{"id":10487,"date":"2014-01-17T00:00:00","date_gmt":"2014-01-17T05:00:00","guid":{"rendered":"http:\/\/localhost\/thenewatlantis.com\/publications\/when-finance-met-physics"},"modified":"2020-09-26T14:04:56","modified_gmt":"2020-09-26T18:04:56","slug":"when-finance-met-physics","status":"publish","type":"article","link":"https:\/\/www.thenewatlantis.com\/publications\/when-finance-met-physics","title":{"rendered":"When Finance Met Physics"},"content":{"rendered":"

J<\/span>ames Owen Weatherall has embarked upon a futile mission, but it is a futile mission to be admired. The Physics of Wall Street<\/i><\/a> is in part an intellectual history, examining the rise of the financial models that have received so much attention over the last half decade, after they were, perhaps unfairly, pinpointed as a central cause of the financial crisis. But the book is also a work of mathematical advocacy: Weatherall\u2019s stated goal is to revive the ailing practice of financial modeling by basing models upon better assumptions and making them more reliable.<\/p>\n

The story of mathematical finance is as much about its practical implications as it is about the evolution of the field itself. While Adam Smith and the other progenitors of modern economics viewed exchange as a component of moral philosophy and so were not disposed to create mathematical models, the neoclassical economists of the early and mid-twentieth century embraced the methods of the physical scientists they styled themselves after. The economist Don Patinkin depicted the new face of his field in his 1956 book Money, Interest, and Prices<\/i><\/a>: \u201cWe can consider the individual \u2014 with his given indifference map and initial endowment \u2014 to be a \u2018utility computer\u2019 into whom we \u2018feed\u2019 a sequence of market prices and from whom we obtain a corresponding sequence of \u2018solutions\u2019 in the form of specified optimum positions.\u201d This mechanistic view of human exchange would have been unrecognizable to Smith, but was emblematic of the neoclassical school\u2019s new reliance on models and mathematics.<\/p>\n

As neoclassical economics progressed and financial economics formed its own sub-discipline, the emphasis on making economics conform to the methodology and rigor of the physical sciences grew. M.I.T. economist Robert Solow averred in 1985<\/a> that \u201cif the project of turning economics into a hard science could succeed, it would surely be worth doing.\u201d The rise of massive computing power in the late twentieth century, and the consequent turn in finance away from stock-picking and toward algorithmic trading, seemed to make the neoclassical dream a reality. Complex models imported from physics and stochastic calculus helped earn fortunes for their creators, and they seemed at long last to bring that most elusive of investor dreams \u2014 certainty \u2014 within reach.<\/p>\n

Financial models are now extraordinarily complex things, and they underpin much of what we see and do not see in the world of finance. Not only have models totally colonized the world of investments \u2014 estimates usually credit algorithmic trading with 60 to 70 percent of all stock trades \u2014 but they are used to price everything from options to bond market movements. To Weatherall, this is undoubtedly a positive development. Models create better efficiency for markets, better profits for investors, and better intellectual progress in the field. Not only are models \u201cnot to blame for our current economic ills,\u201d he says, but more sophisticated and more complex models will help us avoid such ills in the future.<\/p>\n

Much of this story has been told before in pre-recession books like Peter L. Bernstein\u2019s Against the Gods<\/i><\/a> (1996) and Roger Lowenstein\u2019s When Genius Failed<\/i><\/a> (2000), but Weatherall\u2019s version of events is nonetheless enjoyable. And Weatherall is well equipped to tell it: an assistant professor at UC Irvine, he has one Ph.D. in physics, another in the philosophy of physics, and an M.F.A. in creative writing to boot (all earned by the age of 30). Rarely has such arcane material been presented in such lucid and readable prose. But the book is, in the end, an unsuccessful attempt to recuperate a failed project.<\/p>\n

