Mean reversion bollinger

Bollinger Bands

Mean-reversion off the bands. Bullish: price crosses back above the lower Bollinger Band from below (oversold bounce). Bearish: price crosses back below the upper Bollinger Band from above (overbought reversal). Bands = SMA ± N standard deviations.

Signal family

Mean reversion — Oscillator-based signals that fire at overbought or oversold extremes — typically fade the prevailing move.

Parameters

Name Description Default Range
period SMA period 20 5–100
ub_factor Upper band std dev factor 2.0 0.5–4.0
lb_factor Lower band std dev factor 2.0 0.5–4.0

Historical context

2,481,722 triggers on 24,141 tickers, 1988-03-31 → 2026-05-01. Universe: global — all covered exchanges (mcap ≥ $100,000,000, price ≥ $1). Long-only convention: BUY at open T+1, hold the horizon, compare to S&P 500 Equal Weight over the same window.

Methodology footnotes

Benchmarks shown in the detail tables: spxew (S&P 500 Equal Weight — primary, median-stock view, avoids the 2020+ megacap-concentration distortion), spx (S&P 500 cap-weighted, distorted post-2020), msci (MSCI World USD). Per-stock regime tags: trending = ADX(14) ≥ 25, high vol = 20d realized annualized vol ≥ 20%. 1d return = intraday T+1 open→close; 20d = open T+1 to close T+20.

At a glance — alpha vs S&P 500 Equal Weight, global universe

Holding-period sensitivity. Bullish columns: positive = signal worked (long the trigger beat the index). Bearish columns: negative = signal worked (the flagged stock underperformed).

Horizon Bullish α Bearish α
5-day +0.12% -0.06%
20-day +0.09% +0.17%
60-day +0.30% +0.58%
1-year +1.66% +3.51%
Random-date null check (20-day): Bullish: beats random (p=0.005).
Bearish: worse than random (p=0.995).

Where does BOLLINGER actually fire?

The bucket distribution often reveals what the signal really is, regardless of its textbook label. Heavy concentration in "non-trending + high vol" = it's mostly a chop-market event. Heavy in "trending + low vol" = it picks up the smooth grinds. Read the chart before the alpha numbers — context shapes everything that follows.

Bollinger Bands (bollinger) — trigger count distribution by per-stock regime quadrant (trending/non-trending × high/low realized volatility) for bullish and bearish triggers, global universe

Does it work in every regime?

Trigger alpha split by the host stock's own regime on the trigger date — trending or ranging, high-vol or low-vol. This is the 20-day alpha a trade taken on the trigger would have captured. Bars carrying the sign that favours the trade (positive for bullish triggers, negative for bearish) mark the regimes where the signal worked; the opposite sign marks regimes to avoid. One strong bar beside three flat ones is not a "20-day alpha" signal — it is a "20-day alpha when the stock is X" signal. Bar labels carry the sample size; a cell built on a handful of triggers is noise, not a regime finding.

Bollinger Bands (bollinger) — mean 20-day alpha versus S&P 500 Equal Weight by per-stock regime quadrant, bullish and bearish triggers side by side
Trending + Low vol
Stock in a clean directional move with low realized volatility. Textbook "trend-following paradise" — smooth grind with little whipsaw risk.
Trending + High vol
Violent directional moves — parabolic rallies, crisis selloffs. Trend exists but the path is noisy. Signal timing may be imprecise.
Non-trending + Low vol
Quiet chop, summer doldrums, consolidations. No directional bias but also no big swings — small edges become reliable if they exist at all.
Non-trending + High vol
Choppy and violent — the classical "whipsaw zone" for momentum signals. Crossovers and breakouts fire repeatedly without follow-through.

Does it work in every era?

A multi-year average can hide major instability. The sample splits into three windows: 2015–2019 (pre-COVID), 2020–2022 (pandemic + 2022 bear), and 2023+ (post-ZIRP + AI megacap rally). All three carrying the sign that favours the trade means the signal is durable; one era doing all the work means a regime-specific edge that may not repeat. The greater the variance across eras, the smaller the position it justifies.

