“Largely, a waste of time and human potential. It has created jobs, whose value to society is suspect. Why is it that young, bright engineers end up staring at the screens, looking for patterns in asset prices when they could have far better served the society by solving some real problems?”

—Answers to the survey question: “How would you describe quantitative finance at a dinner party?” at wilmott.com

“One can predict the course of a comet more easily than one can predict the course of Citigroup's stock. The attractiveness, of course, is that you can make more money successfully predicting a stock than you can a comet.”

—James Simons

From the 1980s with the increase in trading in derivatives, through the 1990s with the increasing complexity of products, and then the 2000s with the creation of credit instruments and the shift to high-frequency electronic trading, quants have played an ever-more-important role in banking. The educational requirements for quants got tougher, and, as so often seems to happen, the commonsense requirements dwindled to near zero. Quants are the classical boffins, here outside of academia, who do the esoteric mathematics, write the computer code, quantify a bank or hedge fund's risk, and often design the algorithms that actually make the trades. As it has become cool to be a programming nerd, so it is cool to be a quant (the big salary helps). But will it ever be as cool as being a writer?

In this chapter, we're going to lift the lid a little more on what quants actually do – and just as importantly, how much they get paid. We're going to include some feedback and results from a survey we carried out at wilmott.com, so the message is coming straight from the horse's mouth. First though a little more history to bring us up to date and explain how – with the help of technology – these Masters of the Universe reached their current awesome level of power over the world financial system.

In olden times, like pre-1970s, stock markets were places where human traders could meet up in person to buy and sell shares in companies. In the USA the main stock exchange has long been the New York Stock Exchange (NYSE), founded in 1792 by 24 brokers. For the best part of two centuries it had a near monopoly on stock trading. Traders, in brightly colored jackets to indicate their firm, would huddle in trading pits and communicate their intentions with shouted orders and weird hand signals. In 1972 some competition arrived in the form of the NASDAQ, which began as an electronic quoting system but eventually evolved into a proper exchange. Even there, most trading still took place over the phone. This worked well enough until Black Monday, when many brokers just refused to pick up. In response, a computerized trading platform was soon set up. In the UK, Margaret Thatcher's “Big Bang” opened the London Stock Exchange to electronic trading. Thus began a power shift from humans to machines, and from gesticulating traders to writers of code.

As with the rest of society, finance was getting wired. Instead of men yelling at one another over a crowded floor, trades were increasingly being submitted electronically and handled by computers (so traders could yell at them instead). The process was accelerated in the 1990s by technical factors such as the decimalization of US stock prices – which reduced the minimum tick size from 1/16 of a dollar to one cent, thus making it easier to divide trades into small portions – and improved infrastructure for high-speed communications. And it was only a matter of time before it was realized that computer programs could not just help to process human orders, but also make the decisions to buy and sell in the first place.

In 2001, a few years after their Big Blue computer beat Gary Kasparov at chess, a report from IBM gained widespread media attention when it showed that computer algorithms could outperform humans at trading in simulated markets.¹ Mathematicians and physicists, employed by heavyweight firms such as Goldman Sachs or Deutsche Bank, or specialist newcomers such as Automated Trading Desk (later bought by CitiGroup in 2007) or Renaissance Technologies, were soon racing to develop so-called computer robots or “bots” that could track the markets, look for patterns, and execute orders at a pace that humans could never hope to match.

According to the NYSE, the average holding period for stocks declined steadily from 100 months in 1960, to 63 months in 1970, 33 months in 1980, 26 months in 1990, 14 months in 2000, and 6 months in 2010.² By that time trading activity was already starting to be dominated by high-frequency-trading (HFT) firms, which make thousands or millions of stock and option trades every day, often holding them for only a few seconds.³ Originally these concentrated on simple strategies such as exploiting small discrepancies in prices posted by different exchanges, or reacting to changes before human market-makers had time to update their prices, but over time they became increasingly elaborate. Today sophisticated algorithms – which seem to favor computer-game names like Stealth, Dagger, Sniper, and Guerrilla – automatically jump in and out of positions, competing with one another to make tiny profits on huge numbers of transactions, often trying to feint each other out or jam exchanges with fake orders that are cancelled at the last moment.

The electronification of markets initially promised to make the stock markets more accessible and democratic. Buyers and sellers could be matched in electronic barter networks, cutting out the market-maker middlemen of traditional exchanges (those who post both bid and sell prices and profit from the gap between them). Huge amounts of data on transactions were suddenly available to the masses, in easily displayed formats, at least for a fee. However, even as the main exchanges were opening up, dozens of alternative private exchanges, or pools, were set up to cater to large institutions and hedge funds. These were only lightly regulated, so could choose how much information to supply to users about other trades, and at what price. Some pools were open or “lit,” so that trades were freely viewable, but in “dark pools” information was kept secret, or sold at a price to subscribers. Stock exchanges such as the NYSE used to be a closed club, where membership was decided by wealth or privilege; the new system was in theory more open, but in practice access and knowledge were as tightly controlled as ever. The only difference was that now it was the quants, and their computers, who could see what was going on, sending out small buy or sell orders to “ping” the depths, gauge volume, and seek out the presence of large orders. Traditional volume buyers such as mutual funds, or smaller individual investors, were left groping in the dark.

