Volatility

Here’s a time series graph of the CBOE volatility index (VIX) from January 2, 1990 through October 8, 2008:


Today, the VIX today hit an all-time high of 57.64 (after hitting all time highs of 52.05 on Monday and 53.68 on Tuesday). Since the mean of this series is 19.21 (based upon a total of 4,730 daily closing prices dating back to January 2, 1990), and its standard deviation is 6.47, today’s VIX is 5.94 standard deviations to the right of the mean. Obviously this is a very fat-tailed distribution, but it is nevertheless (morbidly) entertaining to point out that if the series were normally distributed, then one would expect to observe this extreme of an outcome once every 683,138,010 days that the financial markets are open. The number of trading days varies from year to year depending on what day of the week holidays fall on, but a rough guess is 52 weeks x 5 days per week = 260 less about 10 holidays = 250 trading days. So if we translate this into the implied number of years, the odds of this happening would come out to roughly once every 683,138,010/250 = 2,732,552 years.

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