Bollinger Bands (bollinger) — 20-day alpha split by historical sub-period (2015-2019, 2020-2022, 2023+) to check consistency across market regimes

↑ Bullish triggers

Bench Metric 1d 5d 20d 60d 252d
spxew Stock % -0.00% +0.33% +1.37% +3.41% +12.78%
Bench % -0.00% +0.16% +1.22% +3.13% +10.90%
Alpha % -0.03% +0.12% +0.09% +0.30% +1.66%
Median alpha -0.09% -0.12% -0.72% -1.72% -6.58%
Hit rate (α>0) 47.9% 48.7% 46.3% 45.1% 41.7%
p (naive) <0.001 <0.001 <0.001 <0.001 <0.001
p (HAC) <0.001 <0.001 <0.001 <0.001 <0.001
N 1,102,436 1,068,209 1,055,380 1,026,908 939,635
spx Stock % -0.00% +0.33% +1.37% +3.41% +12.78%
Bench % +0.00% +0.23% +1.51% +3.67% +14.73%
Alpha % -0.03% +0.06% -0.17% -0.25% -1.92%
Median alpha -0.07% -0.17% -0.99% -2.32% -10.32%
Hit rate (α>0) 48.2% 48.2% 45.0% 43.6% 37.9%
p (naive) <0.001 <0.001 <0.001 <0.001 <0.001
p (HAC) <0.001 <0.001 <0.001 <0.001 <0.001
N 1,108,791 1,075,952 1,071,270 1,037,449 955,796
msci Stock % -0.00% +0.33% +1.37% +3.41% +12.78%
Bench % +0.03% +0.24% +1.32% +3.29% +12.31%
Alpha % -0.04% +0.06% -0.03% +0.13% -0.05%
Median alpha -0.10% -0.19% -0.86% -1.98% -8.23%
Hit rate (α>0) 47.5% 47.9% 45.6% 44.4% 40.0%
p (naive) <0.001 <0.001 0.0128 <0.001 0.3138
p (HAC) <0.001 <0.001 0.0368 <0.001 0.7438
N 1,100,296 1,063,976 1,054,584 1,028,583 938,807
Observed 20-day lift (vertical line) against the null distribution of random-date firing. If the line is deep inside the null cloud, the signal adds no information. If it sits in the right tail, the signal is doing real work in that direction; in the left tail it ran inverted — random dates served the bullish case better than its own triggers did.
Bollinger Bands (bollinger) — bullish 20-day observed lift versus random-date permutation null (200 iterations)
Permutation null detail — all horizons × each benchmark
200-iteration null: for each ticker, sample N random dates from its history (matching observed trigger count) and compute the same alpha. Both observed and null are baseline-centered per ticker (each ticker's own baseline alpha is subtracted), which removes the universe-selection lift that all surviving names share, so the comparison is about the trigger's timing. It does not put the null at zero: that baseline is a median, while a random date's expectation is the ticker's mean, so the null settles at the gap between the two — the right-skew of the ticker's own alpha distribution, positive for equities. Read observed minus null, not the absolute position of either column — which is also why these figures do not match the α columns in the tables above (those are raw, uncentered means). pperm = one-sided fraction of null iters with mean in the "signal was right" tail (right for bullish, left for bearish), so it runs from a floor of 0.005 (trigger dates beat every random draw in the claimed direction) to a 1.000 ceiling (every random draw served the claimed direction better — a reliably inverted signal, not an absent one). The floor is 1/(iterations + 1) and moves with the iteration count; the ceiling does not. Either end says the result was reliable, not that it was large: the gap between the line and the cloud can be a fraction of a percent and still reach an endpoint, and the transaction-cost floor in the caveats below would swallow a gap that small. Read the size off the α and hit-rate columns, the reliability off pperm.
Horizon Bench Observed lift Null mean Null 95% CI pperm
1d spxew +0.11% +0.08% [+0.07%, +0.08%] 0.005
1d spx +0.08% +0.09% [+0.08%, +0.09%] 0.557
1d msci +0.12% +0.09% [+0.08%, +0.09%] 0.005
5d spxew +0.51% +0.34% [+0.33%, +0.36%] 0.005
5d spx +0.48% +0.36% [+0.35%, +0.37%] 0.005
5d msci +0.48% +0.37% [+0.35%, +0.38%] 0.005
20d spxew +1.20% +1.12% [+1.10%, +1.14%] 0.005
20d spx +1.17% +1.15% [+1.13%, +1.17%] 0.030
20d msci +1.21% +1.17% [+1.15%, +1.19%] 0.005
60d spxew +2.67% +2.41% [+2.36%, +2.44%] 0.005
60d spx +2.85% +2.47% [+2.43%, +2.51%] 0.005
60d msci +2.82% +2.49% [+2.45%, +2.53%] 0.005
252d spxew +5.42% +4.76% [+4.68%, +4.84%] 0.005
252d spx +5.85% +5.10% [+5.01%, +5.17%] 0.005
252d msci +5.52% +5.05% [+4.97%, +5.12%] 0.005