Today, most trading takes places not on trading floors, but in massive computer facilities. The NYSE still has a busy-looking floor on Wall Street, which forms its public face on TV, but the real action takes place in its data center some 30 miles away in Mahwah, NJ. Speed has become so important that the speed of light has become a constraint, with hedge funds paying fees to locate their computer servers close to the exchanges, in order to avoid microsecond delays in order times. Others triangulate their location between different exchanges around the world. In 2010, the HFT company Getco spent $300 million to lay a cable connecting its computers near the Chicago Mercantile Exchange to the NASDAQ exchange in New Jersey, thus shaving a good 3 ms off the 16-ms order time.⁴ Microwaves are sometimes preferred, because light is slowed by 31% when it passes through fiber-optic cables, which is irritating if you're in a hurry. Or lasers, which have more bandwidth and are less affected by weather.

Despite its dangers, which we'll discuss further below, algorithmic trading is taking over stock markets around the world (one of the few holdouts so far is China, where humans are protected by government regulations and a stamp duty on trades).⁵ According to the US Commodity Futures Trading Commission, “automated traders are on at least one side of 50 percent of trades for metals and energy futures, and almost 40 percent in agricultural contracts.”⁶ So, who are the brains behind this race of the robots? You guessed it: the quants.

Trading is a statistical exercise, so algorithms and trading strategies must be designed which on average will provide positive returns. At the same time, the massive trading volume means that risk must be tightly controlled, in case it spirals out of control. For example, many hedge funds trade in options which promise a large payoff, but risk must be hedged by owning or shorting stocks – as discussed in previous chapters. And because leverage is often employed to boost returns, attention to downside risk is especially important. Unlike other areas, increased automation has therefore not led to much of a cull in jobs. From coding up trading algorithms, to designing bespoke derivatives, to analyzing and controlling risk, the skills of quants have never been in greater demand. As Jared Butler from the recruitment firm Selby Jennings told the Financial Times: “Traders used to be first-class citizens of the financial world, but that's not true any more. Technologists are the priority now. It's easier to hire a computer scientist and teach them the financial world than the other way around.”⁷

Quants are no longer just helping to write the story, they have stepped into it themselves like a post-modern author experimenting with new narrative forms. The changing status of quants has made the field highly lucrative – and lured away much of the mathematical talent from areas such as science and engineering. Which brings us to an important topic: salaries.

What do Quants Make – and are They Adequately Paid?

Got a degree in mathematics, physics, engineering, or computer science? For the last 20 years there's been only one job for you. And that's quant finance. Got a degree in finance or economics? It's still the same job, but you're going to have to get some hardcore mathematics on your CV if you're to get it.⁸

Why is quant finance such a desirable career? I don't think we are betraying any secrets if we say that the salaries might play a key role here. Let's get these numbers out of the way before we give you the full job description. Keep that envy under control.

Taken from the Jobs Board at wilmott.com:

Junior Quant 1–3 years’ experience / Hedge Fund job in London, $75–99,000

Quantitative Research Analyst (Financial Engineer) job in New York, $200,000

Or how about:

Senior Algorithmic Trading Developer, Hong Kong, $100–150,000.

That's not an annual salary – it's per month.

The record salary for a job advertised on that website is around $2m. That's an advertised job. On a public website. Not the behind-closed-doors, secretly headhunted, privately negotiated salary. You could apply for it. And maybe haggle it up a bit.

And that's before the bonus.

You get the picture?

Not everyone is earning such big bucks. At the junior end you'll be a code monkey, implementing other people's models. But at the top end you'll own the fund, and dine with presidents and dictators. Let's break down the jobs into some detail. This list is in a completely subjective order from least interesting to most, not necessarily in order of salary or importance.

