Bands
Use Bollinger-style bands as a reversion rule · 7 min
- Close
- 20-day mean
- ±2 σ bands
Price rides along the upper band for weeks. Every touch looked "overbought".
A band rule sells short every close above the upper 2 σ band and covers at the mean. What happens on a market like the one above?
Bollinger-style bands draw the mean ± k standard deviations around price. They are a picture of the z-score: a close above the upper band is z above +k. The band width shows volatility, and bands widen in storms and squeeze in calm.
A band rule fades closes outside the bands. It shares the z-score's assumption: the market comes back. When a trend starts, that assumption breaks, and the losses can be far bigger than the usual gains, because nothing caps how far a trend goes. Two defences are common: a stop in z units (give up beyond, say, 3.5 σ) and a regime filter that stands aside when a trend measure is strong.
- Band rule on a range market (most moves revert within days)
Generated markets, not real data. They show how a rule depends on the market it meets; they do not predict how real markets behave.
Band levels and a signal
- 20-day mean, σ, k
- 50.00, 1.50, 2
- Upper band
- 50 + 2 × 1.5 = 53.00
- Lower band
- 50 − 2 × 1.5 = 47.00
- Close 46.60
- below the lower band: buy
- z of that close
- (46.60 − 50) ÷ 1.5 = −2.27
What usually breaks a band rule?
The lower band is 47.00. Today’s low is 46.80 and the close is 47.40. Does a close-based band rule buy?
Mean 120, σ 4, k = 2.5. Where are the bands?
Missed questions come back for review after one day, then three, then a week.
The 20-day mean is 200 and the 20-day standard deviation is 10. Price closes at 180. What is its z-score?
Hint: z = (price − mean) ÷ standard deviation.
Three years of a fresh generated market are on screen; the next two years do not exist yet. Tune the rule on what you can see, commit to two predictions, then generate the future.
- Your rule so far
Over the next two years, after costs, this rule will…
What kind of market is this?
Generated markets, not real data. They show how a rule depends on the market it meets; they do not predict how real markets behave.