFT is the Aquis Exchange’s decision to ban on predatory high-speed trading in order to clamp down on momentum ignition strategies – or what they fear are such. This decisions also enhances Aquis’ public image and trading volumes; it must have been affected by the stereotypical categorization of HFT as venom. Indeed, in 2015, Panther Energy Trading was convicted of rapidly entering large orders into futures markets that were not intended to be executed – which is an ages-old tactic known as “spoofing.” But the scale of this detected market manipulation wrongdoing was small: the prosecutors claimed that Panther made $1.4M in less than three months. To clarify, it is hardly surprising that bad guys exist; as I note in the article “Two Years after ‘The Good, the Bad, and the Ugly’ of Automated HFT,” any statistical population has a share of them.

[5.] In defense of HFT, not all Computer Code (trading algorithms) should automatically be judged bad, even if they would appear to leave traces of malicious trading behind them. Many of the suspicious cases turn out to be rather innocent and done to prevent the trader to be taken advantage of by others. Even fast algorithms have to have the ability to protect themselves against the (probably) more informed players. Truth be told, HFT algorithms can do much good. Market manipulation is found to be mitigated by the existence of HFT. Aitken, Cumming, and Zhan (2015) present evidence of mitigated frequency and severity of end-of-day price dislocations and conclude “the effect of HFT is more pronounced than the role of trading rules, surveillance, enforcement and legal conditions.” Thus, with enough profit incentive, smart and fast HFT algorithms could be applied as “New Surveillance Forces.”

[6.] Let me investigate more carefully the contents of the E-Mail of May 11, 2015. First, it claims that HFTrs participate in over 70% of all the recorded trades on the New York Stock Exchange (NYSE). There would exist much space to discuss how HFT is defined to arrive in this estimate, and why it can easily differ between instruments, but let us now suppose for a moment that it is indeed a true and legitimate claim – which it may be for some stocks, at least momentarily. (For U.S. Treasure Bonds, for example, it does seem like the right ball-park number by volume traded.) But here is the catch: if over 50% of trades would be done by HFTrs, then some of them would be trading against other HFTrs, because wash trades are illegal and detectable. HFTrs do not avoid trading against each other. There exists no evidence of collusion tactics. HFT is mostly proprietary. With whom do the HFTrs trade?

[7.] The high (> 50%) trade execution percentage suggests that HFTrs do not typically take advantage of any specific group of people, and academic research supports this conjecture. Brogaard, Baron, Hagströmer, and Kirilenko (2015) find that aggressive HFT firms tend to pick off any passive traders, including other HFTrs. Aggressive HFTrs are (mostly) liquidity taking while passive HFTrs are liquidity providing, often referred to as market-makers. Empirical research also implies that it is imperative to distinguish between the types of HFT firms: It does not do justice to group HFT firms under a single umbrella titled “HFT.” Many HFTrs do some type of market-making so they are at least partly passively trading. Like in racing, the strategies can be different; HFTrs may use a wide array of algorithms. The use of highly developed trading platforms with low latency do not imply conformity.

[8.] Let me consider the second concrete (refutable) claim of the E-mail of May 11, 2015. It is central to the plot of this ITHOAF III. Intentionally provocatively, the e-mail declares: “Today, my back-of the-envelope calculation is that [high-frequency traders] are raking in $21M a day in profits.” This implies profit of $5.25B/year, which I assume refers only to the size of U.S. market (the e-mail does not specify it). Because this is a big number and may be hard to put into a proper perspective, I will next make a few of  comparisons to other industries, after which I will begin to close in the crux of this article: back-of-the-envelope estimates of HFT income (and profit), including new trading income (profit) distribution results, also concerning Europe. These results will be approximations, and I will have to make a couple of assumptions to reach them, but I will try to assure you that they are reasonable.