Example triggers on US large-caps (2023+, mcap ≥ $30B)

Six recent bullish BOLLINGER triggers on US mega-caps, ranked within this sample of six: the top three and the bottom three, with extreme outliers excluded. Ranking is relative, not absolute — where the signal did well across the sampled names, even the bottom three can have beaten the benchmark, so the alpha printed on each panel is what settles it. Both groups are tail outcomes by construction; read them as the range, not the typical result.

Best three of the six sampled
Bollinger Bands (bollinger) — strongest bullish trigger #1 on a US mega-cap, showing the stock's OHLC candles, moving averages, signal-specific overlays, and the 20-day forward window Bollinger Bands (bollinger) — strongest bullish trigger #2 on a US mega-cap, showing the stock's OHLC candles, moving averages, signal-specific overlays, and the 20-day forward window Bollinger Bands (bollinger) — strongest bullish trigger #3 on a US mega-cap, showing the stock's OHLC candles, moving averages, signal-specific overlays, and the 20-day forward window
Weakest three of the six sampled — not necessarily losses
Bollinger Bands (bollinger) — weakest bullish trigger #1 on a US mega-cap, showing the 20-day forward window where the signal failed Bollinger Bands (bollinger) — weakest bullish trigger #2 on a US mega-cap, showing the 20-day forward window where the signal failed Bollinger Bands (bollinger) — weakest bullish trigger #3 on a US mega-cap, showing the 20-day forward window where the signal failed
Stock-regime quadrants (2×2 per-stock, 20d alpha detail table)
Each quadrant groups triggers by the stock's own ADX(14) and RV(20) at the trigger date — the textbook conditioning variable (not market-level). Stock %, bench %, alpha %, and HAC p-value shown for each benchmark.
Quadrant N Stock % (spxew) Bench % (spxew) Alpha % (spxew) p (HAC) Stock % (spx) Bench % (spx) Alpha % (spx) p (HAC) Stock % (msci) Bench % (msci) Alpha % (msci) p (HAC)
Trending + Low vol Clean directional grind, low whipsaw 90,593 +0.19% +0.91% -0.67% <0.001 +0.19% +1.16% -0.96% <0.001 +0.19% +1.00% -0.80% <0.001
Trending + High vol Crisis selloff or parabolic rally 401,207 +2.26% +1.39% +0.75% <0.001 +2.26% +1.79% +0.41% <0.001 +2.26% +1.52% +0.63% <0.001
Non-trending + Low vol Quiet chop, summer doldrums 140,021 +0.20% +0.92% -0.68% <0.001 +0.20% +1.17% -0.95% <0.001 +0.20% +1.05% -0.82% <0.001
Non-trending + High vol Classical "whipsaw zone" for momentum 509,367 +1.21% +1.30% -0.07% 0.0001 +1.21% +1.52% -0.27% <0.001 +1.21% +1.36% -0.17% <0.001
Sub-period breakdown table (20d alpha)
Historical clustering check. If alpha concentrates in one era, the signal's robustness is questionable.
Period N Alpha % (spxew) p (HAC) Alpha % (spx) p (HAC) Alpha % (msci) p (HAC)
2015-2019 2015-01-01 → 2020-01-01 347,704 -0.12% <0.001 -0.19% <0.001 +0.02% 0.3053
2020-2022 2020-01-01 → 2023-01-01 349,798 -0.04% 0.0657 -0.02% 0.5113 +0.24% <0.001
2023-2026 2023-01-01 → 2099-01-01 443,216 +0.36% <0.001 -0.29% <0.001 -0.28% <0.001

