Five sigma or "black swan" events have become increasingly more prevalent. The chart here shows just how much more.
Five sigma or larger events are supposed to occur only once every 1.7 million instances -- or once about every 7,000 years in terms of trading days.They've actually occurred 104 times in just the past 60 years.
The chart shows the rolling one-year sum of absolute daily percent changes in the S&P that have exceeded five standard deviations over the past 60 years. The largest of these events occurred on Oct. 13, 2008, when the S&P 500 gained nearly 12 percent in a single day, registering a z-score of 15.6. This followed several days of large declines, with the biggest, of 7.6 percent, occurring on Oct. 7, 2008 and registering a z-score of more than 10.
Banks or hedge funds in the past viewed five-plus sigma events as exceedingly unlikely, and were ill-prepared to cope with them, which likely facilitated the fall of Lehman Brothers and others that under-estimated the potential downside risk in the U.S. subprime mortgage market.
Many trading institutions now view these events as more likely, and have taken steps to hedge against their occurrence. This should cause the cost of hedging to rise. One product that allows investors to price in risk is variance swaps, which allow bets to be placed on volatility.
Traders are pricing in a high level of S&P 500 volatility of 27.2 percent from now through 2018 via variance swaps. The last time actual volatility attained this level for a seven-year period was in the 1930s, after the 1929 equity market crash.
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Disclosure: I am long SDY.