Posts tagged ‘Fat Tails’
Full length video of all four episodes can be found at PBS FRONTLINE
We sure live in interesting times..
“We examined 50-years of historical S&P 500 Index data and compared the actual tail risk frequency and magnitude to the expectations of a typical investor operating under modern portfolio theory. The difference between the two is surprising, and it suggests that investors have significantly underestimated tail risk frequency and severity”
“…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.
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):
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):