Essentially all "insurance" is tail-stuffing. When you purchase insurance, you pay a modest premium which covers your losses (typically up to some maximum limit), which insurance eliminates your losses during the period of coverage (at least until you reach the maximum limit). In some cases where the probability distribution function is well-understood and the tail can be integrated -- e.g., a "normal" distribution -- then one could conceivably remove the need for a maximum limit, since the probability of achieving an event of many, many sigmas away from the mean would be less than 1/the number of elementary particles in the universe. Since most of us believe in thermodynamics, we know that while it is theoretically _possible_ for all of the air molecules in the room where we reside to group into one small corner, leaving us to suffocate, the likelihood of this happening exceeds a large number of lifetimes of the universe. So truly normal curves are pretty safe bets. A party which "writes" insurance integrates the most likely portion of the distribution curve, includes a profit margin, and that becomes the basis for the premium; the insurance writer also includes the integration limits as its maximum limits in the insurance policy. Insurance writers often write insurance whose limits are too large for them to handle. In these cases, they will "reinsure" the portions of the tail that they are still on the hook for with another party. If reinsurers do their homework, they make sure that the risks they are being asked to insure are uncorrelated. However, this is really, really hard to discover. An analogy is in order. A company wishing to have redundant fiber optic communications between New York and Boston will go to a lot of trouble to purchase fiber from two different companies. However, they may have no way of knowing that both companies route their fiber through the same physical bridge in Connecticut. A gasoline truck hits the bridge & burns it down & wipes out both fibers. (This is a true story.) As reinsurance gets passed through more & more levels, it becomes impossible to know or find out exactly what correlations there are between policies. A number of reinsurers were wiped out in the 1980's in this way. AIG became a big writer of insurance on debt defaults -- so-called "credit default swaps" (none dare call it "insurance", since that would put these derivatives under the control of a different regulator who actually did understand insurance, and would have required much higher reserves) -- and due to AIG's size, there wasn't anyone else big enough to purchase reinsurance from. But because of the number, size and connectedness of AIG's customers, AIG became TBTF (too big to fail), and de facto put a number of govts on the hook as the reinsurers of last resort. We know in hindsight that the premiums AIG received were probably far too low to cover even their foreseeable risks, much less the really fat tail risks. And those fat tail risks should have required far higher reserves to cover them. For example, some special purpose companies (by definition "limited liability") were capitalized with something like $1-2 million, and proceeded to write insurance on billions of dollars of debt. The folks at Goldman Sachs, et al, try to achieve an essentially "neutral" position every evening, so if the overnight markets either go up or down sharply, they won't take losses from movements in either direction. GS et al utilize huge computers & lots of clever people to try to minimize the correlation of all of their bets, and buy & sell derivatives to achieve these ends. If their models are good & their software is accurate, they minimize risks to themselves and pass that risk onto their counterparties, who also try to do the same thing for themselves. Since each party is trying to insure itself against losses, it builds up a web of interconnected counterparties who are all tied together, like mountain climbers with rope. If any one climber loses his footing, the rope to the others will easily hold his weight & he is saved. However, if a large enough subset of climbers all fall at the same time, their sheer bulk will take down the remainder. The only solution is to have the rope tied to a much more massive object -- e.g., the mountain itself, or more likely Uncle Sam. But Uncle Sam didn't realize he was on the hook for these potential losses, and didn't charge any insurance premium at all. At 05:30 PM 2/4/2010, Dan Asimov wrote:

Having worked for 4 years as a rocket scientist in high finance myself (which apparently qualified me for my next job -- at NASA), I don't think that's how it works.

The fact is, no one knows how to estimate those risks, even close. As most people know, probability applies to the real world only in special cases. The status of financial markets is constantly changing over time, in different statutory and regulatory and economic environments, most of which have never been seen before. Smart quants will make their best effort to model risks accurately, but no one really knows how to do it.

The blame, IMHO, belongs to the people directly above them, who give them their marching orders and who are or should be well aware of the impossibilty of quantifying risk, or even quantifying the error in the best estimates of risk.

--Dan

<< The math wizards of Wall Street are employed at enormous salaries to do "tail-stuffing", wherein all minor risks (i.e., those that might reduce their bonuses) are pushed down into the probability distribution "tail", where the probability remains low, but the expected value is significantly increased. Net result: nice (more-or-less) smooth privatized profits, with state-subsidized catastrophic losses. "I be gone, you be gone, we all be gone".

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