[9.] First, the points of comparison to gain some more perspective: In 2014, Coca-Cola Co. paid Monster Beverages $2.2B for a 17% stake of its shares. So, one full year of HFT U.S. market profits could buy only about 40% of one global beverage company – assuming the estimate in the E-Mail of May 11, 2015, is right. Or, consider that in 2013, SoftBank paid $1.53B for a 51% stake of Supercell, a Finnish mobile gaming company – about as much as is the cost of the home of Super Bowl 50, Levi’s Stadium in Santa Clara, California. In fact, since 1986, U.S. taxpayers have spent as much as $17B to build football stadiums, of which Levi’s ($1.3B) is among the most expensive. Tesla’s glorious “Gigafactory” outside Sparks, Nevada, costs about four times more to build. Apple made around ten times more in profit ($11.1B) in the last quarter of fiscal year 2015. HFT is like the 1849’s gold rush: over-hyped.

[10.] Another side-track to do before putting the pedal to the metal is to define “profit.” Google defines profit as “a financial gain, especially the difference between the amount earned and the amount spent in buying, operating, or producing something.” Since there is no way I can be 100% certain of the definition of profit of the [yet undisclosed] sender of the E-mail of May 11, 2015, I assume that it is line with Google’s. To play it safe, it could also potentially refer to trading income and meaning “money received, especially on a regular basis, for work or through investments” excluding fixed costs. This would then give an upper bound for profit; buying, operating, or production costs are excluded from the definition. In this article, my approach is to first calculate the upper limit of HFT profits and then iron out the details. I will use Net Trading Income as a yardstick to see if the implied $5.25B per year is realistic.

[11.] Here comes the nine paragraphs long drifting part (11-19, which you can skip at the first reading): What is the cost of building a faster racing car? What is its intrinsic value? When I initially presented my estimates on 5th of October, 2015, at Symposium on High-Frequency Trading at the Copenhagen Business School, I was inquired about the “social costs of HFT.” I shortly replied it would consist of the costs that slow moving institutional investors pay to upgrade their rusty technology to meet the modern standards: chunks of assets traded efficiently by algorithms. In a zero sum game like the stock market, if HFTrs make a profit, someone has to lose. Since retail investors are among the large winners due to tighter spreads and generally more liquidity, the less tech-savvy institutional investors, hedge funds, and other professional traders (including some HFTrs), must be partly losing.

[12.] Could HFT’s social cost be easily and accurately estimated? And is there a social cost? After all, economic activity tends to create new business, although sometimes only for the small yet unknown startups. Upgrading rusty trading technology is not necessarily a cost. It can be progress. But let me suppose that there is a social cost. A simple and transparent way to think about this is to compare to what the cost was in the past. I start by reviewing how much the market-makers made around the turn of the 21th century. If the profit was smaller than now, then there are grounds to argue that the HFT market-makers may produce a social cost. But if the profits of market-makers were actually bigger in the end of 1990s, then the social cost problem should have been alleviated relatively. Then it will be important to demonstrate that the social benefits of HFT outpace the remaining costs.

[13.] A comparison between Formula 1 racing and HFT may be a cliché. Nevertheless, it illustrates some of the potential intrinsic value of HFT. In both F1 and HFT, technology is ideally (a) tested in a state-of-the-art offline (wind-tunnel) environment, (b) confirmed in controlled (test driving) conditions, and finally (c) put in (real racing) production. Weak solutions are wrecked. The winners become more cost efficient to use – the new standard. Any investors will soon be allowed to use the most proven HFT technology, similarly to F1 technology made available in regular cars. The users may not appreciate the development, though; the best F1 and HFT solutions are not easy. F1 has been regulated to be safer and more even, but it has caused the ultimate motor sport to be not that attractive anymore. Also HFT is being scrutinized more carefully and the effect on market health is a gamble.

[14.] According to Adam Smith’s (the drift star of ITHOAF III) Invisible Hand Hypothesis, benevolence is not necessary to advance the public interest if people are free to engage with each other in voluntary economic interaction. But as portrayed in The Economist’s article “Profit and the Public Good” in 2005, to create value and advance the public good it is first (1) necessary that firms must compete with each other for profit and that (2) prices have to reflect true social costs and benefits. So, what are the measurable externalities of HFT? A positive externality could be (a) the technological architecture developed in microwave networks, which could in the future be used to serve the public good by fast, efficient, and clean data transfer. Or, maybe (b) Global Position System with an unprecedented accuracy using quantum entangled states synchronizing every exchange worldwide in one real time.

