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|
|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.