Chance of Having Seen HOD/LOD by bar X

According to BPA, a breakout of an 18 bar range has a 20% chance of breaking out of the other side [of the range] before EOD. There's a probability like this associated with every bar of the day. Bar 18 became famous simply for occuring around the time when this probability becomes enticing enough in a day to act upon. This study attempts to confirm this and also to calculate the exact probabilities for all 81 bars of the day. All code and some sample historical data is provided for replication. Feedback and collaboration are welcome!

“There is nothing magical about 18 bars. I could have picked 16 or 23. The idea is that if the market has been in a range for about 20 bars and it breaks out, there is only a 20% chance that there will be a breakout of the opposite side of the range by the end of the day. Also, if the range is about half of the average recent daily ranges, traders will look for the day’s range to approximately double.” webinar: Trading Opening Breakouts and Reversals Slide 3


For each of the 81 bars of every day the code records whether HOD or LOD up to that bar's range was broken before EOD. If both HOD and LOD for that bar's range were broken it records that case as a failure. If at least one held to EOD then it records that as success. Processing all the historical data creates a record of all the days where Bar 1 failed or succeeded at keeping HOD or LOD, same for Bar 2, Bar 3 ... up to Bar 81. All bar results from all the days are then grouped by bar index and statistics are calculated to arrive at the final probability of having seen either HOD or LOD by Bar X before EOD.

But what is the exact probability?


The following chart is based on historical data range from Sep 27, 2005 - Oct 14, 2022 or 4410 days. Those with programming knowledge are encouraged to replicate these results. All the code is freely available on GitHub.

According to this, the chance of having seen HOD/LOD by bar 18 comes out close to 81%.

Risk Disclosures

CFTC Rule 4.41: Hypothetical or Simulated performance results have certain limitations, unlike an actual performance record, simulated results do not represent actual trading. Also, since the trades have not been executed, the results may have under-or-over compensated for the impact, if any, of certain market factors, such as lack of liquidity. Simulated trading programs in general are also subject to the fact that they are designed with the benefit of hindsight. No representation is being made that any account will or is likely to achieve profit or losses similar to those shown.

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