[15.] It is harder to tell how HFT would harm the economy or the health of people at least so long as HFTrs compete with each other freely. Naturally, there does exist a threat if the infrastructure central in trading, and data especially, become concentrated “In the Hands of a Few.” Fairness could then be violated. In this sense, some things in “Flash Boys” are legit, but unfortunately name HFTrs the culprits to the loss of transparency. The problem is not so much about speed, but data; more specifically the access to Good Big Data. This is closely analogous to a race where speed can be improved by gaining better traction, more powerful engines, and smoother aerodynamics, but they are dwarfed in importance by the access to fuel – the one who controls the fueling system controls the race, too. Smart and agile market data surveillance techniques could improve the conditions of public interest.

[16.] In “F&F III: Tokyo Drift,” Uncle Kamata quotes an old saying, “For want of a nail, the horseshoe was lost. For want of a horseshoe, the steed was lost. For want of a steed, the message was not delivered. For want of an undelivered message, the war was lost.” Set in our context, Kamata warns about the effects of small regulatory changes on market health. Sensitive dependence on initial conditions – the Butterfly Effect as first described by Edward Lorenz in 1963 – is the essence of chaos theory. A small adjustment turns into a disproportionate effect through non-linear trading dynamics. Highly complex dynamic systems’ main trait is not normal stability, unpredictable phase transitions are. Thus, in Florida’s slick racing conditions, allowing just one of the “F&F II: 2 Fast 2 Furious” semi-truck too close to the red 2013 S281-E (analogously, HFT) can have chaotic consequences on market well-being.

[17.] Need for Speed has existed in the financial markets long before HFT. Another quote from the same The Economist article describes a situation that should be avoided overall: “Producers of all manner of goods and services are more likely to call for the introduction of licences and controls to protect their existing positions in their markets than to demand that newcomers should be permitted and even encouraged to contest those markets.” Heterogeneity (dissimilarity) of trading firms should thus be welcomed. Visionary firms would make the competition harder and the whole economy more productive. Excessive requirements on trading capital and disclosure of innovations and trading algorithms just make it hard for the new agile garage level firms to enter a technology laden industry. It is likely that “Bad Reg” would mainly help to fuel the formation of Superpowers of Trading and Technology.

[18.] In January, 2016, the World Economic Forum met to discuss the topic of “Mastering the Fourth Industrial Revolution” (and to ski, obviously) in Davos, Switzerland. Professor Klaus Schwab wrote: “Given the Fourth Industrial Revolution’s rapid pace of change and broad impacts, legislators and regulators are being challenged to an unprecedented degree and for the most part are proving unable to cope.” This certainly rings true in the financial industry, particularly in HFT. In HFT, regulators inability to operate efficiently enough has caused unnecessary stress, uncertainty, and heated debate. Market surveillance techniques for observing abuses and malfunctions have been, and still mostly are, inferior to what the private sector has. Regulators do not have the necessary agility. In this sense, they have Need for Speed. One solution could be to give HFTrs a profit incentive to do surveillance.

[19.] Need for Agility has long existed in information technology, partnering with HFT, but this need has not typically existed everywhere. In 1976, Bruce Henderson, founder of Boston Consulting Group, wrote an article on structural stability. His “Rule of Three and Four” (R3&4) – not to be confused with the poker’s “Rule of Four and Two” (R4/2) – says there should always exist three large firms with relative market shares decreasing at a rate 4:2:1. R3&4 is in trouble in industries with rapid technological progress or regulatory intervention – the hallmarks of HFT. R4/2 could actually be more applicable, giving a quick statistical decision criteria whether to call (stay in a new market, for example) or fold with a draw. But in any case, the ratio of HFT income I will use below is in “Henderson’s spirit”: the HFT industry income distribution will be assumed to follow a power law with a rate 3:1.

