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2000issue C071-3

Constructing next-close envelope targets for breakout stops

A moving envelope can be written as an equation in the unknown next close. The resulting next-bar band targets can be placed as anticipatory breakout stops or reused as inverted same-bar limits.

  • A next-bar band target is the unknown future close that would make price equal a moving mean plus or minus a stated multiple of moving standard deviation.
  • An anticipatory breakout stop is priced at that projected envelope so a fill can occur on the bar that first satisfies the envelope cross.
  • Quadratic band roots give an upper price and a lower price, so both sides of a breakout system share one construction.
  • The same prices can be reused as inverted target limits that buy at the lower target and sell at the upper target.
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Current trackBreakout system74 readingsBollinger Bands88 readings

A reusable band-relative measure

A band-relative percentage is the share of a plus-or-minus two-standard-deviation envelope, around a mean over a chosen lookback, that current price occupies. The window must be greater than one bar.

Once built as reusable custom measures, those envelope transforms can be placed in a chart, a prediction workflow, or a coded trading strategy.

The next close as the unknown

A next-bar band target is the unknown future close that would make price equal a moving mean plus or minus a stated multiple of moving standard deviation. An exact next-bar target is therefore the unknown close that would meet a moving standard-deviation band.

A sample-deviation form uses sample-deviation length, the denominator of lookback minus one, when the moving dispersion is a sample standard deviation rather than a population standard deviation. A population form replaces Length minus one with Length and replaces (Length-1)/Length with one.

The unknown next close that touches a moving envelope satisfies a quadratic with two real roots, one for the upper band and one for the lower band. Those quadratic band roots are the pair of real solutions to the next-close envelope equation.

One construction for both sides

Closed-form target formulas take three parameters: the envelope lookback, illustrated as 20; that lookback minus one, illustrated as 19; and the deviation multiple, illustrated as 2.

Clearing an upper-band switch in that target formula yields the matching lower-band price, so both sides of a breakout system share one construction.

An iterative search from the prior close

An iterative alternative extends the series by one bar and searches up or down from the prior close in steps of one hundredth, for as many as 10000 increments, until the moving two-deviation envelope is crossed or just retained.

An anticipatory breakout stop

One complete long procedure places a buy-stop at an upper-envelope target computed from the close with a 15-bar lookback and a two-standard-deviation width, then trails the position with a 10 percent trailing stop.

Pricing that stop at the projected next-bar envelope lets the entry trigger earlier than a rule that waits for a completed close beyond the band. That placement is an anticipatory breakout stop: an entry stop at the next-bar band target so a fill can occur on the bar that first satisfies the envelope cross.

Inverted target limits

The same target prices can be reused as inverted target limits: same-bar buy and sell limits placed at the lower and upper next-bar targets, reversing the timing of the trend-following breakout version.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
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20011-2 pp.Next on Breakout systemFebruary soybean high breakout and June trailing stopThe soybean procedure is long-only and may enter only in February, when a fifty-day high breakout is allowed inside that seasonal permission window.
All readings on this track · 23 readings
  1. 1995Range breakout rules with an expansion filter and moving-average exits
  2. 1995Write a weekly breakout as one parameterized entry and exit
  3. 1995Combining a trend rule, a breakout trigger, and a seasonal filter
  4. 1996Constructing a two-bar clearance breakout from a twenty-session exponential average
  5. 1996Two-bar exponential-average breakout as setup, stop, and flatten
  6. 1998A noise-offset breakout judged after walk-forward re-estimation
  7. 1998Gating a weekly average crossover with stored support and resistance
  8. 1998Moving-average candidates gated by support and resistance
  9. 2000Constructing next-close envelope targets for breakout stops
  10. 2001February soybean high breakout and June trailing stop
  11. 2005Box-and-breakout states written as ordered entry and exit rules
  12. 2007Match trend and breakout rules to the market condition
  13. 2010How a JM internal band becomes long and short entry and exit rules
  14. 2013Constructing a three-average trend-aligned breakout system
  15. 2016Volume-confirmed breakout entry rules
  16. 2017How to construct exponential standard deviation bands
  17. 2017Four-day green candle breakout as one swing procedure
  18. 2018Constructing inverse ETF breakouts above a 200-day average
  19. 2018Evaluating trend, breakout, and regression rules by average robustness
  20. 2019A crypto pair breakout after a sideways range
  21. 2019Next-session breakout rules after a high-volume close
  22. 2020Altcoin dual-stop breakout with a timed exit
  23. 2020Critiquing required stops in mechanical breakout systems
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