One of the weaknesses of the book is Weatherall\u2019s proclivity for tangential anecdotes \u2014 the chapter on physicists and mathematicians trying to beat the casino can be a slog \u2014 but he redeems himself with his sympathetic portraits of a wide range of fascinating eccentrics. Take, for example, the almost comically tragic story of Louis Bachelier, the now-famous mathematician who essentially invented mathematical finance. This woebegone Frenchman wrote an astonishingly original dissertation that challenged the dominant approaches of his field, inevitably resulting in professional banishment. Even with Henri Poincar\u00e9, the famous mathematician and theoretical physicist, to advise and support him, Bachelier earned no respect from his peers or his evaluators. After several wanderlust years, he finally secured a lecturing appointment at the University of Paris \u2014 but without a salary. Finally, after five years of academic penury, he was to be offered a permanent position. But the small matter of Germany\u2019s invasion of France intervened, and Bachelier was drafted to fight in World War I. He survived, but his career never reached the altitudes that his brilliance merited.<\/p>\n

The book is full of stories like these: tales of misunderstood geniuses and stymied academics who challenged prevailing standards and were ostracized for their trouble. Weatherall presents the story of mathematical finance as a sort of Whig history, in which refinements are continually made by successive generations of brilliant misanthropes and hippie physicists, getting closer to the goal of making finance more like physics, until eventually we achieve the ability to predict the ostensibly unpredictable.<\/p>\n

Though it is a story of scientific advancement, the later thinkers\u2019 penchant for turning their scientific discoveries into proprietary investment tools and untold riches mars the image of pristine intellectual pursuit. Weatherall concludes the story with a call to import more<\/i> lessons from physics into finance \u2014 to perfect mathematical finance by further refining models, and to regard as symbiotic the psychological study of human behavior and the mathematical modelling of financial markets. It\u2019s a compelling argument, but ultimately an unpersuasive one.<\/p>\n

T<\/span>here are several reasons not to readily accept Weatherall\u2019s arguments. The first is the most obvious one, and has been circulated in these pages (\u201cThe Financial Crisis and the Scientific Mindset<\/a>,\u201d Fall 2009\/Winter 2010) and elsewhere since the financial crisis of 2008: human beings are decidedly not quarks. Whereas the particles and atoms studied by physicists generally behave according to more or less predictable patterns, human beings are foolish and irrational and often do unexpected things. The best model in the world cannot fully predict when a group of human beings will engage in collective irrationality: consider, as Weatherall does, the bank-run scene in It\u2019s a Wonderful Life<\/i>, or the Dutch tulipomania.<\/p>\n

Weatherall is canny enough to address this objection directly. He is not of the scientistic variety of thinkers who promote math, method, and models as the ultimate explanations of all phenomena; he merely argues that financial models should take psychology and sociology into account. This, he says, is the approach of behavioral economics, which offers a more complete view of human behavior than physics or purely utilitarian economics.<\/p>\n

But do they? The biggest elephant in the modern academic room is the questionable methodology of the social sciences. Psychology, for example, is in the midst of a major rethinking of the validity and reproducibility of many of the fundamental findings of the discipline. The Open Science Framework\u2019s Reproducibility Project is attempting to replicate major studies<\/a> in the field because of widespread, longstanding skepticism of the conclusions of psychology studies in general \u2014 most of which are never subjected to this basic test.<\/p>\n

The best research in psychology and social science draws on large, longitudinal samples, or is repeatedly verified across multiple studies and by multiple researchers. The famous work of Daniel Kahneman and Amos Tversky on cognitive biases, and the more recent work of Richard Thaler and Cass Sunstein<\/a>, are examples of this kind of impressive and methodologically robust research. But too many social science studies rely for their research subjects upon a small pool of college students compelled or strongly induced to participate, and the results are too often reported as solid fact.<\/p>\n