[20.] Let us get back to the race track. The estimation of HFT industry profit based on two data sources made available by the two recent successful Initial Public Offerings (IPOs) in 2015: (i) Virtu Financial Inc. (US, Nasdaq: VIRT) and (ii) Flow Traders BV (Europe, Euronext Amsterdam: FLOW). According to their respective IPO prospectuses, these two companies represent the best, largest and technologically cutting-edge HFTrs. Most of the other HFT firms are more secretive about their performance. So my goal next is to give you the upper distribution estimate of the aggregate HFT industry in the U.S. and Europe, then to use those distributions to calculate different characteristics of the HFT industry – such as the average profits/income of an HFT firm – and to deduce how competitive the market is. It will also allow the new estimates to be compared to the historical data of market-makers.

[21.] Let me consider Virtu Financial. Its Q2/2015 Adjusted Net Trading Income (AdjNTI) was reportedly $105.9M. Assuming 250 trading days per year, this implies $105.9M/(250/4) == $1.7M per day for trading all around the world. For only “America’s Equities,” AdjNTI was $27.3M, implying $27.3/(250/4) == $0.4M per day (rounded), which translates to about $100M per year. Now recall the E-Mail of May 11, 2015, which claimed the HFT industry to make about $21M per day in profit (in the U.S.): If the other HFT firms would be of VIRT’s size, there would have to be $21M/$0.4M == 52 such firms. If the $21M per day estimate is a worldwide HFT estimate, then there should be $21M/$1.7M == 12 HFT firms like VIRT. A  much more realistic number than 52 alright, but still too high to be realistic. Another key factor in estimating the aggregate HFT profit is the cost structure that HFTrs have to bear.

[22.] You may be familiar with VIRT’s “incredible” daily AdjNTI distribution, attached for your convenience below. Upon its release in 2014 (part of their IPO prospectus), it was big news, because it revealed that VIRT had “lost money” only on one day in its history. This AdjNTI distribution has more interesting features: the distribution has a long right-hand tail reaching a value more than $5M per day, otherwise it is like a Gaussian distribution. The daily trading income I just roughly estimated above ($1.7M) sits close to the middle of this distribution. Its mode is the bin $1.3-1.5M. It should be stressed that this distribution is for VIRT’s all trading operations; its positiveness relies on VIRT’s large-scale market-making in numerous venues and countries (230 in 35 countries in Q4/2015), fast, efficient, reliable trading operations and sound risk management with respect to asset inventories.

[23.] VIRT’s statement of revenue, profit, and cost illustrates some of the key challenges. In fact, the numbers raise concerns about the solidity of HFT profitability. The condensed consolidated statement of VIRT’s comprehensive income, attached here for convenience, demonstrates, for example, that a large part of their total revenues – around 1/3 – is taken by operating expenses “Brokerage, exchange, and clearing fees.” Another large component is “Communication and data processing” costs. Perhaps surprisingly, VIRT employs only about 150 persons, making it relatively efficient in comparison to most in the industry. But VIRT (and all others) still has to pay a lot to brokers, exchanges, and clearing firms to keep their top fuel engine running. Their profit after all their operating expenses is rather modest. So in summary,  that the costs of operating a HFT firm are high and are expected to stay high.

[24.] It should be obvious by now that basing the aggregate HFT AdjNTI estimation on VIRT as the representative HFT firm would not work well. The simple formula [Number of HFT Firms Operating in the U.S.] x [Daily AdjNTI of a Representative HFT Firm] would overestimate the true unknown AdjNTI: it would predict about 400 x $0.4M == $160M per day. Alternatively, if you believe that there are 400 HFT firms operating in the U.S., and trust in the daily profit estimate of the E-Mail of May 11, 2015 ($21M), the average profit of an HFT firm would be $21M/400 == $52.5k. But the results of Baron et al. (2012) suggest this daily average is too high (among HFTrs): they find that in 2010-12 average $45K gross trading profits were made trading the E-mini contract on the Chicago Mercantile Exchange by aggressive HFTrs while mixed and passive HFTrs earned only $19K and $2K, respectively.

