Actuaries, Stochasticity and Risk Management: The Real Lesson of Long-Term Capital Management

Actuaries, Stochasticity and Risk Management: The Real Lesson of Long-Term Capital Management

A discussion about how outside forces make models inaccurate.
Bob Crompton

Max Rudolph's "ERM As A Competitive Advantage: Moving Beyond PBA to Add Value" (The Actuary, April/May 2007) is an interesting and thought provoking article, but if it is read casually it may give the wrong impression. The reader may come away with the idea that the solution to risk management is simply to develop more sophisticated models. I believe the key to understanding this article is found in the section where Rudolph discusses lurking developments, changing stochastic parameters and events such as the collapse of Long–Term Capital Management. This section is critical because it points to some important issues often overlooked in discussions of enterprise risk management.

Its principals glibly dismissed the collapse of Long–Term Capital Management as a "10 sigma event." This is a patently false and self–serving statement. The real lesson of Long–Term Capital Management is not a lesson in how to rationalize our mistakes. The real lesson is that in a stochastic world our models will be wrong in surprising ways and that the sophistication of our models may blind us to important contingencies. The following statement from a former Long–Term Capital Management executive is enlightening: "Look, when I drive home every night in the fall I see all the leaves scattered around the base of each tree. There is a statistical distribution that governs the way they fall, and I can be pretty accurate in figuring out what that distribution is going to be. But one day I came home and the leaves were in little piles. Does that falsify my theory that there were statistical rules governing how leaves fall? No. It was a man–made event."1

The models used at Long–Term Capital Management were extremely sophisticated models built by extremely bright people. These models were excellent as far as they went. But they did not go far enough. They took no account of the possibility of the leaves being raked into little piles.

Because our understanding is ultimately experience based, there is a danger that we will mistake everything that has been for everything that can be. Although scenario based stochastic models can generate scenarios that have never been observed in real life, these scenarios are qualitatively similar to what we have observed. What if something qualitatively different occurs? What if someone comes along and rakes all of our leaves into piles?

True enterprise risk management incorporates the realization that there are potentialities not yet observed–that no matter how sophisticated our models are, the potential for disaster exists from events not captured by our models.

The ability to conceptualize potentialities not yet observed might be what we mean when we speak of actuarial judgment. So how does an actuary gain an understanding of the potentialities?

Gravity–Not Just a Good Idea, It's the Law!

Gravity and other effects in the physical world arise from the nature of the stuff that makes up our universe. These effects are predictable to a high degree of accuracy and they are inescapable. You can't "break" the law of gravity the way you can break traffic laws.

If all of the stochastic distributions that actuaries were interested in were those arising from the physical realm, our jobs would be easier. But many of the distributions that we are interested in arise from the sociological constructs that we call culture and society. The laws that govern our culture and society are different from the laws that we find in physics. These laws can be broken, bent or changed. And they are not inescapable, that is, we can always find loopholes or another jurisdiction. This ability to go beyond the boundaries also applies to our habits, conventions and mores. These govern more of our behavior than do statutes and regulations. When Alexander the Great solved the problem of the Gordian Knot, he cut it rather than untied it.

Strong motivation enables the ability to find loopholes or bend laws. This was borne–in on me when I was a young product development actuary. One of our home office marketing executives sat me down and explained to me all the ways in which an agent could game the system in order to maximize commissions. I was stunned because the possibilities were so far beyond anything I had considered up to that point.

This leads me to the following saying that I have shamelessly plagiarized from Dr. Samuel Johnson: "Depend upon it, sir, when a man knows he can make a fortune in a fortnight, it concentrates his mind wonderfully."

When our strongest motivations are engaged, it concentrates our minds wonderfully on how we can change or avoid those constraints that keep us from realizing our desires. Therefore, realization of potentialities not yet observed are likely to occur in those transactions where our strongest motivations are involved–money, power, sex, glory and, perhaps, religious fervor. The actuary is qualified by his training to investigate transactions involving the first of these motivations.

The motivation of making a lot of money in a short amount of time can be seen in the blindingly complex transactions associated with Enron. Money motivations as well as political motivations were behind the Russian bond default that triggered the fall of Long–Term Capital.

Our quest for potentialities should focus on those areas of our culture and society where the exercise of human ingenuity can result in significant augmentation of wealth (or one of the other satisfiers of our desires).

Actuarial Science–Prophecy or Hocus–Pocus?

It seems at first glance that the most an actuary can do is to identify potentialities. Predicting when they will happen or even assigning probabilities to the potentialities seems to be in the realm of prophecy rather than actuarial science.

But there may be some actuarial strategies that will give us some insight. If we can identify a sufficient number of these critical events–these "leaf raking" episodes–and if we can classify the significant features of culture and society at the time of the critical event, we may be able to identify commonalities. These commonalities would then serve as concurrent indicators, or possibly even leading indicators of the high potential for another critical event. This is the sort of analysis for which neural networks were made. Neural networks are trainable systems that can "learn" to solve complex problems from a set of examples and then generalize to solve unforeseen problems. Neural network analysis may lead to some interesting and valuable insights into critical events.

Or maybe not. Maybe stochasticity is too deeply embedded in life for us to make any headway. Choose your metaphor:

  • Stochasticity is like a rain–bow–it recedes from us just as fast as we approach.
  • Stochasticity is like a waterbed–you can push a bump down, but it will just pop up somewhere else.
  • Stochasticity is like a donut. I don't really know how stochasticity is like a donut, but it ought to be, somehow.

Maybe the best thing we can say about this approach is that we should do it so our competitors don't know more than we do.

There is a flip side to stochasticity. If stochasticity implies the potential for disaster, it also implies the potential for serendipity. This is why genius is 90 percent perspiration. In order to reach serendipity, we have to be experimenters, tinkerers, people who are always wondering, "What if I do this instead?" Thomas Edison may not have been trained in stochastic science, but he was convinced that if he tried enough different things, he would eventually find something new.

The flip side of enterprise risk management might be termed enterprise enhancement management. The goal of enterprise enhancement management is to reach serendipity by institutionalizing experimentation and tinkering. Because we cannot predict when or where potentialities not yet observed will occur, experimentation and tinkering needs to be implemented in all areas of the enterprise: product, distribution, finance, organization, management and human resources.

If neural network analysis provides any guidance on risk potential, it may also provide guidance on serendipity potential.

It may be that we live in a world where all the distributions that are interesting to actuaries are ill–behaved. If so, this is the worst possible world for actuarial models and projections. On the other hand, it just may be the best possible world for serendipity.

Bob Crompton, FSA, MAAA, is a consulting actuary for Actuarial Resources Corp. He can be contacted at

Footnotes: 1"Blowing Up" by Malcolm Gladwell, New Yorker, April 22 2002.