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2003issue C101

Constructing volatility-scaled Bollinger envelopes

The envelope is three lines: a middle moving average and outer lines placed two standard deviations away from that path. Width can change with volatility, and the relative strength index is specified only to confirm what the finished bands show.

  • Build the envelope as a middle moving average with a customary 20-day lookback, then place the upper and lower lines two standard deviations from that path.
  • Use a standard-deviation offset instead of a fixed-percentage offset so the envelope can change width with market volatility.
  • Read price at or beyond the outer lines as a possible overbought-oversold condition, then apply the stated tightening, continuation, and reversal rules.
  • Leave the relative strength index out of the band arithmetic; it is specified only to confirm what the finished envelope shows.
Entries in this reading3 entries
Current trackBollinger Bands84 readingsRelative Strength Index186 readingsMoving average449 readings

A three-line envelope

The envelope is drawn as three lines: a middle moving average, an upper line, and a lower line. That sandwich is meant to frame a range of price movement. The outer lines sit a stated number of standard deviations away from the central moving average so the width can change with volatility.

Daily EBH with a 20-day two-sigma envelope

On daily EBH the 20-session average is flanked by rails two standard deviations away. The envelope stays tight through the spring coil, then gapes open on the June advance and is still wide into August, with the last printed rails at 137.13 and 124.59 around a 130.86 midline. Weekly samples were read from the published figure; those three closing prints were taken from the scale.
On daily EBH the 20-session average is flanked by rails two standard deviations away. The envelope stays tight through the spring coil, then gapes open on the June advance and is still wide into August, with the last printed rails at 137.13 and 124.59 around a 130.86 midline. Weekly samples were read from the published figure; those three closing prints were taken from the scale.EBH · Daily · 2003-02-24T00:00:00.000Z to 2003-08-18T00:00:00.000Z

The source fixes the middle path at a 20-day moving average and the offsets at two standard deviations. Only month ticks are dated on the figure; weekly x values are interpolated from those labels. The year 2003 is taken from Stocks & Commodities V. 21:10 (October 2003), not printed on the plot. Intermediate levels are approximate; do not treat them as ticks.

How the middle path and offsets are built

The middle line is specified as a moving average with a customary 20-day lookback. That moving average is the central path of the envelope. The upper line is the middle moving average plus two standard deviations. The lower line is that same average minus two standard deviations.

Those outer placements are the standard-deviation offset: the volatility measure added to and subtracted from the central moving average to locate the upper and lower lines.

Why width is tied to volatility

The outer offsets use standard deviations rather than a fixed percentage so the width can change with market volatility. A fixed-percentage envelope, illustrated with a 3 percent offset, is described as adjusting poorly during extreme advances or declines. Tying band width to the standard deviation of the moving average is presented as making the envelope more adaptable and better at containing prices.

How the finished envelope is read

Price at or above the upper line is treated as a possible overbought condition. Price at or below the lower line is treated as a possible oversold condition. That overbought-oversold reading comes from the construction itself: price at or beyond the upper line may be treated as stretched upward, and price at or beyond the lower line as stretched downward.

Stated reading rules include sharp moves after the bands tighten, continuation when price leaves the bands, reversal after extremes print outside then inside, and a tendency for a move that starts at one band to reach the other.

A confirmation companion, not a band input

The envelope is intended to be used together with the relative strength index to confirm what the bands show. In that role the relative strength index is a companion oscillator used alongside the bands to check observations rather than to compute the bands themselves.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
22 of 45 in the Bollinger Bands track
20031-5 pp.Next on Bollinger BandsWhy tick breadth fails as a market personalityEach tick still pairs a buyer with a seller, so the tape-wide up-versus-down count is not a direct read of leftover supply.
All readings on this track · 45 readings
  1. 1992Constructing volatility-scaled bands with relative strength index confirmation
  2. 1994Implied volatility as a band-defined regime filter for index options
  3. 1995Constructing projection bands from least-squares slopes
  4. 1995Constructing regression projection bands and range oscillators
  5. 1996Constructing Bollinger bands, percent-b, and stochastics
  6. 1996Constructing mechanical rules from Bollinger Bands and stochastics
  7. 1996Constructing a standard-error envelope around a linear regression
  8. 1996Dual-horizon ratio envelopes and regression error channels
  9. 1997Rational group structure with a trend screen, RSI, and bands
  10. 1997Asymmetric volatility band construction
  11. 1998Constructing three-state filters from Bollinger band envelopes
  12. 1999Combination filters with Bollinger Bands and the relative strength index
  13. 1999Constructing stochastic timed exits and band-RSI reversals
  14. 1999Evaluating Bollinger Bands against fixed-width and range-based envelopes
  15. 2000Constructing a Bollinger Band target as a forward price
  16. 2001Numeric candlestick encoding with local size bands
  17. 2001Ranked candlestick sentiment to band-cross entries
  18. 2002Combining Bollinger Bands, RSI, and a stop-loss
  19. 2002Bollinger Bands remain filters, not forecasts
  20. 2002Constructing a stochastic RSI with Bollinger bands
  21. 2002Constructing a StochRSI and Bollinger mechanical system
  22. 2003Constructing volatility-scaled Bollinger envelopes
  23. 2003Why tick breadth fails as a market personality
  24. 2005Constructing Bollinger bands versus fixed trading bands
  25. 2006Squared versus absolute deviation in envelope construction
  26. 2006Confirming yen crossovers with implied volatility and bands
  27. 2006A daily candle reversal is a hypothesis until shorter sessions fail at the same zone
  28. 2008Rebuild the Relative Strength Index as price-scale bands
  29. 2008Reading Relative Strength Index extremes on one price axis with Bollinger Bands and moving averages
  30. 2011Three-filter confirmation for short-swing futures
  31. 2011Constructing an inverse Fisher stochastic with bands and averages
  32. 2012Constructing a Bollinger Band indicator suite
  33. 2012Stacking price extremes, crossovers, bands, and MACD
  34. 2012Adaptive Bollinger band impulse, trend, and momentum filters
  35. 2013Rescaling stochastic, percent-B, and wave-count parameters
  36. 2014Industry-group quartile pivots as a Bollinger Bands case study
  37. 2014Bollinger Bands as adaptive price envelopes: a 2014 classroom case
  38. 2016Trend-channel entry rules from stacked moving averages
  39. 2016A permission stack for Bollinger, RSI, and the 50-period average
  40. 2017Constructing weighted Bollinger bands and volume averages
  41. 2017Four swing-entry rules that share a timed exit
  42. 2017Two-wave monthly cycles as a regime filter
  43. 2019Constructing exponential-deviation-bands from a midline-average
  44. 2020Critiquing exponential variants of Bollinger Bands
  45. 2020Constructing selectable volatility and moving-average bands
By fieldIndicators and filters682 readingsBy year2003104 readings
All 84 readings tagged Bollinger Bands
Also on Bollinger Bands5 readings
1992Constructing volatility-scaled bands with relative strength index confirmation2008Reading Relative Strength Index extremes on one price axis with Bollinger Bands and moving averages2016A permission stack for Bollinger, RSI, and the 50-period average1997Rational group structure with a trend screen, RSI, and bands1999Combination filters with Bollinger Bands and the relative strength index