• Junior quant. As a junior quant you will probably be straight out of university. That probably means you will have done something scientific or financial as an undergraduate, followed by a postgraduate degree in something more specifically in mathematical finance. Perhaps that will be a Masters, increasingly it will mean a doctorate. So you are probably in your mid-twenties. You will have taken quite a chance by pinning your hopes on getting the banking job. A lot of your contemporaries won't have been as lucky as you, many will have ended up in software companies, consultancies, or insurance. Fine places to work, and in many ways better than banks in terms of work/life balance, but still not perceived as being glamorous, if we can use that word. A PhD is not strictly necessary for quant finance work, technically all you need is second-year undergraduate mathematics, but banks do often ask for that qualification. Maybe it shows you can work independently… strike that, this is not the twentieth century any more, PhD students aren't what they used to be… but more probably simply because they can. And if the employer has a PhD himself he's probably more likely to hire someone similar. As part of your graduate studies you will have learned to write computer programs. And to maximize your chances of getting a quant job you will take the coding very seriously. At a minimum you'll be extremely comfortable with the C++ programming language. Ideally you'll be au fait with other languages as well. Fashions change in programming, new languages come, and then often go. These days it's Python.⁹ You are a code monkey. You'll be tinkering with code that others have written. You'll be implementing models that other people have created. You'll be working long hours, but that applies to everyone in banking.
• Model validation. Model validation is, as the name suggests, checking that models are implemented correctly. As discussed further in the next chapter, it's not really about whether those models are any good, sadly. We can't do better than take a few quotations from wilmott.com concerning this least interesting of jobs. One member, katastrofa, says: “Model validation is where quants go to die.” Another member, deimanteR, adds some flesh to this: “My impression is Model Validation can be particularly dull in big banks – you will be pressing Shift-F9 mainly. In smaller places you might be developing alternative models that no one uses. Still the best you can hope for. Moving out might be difficult – the longer you stay there the harder is to get out.” How depressing is that? (Shift-F9, by the way, refers to the Excel command that recalculates a spreadsheet.) Member Gamal is a bit, just a bit, more upbeat: “If you like browsing net 8 hours per day, it's a perfect place.” Only 8 hours? Model validation is quite a new role in banks, really coming into vogue following the crisis of modeling that started in 2007. Because it lacks any creativity, it's rather dull. And because it's not close to the money (and if anything it can be a source of frustration for those who are) it is very poorly paid, relatively speaking.
• Quant developer. This is almost the default quant job, in that there seem to be lots of them around. The job is implementing models in the programming language du jour. It is a grand title for someone who is a little bit more senior but is essentially just programming, that's the “developer” bit. In another company, Google for example, you might be called a software developer. As well as being extremely good at coding, you will know something about numerical algorithms. That means you will know about Monte Carlo simulations, and some of the theoretical basis for this. Or maybe numerical solutions of partial differential equations. Increasingly, as discussed below, it may also involve analyzing “big data” and applying machine learning techniques to everything from Internet search terms to weather patterns. If you have anything to do with portfolios of assets or investments, you'll be called upon to write the code to optimize asset allocation.
• Risk management. As a risk quant you will be measuring the amount of risk in contracts and portfolios. You won't be the most popular quant in the bank, since you will be the guy telling people that they have to cut down on their risky positions, and thereby probably decrease their bonuses. But look on the bright side, the traders won't want to listen to you anyway.
• Research quant. Like unicorns this is a mythical creature, a thing of beauty and envy. Almost. The few research quants still in existence are supposed to invent new models, to improve those that already exist and have perhaps failed. Or maybe you'll be trying to speed up models, or make them more accurate, or uncover new sources of data. You will undoubtedly have a PhD, you will be a whizz at stochastic calculus. It is highly unlikely that your research will be all that different from what others are doing, and although your job will feel a little bit like academia you will have to work much longer hours, and you won't have free rein for much blue-sky research. In a perfect world you would be creating genuinely original models and techniques, but in the real world banks don't like too much originality. You will sometimes publish papers in learned journals, and speak at international conferences. You will become famous among quant newbies who will look up to you. However, if your research turns out to be wonderfully clever but somewhat lacking in the profit arena, then expect to be “let go.” Don't despair though, there are plenty of MSc programs that will take you on as a professor in the blink of an eye.
• Front office or desk quant. As one of these you are close to the money, and you'll work closely with the traders. Make no mistake, you may have better qualifications and a higher IQ than them, but you are very much lower down in the food chain. Expect to get the blame when things go wrong. A thick skin is needed in this role. But the pay can be good. There'll always be a need for such employees. The coding can vary from simple tweaking of existing programs, to debugging major code, to implementing new models from scratch. The trader doesn't care whether the theoretical foundations for his ideas are sound. Does it make money? Check. Is it fast? Check.
• Quant trader. This is the holy grail of quant jobs, managing your own trading book. You are a trader who uses quant tools to assist in decision making, portfolio allocation, etc. It takes a very special type of person to do this job well. First of all you'll have lots of technical mathematical skills, especially statistical. And you'll need nerves to take the risks. You won't be too obsessed with the mathematics. If something works (i.e., makes money) then the possibility of it being incorrect is of minor concern. Hey, if you've got a plus sign where it should be a minus and it's making money then you'd be stupid to correct it. You are pragmatic. And very smart. And since you are probably doing your own programming then you are just some legal paperwork and a few hundred million dollars away from starting your own hedge fund.

We've sprinkled some of the feedback from our informal and highly unscientific quant survey at wilmott.com throughout the book, but here are some statistical findings from the hundreds of people from 47 different countries who endured a detailed, 50-part questionnaire and psychological probing, which we performed in order to get the pulse of the quant community and also as a blatant attempt to get ideas and material.

Average estimated IQ (self-reported!): 122. David once did an IQ test at school. The separate computer-readable answer sheet had two sides, and there was only one instruction, which was to record the answers on the green side first and then the red side. And ever since, his IQ has been one of those statistics with an asterisk by it. (Another test showed he was color blind, but that's not really an excuse.)

• 95% attended college.
• 42% have a doctorate.
• 72% have a professional qualification.
• 12% are female.
• 11% think there are gender inequality issues where they work (about as many as there are females, then).
• On average they thought the highest tax rate should be 27%.
• One-third of respondents thought that their company would consider relocating if taxes were to rise.
• 70% donated to charity.
• 66% prefer non-fiction over fiction. We think this book qualifies as 66% non-fiction. Those that like fiction seem to prefer sci-fi.
• Movies popular among quants include The Godfather and Dr Strangelove. One person favored Happy Gilmore.
• 93% describe their recreational drug of choice as “none,” and 6% say “aspirin,” which may invalidate our other results.
• Half of quants are teetotal.
• 43% agreed with the statement that the efficient market theory is true. We're using the past tense in case we change anyone's mind.
• 70% agree with the statement that the recent crisis was “Just a warm-up.”
• The quants’ car brand of choice is Toyota.

We also asked about their religion. Sadly, not a single Jedi was among them. Although Pastafarianism is big on wilmott.com.