The flaws of behavioral economics studies are more troubling because of their use in public policy. Andrew Ferguson, in a 2011 article for the Weekly Standard<\/i><\/a>, notes that the rationale for the tax-cut component of the 2009 stimulus bill rested largely on a single behavioral economics study. Published by two researchers at Texas A&M\u2013Corpus Christi<\/a>, the study simply asked a group of 141 students to imagine receiving a refund, and found that they were more likely to spend it if it came in monthly increments. But the study cast this weak tea as bold scientific fact: \u201cresults … confirm that monthly refunds stimulate current spending significantly more than yearly refunds.\u201d<\/p>\n

Weatherall himself locates several areas of social science research that he claims will be greatly beneficial to mathematical finance. For example, he praises the French physicist-turned-economist Didier Sornette\u2019s research on herding effects \u2014 the ways a crowd, based on the desire to imitate others, can create a feedback loop and magnify a price drop or rise \u2014 and says this work can help make finance more predictable. But, as Weatherall points out, though Sornette\u2019s quantitative methods have allowed him to discern when these herding effects have taken over, Sornette \u201cdoesn\u2019t have an answer\u201d to the more important question of why the ordinary tendency to imitate leads to herding effects at some times and not others.<\/p>\n

Weatherall emphasizes that models are only as good as their assumptions. But he nonetheless makes his argument by drawing on lessons from fields that pile assumption on assumption, so deep that their practitioners typically do not even realize that they can\u2019t see the bottom. Weatherall aims to strengthen the scientific bases of financial models, but by incorporating research from areas that are very much not scientific \u2014 at least not in the way his own field of physics is.<\/p>\n

T<\/span>here have been some figures in mathematical finance who have recognized that it does not yet amount to a science \u2014 but they are rare. Weatherall spends a chapter with Fischer Black, the polymath who helped form the famous Black-Scholes-Merton options pricing formula. Black-Scholes-Merton, perhaps the most influential financial formula of the past few decades, offered its users a way to price options accurately even in the face of uncertain information regarding price, volatility, and market conditions. Emanuel Derman, a former quantitative risk analyst, described it thus in his 2011 book Models Behaving Badly<\/i><\/a>: \u201cIt\u2019s like a recipe that tells you how to make fruit salad (an option) out of fruit (stocks and bonds)\u201d but also tells you \u201cwhat the fruit salad is worth.\u201d The formula revolutionized options and indeed much of modern trading, and its central idea of fully hedging risk helped underpin some spectacular successes and disasters on Wall Street.<\/p>\n

Black was never as certain as Myron Scholes and Robert Merton of the seamlessness of the model. Weatherall does not consult Black\u2019s \u201cNoise<\/a>,\u201d a speech delivered to the American Finance Association in 1985. Whereas other efficient market theorists saw all information as helping create an accurate price, Black distinguished between \u201cinformation\u201d traders and \u201cnoise\u201d traders. The latter, he thought, trade on behaviors arising from speculation and uncertainty as if it were real information, and thus create inefficiencies and unnecessary volatilities in pricing. Because modern markets are so unfathomably complex, there is no pricing model \u2014 Black-Scholes-Merton very much included \u2014 that can fully block out the noise.<\/p>\n

Separating the information from  the noise is precisely the problem that Weatherall is trying to solve \u2014 and yet it remains as much a problem today as when Black gave his speech, despite a quarter century of technological progress. The trouble has as much to do with inherent limits on our predictive power as with our constant failure to recognize those limits. As Weatherall notes, \u201cone can convince oneself that a model that has worked before is a kind of magical device that will continue to work, come what may.\u201d And one may gain \u201ca false sense of confidence that, because you have some theoretical justification for a model, the model must be right. Unfortunately science doesn\u2019t work this way.\u201d But the most glaring truth Weatherall overlooks is that, although science doesn\u2019t work in this magical way, our minds still do.<\/p>\n

