Markets and Black Swans
I began studying complexity theory as a consequence of my involvement with Long-Term Capital Management, LTCM, the hedge fund that collapsed in 1998 after derivatives trading strategies went catastrophically wrong.
After the collapse and subsequent rescue, I chatted with one of the LTCM partners who ran the firm about what went wrong. I was familiar with markets and trading strategies, but I was not expert in the highly technical applied mathematics that the management committee used to devise its strategies.
The partner I was chatting with was a true quant with advanced degrees in mathematics. I asked him how all of our trading strategies could have lost money at the same time, despite the fact that they had been uncorrelated in the past.
He shook his head and said, “What happened was just incredible. It was a seven-standard deviation event.”
In statistics, a standard deviation is symbolized by the Greek letter sigma. Even non-statisticians would understand that a seven-sigma event sounds rare. But, I wanted to know how rare. I consulted some technical sources and discovered that for a daily occurrence, a seven-sigma event would happen less than once every billion years, or less than five times in the history of the planet Earth!
I knew that my quant partner had the math right. But it was obvious to me his model must be wrong. Extreme events had occurred in markets in 1987, 1994 and then 1998. They happened every four years or so.
Any model that tried to explain an event, as something that happened every billion years could not possibly be the right model for understanding the dynamics of something that occurred every four years.
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