So, picture a teetotal male, high on aspirin, driving a Toyota, and you won't be far off.

Quants vs. Regulators

We wanted to compare these quant salaries and education levels with those of regulators, but found it hard to get a straight answer about the latter group. The two main financial regulatory bodies in the UK are the Prudential Regulation Authority (PRA), which is a subsidiary of the Bank of England and is responsible for supervising the finances of banks, insurance firms, etc. and the Financial Conduct Authority (FCA), which deals more with things like business conduct and consumer issues (there is a degree of overlap in their responsibilities). We bombarded both of them with Freedom of Information requests, asking them questions about education levels, median salaries, and other topics such as criminal prosecutions, but unfortunately the information content of the responses was rather low. Neither group had anything useful to say about prosecutions against quants, which is unsurprising given that it doesn't seem to be something they go in for. When asked about education levels, the PRA said: “we would need to go through each personal record of the 1241 people working in the PRA to determine whether we hold the specific information about their education such as, where and how each person was educated and to what level.” (Seriously? They might actually not know what level of education people working for them have?!!)

The FCA was more forthcoming, and told us that although finding the information about staff education levels for us would be too time consuming, an internal survey did show that 44 of their 2169 employees self-reported having a PhD, with 252 not answering about their education level. Now that's very nice for us, but why were they asking their employees about their education level in an internal survey? Surely they had access to that data. Typically, one asks for qualifications before hiring. And who were the 252 employees who declined to tell their employers their education level? (FYI that's on top of the employees who didn't respond to the internal survey at all, which makes it a deliberate act rather than apathy.) Strange way to run a regulator. Anyway, call it between 2% and an unlikely maximum of 10% of their workforce with PhDs. Compare that with a hedge fund, where typically a third of the employees might have PhDs (and nearly everyone working at the quant end does). And there are a lot of hedge firms to regulate.

For salaries, the FCA told us that the salary range for their regulatory jobs started at £20,000–£40,000 for a Junior Associate. A Senior Associate, who “may act as a team leader or mentor,” can expect £46,000–£81,000. Managers get anything from £65,000 to as high as £118,000. The PRA only referred us to their annual report, which stated that remuneration in 2015 ranged from £18,578 to £266,777 for their CEO, with a median of £67,952, but didn't break it down by job category as we had asked.

These are very respectable salaries, and compare favorably with those in science or engineering. But with salaries in quant finance, not so much. We don't like to use the expressions “order of magnitude smaller” or “apparently missing a digit” when it comes to people's earnings, but it's in that ballpark. This says less about regulators than it does about quants – but it means that recruiting the best experts is always going to be a challenge. And it's easy to see the problems that can arise when regulators don't have enough qualified personnel. For example, in a 2015 survey of hedge funds, the FCA wrote: “Value at Risk (VaR) is a measure of the potential loss of a portfolio at a given level of confidence. We asked firms to provide us with their own VaR calculations for their funds.”¹⁰ So no chance of fraud there, then (we will show later how such measures are easily adjusted to give the right answer).

Writer-nomics

Working our way down the salary scale, it is interesting, if only for the sake of humor, to compare all this to another, very different occupation of which we both have some experience: writing. Writing is a great job. Writers can make up their own projects and set their own deadlines. They can work from home and have no one to report to but themselves, their readers, and the occasional editor. There are only two catches. The barrier to entry is high, and the pay is a little unreliable. But that's not what you're in it for.

The odds of an unsolicited manuscript being accepted by a publisher has been estimated at about 1 in 10,000.¹¹ Similar for the chances of having a screenplay turned into a film.¹² Even authors who later went on to great success have had trouble getting a foot in the door. J.K. Rowling of Harry Potter fame, for example, only got lucky with her thirteenth publisher. Having a polished CV or a degree from a fancy institution is no help here. Contacts aren't much use either. Being famous for doing something else is better. Acquiring a literary agent is useful, but “is even harder than finding a publisher!” as one publisher informed Rowling, when she later submitted a novel under the pen name Robert Galbraith.¹³ You can always self-publish, as we have both done, but the challenge of finding a readership is harder.¹⁴

And then, even when you get your first work published, that is just the start, because the chances that it will actually sell are minimal, book sales being dominated by a small number of titles.¹⁵ As discussed earlier, neoclassical economics and most risk assessment tools are based on the normal distribution, which is a shame because many important economic phenomena, from sales to stock-market fluctuations to wealth distribution to company size, are better described by a highly skewed power law. If book sales followed a normal distribution, authors could safely expect to sell, within a certain range, an average number of copies per year. The reality is quite different. It is possible to make good money if you have a bestseller, or sell lucrative movie rights, or win a prestigious award such as the hedge-fund-sponsored Man Booker Prize (the 2015 prize went to Marlon James, whose first book was rejected 78 times before being published). But there is no base salary or steady income, and as a general money-making strategy, writing is not recommended. A 2015 survey of about a thousand published authors, fiction and non-fiction, by the Writers’ Union of Canada showed that their average annual income from writing was, er, $12,879 Canadian, or about $10,000 US.¹⁶ Roughly an order of magnitude smaller than regulators, then. The numbers are also in decline, probably because no one (apart from you – thanks!) buys books anymore.¹⁷ Of course the average doesn't mean much, because the distribution is so highly skewed (the median is under $5000 CAD) – but if reliable income is the goal, then definitely go with the quantitative finance if you can.

