"Tail Risk," Economists' Predictions, and Credit-Default Swaps

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There is much criticism of the banking industry for having failed to take account of "tail risk." The reference is to parts of the normal distribution and of variants such as the student t distribution. These probability distributions form a bell-shaped curve. The ends of the bell, or "tails" of the distribution as they are called, denote very small probabilities. If the mean of a normal distribution is 500 and the standard deviation from the mean is 100, then 99.7 percent of the observations comprising the distribution will fall between 200 and 800, and hence fewer than one-third of one percent of them will be smaller than 200 or larger than 800.

The probability, say in 2005, that there was a nationwide housing bubble that would burst and drive the banking industry into a condition of near insolvency (indeed, without the bailouts, the banking industry might have been insolvent) was small--a "tail risk." And we are told that the industry was "reckless" to fail to take precautions against such a risk.

Yet recently a distinguished macroeconomist at Northwestern University, Robert Gordon, has predicted that the current depression will bottom out either this month or next, without worrying about tails. On May 1 he wrote that he had

discovered a surprisingly tight historical relationship in past US recessions between the cyclical peak in new claims for unemployment insurance (measured as a four-week moving average) and the subsequent...trough...It is always too early to make definitive conclusions, but the recent 2009 peak in new claims looks sufficiently similar to previous recession peaks to allow a conclusion that it is highly probable that the new claims peak has now occurred...My reasoning leads me to conclude that the ultimate...trough of the current business cycle is likely to occur in May or June 2009, substantially earlier than is currently predicted by many professional forecasters.

His prediction is based entirely on past data. It is an exercise in induction. It therefore assumes that the future will be like the past. Maybe so. But there is a "tail risk" that the future will not repeat the past, and he makes no effort to estimate it. How could he? History is not a normal distribution.

Just to speak of "tail risks" is to prejudice a sensible assessment of the bankers' behavior leading up to the crash. The idea of statistical "tails" is associated with the normal (or closely related) distributions, in which tail risk is a quantitative probability, as in my earlier example. The risk of an economic collapse, like the risk of a terrorist attack or of an attempt to assassinate the Pope, cannot be quantified. It belongs to the realm of uncertainty, when "uncertainty" is used to denote a risk that is not calculable.

As Keynes famously wrote, the "urge to action" induces businessmen to take noncalculable risks. It induced Professor Gordon to predict when our current economic downturn will reach its nadir. And it motivated, and motivates, risky lending.

Which brings me to the criticism of American Insurance Group and other issuers of credit-default swaps for having failed to maintain adequate (in A.I.G.'s case any) reserves. Credit-default swaps are unregulated insurance contracts, insuring businesses against losses due to defaults. When the international banking system collapsed last September, the number of defaults exceeded the ability of A.I.G. to honor its obligations, and the government bailed it out, to the tune, eventually, of almost $200 billiion. The credit-default swap market as a whole, however, functioned throughout the crisis quite well.

Should A.I.G. have had reserves? Probably. But they would have been overwhelmed by the financial crisis. Insurance companies cannot be required to have reserves (or reinsurance backed by reserves) against risks that cannot be estimated and if they materialized would cause a global depression or some equivalent catastrophe. If a nuclear attack killed 50 million Americans, the entire life insurance industry would be bankrupt, but the industry would not be criticized for having failed to maintain adequate reserves against such an eventuality.

The responsibility for preventing, or remedying, disasters that transcend the capabilities of the private market is a governmental responsibility, which our government failed to discharge. I continue to be perplexed by how government has managed to escape most of the blame for our current economic state.

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Richard A. Posner

Richard Posner is an author and federal appeals court judge. He has written more than 2500 published judicial opinions and continues to teach at the University of Chicago Law School. More

Richard A. Posner worked for several years in Washington during the Kennedy and Johnson Administrations. He worked for Justice William J. Brennan, Jr, the Solicitor General of the U.S., Thurgood Marshall, and as general counsel of President Johnson's Task Force on Communications Policy. Posner entered law teaching in 1968 at Stanford and became professor of law at the University of Chicago Law School in 1969. He was appointed Judge of the U.S. Court of Appeals for the Seventh Circuit in 1981 and served as Chief Judge from 1993 to 2000. He has written more than 2500 published judicial opinions and continues to teach at the University of Chicago Law School. His academic work has covered a broad range, with particular emphasis on the application of economics to law. His most recent books are How Judges Think (2008), Law and Literature (3d ed. 2009), A Failure of Capitalism: The Crisis of '08 and the Descent into Depression (2009). He has received the Thomas C. Schelling Award for scholarly contributions that have had an impact on public policy from the John F. Kennedy School of Government at Harvard University, and the Henry J. Friendly Medal from the American Law Institute.
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