Commentary Magazine

Physics and Finance

To the Editor:

Jeremy Bernstein’s “The Einsteins of Wall Street” [September] gives a dramatic account of the mismatch between the theories of quantitative finance and the achievements of those theories in practice. My book My Life as a Quant, which Mr. Bernstein refers to, was written in part to explain the limited (but not negligible) efficacy of the techniques of theoretical physics in finance.

When I started working on Wall Street twenty years ago after a career as a theoretical physicist, I simply assumed it made sense to apply the techniques of physics to financial modeling. Why should differential calculus and Fourier series not be as appropriate for describing the movements of stocks and yield curves as they are for particles and electromagnetic fields?

After several years in the hurly-burly world of securities trading, my naiveté faded. In physics, a model can come so close to describing reality as to be almost indistinguishable from it. In economics, any model is merely a toy. Physics is not “better”; finance is simply harder. In physics you are playing against God, Who does not change His laws very often. In finance you are playing against God’s creatures, who value assets based on their ephemeral opinions. A financial theorist is ultimately trying to represent how people think.

Still, financial models can be useful. I like to think of them as analogues of the gedanken (thought) experiments used by physicists in the early part of the 20th century. These were imaginary investigations, a sort of mental stress-testing of the physical world, conducted in one’s head because they were too difficult to do in practice. Their aim was to force a conceptual picture of the world into a contradiction. Einstein imagined what he would see while sitting on the edge of a moving light beam in order to gain insight into the contradictions between the Newtonian description of matter and Maxwell’s description of light.

In this spirit, financial models should be viewed as a collection of parallel thought universes you can explore. Each individual universe should be consistent, but the world of finance and people, unlike the world of matter, is infinitely more complex than any model you make.

The appropriate way to engage with a model is with an initial dose of hubris: temporarily suspending disbelief and pushing the model as far as possible. But then, you must remember that you are only theorizing. Catastrophe strikes when theories take on a life of their own and hubris evolves into idolatry.

Emanuel Derman

Columbia University

New York City


To the Editor:

I hope Commentary’s readers came away from Jeremy Bernstein’s article with a better appreciation for what all those articles about “risky derivatives” are about; derivatives are sufficiently important to modern finance that greater public understanding is certainly desirable. But I am a bit disappointed that Mr. Bernstein focused on derivatives modeling as the cause of the collapse of Long Term Capital Management (LTCM). The LTCM debacle was fundamentally about a failure of risk-management. As such, it was a cultural failure rather than a scientific one.

Pricing models do not tell the “true” value of a derivative instrument. What they do is transform the problem of pricing into the problem of predicting a factor that determines pricing.

Based on the assumption that, in ordinary market conditions, stock-price returns form a normal distribution, the Black-Scholes formula reduces the price of a stock option to a variety of observable and hedgeable factors (stock price, prevailing interest rate, etc.) plus one unobservable and—except with another stock option—unhedgeable factor: future stock volatility.

But isolating this factor is not the same as knowing its value. The market’s estimate of future volatility can be as erratic and as wrong as its estimate of anything else. The estimate of future volatility as implied by option prices can fluctuate as much as stock prices themselves.

Everyone at LTCM certainly understood this, and the company did not lose vast amounts of money because it mis-modeled securities—something other dealers have done, at a steep cost. Rather, the problem for the team at LTCM was managing risk. They did not rigorously stress-test their positions, which might have helped them anticipate that all their positions could go against them at once in a distressed market.

And they ignored their own impact on the market. Other market participants knew LTCM’s reputation and also something of its strategy. Many went after the same trades, attempting to piggy-back on LTCM’s vaunted genius. LTCM should have realized that, if it were ever squeezed and forced to sell, few others would have an appetite for taking on its losing positions.

None of this relates to whether derivatives modeling is a good or bad approximation of the real world. If LTCM had had independent, professional risk-management, it could have used the same models to identify trades but without running such an extraordinary amount of risk in executing them.

Two other points are worth airing. Mr. Bernstein mentions in passing that there have been proposals to regulate hedge funds and derivatives, but he does not give any details about these proposals or weigh their potential effects. Lack of transparency in the derivatives market was a major contributor to the LTCM catastrophe. To some extent the market has self-regulated to solve this problem, but it is worth further discussion.

Finally, Mr. Bernstein asserts that LTCM’s collapse was more serious than Enron’s or WorldCom’s in terms of its impact on the financial system. I cannot agree. LTCM triggered a panic, but it was quickly quelled, leaving no lasting damage. Alan Greenspan did just what J.P. Morgan did in the panic of 1907: he got the major players together and brokered a deal that ended the crisis. The system was fully able to absorb LTCM’s losses, once everyone was secure that he alone would not be left holding the bag.

By contrast, Enron and WorldCom did major harm to the American economy. After seeing the amazing gains Enron and WorldCom were making by trading subsidiaries and investing heavily in broadband and other next-generation telecom services, other companies began to emulate them—and did so with borrowed money.

When it came out that both companies were towering frauds and not making any money at all, not only were the direct losses from their bankruptcies bigger than the losses sustained by LTCM, but the revelation that many other utilities and telecom companies had business models that were built on fraud triggered numerous bankruptcies and near-bankruptcies.

Noah Millman

Brooklyn, New York


Jeremy Bernstein writes:

I appreciate Emanuel Derman’s letter, written with the same grace and clarity as his book. Noah Millman’s thoughtful argument deserves a response by other financial experts and not by a theoretical physicist. In reading about the LTCM disaster, I, at least, was struck by how close a call it was. Others might have the impression that Alan Greenspan was some sort of philosophical Svengali who got the disparate parties to reason together; to me, it seemed more like herding pigs at a trough. Only at the last minute was a deal brokered that kept the entire marketing system from collapsing. Common sense tells me that these funds should be regulated.

Let me enter a correction and an addendum to what I wrote in Commentary. The correction: my meeting with Myron Scholes happened as I said it happened, but not when; in reconstructing the occasion, I confounded some dates. The addendum: the first person to do the sort of financial engineering that formed the subject of my essay was a French mathematician named Louis Bachelier, in the faraway year of 1900(!). I have explored Bachelier’s work in an article to be published elsewhere.



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