A model is at heart a simplification, a reduction, and a metaphor that relies upon assumptions. As Weatherall says, \u201ca few simplifying assumptions can go a long way toward making an otherwise intractable problem solvable \u2014 and once you solve the simplified problem, you can begin to ask how much damage your simplifying assumptions do.\u201d The trouble arises when we fail to make the move from our abstract sketch to a whole picture. We let models stand in for reality in finance because it\u2019s more efficient to base everything on simplified assumptions and reduced data.<\/p>\n

The central shortcoming of Weatherall\u2019s book is its failure to emphasize just how persuasive metaphors \u2014 and thus financial models \u2014 really are. Analysts choose one portion of reality and operate from it. But the problem is not just that they fail to accurately describe the entire picture, but that they fail to realize their own failure. Ushered along by the thought that yet-uncertain developments will eventually become known, once investors have some convincing model they can easily begin to operate as if they have already achieved total certainty. Weatherall is not unaware of this problem. While promoting his book, he told the science writer John Horgan in an interview<\/a>, \u201cI think that some economists have been blinded by the rigor of their work: if the mathematics is right, the theories must be true. But the relationship between mathematical theories and the world is more complicated than that.\u201d It would have been nice if he had struck that cautionary tone more often in his book.<\/p>\n

One result of false certainty in models is that the models wind up actively molding the very thing they purport to passively describe. Though Weatherall mentions this only briefly \u2014 and seems to see it as a feature, not a bug \u2014 the sociologist Donald MacKenzie convincingly demonstrated the molding effect of financial models in his aptly titled 2006 book An Engine, Not a Camera<\/i><\/a>. In one example from the 1990s, theorists at the hedge fund Long-Term Capital Management (LTCM) based their models on the efficient-market hypothesis, which holds that markets are good at reflecting available information about pricing. Yet they also exploited arbitrage profits, in which goods are purchased from one market and resold in another where they are priced higher, in contradiction to the efficient-market hypothesis. MacKenzie argues that LTCM\u2019s models forced a certain set of behaviors in other market actors that altered the very conditions upon which the model was based.<\/p>\n

A second fundamental problem in the LTCM case relates to its use of the Black-Scholes-Merton formula. The influence of the formula in finance even today would be difficult to overstate; in the 1990s, it was central to LTCM\u2019s entire system, which is understandable insofar as Scholes and Merton were both on the LTCM board. In order to make the formula work smoothly, its creators had to assume so-called \u201ccontinuous time\u201d in share prices. As Roger Lowenstein puts it in When Genius Failed<\/i>, Black-Scholes-Merton assumed that \u201cthe price of a share of IBM would never plunge directly from 80 to 60 but would always stop at 79\u200a3<\/sup>\u20444<\/sub><\/span>, 79\u200a1<\/sup>\u20442<\/sub><\/span>, and 79\u200a1<\/sup>\u20444<\/sub><\/span> along the way.\u201d Black-Scholes-Merton not only failed to foresee huge price jumps but also minimized their importance, diverting attention away from consideration of what might happen if they actually did occur. Finance failed to see where the assumptions could not<\/i> be applied, because that would have disrupted the model. Irrationality on a large scale, creating the conditions of a feedback loop, did not fit neatly inside a model. So when irrational behavior actually did occur, its effects were amplified by the very rationalist models that had assumed it wouldn\u2019t \u2014 and this combined effect contributed not only to the collapse of LTCM in 1998 but to the financial crisis of 2008.<\/p>\n

S<\/span>o why do these financial models, which are really just elaborate, reductive metaphors, continue to persuade financial professionals? Because they are elegant forms, and the field has been expressly searching for elegant forms that boast explanatory power. Irving Fisher, the famous Yale economist, referred bluntly in the 1940s to \u201cthe goal on which my heart has been most set, the goal of economics becoming a true science comparable with physics.\u201d Finance and economics took up this challenge, reducing a huge swath of human interaction to simplified formulas reflecting utility maximization.<\/p>\n