↓ Bearish triggers negative alpha = signal was right (stock underperformed market)

Bench Metric 1d 5d 20d 60d 252d
spxew Stock % -0.01% +0.13% +0.81% +2.63% +13.25%
Bench % +0.03% +0.19% +0.69% +2.09% +9.90%
Alpha % -0.04% -0.06% +0.17% +0.58% +3.51%
Median alpha -0.11% -0.36% -0.85% -1.93% -5.82%
Hit rate (α>0) 47.3% 46.3% 45.9% 44.7% 42.8%
p (naive) <0.001 <0.001 <0.001 <0.001 <0.001
p (HAC) <0.001 <0.001 <0.001 <0.001 <0.001
N 1,287,604 1,239,226 1,233,197 1,205,768 1,053,050
spx Stock % -0.01% +0.13% +0.81% +2.63% +13.25%
Bench % +0.02% +0.20% +0.89% +2.92% +13.64%
Alpha % -0.03% -0.07% -0.04% -0.27% -0.41%
Median alpha -0.10% -0.40% -1.10% -2.84% -9.85%
Hit rate (α>0) 47.3% 45.9% 44.7% 42.4% 38.5%
p (naive) <0.001 <0.001 <0.001 <0.001 <0.001
p (HAC) <0.001 <0.001 0.0025 <0.001 0.0398
N 1,299,164 1,259,132 1,244,496 1,221,418 1,065,817
msci Stock % -0.01% +0.13% +0.81% +2.63% +13.25%
Bench % +0.04% +0.19% +0.78% +2.50% +11.17%
Alpha % -0.04% -0.05% +0.08% +0.17% +2.03%
Median alpha -0.12% -0.38% -0.98% -2.41% -7.43%
Hit rate (α>0) 47.0% 46.1% 45.2% 43.4% 41.2%
p (naive) <0.001 <0.001 <0.001 <0.001 <0.001
p (HAC) <0.001 <0.001 <0.001 <0.001 <0.001
N 1,290,758 1,249,550 1,241,787 1,212,349 1,060,619
Observed 20-day lift (vertical line) against the null distribution of random-date firing. If the line is deep inside the null cloud, the signal adds no information. If it sits in the left tail, the signal is doing real work in that direction; in the right tail it ran inverted — random dates served the bearish case better than its own triggers did.
Bollinger Bands (bollinger) — bearish 20-day observed lift versus random-date permutation null (200 iterations)
Permutation null detail — all horizons × each benchmark
200-iteration null: for each ticker, sample N random dates from its history (matching observed trigger count) and compute the same alpha. Both observed and null are baseline-centered per ticker (each ticker's own baseline alpha is subtracted), which removes the universe-selection lift that all surviving names share, so the comparison is about the trigger's timing. It does not put the null at zero: that baseline is a median, while a random date's expectation is the ticker's mean, so the null settles at the gap between the two — the right-skew of the ticker's own alpha distribution, positive for equities. Read observed minus null, not the absolute position of either column — which is also why these figures do not match the α columns in the tables above (those are raw, uncentered means). pperm = one-sided fraction of null iters with mean in the "signal was right" tail (right for bullish, left for bearish), so it runs from a floor of 0.005 (trigger dates beat every random draw in the claimed direction) to a 1.000 ceiling (every random draw served the claimed direction better — a reliably inverted signal, not an absent one). The floor is 1/(iterations + 1) and moves with the iteration count; the ceiling does not. Either end says the result was reliable, not that it was large: the gap between the line and the cloud can be a fraction of a percent and still reach an endpoint, and the transaction-cost floor in the caveats below would swallow a gap that small. Read the size off the α and hit-rate columns, the reliability off pperm.
Horizon Bench Observed lift Null mean Null 95% CI pperm
1d spxew +0.09% +0.08% [+0.07%, +0.08%] 1.000
1d spx +0.09% +0.09% [+0.08%, +0.09%] 1.000
1d msci +0.10% +0.09% [+0.08%, +0.10%] 1.000
5d spxew +0.31% +0.34% [+0.33%, +0.36%] 0.005
5d spx +0.34% +0.36% [+0.35%, +0.37%] 0.005
5d msci +0.35% +0.36% [+0.35%, +0.37%] 0.015
20d spxew +1.14% +1.11% [+1.09%, +1.13%] 0.995
20d spx +1.17% +1.14% [+1.12%, +1.16%] 0.990
20d msci +1.18% +1.15% [+1.13%, +1.18%] 0.970
60d spxew +2.33% +2.41% [+2.37%, +2.45%] 0.005
60d spx +2.23% +2.48% [+2.44%, +2.52%] 0.005
60d msci +2.26% +2.50% [+2.46%, +2.54%] 0.005
252d spxew +4.43% +4.59% [+4.51%, +4.65%] 0.005
252d spx +4.65% +4.94% [+4.87%, +5.01%] 0.005
252d msci +4.72% +4.89% [+4.82%, +4.95%] 0.005

