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Power Laws & the New Science of Complexity Management

It is possible to deal with extreme financial risks in a more considered way. “LTCM’s risk management was appalling,” says statistical physicist Jean-Philippe Bouchaud, CEO of the Paris-based hedge fund Capital Fund Management (CFM). CFM relies on ideas from physics to take power-law fluctuations explicitly into account when building investment portfolios and when calculating VaR. Typically, the contract between a hedge fund manager and an investor states that the latter has a 1 percent chance of losing something like 10 percent of the total invested value. The manager has to make sure that this estimate of 10 percent is realistic. “The power law is much better than the bell curve at establishing this risk,” says Dr. Bouchaud. It is also better at helping hedge fund managers avoid the painful consequences of “unexpected” fluctuations.

Over the past decade, physicists have been instrumental in drawing attention to the power-law character of financial returns and its implications. “Physicists have taken the fat tails seriously,” says Doyne Farmer of the Santa Fe Institute, another pioneer in the study of complexity. Physicists have also explored power-law implications in other areas such as portfolio optimization and option pricing. But this “heads-up” approach to extreme fluctuations has yet to penetrate to the core of international finance. Partly in response to the LTCM debacle, the Basel II accord on international banking, currently under development, will require financial institutions to set aside larger capital reserves to protect against surprises.

Unfortunately, the analysis behind these guidelines remains firmly based on the bell curve. “They just add a large fudge factor at the end,” Dr. Bouchaud complains. It would be more appropriate, he suggests, for the empirical reality of market fluctuations — as captured by the power law for financial returns — to be incorporated in the analysis of banking risk from the outset.

The insurance industry is facing a similar challenge to reorient itself toward discontinuity risks. Chris Barton, a research geologist with the U.S. Geological Survey, has studied insurance losses due to extreme weather events. If these followed the bell curve, then insurance companies would legitimately be able to estimate future claims on the basis of an average over past claims. But the data for extreme weather events instead shows a power law — extreme losses are far more common than one might expect. In one such event, in August of 1992, Hurricane Andrew smashed through southern Florida and Louisiana, creating insured losses exceeding $16 billion and total losses of more than $30 billion, even though the worst part of the storm missed Miami. This one event bankrupted several insurance companies and significantly depleted the insurance capital available for natural catastrophes.

Several experts have concluded in a review of the situation that “the basic assumptions underpinning most of the insurance industry are violated by the laws of nature that apply to climate and tropical cyclones.” The bell curve does the job with automobile insurance and other risks that reflect independent events, but it fails miserably when assessing large catastrophic losses due to hurricanes and earthquakes. Like the financial industry, however, the insurance industry is learning to plan for dramatic discontinuities. New financial instruments such as catastrophe bonds now help to spread risk into the capital markets, where resources are adequate to cover the potentially massive losses — as high as $100 billion — associated with a hurricane hitting a major city in the U.S.

Dealing with Discontinuity
Even in situations where a power law is not clearly evident — as in most real-world business settings — one can expect abrupt discontinuities to define the rhythm of the unfolding future. Many executives recognize that the greatest risks they face are those associated with these singular events — with the sudden loss of a major earnings driver, market destabilization linked to new technology, or unexpected governmental regulation. Successful companies have learned how to manage and prepare for discontinuities and recognize that these events also offer opportunities, as their competitors may take a big hit.

 
 
 
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Resources

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