Writers must also accept that sales are unpredictable, and only partially within their control (though having one bestseller raises the author's profile and increases the chances that the next book will sell well too). They are like a nice kind of economic crash – you never know exactly how big they are going to be, or where they are going to come from. Who would have thought that a 700-page tract on inequality by a little-known French economist would be one of the bestselling books of 2014 (Thomas Piketty's Capital in the Twenty-First Century)?¹⁸ Even Miguel de Cervantes, credited with the best-selling novel of all time, was considered a bit of “a loser” in his time according to one historian – his first novel flopped, he spent time in jail, and Don Quixote only became a phenomenon after he died.¹⁹ One reason writers are dangerous is that you can deprive them of money, put them in prison, and they will keep writing.

Many writers support themselves by teaching writing to other would-be writers, at one of the creative-writing programs that have sprung up in universities (or in jails, for that matter) around the world. The economics of this are unclear – hiring a few writers to produce a lot more of them doesn't exactly seem like a long-term solution to the problem. But even if students were told upfront about their salary prospects, it probably wouldn't make much difference. David once attended a meeting for aspiring screenwriters where a writer, who was considered massively successful because he once had a screenplay made into a film, told the audience what the statistical chances were of one of their screenplays being similarly accepted. No one cared, because everyone there thought they were the one with the brilliant and marketable idea. It was like explaining to a quarter-billion spermatozoa that statistically speaking, they are probably wasting their time. (David's idea, since you ask, was a story in which the Earth was the villain! It went through some iterations with a production company, but didn't go anywhere, so he turned it into a book, which got him an agent.)

So what does this have to do with quantitative finance (the subject of this particular piece of writing)? For one thing, the economics of writing gives a different perspective on efficient market theory, and particularly the idea that market price reflects “intrinsic value.” When Eugene Fama was asked in a 2007 interview to comment on average CEO pay – which in the USA is now 354 times that of an unskilled worker – he said “you're just looking at market wages. They may be big numbers; that's not saying they're too high.”²⁰ By the same argument, average writers’ salaries are just market wages. They may be small numbers; that's not saying they're too low. Which may be one reason why writers, like quants, take efficient market theory less seriously than tenured business school professors.

Writers, with their hands-on experience of free markets, also know that the world is not “normal,” that there is not a neat relationship between risk and reward, and that markets are affected by powerful feedback effects – so, for example, having a book on a bestseller list encourages further sales, mentions, reviews, and better placement in stores, which in turn drive more sales. This kind of winner-takes-all dynamic is common in many areas. The earnings of visual artists, for example, are in the same ballpark as those of writers, but the distribution is even more skewed – at least if you count dead artists.²¹ At the time of writing, the record price for a painting was about $300 million for a particularly fetching (we assume) Gauguin. The purchaser was reputed to be the State of Qatar, but hedge-fund owners are also big buyers. Winner-takes-all applies even to the world of quantitative finance, with the important difference that it is winner-takes-all above base salary plus bonus.

Why then would anyone choose to become a writer, apart from the adulation, the groupies, the thrilling risk, and the occasional free books from publishers? It's a chance to do something authentic, that you believe in. It has “intrinsic value” of the sort that doesn't appear as a number on a pay check. You can do other things at the same time, including banking (T.S. Eliot penned The Wasteland while employed at Lloyds). And you can set your own hours.

Blinding us with Science

While some quants like to invest in art, others find science more appealing. David Harding, who founded Winton Capital, has for example generously funded The Winton Programme for the Physics of Sustainability at Cambridge; The Harding Center for Risk Literacy at the Max Planck Institute for Human Development in Berlin; £5 million towards building a new mathematics gallery at the Science Museum in London; and for science writers the Royal Society Winton Prize for Science Books. Winton Capital also funded a science competition to improve on algorithms for the mapping of dark matter, the mysterious, elusive substance which is thought to permeate the universe, as well as areas behind the fridge.²²

David E. Shaw gave up day-to-day operations of his hedge fund in 2001 to concentrate on D.E. Shaw Research, which carries out biochemistry research. The firm's job ads helpfully point out that of successful applicants, a considerable number have “competed successfully in the United States and International Math Olympiads as well as the Putnam Competition.” This is like saying “many of our fitness instructors are Olympic medal holders,” or “most of our drivers are Formula One champions.”

Another heavyweight in the science market is the Templeton Foundation, which is propped up by a $3 billion endowment from the estate of the famed investment manager John Templeton. Each year it hands out grants worth over $100 million, with a significant portion going toward high-energy physics, and in particular supporters of string and multiverse theory. For comparison, the US National Science Foundation's budget for high-energy physics is about $12 million. Whether his foundation is as good at spotting scientific theories as Templeton was at picking stocks remains to be seen. (The physics of string and multiverse theory, as opposed to the mathematics behind it, was critiqued in David's willfully obscure treatise on science called Truth or Beauty. Its sales – since we were on that topic – were unexciting everywhere except in China, where the translated version was unaccountably chosen by Xinhua, the press arm of the Chinese state and mouthpiece of the Communist Party, as recommended New Year holiday reading. As we said, unpredictable.)