[25.] As a reality check, let me make the $46K gross trading profits a benchmark. Keep in mind that this average is statistically “In the Hands of a Few,” because the trading profit distribution is skewed to the right. Subtracting 1/3 of $46/day to account for infrastructure costs yields $30k. Should the costs be 1/2 on average, profit would decrease to $23k. If there are 400 HFT firms earning in aggregate $10M/day (UCSC Astrophysics Professor Greg Laughlin’s estimate) then the average is $10M/400 == $26K, matching the range $23-30K. The simplest theoretical approach I take below matches the $10M/day estimate, although it may be lower at $4M – only one fifth of the estimate of the E-Mail of May 11, 2015, and landing the yearly trading income of the U.S. HFT industry, $1B, to a third of Supercell’s value in 2013, and about twenty times less than JPMorgan Chase & Co’s 2015 Net Income.

[26.] HFT profits have been reported to be declining in the past few years. The two main oft-cited reasons for “How the Robots Lost: High-Frequency Trading’s Rise and Fall” are low price volatility and small trading volumes compared to a decade ago (especially in the equity space). As shown above, trading infrastructure and data costs have become serious concerns, and not only for the entrant HFTrs but also for the incumbent HFTrs now trying to cut the costs. In fact, TABB Group has shown that while exchange data revenues have increased about 40% during the past five years, market-making revenues have declined about 75%. Effectively, Big Data – even Bad (Bug or Hack) Big Data – has made many data providers the “New Kings of the Hill.” That is a new club that, for example, Nasdaq has a desire to acquire a VIP membership at by the acquisition of news distributor Marketwired.

[27.] Just consider Knight Capital Group (NYSE: KCG) – a large, well-known, independent market-maker, and an officially designated NYSE market-maker – whose Q4/2015 profit turned in the red by -$6.4M when their equity market-making business still made $146M in Net Trading Revenue (VIRT: $167M). About half ($96M) of that in the U.S. In a striking contrast to VIRT (numbers reported in parenthesis), KCG’s “Brokerage, exchange, and clearing fees” $67M ($53M) and “Communication and data processing” $36M ($17M) were all higher. KCG’s employee costs $68M ($21M) were three times as high. Again low volatility, declining trading volumes, and tough competitors were said to play a big factor in the loss. More seriously, KCG should be recognize the two semi-trucks of “F&F II: 2 Fast 2 Furious,” “Bad Tech” and “Bad Reg,” which could increase their costs further and force KCG to quit.

[28.] “It is a cruel world,” ended Albert Hirschman his comment article entitled “Paternity of an Index” in reference to the so-called Herfindahl Index, sometimes known as the HHI. It appears that the true originator of the HHI was Hirschman and not Herfindahl – a rather common injustice in the scientific world. It can get a lot more unjust in finance: As late as the turn of the 21th century, designated market-makers (“specialists”) hold an officially mandated monopoly on the NYSE to act as price smoothing middlemen. As Exhibit “Top NYSE Specialists” shows, in 2000, the Top-5 controlled in total 98% of the dollar volume. Perversely, this cruelty can now be expressed handily by the HHI: the higher the HHI, the more concentrated the industry is, and the lower the HHI, the more competitive it is. Here the HHI can be used to illustrate the cruelty done with respect to the HFT market-makers.

[29.] To see this injustice, calculate the HHI using the (NYSE) specialists’ market shares: sum over all the squared percentages of the specialists to arrive at HHI == 0.18. Now recall that the U.S. Department of Justice defines HHI > 0.15 to imply a “moderately concentrated market.” Thus, 0.18 implies that market-making on the NYSE was “In the Hands of a Few.” (Indeed, a specialist even has a mandated monopoly in the stocks they make.) To calculate a comparable HHI over all HFT market-makers, I have to have a distribution of something similar to the market share. I use my estimate of the HFT income distribution, the implicit assumption being that the larger is the volume share, the larger is the income. Since there are no open data on the distribution of HFT incomes, I have to resort to statistical theory. But I will first demonstrate what kind of profits the NYSE specialists made in their heyday.