Economics and finance did not simply evolve to become mathematical: its practitioners set out to make it so. And as in the physical sciences, elegant formulas that explain complex subjects have great persuasive currency among their fallible human users. As the literary theorist Kenneth Burke put it<\/a>, \u201ca yielding to the form prepares for assent to the matter identified with it.\u201d Once economics and finance made it their goal to boast the elegant model form, they assented to the simplified assumptions of that form. They mistook the map for the territory, and still do.<\/p>\n

This mistake pervades finance and economics. We let the Case-Schiller index, a metric of housing prices, stand in for the state of the housing market as a whole, at the expense of paying attention to the plight of defaulting homeowners. We let a narrow index of thirty stocks, the Dow Jones Industrial Average, stand in for the health of financial markets. We let figures like the gross domestic product stand in as true measures of the nation\u2019s economic health despite being rife with well-known flaws<\/a>. We simplify assumptions because it\u2019s easy, and we don\u2019t expand our descriptions because it\u2019s difficult. The trouble is not so much that we cut corners as how steadfastly we fail to realize that we do so.<\/p>\n

These problems with financial models undermine Weatherall\u2019s basic idea of what science is, what it does, and what it should be. In his telling, science gradually moves us from the apparent chaotic disarray of the world to perceiving the world\u2019s underlying order. This is a reasonable description of the physical sciences. But human affairs are messier and involve complicated moral dilemmas. Weatherall, though, seems to think that virtually anything the scientist does is good, and any transformations resulting from scientific work are even better. He sees advancement and progress virtually wherever physicists and mathematicians put pen to stock purchase. His story is one of slow and beneficial infiltration: \u201cquants\u201d (the mathematicians who work on Wall Street) move in to profit from inefficiencies that the old guard is too dim to spot. The scientists are the crusading heroes bringing order to an unruly world.<\/p>\n

Weatherall is also all too hasty to credit science for developments he deems good. In one example, the \u201chighly secretive Chicago firm\u201d O\u2019Connor and Associates spotted a flaw in Black-Scholes-Merton and adjusted its models accordingly, giving it a competitive advantage while largely sparing it from the 1987 crash. In the book\u2019s endnotes, Weatherall says the firm\u2019s success proves that the flaw \u201cdidn\u2019t appear so suddenly after all, if you knew to look for it!\u201d For him, this case constitutes proof that continual scientific refinement and hypothesis-testing can save the day, averting the problems that models produce. But perhaps there\u2019s another explanation: luck. In O\u2019Connor\u2019s case, the firm hired a man who had once worked for Black and so had some inkling of the formula\u2019s flaws. Depending on one\u2019s perspective, this is either a case of scientific refinement or of fortuitous insider information.<\/p>\n

T<\/span>he biggest question that goes unasked in this book is whether this is what we want<\/i> finance to look like. Weatherall emphasizes the good that finance has done for the U.S. economy while giving short shrift to the ills it has created, and claiming that those failures show that finance needs to be more<\/i> like physics rather than less. In the book\u2019s epilogue, Weatherall notes that models underlie all science and engineering, and if we doubt their basic validity, we \u201cshould never drive over the George Washington Bridge or the Hoover Dam.\u201d It\u2019s \u201chard to see why,\u201d he says, finance is \u201ca different kettle of fish from civil engineering or rocket science.\u201d But this is a specious analogy. The engineers who perfect load-bearing formulas for bridges don\u2019t profit from them in the same way that Wall Street quants do. The incentive structure is different. The model underlying the bridge has one purpose: to provide a conveyance for transportation. A trading algorithm has a very different purpose: to earn money for the designer.<\/p>\n

