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The Interdisciplinary Quest for New Ideas in Economics

By James Case

BOOK REVIEW: The Physics of Wall Street: The History of Predicting the Unpredictable. By James Owen Weatherall, Houghton Mifflin Harcourt, New York, 2013, 304 pages, $27.00.

Anyone wishing to understand the world of finance must be aware of the role that mathematical models now play in it. Twenty years ago, Peter Bernstein’s instant classic Capital Ideas: The Improbable Origins of Modern Wall Street was the place to learn. But because financial thinking and practice continue to evolve, the story requires periodic updating. Weatherall’s ambitious new book begins with an attempt to fill this need.

Several of the early chapters (particularly the third and sixth) summarize material described elsewhere at book length. The third describes the life and times of the late Benoît Mandelbrot, who covered much of the same ground several years ago in a book [3] written with Richard L. Hudson, and whose autobiography [2] has since appeared. The sixth is a brief history of the Prediction Company of Santa Fe, New Mexico, which has been the subject of at least one full-length book [1]. Although the firm’s original workforce—including founders Doyne Farmer and Norman Packard—has long since moved on, “Predco” remains an active (and perhaps wildly successful) subsidiary of UBS, the Union Bank of Switzerland.

It is difficult to gauge the degree of Predco’s success because—perhaps in an effort to discourage imitation—man-agement has chosen to remain secretive about the firm’s actual earnings. The best assessment Weatherall could elicit is a quote from a “knowledgeable source” to the effect that, over the firm’s first 15 years, “its risk-adjusted return was almost a hundred times larger than the S&P 500 return over the same period.” If so, the firm’s performance compares favorably with Warren Buffett’s at Berkshire–Hathaway, or Ed Thorp’s at Princeton–Newport Partners, though none of the three (according to Weatherall) can match the achievement of James Simons’s Renaissance Technologies.

James Simons graduated from MIT in 1958, completed his Berkeley PhD (under S.S. Chern) in 1962, and worked as a code breaker at IDA during the run-up to the Vietnam war. He became chair of the Stony Brook mathematics department in 1968, and received the 1976 AMS Oswald Veblen Prize in Geometry, largely on the strength of the book Characteristic Forms and Geometrical Invariants he co-authored with Chern. The theories presented lie at the forefront of theoretical physics, especially string theory. In 1982 Simons took leave of academic life to found Renaissance Technologies, a hedge fund management firm that uses computer modeling to find inefficiencies in highly liquid securities. Its flagship product, the Medallion Fund, is a high-risk high-return vehicle in which only the firm’s executives may invest. It regularly outperforms the firm’s other funds, which are open to outside investors. According to Weatherall, Renaissance employs many mathematicians and physical scientists capable of understanding and improving the algorithms on which the firm relies, but no one trained in finance or economics. In 2006, Simons was named Financial Engineer of the Year by the International Association of Financial Engineers.

Benoît Mandelbrot is a central character in the book, due in part to his admiration for Louis Bachelier—the founder of mathematical finance and, arguably, of the entire theory of stochastic processes—which caused him to ferret out much of what is known of Bachelier’s family background and early years. But Mandelbrot is significant mainly, at least in Weatherall’s eyes, as a skeptic who warned tirelessly of the perils of over-reliance on derivative securities evaluated in a “Black–Scholes environment.” In that environment, all stochastic processes are Gaussian normal processes, which exhibit significantly fewer extreme variations (either extremely large or extremely small) than do the historical price series they are intended to model. So it is hardly surprising that derivatives evaluated in such an environment appear less risky than they really are. Mandelbrot championed the substitution of “Levy-stable distributions,” a one-parameter class that includes the slender-tailed normal distribution (for parameter value \(\alpha = 2)\), the fat-tailed Cauchy distribution (for \(\alpha = 1)\), and an entire continuum of intermediate distributions for intervening values of \(\alpha\).

Mandelbrot was not alone in observing the inadequacy of valuations performed in a Black–Scholes environment. The highly secretive firm O’Connor and Associates was founded in 1977 to exploit opportunities then becoming available on the newly opened Chicago Board of Trade. Realizing that the assumptions underlying the Black–Scholes formula were a first approximation at best, the founders set out to develop—in collaboration with first-generation quants Michael Greenbaum and Clay Struve—a modified Black–Scholes model that would be able to account for the sudden and dramatic price changes that can lead to fat-tailed distributions. The firm was famously successful, first in options and later in other types of derivatives, in part because their modification of the Black–Scholes model tended to outperform its parent.

The true worth of the O’Connor model went undemonstrated until the stock-market crash of 1987, during which the S&P 500 index lost more than 20% of its value in a single afternoon. By anticipating the conditions under which the Black–Scholes model would fail, the firm not only survived but prospered. By 1992, it was among the largest players on the Chicago commodities market, with more than 600 employees and billions of dollars under management. Around that time, two O’Connor associates became aware of Predco, and persuaded their partners to invest in it. Whereas Farmer and Packard had rejected other suitors, they welcomed acquisition by O’Connor and Associates, in part because they needed the money to increase the scope of their operations, and in part because the acquiring firm seemed technically sophisticated enough to understand what they were up to. The deal was unexpectedly sweetened when, later in 1992, O’Connor was purchased outright by the giant Swiss Bank Corporation, and sweetened again when (in 1998) SBC merged with the even larger UBS.