[30.] In year 2000, the NYSE was the world’s largest equity market with 1.042B average daily volume for 2,862 companies and with about 80% market share in the U.S. equities. The 15 NYSE specialists had aggregate revenues of $2.8B and after-tax profits of $988M. They made the same of amount of profit than HFTrs had income in the U.S. in 2015 ($1B, as shown below). If TABB Group’s estimate of 2014 should be considered more accurate, HFTrs did even worse: $1.3B in revenue, a drop of 80% from year 2008 ($7.2B). It appears the NYSE specialists themselves enjoyed a “rigged market.” By comparison, in 2015, the NYSE Group (NYSE, Arca, and Euronext) facilitated about the same number of trades per day of NYSE-listed stocks as 15 years ago. However, because of the fragmented markets, the NYSE market share in the U.S. equity market has slowly decreased to a modest 20%.

[31.] It is the same but different: Virtu trades more than 12,000 financial instruments. In the 1990s, the NYSE specialists made more money making markets in fewer stocks. For example, in 2000, the largest specialist on the NYSE, LaBranche & Co, traded (“only”) 514 stocks. In 2010, LaBranche was bought out by Barclays Plc for $25M, later agreeing to sell all of its NYSE floor market-making operations  to Global Trading Systems LLC (GTS). A new time officially started: GTS, VIRT, KCG, IMC, and Citadel (all well-known HFTrs) will manage almost all of the designated NYSE market-making business. Thus, the “Old Kings of the Hill” are surrendering their designated roles to the “New Market-Makers.” The crucial difference is that these HFTrs are officially responsible middlemen in a now highly competitive highly competitive market, which more tech-savvy firms could enter.

[32.] But are “we talking or we racing?” Finally, the estimate for the aggregate HFT income distribution: Zipf’s Law (ZL) is a famous statistical distribution describing a wide array of phenomena, and which can be traced back to at least the 1930s when George Kingsley Zipf modeled English word counts. Since that time, ZL has been found to fit the distribution of market shares, firm sizes, and so on. Related to HFT, Biais et al. (2011) apply it as a part of their HFT equilibrium model. In the current article, I use the roughly ZL obeying empirical density estimates that were reported in Axtell (2001) for U.S. firm sizes. This produces the AdjNTI distribution shown below, where I have calibrated the right-hand tail with respect to VIRT assuming there is only one HFT firm in the U.S. making $400K/day. The rest of the right-hand tail is aggregated to one (eight) bin averaging $1200K/day (equally, 3 x $400K).

[33.] Two yellow flags arise: The income distribution is estimated assuming 400 HFT firms operating in the U.S., which is itself related to the total number of trading firms in the U.S. The estimate of 400 is from year 2009 (Wall Street & Technology) and it amounts to 2% of 20,000. Secondly, I have excluded all clearly “non-profitable” firms in the application of ZL; I only consider firms with AdjNTI > 0. The exclusion of the negative tail region means that I show conservative estimates – the upper bound of HFT profits. Here, the exclusion of non-profitable firms can as well be justified by an academic empirical study observing that HFT entrants that are unsuccessful exit the industry shortly (see Baron et al. (2014)). The HFT income distribution could, of course, be of a different form, and I will present a few robustness checks below to show the potential range of the aggregated HFT industry.

[34.] Now let me do a quick robustness check on whether the calibration of the income distribution at $400k/day is reasonable. In this respect, one useful piece of information can be found in the Q3/2015 report of Flow Traders – the European counterpart to Virtu Financial – that also sheds some light onto the differences between the U.S. and Europe. For comparison purposes, I have taken the rather volatile Q3 where FLOW’s Net Trading Income was reported to be e93M – the best quarter in their history, actually. Similarly to VIRT, too, Flow Traders report that they had no loss days in the first nine months of 2015. Obviously this can only be a rough estimate, because the two firms trade with a different focus in HFT: As they describe it, FLOW is the “leading liquidity provider of Exchange Traded Products globally,” and a widely acknowledged market-maker of Exchange Traded Funds.

