Sunday, November 2, 2014

Does 3 standard deviation move of an ETF match reality?

It was a fantastical test in the last couple of weeks for the premium selling strategy that I'm working on in both real and paper trades, as the market went extremely turbulent. It will take a while for me to digest the trades to firm up my trading rules.

In preparation to analyze my TLT trades as it ventured above the 3 Standard Deviation (SD) line intraday on 10-15, I studied the historical data. I think 3 SD corresponds to 99.7% probability approximately as I outlined in a post before. If I understand it correctly, there will be a 3 SD event every 1 year 7.5 months which corresponds to 333 (1/0.3%) trading days on average (assuming there are 200 trading days per year).

I'm interested how these numbers matching the reality. So I went through the TLT history using Prophet Chart available from TOS. I created the Bollinger bands with 30 day MA & 3 SD on TLT chart, scrolled through the entire price chart whose data started at 2002-7-26 for over 12 years. I found the follow 3 SD occurrences where prices closed outside the Bollinger bands by visual inspections only.

Number Date Days Up/Low Days outside 3 SD
1 7/2/2004 0 Up Just 1 day
2 2/27/2007 970 Up Just 1 day
3 11/20/2008 632 Up Just 1 day, but continued to rise
4 5/6/2010 532 Up Just 1 day
5 8/16/2010 102 Up Just 1 day
6 8/2/2011 351 Up 3 days
7 3/14/2012 225 Low Just 1 day
8 4/5/2013 387 Up Just 1 day

From 2004-7-2 to 2014-10-31, there are 4480 calendar days. That is a period of 12 years and 3 month. I equated it to 2460 trading days roughly. With the 0.3% probability, we should have 7.3 (2460 x 0.3%) occurrences outside 3 SD in the period. In reality, we've had 8 occurrences as shown in the above table. I think this is very surprisingly close to the theory.

I have a couple of other findings that should be recorded here.
  • 6 out of 8 times the price came back to Bollinger bands in the next day
  • 1 out of 8 times the prices fell below the lower Bollinger band
    • I guess there will be more events that the prices fall below the Bollinger band in the next 10 to 20 years.
I'm running out of time today. So I have to present my trade analysis (Lessons from surviving the test of 3 SD events) next time.


  1. It would be interesting to see what the market was doing just before the 3SD event. If you can find a common thread then you could use this a warning sign to prepare.