As Adam Smith realized long ago, economics and finance are not context-free mathematical activities in the way an engineering model could be, for they are inescapably bound within human relations. If I am the chief engineer of the Hoover Dam, I might be able to make some illicit money with my model \u2014 perhaps I shift the flow a bit to favor a real estate investment downriver \u2014 but I can\u2019t design the model to exploit an inefficiency in structural dynamics that will enrich me thanks to my hugely leveraged options contracts. The purpose of the model is still to regulate the flow of water and provide a way for traffic to cross. I make money from how well the model conforms to these physical requirements. No matter how much the financial engineers borrow from physics and calculus, their motives will always be fundamentally different from those of physicists and mathematicians. You don\u2019t design models that exploit market inefficiencies for the sake of building an accurate representation of the world; you do it to make money.<\/p>\n

And having made that money, the foundations of your model, and others\u2019 models, are liable to shift. This is the ultimate trouble with pretending we can make finance as robust as physics: while matter is manipulable, the laws governing that manipulation remain absolute. But in finance, the stuff we are manipulating with our abstractions is itself an abstraction, and the laws governing it can themselves be manipulated, accidentally or deliberately. Tweaking the very rules of the game is in fact one of the best ways to win it \u2014 and to wind up destroying it.<\/p>\n

Financial models will forever lack the solid foundations of bridges, but their failure can be even more catastrophic. As we saw in 2008, pensions are dissolved. Jobs are lost. Lives are ruined. Models are not contrivances in a social vacuum; they are simplifications with consequences, hopelessly intertwined with the motives of the designer and existing in a world of greed, dishonesty, and irrationality.<\/p>\n

In a limited sense, Weatherall\u2019s basic mission \u2014 to make our models work better, and to use them to develop new economic tools \u2014 is admirable. But in practice, financial models can leave us unable to see many of the most important aspects of financial markets. And in that blindness lie the roots of catastrophe. Weatherall\u2019s endorsement of \u201can economic Manhattan Project\u201d \u2014 a massive project of \u201ccollaboration between economists and researchers from physics and other fields\u201d \u2014 amounts to a utopian dream to create the heaven of an orderly model in our disorderly world. On the last page of the last chapter of his book, Weatherall claims that, before the 2008 financial crisis, \u201cthere was no one there to point out that the shadow banking system was built on a house of cards.\u201d To Weatherall, the failure was merely an empirical one, for which \u201cmathematical sophistication is the remedy, not the disease.\u201d He does not seem to wonder why the people who couldn\u2019t see the house of cards for what it was were the ones who built it in the first place.<\/p>\n","protected":false},"excerpt":{"rendered":"

Stock trading has become a form of mathematical modeling, with sometimes disastrous results. R. McKay Stangler reviews a new book that claims we need yet more and better models.<\/p>\n","protected":false},"author":1,"featured_media":0,"template":"","article_type":[14],"noteworthy_people":[],"topics":[5007,2266,5008,5004],"_links":{"self":[{"href":"https:\/\/www.thenewatlantis.com\/wp-json\/wp\/v2\/article\/10487"}],"collection":[{"href":"https:\/\/www.thenewatlantis.com\/wp-json\/wp\/v2\/article"}],"about":[{"href":"https:\/\/www.thenewatlantis.com\/wp-json\/wp\/v2\/types\/article"}],"author":[{"embeddable":true,"href":"https:\/\/www.thenewatlantis.com\/wp-json\/wp\/v2\/users\/1"}],"version-history":[{"count":0,"href":"https:\/\/www.thenewatlantis.com\/wp-json\/wp\/v2\/article\/10487\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.thenewatlantis.com\/wp-json\/wp\/v2\/media?parent=10487"}],"wp:term":[{"taxonomy":"article_type","embeddable":true,"href":"https:\/\/www.thenewatlantis.com\/wp-json\/wp\/v2\/article_type?post=10487"},{"taxonomy":"noteworthy_people","embeddable":true,"href":"https:\/\/www.thenewatlantis.com\/wp-json\/wp\/v2\/noteworthy_people?post=10487"},{"taxonomy":"topics","embeddable":true,"href":"https:\/\/www.thenewatlantis.com\/wp-json\/wp\/v2\/topics?post=10487"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}