Example triggers on US large-caps (2023+, mcap ≥ $30B)

Six recent bearish BOLLINGER triggers on US mega-caps, ranked within this sample of six: the top three and the bottom three, with extreme outliers excluded. Ranking is relative, not absolute — where the signal did well across the sampled names, even the bottom three can have beaten the benchmark, so the alpha printed on each panel is what settles it. Both groups are tail outcomes by construction; read them as the range, not the typical result.

Best three of the six sampled
Bollinger Bands (bollinger) — strongest bearish trigger #1 on a US mega-cap, showing the stock's OHLC candles, moving averages, signal-specific overlays, and the 20-day forward window Bollinger Bands (bollinger) — strongest bearish trigger #2 on a US mega-cap, showing the stock's OHLC candles, moving averages, signal-specific overlays, and the 20-day forward window Bollinger Bands (bollinger) — strongest bearish trigger #3 on a US mega-cap, showing the stock's OHLC candles, moving averages, signal-specific overlays, and the 20-day forward window
Weakest three of the six sampled — not necessarily losses
Bollinger Bands (bollinger) — weakest bearish trigger #1 on a US mega-cap, showing the 20-day forward window where the signal failed Bollinger Bands (bollinger) — weakest bearish trigger #2 on a US mega-cap, showing the 20-day forward window where the signal failed Bollinger Bands (bollinger) — weakest bearish trigger #3 on a US mega-cap, showing the 20-day forward window where the signal failed
Stock-regime quadrants (2×2 per-stock, 20d alpha detail table)
Each quadrant groups triggers by the stock's own ADX(14) and RV(20) at the trigger date — the textbook conditioning variable (not market-level). Stock %, bench %, alpha %, and HAC p-value shown for each benchmark.
Quadrant N Stock % (spxew) Bench % (spxew) Alpha % (spxew) p (HAC) Stock % (spx) Bench % (spx) Alpha % (spx) p (HAC) Stock % (msci) Bench % (msci) Alpha % (msci) p (HAC)
Trending + Low vol Clean directional grind, low whipsaw 116,618 +0.59% +0.35% +0.28% <0.001 +0.59% +0.64% -0.04% 0.1562 +0.59% +0.50% +0.12% <0.001
Trending + High vol Crisis selloff or parabolic rally 578,778 +0.97% +0.72% +0.33% <0.001 +0.97% +0.94% +0.09% 0.0004 +0.97% +0.81% +0.22% <0.001
Non-trending + Low vol Quiet chop, summer doldrums 151,671 +0.53% +0.42% +0.11% <0.001 +0.53% +0.68% -0.16% <0.001 +0.53% +0.54% -0.01% 0.6075
Non-trending + High vol Classical "whipsaw zone" for momentum 493,454 +0.83% +0.82% +0.02% 0.2677 +0.83% +0.96% -0.11% <0.001 +0.83% +0.88% -0.01% 0.6020
Sub-period breakdown table (20d alpha)
Historical clustering check. If alpha concentrates in one era, the signal's robustness is questionable.