[35.] Based on FLOW’s Net Trading Income, FLOW is almost in par with VIRT. They are also roughly speaking similarly profitable: For example, in Q3/2015, FLOW reported Adjusted Net Profit of e37.9M. Moreover, FLOW’s costs were about 60 percent, or almost 2/3, of the Net Trading Income. Unfortunately, for Europe, I am not aware of an estimate of operative HFT firms, so the AdjNTI distribution estimation is more difficult. A rough estimate would be half of the number of firms operating in the U.S. (400). If there are more than 200, they should be of minor importance, and at the aggregate level with AdjNTI < 0, so they cannot stay operative for long; some will exit, some merge, and some replace a firm with AdjNTI > 0. Now, if the AdjNTI distribution is assumed to be of the same rough ZL shape, but with half of the number firms in the U.S., the European aggregate daily AdjNTI becomes e5.2M.

[36.] What if the statistical model we use does not apply here? There is empirical evidence in the literature showing that ZL does not always fit well in the full range of market shares (this is also true for the first two bins in the Axtell (2001) study, although not pointed out). The power law may have an exponent significantly different from 1 (ZL). So let me do more robustness checks with the U.S data. An applied use of R3&4 suggests the Top 3 HFT firms’ AdjNTI are decreasing with a rate 4:2:1. Using geometric series (to base 2) for the number of HFT firms yields the exact theoretical ZL (slope 1) aggregate AdjNTI and $10M/day – a rate 9:3:1 yields $3.5M/day. If the ZL exponent is smaller than in Axtell (about -0.6, see cola-brand industry market shares), then $4M becomes $5.5M due to a heavier tail. Depending on the distribution and calibration, the AdjNTI estimate varies in the range $3.5-10M/day.

[37.] The same can be done worldwide. First, an estimate for the number of HFT firms is needed. A reasonable ball-park estimate is 800. But rather than estimating the AdjNTI distribution as I have done above, now I directly estimate the profit distribution. To do the calibrationn, I use VIRT once more: its 2014 profit is reported to be e170M (see below), that is, e680K/day. To better comprehend the worldwide profit distribution, I reproduce a figure of the linked yearly profits of four big HFT firms, which demonstrates the scale of yearly profits for four renowned HFTrs since year 2009 – note that profits get consistently larger for two Dutch firms, IMC and Optiver. Importantly, however, profit depends not only on trading income but also on costs, which can be very high for inefficiently operating firms, suggesting that the HFT industry is becoming more concentrated “In the Hands of a Few.”

[38.] ZL yields a range for the worldwide HFT profits by using scaling $680K/$400K ==  1.7: $6-17M/day ($1.5-4.25B/year), and assuming EUR/USD in par, 400 firms, and a profit floor (about $1000/day). If 800 profitable firms operate (others cancel out), the range doubles to $12-34M/day ($3B-8.5B/year). A good, still conservative (pictured below), estimate lays at the lower end of this spectrum: $14M/day ($3.5B/year). The last bin aggregates probability masses beyond the seventh bin. Use of caution advised. If HFT firms would be left to freely compete with each other, and the industry would mature without regulatory intervention, merges and buy-outs would naturally take place. The firms in the eight bin would become larger and approximate Henderson’s R3&4. “Normal accidents” and regulations – the two F&F II semi-trucks I called Bad Tech and Bad Reg – would affect when and if that happens.

[39.] Nowadays, HFTrs do most of the market-making, and thus the level of competition can be measured by applying the HHI to the HFT income distribution, giving HHI == 0.15. The U.S. Department of Justice says that this is associated with an unconcentrated market. Like in the NYSE specialist case, I do not take into account the market shares of any other potential market-makers – I regard them as too insignificant. Based on the NYSE estimate (0.18), the estimate of New Market-Makers indicates that competition has increased, and the U.S. equity markets have in fact progressed from a moderately concentrated market to an unconcentrated market. So, if Adam Smith is correct, this is good for the U.S. society. In this sense, the U.S. equity markets are now fairer than they were before, and should be considered less rigged. There has been, and still is, “2 Fast 2 Furious Need 4 Speed Antidote.”