And then there is James Simons of Renaissance Technology – one of the biggest patrons of scientists since the Medicis hired Galileo as a tutor. Ranked 76 on the 2015 Forbes list of the world's billionaires (another list which follows a power law²³), he has a personal fortune estimated at $14 billion, and seems intent on giving much of it away to promote a range of scientific research through his Simons Foundation.²⁴ Its “Mathematics and Physical Sciences” program focuses on computer science and theoretical physics, doling out million-dollar grants to leading scientists. “Life Sciences” supports research on the boundary between physics and biology, including a brain-modeling project known as the Global Brain. “Education and Outreach” features a program aimed at secondary schools and teachers called Math for America. In addition, there is an Autism Research Initiative and a Center for Data Analysis, which explores big data in areas such as genomics and neuroscience. The Foundation even has its own online science magazine, Quanta, so employs a few science writers.²⁵

While any source of science funding is probably to be welcomed, not everyone is comfortable with the idea that scientific research is being shaped by the tastes of hedge-fund owners. The Templeton Foundation, for example, has been accused of blurring the line between science and what cosmologist Sean Carroll called “explicitly religious activity” (which may explain that weird multiverse stuff).²⁶ There is a risk that billionaires may distort the science market the same way they distort the art market, by turning it into something like the luxury goods sector. Instead of a Gauguin, or a Jeff Koons, you can get the latest version of a Theory of Everything. However, the Simons Foundation seems to be a solid and broad-based extension of public funding for high-quality science. It probably helps that Simons is an accomplished scientist himself. He doesn't just fund things like string theory: as a young mathematician, he co-developed the Chern–Simons theorem, which was popularized by string theorist Edward Witten, and serves as an important mathematical tool in that area.

Bots

Simons has had an interesting career path, and – getting back to the topic of quantitative finance – if there is one firm that exemplifies the field's rise, it is his Renaissance Technology.

After receiving his doctorate in mathematics at the age of 23, Simons celebrated with two friends by buying Lambrettas and motor scooting from Boston to Bogota. A few years later, together with Simons's father, the group teamed up to buy a Columbian floor-tile factory, as one does. The same year, 1964, Simons started work as a code-breaker with the National Security Agency (NSA). In 1967, General Maxwell Taylor wrote an article for the New York Times Magazine in favor of the Vietnam War. Simons penned a reply for the same magazine, arguing the opposite. Shortly after he was fired by the NSA.²⁷ However, he was welcomed by academia, and was soon appointed chairman of the mathematics department at Stony Brook University. There he began to build up what would become a formidable group of mathematicians.

Simons also dabbled with trading on the side. The Columbian factory had done quite well, so in 1974 Simons and his partners decided to take out some profits, and invest $600,000 with a commodities trader, making leveraged bets on the price of sugar. In the space of a few months, it became $6 million.²⁸ Figuring he could do this himself, Simons left Stony Brook in 1977 and went into trading full time, setting up a firm called Monemetrics in a strip mall in the Long Island town of Setauket, close to Stony Brook. Two of his first hires were Lenny Baum, a former colleague from the IDA, and a mathematician called James Ax.

Baum was co-inventor of the Baum–Welch algorithm, which is used to build models of hidden Markov processes. A Markov process is an iterative process in which the rule governing the transition to the next step depends on nothing more than the current state. A simple example is a random walk. When you take a step, your position depends only on where you just were, along with the rule for the random step (e.g., the standard deviation of the step size). A hidden Markov process is one that you have lost somewhere on your desk. Or alternatively, it's one where the rules are hidden. There could be something going on in the background, but all you see are the observed states at each step. Baum–Welch is a mathematical process for teasing out the hidden parameters. The algorithm was used in everything from code-breaking to speech recognition, but Simons thought it could work in finance as well. The markets were a giant hidden Markov process; all you had to do was figure out the rules.

James Ax took over the task, and tried applying the technique to futures contracts. In 1988 he and Simons started a new hedge fund call Medallion, naming it after mathematics awards they had won. But the bugs weren't all worked out and in 1989 the fund was losing money. Ax left, went back to fundamental research on quantum mechanics, learned to play golf, took a screenwriting class, and wrote a screenplay for a scientific thriller called “Bots.”²⁹ Simons – whose recruitment skills had been honed at Stony Brook – hired a string of mathematicians to take over. In 1990 the Medallion fund returned over 50% after fees, the first of a long series of stellar results. In 1993 the fund was closed to outside investors, and now serves only as an investment vehicle for Simons and his staff.

We haven't seen James Ax's screenplay – he died in 2006 – but the word “bots” usually refers to the software robots that run automated tasks on computer networks including the Internet. Maybe the bot is the villain. If so, it is fitting that the co-founder of the Medallion fund came up with the idea, since in many ways the fund resembles a kind of sophisticated robot, its artificial intelligence automatically learning about the markets as it goes along, buying and selling with each millisecond pulse of its digital brain.

Global Brain

In the early 1990s, Simons poached two machine translation experts, Robert Mercer and Peter Brown, from IBM's speech recognition group, by offering 50% more pay (it would turn into a lot more than that).³⁰ They were soon followed by much of the rest of the group, leading some to complain that Renaissance set the field of machine translation back by five years.³¹ The firm's interest in speech recognition also led to speculation that they had worked out a way to listen in on Wall Street conversations. But their approach probably has as little to do with that as it does with string theory (although a number of firms now automatically scan news reports and twitter feeds to divine market sentiment and generate buy or sell recommendations).

