"Black Swans" and the Financial Crisis

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Post-mortems of the financial crisis typically mention "black swans" as the rare events that were the Achilles heel of financial models, manifesting themselves as "25 standard deviation events occurring several days in a row". Here, we briefly discuss the implications of "black swan" events in asset pricing and risk management. We then show that the "black swans" problem virtually disappears for S&P Index returns when surprises are measured relative to the standard deviation of the conditional S&P distribution. In our illustration, we use the one-day-lagged VIX as an easy-to-understand measure of that conditional S&P standard deviation.