[40.] The E-mail of May 11, 2015, is correct in (implicitly) wanting for more transparency. Trading firms should ideally be able to evaluate different technological solutions and data. Small HFT firms cannot realistically hope to compare different data feeds due to resource consuming user data interfaces and protocols. Insufficient resources to search for Good Big Data is one of the main reasons why only a few firms get a solid foot hold. So should financial authorities help to enhance data quality? In addition to lighter disclosure and reporting requirements to small HFT firms, data producers could be made responsible for delivering Bad (Bug or Hack) Data – Big Data plays such a big role in the development of trading algorithms in back-testing and production. Impure Big Data may increase the systemic risk more than bad trading. It should make Jim Cramer a happier man, as well.

[41.] It is a different story to react wrongly to correct data than to react correctly to wrong data. Knight Capital’s costly algorithmic error in 2012 can be considered to be their own fault: wrong reaction to correct data (albeit the data may have been in a different format). The second error type is however potentially more damaging, because it may affect a large group of traders and investors simultaneously – a systemic risk. One weakness of trading algorithms is that they do not easily detect if Big Data is impurely Bad or purely Good. This is something I have discussed at some length in my earlier “Big Data Brother” article. If there are going to be tighter rules and regulations controlling HFT and other automated trading firms, the important data feeds HFT technology use should be similarly ruled and regulated. And if authorities are not able do it, the data feeds should be made transparent.

[42.] As the New Kings of the Hill gain more power over trading (and market efficiency), their social costs should be compared to the social costs of HFT. Market-making passive HFTrs mostly need accurate real-time order-book data, but more complex strategies will require connectivity to more insightful data feeds. The New Kings stand at this crossroad. Their social cost may be much higher than HFTrs’: they can affect – deliberately or not – the efficiency, volatility, and transparency of future markets. They need to have a “Code of Conduct.” In 2015, Senior Supervisors Group released Algorithmic Trading Briefing Note, which lists several risk based principles that HFTrs, and other “algorithmic firms,” should follow. It is descriptive, but it is correct in requiring more comprehensive control. The code should not only be targeted at HFT firms, but also at the data trading New Kings.

[43.] Here comes the last 1/4 of a mile. The Code of Conduct is about principles. I will list five here and leave the details to the SSG Briefing Note: (1) HFT firms should use a multi-layered defense-in-depth approach “increasing control redundancy and diversity” and which  “can reduce the risk that an erroneous or destabilizing order will reach financial markets.” (2) Testing should be a continuous liability from (a) its initial testing to (b) controlled roll-out to (c) production environment with different market conditions closely monitored. In management, it must be understood that (3) insufficient oversight and conflicts of interest create internal risks and that (4) the intraday risk profile must be correctly accounted for. Finally, to strengthen the control for risk, the management should (5) see all near-misses. Similarly, the New Kings of the Hill should meticulously control all of their data products.

Conclusion. “This time it ain’t just about being fast” – my final quote from the final F&F VII. DeLorean DMC-12 was lighting fast stainless steel (and beautiful), but it just was not enough: DeLorean Motor Company went bankrupt in 1982. The same can happen to Saleen in 2016. Similarly, HFT firms need to be managed carefully following Code of Conduct, not only for managing risks, but for making sound business decisions. The best HFT firms understand this and have the capacity to better their status in hard times. If regulators do a bad job of protecting competition by tightening their leash too much by misjudged Computer Code, the industry will end “In the Hands of a Few.” In 1982, The Federal Bureau of Investigation tactfully shot down the vision of John DeLorean on (what probably are) false allegations of drug trafficking involvement. Now, the vision of healthy markets is cruelly endangered. □

[Signed: 7/.V]