The two main components of a hedge fund's strategy are figuring out what the markets will likely do next, and integrating that prediction into a trading platform. Especially for large firms, these are connected since making a significant trade can affect the market. Both steps need to take into account not just expected profits, but also risk analysis and expenses including taxes. Some hedge funds, such as the ill-fated LTCM, take a “convergence” approach where they look for two different assets whose prices are related – for example, stocks of companies in a similar area – but where one appears underpriced relative to the other. They can then buy the underpriced asset, short the overpriced asset, and wait for their prices to converge. Unfortunately, convergence may take forever, or not happen at all. It is like picking bestsellers based on rational criteria such as the performance of similar books, which as we've seen would miss a lot of candidates.

Renaissance's approach is to throw away any preconceived notions and just look for short-term patterns in the data, which may reflect artefacts to do with trading as much as fundamentals. The Medallion fund, for example, appears to be Catholic in its tastes, and trades international commodity futures, equities, currency swaps, bonds, mortgage derivatives, and so on. The fund has its own trading desk, which employs about 20 traders. In one year, the firm executes tens of millions of trades, with many of them held for only a few seconds (the firm pioneered many of the high-frequency trading techniques described by Michael Lewis in Flash Boys).³² As Simons told the Greenwich Roundtable in 1999, “we look at anomalies that may be small in size and brief in time. We make our forecast. Then, shortly thereafter, we re-evaluate the situation and revise our forecast and our portfolio. We do this all day long. We're always in and out and out and in. So we're dependent on activity to make money.”³³

Much of this activity takes place in private “dark-pool” exchanges, in order to avoid telegraphing transactions, which would affect prices. Results are also boosted through leverage: the firm deposits money with a broker, say Barclays or Deutsche Bank, who in turn loan further money. Renaissance manages the whole pot for a year, repays the broker its loan plus fees, and keeps the proceeds. The process can be structured as buying an option on a basket of assets, where Renaissance manages the basket and always chooses to exercise the option; and as discussed below, Renaissance argued exactly that in order to qualify for lower tax rates.³⁴

The forecast model therefore has less to do with analyzing fundamentals than using machine learning to find patterns in big data and execute on them rapidly. As Mercer tells the story: “RenTec gets a trillion bytes of data a day, from newspapers, AP wire, all the trades, quotes, weather reports, energy reports, government reports, all with the goal of trying to figure out what's going to be the price of something or other at every point in the future… The information we have today is a garbled version of what the price is going to be next week. People don't really grasp how noisy the market is. It's very hard to find information, but it is there, and in some cases it's been there for a long, long time. It's very close to science's needle-in-a-haystack problem.”³⁵

Another source of information for Renaissance, as revealed in transcripts of a legal case involving former employees, is limit order book data from public exchanges, which list all the orders that are in place to buy and sell an asset at particular prices.³⁶ One of the best indicators of market changes is the activity of other traders. For example, if there is a queue of orders to buy a stock, then a nimble trader can insert themselves into the order by buying the stock and then quickly reselling it – much as a scalper can profit by being first in line to buy tickets at a popular concert. And part of the prediction is knowing what effect one's own trades will have on the market. Any large order will be sensed by other bots, which will try to profit from them, either by selling into them or buying ahead of them. Strategies have to evolve constantly, as copycats appear and markets change.³⁷ Because most of the trading is carried out by bots, machine learning algorithms have to learn the behavior of other machine learning algorithms, in a kind of regressive loop, as if the markets are becoming self-aware. The complex technical nature of the problem – akin to building a global brain for finance – is why Renaissance hires mathematicians, statisticians, physicists, and other scientists, but not people from a finance background.³⁸ (It is ironic that Mercer, who now shares CEO duties with Simons and Brown, went into speech recognition, since he seems to fit into the typical quant mold of being somewhat uninterested in light conversation. As he told the Wall Street Journal: “I'm happy going through my life without saying anything to anybody.”³⁹)

Creative Finance

While the exact workings of Renaissance are a closely guarded secret, its financial performance is not. In 2008, at the heart of the financial crisis, when the S&P 500 lost 38.5%, Medallion nearly doubled, with a gain of 98.2%. In the decade from 1994 to mid-2014, the fund made an average annual gain, before fees, of 71.8%. (Fees take about half that, but since the fund is employee-owned, they are just paying themselves.) Its other funds that are open to outside investors also posted consistently positive, if less spectacular, returns. (One dud was the Renaissance Institutional Futures Funds, which was closed in 2015 after returning an average of only 2.86% since its establishment in 2007.⁴⁰)

Taxes aren't a problem either. In 2015, after four years of intensive legal work, the company got the Labor Department's permission to shield Medallion inside Roth IRAs, which means it can grow completely tax-free.⁴¹ The firm's aggressive tax stance met with controversy in 2014, when the Senate took it to task for using basket options to avoid more than “$6 billion in taxes by disguising its day-to-day stock trades as long term investments,” according to Senator John McCain.⁴² There seems to be a disconnect between the tight-fisted approach to taxes on the one hand, and the philanthropy of the Simons Foundation on the other. The Foundation presumably believes that it can do a better job of handing out money and promoting mathematics education and science than the government can. It all fits with the idea of rational, efficient markets, where the biggest winners are the most rational and enlightened of all. Or it would, except that co-CEO Robert Mercer's own foundation donated $2.5 million to the Koch brothers’ Freedom Partners Action Fund, and $11 million to the presidential campaign of Tea-party candidate Ted Cruz, neither of which are renowned for their pro-science stance.⁴³ And it also points to a wider contradiction between the interests of firms such as Renaissance, and those of the economy as a whole.