The algorithms brought by Farmer and Packard to the analysis of financial data began as data-mining techniques designed by physicists like themselves to find small islands of predictability amid the vast oceans of apparently patternless variation characteristic of chaotic time series. By allowing different algorithms to operate simultaneously on the same data stream, and to “vote” on proposed trades, they were frequently able to identify opportunities worth pursuing. They were thus among the first to employ the “black box” and “algorithmic” trading methods on which the hedge fund industry has come to rely.

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The last three chapters in the book are the ambitious ones. The first of the three describes, in decidedly nontechnical language, Didier Sornette’s efforts to discover warning signs that might predict impending catastrophes. One of Sornette’s earliest projects involved ruptures in the high-pressure Kevlar tanks in which rocket fuel is sometimes stored during space flight. Such tanks performed admirably most of the time, but had a distressing tendency to explode, on rare occasions, without warning.

Lab tests revealed that, under pressure, the tanks routinely developed microscopic fractures that sometimes grew, by connecting with other fractures, to potentially dangerous size. Even the smallest fracture could potentially do this, much as liquids can sometimes percolate through marginally porous media. Sornette and his colleagues noticed that the tanks would begin to “rumble” as fractures began to appear, and that if the intervals between rumblings became “log-periodically” shorter—meaning that the peaks and valleys were roughly coincident with those of a function of the form \(\mathrm{cos}(\omega~\mathrm{log} (t_c – t))\)—a critical event was likely to occur at or about the critical time \(t_c\).

Later, in collaboration with his wife, Anne Sauron-Sornette, a geophysicist, Sornette observed that a sequence of small earthquakes is more likely to presage a large one if the intervals between the small ones become log-periodically shorter. And in the summer of 1997, in collaboration with friend and management scientist Olivier Ledoit, he observed log-periodic fluctuations in various stock market indices. The two responded by buying up a host of cheap “far-out-of-the-money” put options, entitling them to sell the underlying securities in October at August and/or September prices. When the Dow fell 554 points on Monday, October 27, and both the NASDAQ and S&P 500 indices dropped by comparable amounts, the two earned a 400% profit and documented the fact by releasing their Merrill Lynch trading statement. Sornette makes no claim that all catastrophes can be predicted in this way. But some of them obviously can, and the rewards for so doing are often substantial.

Weatherall’s penultimate chapter concerns a second husband–wife team, consisting of mathematical physicist Eric Weinstein, now a hedge fund manager and financial consultant in Manhattan, and economist Pia Malaney. At Weinstein’s suggestion, Malaney wrote her Harvard thesis on the applicability of gauge theory to the construction of economic indices, such as the NASDAQ, the S&P 500, the Dow, and (especially) the Consumer Price Index. The CPI is particularly important to ordinary citizens, as a variety of pension, health care, and Social Security benefits are adjusted annually to keep pace with the CPI. Gauge theory has not caught on in the economics community, despite the prominence and support of Malaney’s thesis adviser, Eric Maskin (a 2007 Nobel laureate). Yet Weinstein remained convinced that the idea has merit, and eventually persuaded Lee Smolin, a physicist at Canada’s Perimeter Institute (and author of a book titled The Trouble with Physics), that the proposal deserved a hearing.

Smolin responded by organizing a conference, held at Perimeter in 2009, and attended by physicists, mathematicians, biologists, mainstream economists, and financiers. His hope was to persuade all in attendance that economic theory is inadequate and in need of an extensive overhaul. Furthermore, he believed, nothing less than a giant research effort—on the scale of the World War II-era Manhattan Project—could reasonably be expected to produce the necessary revision. The conference itself, Weatherall writes, was quite successful. Those in attendance readily agreed that economic theory is inadequate. They failed, however, to reach consensus as to where the key deficiencies lie or how to fix them. Then too, lurking in the background, was the funding problem. How, if it were even possible to obtain support for something as vast as a new Manhattan Project, would the funds be split among cooperating disciplines? In the absence of any assurance that theirs would get its due, attendees lost interest and returned to their accustomed activities. Even Smolin has gone back to doing physics, having apparently decided that economics is a waste of scientific resources. Though economic problems seem reasonably tractable, he found the economics profession hostile to new and unfamiliar ways of thinking!

Today, Weatherall writes, even as Weinstein, Malaney, Sornette, Farmer, and a handful of others continue to develop nontraditional economic models, the world economy remains a shambles. The so-called recovery from the collapse of 2007–2008 lags far behind schedule. What, he asks, can be done to expedite real recovery and delay the next recession? His answer appears  in the book’s final chapter “Epilogue: Send Physics, Math, and Money!” The world, he submits, needs new and more fruitful economic ideas. To discover them, he sees no alternative to a monumentally large, copiously funded, interdisciplinary research initiative. Good luck selling that inside the beltway!

[1] T.A. Bass, The Predictors, Allen Lane, New York, 2000.
[2] B. Mandelbrot, The Fractalist: Memoir of a Maverick Scientist, Pantheon, New York, 2012.
[3] B. Mandelbrot and R.L. Hudson, The Misbehavior of Markets, Basic Books, New York, 2004.

James Case writes from Baltimore, Maryland.

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