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08/26/2010

In Defense of a Quant (Part I)


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The public likes simple explanations, especially if they are argued with bombast. For instance, the financial crisis happened because “the young boys with PhDs in physics were conceiving a financial hydrogen bomb” (attributed to F. G. Rohatyn of Lazard Fréres). To me, it sounds like “the laws of fluid mechanics sunk the Titanic.” This is literally true, of course, but the substantive reason was much more mundane (and universal): hubris and the human propensity to throw all caution to the wind—literally and idiomatically—when big money is involved.

Among popular stories of the Wall Street collapse, which one sees on TV or bookstore shelves, some are especially persistent:

 

  • First, the existing financial models are too simplistic to describe the markets. Particular abuse is hurled at VaR, value at risk, as a supposed method of organized deception.
  • Second, the quantitative models systematically underestimate the risk inherent in portfolios.
  • Third, mathematical approaches are, in general, unsuitable to describe such complex systems as financial markets.
  • Fourth, there are nefarious instruments called “derivatives,” which supposedly played a major role in the market collapse of 2008–09.
  • Fifth, all mainstream economists and financiers missed the signs of impending financial turmoil.

 

Some of these arguments are philosophical; others require more technical discussion. Let us start with the first—how the mathematical models relate to reality. Nassim Taleb writes in The Black Swan: “Minutely small uncertainty, at the level of the slightest parameter, might, because of nonlinearities, percolate to a huge uncertainty at the level of the output of the model … Even if we had the right model (which we, of course, don’t), a small change in one of the parameters, called calibration, can entirely reverse the conclusions.”1 Then he goes on and on, demolishing VaR, Greeks, and the rest of stuff conventionally called quantitative finance.

I agree that VaR metric is a rather simplistic method to look at market risk. However, if the right honorable gentleman peeks into a textbook of fluid mechanics for civil engineers, he may realize that the students are typically required to do exercises with the pipes of uniform width, stationary flows, and perfectly circular connectors. Following the logic of the above-cited bestseller, we have to wait for a comprehensive model taking into account the molecular motions, rusting of tubes, solid matter in flows, transient processes at switching faucets on and off, and all the way up, to the full geophysical description of Mississippi with all its tributaries, dams, and locks. Even the harshest critic of quantitative approaches cannot postpone using his toilet that long. If I tell chary readers of older generations that the computational aerodynamics learned to simulate structures more complex than an infinitely long wing in a stationary flow—practical enough for you?—only on the eve of 1980s, when the Jumbo jets already plowed the sky, especially sensitive ones can faint.2

In fact, all models are simplified descriptions of real life situations. That’s why they are called models. Models can not be substituted for a common sense and trial-and-error type experiments.3

Let me recite a stylized, but real, business situation in which I was involved. The managers of a start-up trading firm decided to sell short a rather exotic commodity and asked the analyst to produce volatility estimates, to determine whether the risk was worth it or not.4 In vain, the analyst pleaded to the superiors to let her/him address the “deciders” and explain that no trade should be executed on the basis of quantitative analysis alone without an underlying business purpose.5 The analyst was told to produce the numbers and not to raise questions above his/her pay grade. Of course, the short sale went through and the amount of money, relatively large for the start-up, was lost. Guess, whom managers blamed for the “wrong numbers” and the debacle—themselves or the risk department?

Indeed, no amount of high-tech wizardry can make sound an unsound business model. But this, rather trivial, conjecture has nothing to do with deficiencies of the normal distribution, VaR, and copulas—and everything with greed and hubris—as does the sinking of the big ships.

 

–Peter B. Lerner, MBA, PhD is a semiretired financial researcher currently teaching one business class in Manhattan and residing in Ithaca, NY. The second, more technical, installment of this article will appear if the author survives his planned trip to Moscow in mid-September.

 

1. It obviously never occurs to him that mechanical chronometers, expensive toys so beloved by the Wall Street, are one of the most nonlinear devices one can imagine. Yet, their movement is quite regular, despite or because of the nonlinearities involved in their operation.

2. I also challenge critics to browse the copy of R. Serber’s The Los Alamos Primer written in 1942 to bring new arrivals at Los Alamos up to speed on how to build a nuclear bomb. None of it uses math above a level of the first/second year undergraduate in technical disciplines. But alas, the likes of R. Oppenheimer and H. Bethe simply knew what they were doing, not just mindlessly crunching numbers.

3. Three olden books are especially instructive in this respect. First, is Henri Poincaré’s The Value of Science and Science and Method, written on the eve of the 20th Century but still a classic. Poincaré, one of the greatest mathematicians of his time, participated in the birth of mathematical finance by the merit of being an adviser of Louis Bachelier, who discovered most of what is now known as the Black-Scholes theory in his 1900 PhD dissertation. Ironically, Nassim Taleb, while dedicating so much space to the discussion of Poincaré own work on qualitative theory of differential equations, avoids his insight on the connection between theoretical formulas and empirical reality. Another book is Robert Feynman’s The Character of Physical Law. Feynman invented the celebrated Feynman-Katz formula, which is the basis of many proofs and computational devices in quantitative finance.

4. Some commodities like environmental permits tend to hover at near-zero prices for prolonged periods of time. Hence, a risk-neutral estimate for an American put should produce a number close to the strike price independently of the pricing method.

5. The caveat to this author’s statement is that it refers to the “real business”, i.e. the business that has customers. Maverick speculators can do what they wish.


As an impartial, nonprofit forum for the finance and banking industries NYSSA encourages discussion and debate among its member and other professionals. Commentaries, however, should be taken as the sole opinion of the author(s) and not of NYSSA. If you would like to submit a commentary to the Finance Professional's Post, send your article to the editor.

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Very nice article

Very good article.

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