A loss quantile such as value at risk does not specify the severity of losses beyond that quantile, and a capital assessment that ignores dependence can miss the damage from repeated crises.

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Fortunately, bankers and regulators now realize the system is flawed, so the world's central banks have been pushing for more sophisticated risk models, one gaining popularity based on something called extreme value theory and borrowed from the insurance industry, is on the right track. It assumes prices very wildly, with fat tails that scale. But it does not commonly take account of a further source of risk I have been describing, long-term dependence, or the tendency of bad news to come in flocks. A bank that weathers one crisis may not survive a second or a third. I thus urge the regulators, now drafting a new Basel Capital Accord to regulate global bank reserves, to encourage the study and adoption of yet more realistic risk models. If they do not, Summers' list of six crises will just keep growing. It is gratifying to find I am no longer alone on this point.

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That means you want to structure your bank's investments so there is, by your models, a 95% probability that the losses will stay below the danger point, and only a 5% chance they will break through it. To use an example suggested by some Citigroup analysts, suppose you want to check the risk of your euro-dollar positions, with a few strokes on your PC keyboard, you calculate the volatility of the Euro-Dollar market, assuming the price changes follow the bell curve. Let us say volatility is ten percent. Then with a few more strokes, you get your answer. There is only a five percent chance that your portfolio will fall by more than twelve percent. Forget about it. The flaw should be obvious by now. The potential loss is actually far, far greater than twelve percent. The problem is not merely that the bell curve leads us to underestimate the volatility. That would be bad enough, as it would underestimate the odds of loss. The problem is worse than that.