As we've seen, quants add value by calculating prices for financial instruments such as derivatives, which are used by a diverse range of users. But as the OECD noted in a 2015 report, “there can be too much finance. When the financial sector is well developed, as has been the case in OECD economies for some time, further increases in its size usually slow long-term growth.”⁴⁴ One reason is that, while banks, investment funds, and stock exchanges have an essential role in supplying capital to companies and individuals, most of those recipients in practice turn out to be – other financial firms. In other words, banks are funding one another and trading each other's shares and debts in a kind of merry-go-round. And while this activity is profitable, most of it is not inherently productive.

Hedge funds, for example, don't build anything in the normal sense; instead, they take in techniques and experts from other areas and use their skills to take lots of tiny cuts out of markets (like black holes, information goes in, but little leaks out). Something like high-frequency trading is pretty much a zero-sum game: if Renaissance is making billions, then others – for example, people with retirement funds – are losing billions. While it adds liquidity to certain assets, as discussed in Chapter 10, this apparent liquidity is somewhat illusory, and is not a priority for long-term investors.⁴⁵ At the same time, it carries a very real risk to system stability – as illustrated by the trillion-dollar Flash Crash of 2010, which began on May 6 at 2:32 EST, and was all over a little more than half an hour later at 3:08. In that time the Dow Jones lost about 9% of its value, but recovered most of that by the end of the day.

As with most financial crashes, the exact cause of the Flash Crash is uncertain and has been blamed on a number of factors – first on an accidental order which triggered an over-reaction, then five years later on a London-based high-frequency trader using spoof sell orders to drive the markets down – but algorithms certainly played a part, since they dominate most normal trading. Many just turned themselves off as prices began to plummet, which is the computer equivalent of not answering the phone. Computers gave markets an even quicker jolt on October 15, 2014 at 9:33 in the morning, when the prices of US Treasuries spiked up by over seven standard deviations, but were back to normal within twelve minutes. An investigation by regulators showed the activity was mostly “aggressive” momentum-chasing algorithms selling to “passive” algorithms that were acting as market makers. In many cases these algorithms belonged to the same outfit – some 15% of the total activity was firms “self-trading” (i.e., selling to themselves), so “no change in beneficial ownership results.”⁴⁶ Smaller versions of such “flash” events have become regular occurrences, even in previously staid markets such as corn futures.⁴⁷ While computer algorithms may seem to be the perfect realization of the type of rational behavior imagined by theorists, the fact that computers do not feel emotions such as fear or greed does not mean that the end result of their actions is rational or optimal.

Hedge funds have their place in the financial ecosystem, and their activities have certainly made it more “efficient” in the narrow sense that prices are consistent and there are fewer arbitrage opportunities for other traders; but anyone who thinks that is what they are being paid for probably also believes in efficient market theory and has stopped reading by now (words being cheap, as we've seen). They aren't about wealth creation, they are about wealth redistribution – like taxes but in reverse. In a world where economic rewards are becoming increasingly skewed and asymmetric – where more and more professions are beginning to look like writing – this is not universally perceived as a good thing, as Piketty pointed out in his book. Which is one reason hedge funds channel much of their largesse toward lobbying politicians (and in some countries dominate political contributions).⁴⁸ They shape/influence/game elections the same way they do markets.

Another problem, as a paper from the Bank for International Settlements (BIS) notes, is that “a bloated financial sector can also suck in more than its share of talent, hampering the development of other sectors.”⁴⁹ In countries such as the USA and the UK, a substantial portion of mathematicians from elite institutions go into finance: “people who might have become scientists, who in another age dreamt of curing cancer or flying to Mars, today dream of becoming hedge fund managers.”⁵⁰ (BIS – known as the central bank of central banks – often seems to enjoy criticizing the financial system which, as much as any organization, it helped design.) And once firms such as D.E. Shaw hire up all the Math Olympiad champions, most of those skills don't get used in a productive way, if at all. The mathematics used by hedge funds can be tricky and sophisticated, but in the scale of things it isn't that deep, as even Simons admits.⁵¹ Instead, as we noted above, degrees from top-flight institutions act primarily as a barrier to entry, and add to the field's aura of mystique. Training people in mathematics only so they end up in hedge funds is therefore rather like creative writing classes: in either case, from a global perspective, it doesn't make a lot of economic sense, but that isn't the point.⁵²

Quants, scientists, and writers all share some of the same impulses: to do something authentic and creative; to test themselves; to achieve a kind of freedom. And they are driven by a similar kind of passion and curiosity. As quant Tom Hayes – on charge for manipulating Libor – said on the stand: “when you get it right, it's like solving that equation. It's make money, lose money, and it's just so pure.”⁵³ But if hedge fund owners really wanted to help scientists do their work, the best way would be to stop recruiting their top students by offering them eye-watering salaries. A more realistic alternative, of course, is that the financial sector becomes a less dominant source of employment for other reasons. We will return to this topic in the final chapter. We first turn to the role of quants in creating, and maintaining, a different kind of fiction: the sort that consists of mathematical models.