“…whereas the normal distribution of the daily return of the S&P would suggest a negative three-sigma event (between -3.56% and -2.36% daily returns) should have occurred 27 days over the last one hundred years, this has actually occurred over a hundred times in the 81 years since 1927. And the “normal” likelihood of a negative four-sigma event is one day every one hundred years; yet we have seen this take place an astounding 44 times since 1927…”
On October 19, 1987 the DJIA dropped 508 points (-23%) in the largest single-day crash in history. This Nightly Business Report clip was broadcast that evening.
The S&P futures trading pit audio feed during the May 2010 Flash Crash.
Based on some of the charts over at C2, Summer 2011 was a pretty rough period for many trading systems. The S&P500 fell 16 % in just the first nine days of August, and continued to slide during the next two months:
During the carnage the market spanked many a trading system, sucking down their equity curves with double digit drawdowns. Here’s a few examples (click on the charts for more info):
At least once in their lifetime, every trader has been tempted by the seductive lure of the high win percentages and “easy” profits offered by Martingale money management (doubling/averaging down).
Its all nonsense of course, and every time I think about revisiting the Martingale, I force myself to take a look at the equity curve of a particular ES strategy on C2:
My previous post on S&P500 Black Swans got me thinking: The S&P500 index is a weighted average of 500 companies, right? And if the average is routinely making 6-sigma moves, what kind of crazy shit are the underlying stocks up to?
Let’s take a look at AAPL. Solid company, huge market cap, lots of trading volume. Given its size, it should move almost like an index, right?
WRONG. Take a look at a histogram of daily AAPL returns over the past 12 years (click to zoom):
After surviving the August 2011 meltdown, it occurred to me that the market is experiencing six sigma events (crashes) these days with increasing frequency. To wit: In just the past 3 years we’ve had the 2008 Mortgage Meltdown, the Flash Crash, the Japanese Tsunami, and the Debt Ceiling Crisis. That averages out to around one market crash per year.
I was curious to see how fat these “fat tails” actually get, so I ran some quick tests. Here’s a histogram of the daily returns for SPY (the S&P 500 index ETF) over the past 12 years (click to zoom):