Period N Alpha % (spxew) p (HAC) Alpha % (spx) p (HAC) Alpha % (msci) p (HAC)
2015-2019 2015-01-01 → 2020-01-01 400,529 -0.37% <0.001 -0.65% <0.001 -0.43% <0.001
2020-2022 2020-01-01 → 2023-01-01 395,813 +0.06% 0.0329 +0.28% <0.001 +0.40% <0.001
2023-2026 2023-01-01 → 2099-01-01 543,666 +0.67% <0.001 +0.19% <0.001 +0.25% <0.001

Methodology and caveats

How to read. Entry at open of T+1 (one trading day after the signal fires on close of T). 20d = open T+1 to close T+20. Alpha = stock return − benchmark return over the same window (Convention A, single-sided, textbook). For bullish triggers, POSITIVE alpha = signal was right. For bearish triggers, NEGATIVE alpha = signal was right (stock underperformed market). No sign-flipping; the direction of the bet determines what "good" looks like. Per-stock regime is each stock's own ADX(14) and RV(20) at the trigger date — not market-wide state.

Three p-values, three robustness tests. (a) p_naive: scipy one-sample t-test on winsorized alphas. Optimistic because overlapping 20d windows on the same ticker inflate effective N. (b) p_hac: Newey-West HAC with lag = horizon — corrects for the overlap and is the academic-finance standard. (c) p_perm: one-sided fraction of 200 random-date null iterations falling in the “signal was right” tail (mean ≥ observed for bullish; mean ≤ observed for bearish). Tests whether the signal beats random date selection at all. A signal that clears all three (pnaive, phac, pperm all < 0.05) has real information; a signal that fails pperm has not beaten random timing whatever the t-test says — and because the test is one-sided, a pperm up at its 1.000 ceiling is not "no edge" but inverted edge: every random draw served the claimed direction better than the trigger dates did.

Caveats. (i) Universe reflects today's active tickers; delisted losers pruned → survivorship bias. (ii) Mcap ≥ $100M filter uses today's snapshot, not point-in-time — mild lookahead on which stocks enter the sample, not on returns. (iii) Means and p-values use winsorized alphas (1/99 percentile) to prevent data errors from dominating. Medians and hit rates use raw data. (iv) Zero transaction costs assumed. Realistic bid-ask + commissions remove 20–40bps from 20d alpha on US large-caps, more on small-cap. Sub-20bps alpha is noise in practice. (v) Past performance does not predict future results.

How to use this

1 · When to reach for this signal

Statistically real but thin at 20 days. Bullish 20d alpha is +0.09% and beats random , but sits below the ~20bps cost floor from the caveats — screening context, not a standalone edge. Bearish 20d alpha is +0.17% — worse than random : firing on random dates would have done better. Fires are screening context inside a composite (section 4), not entries.

These verdicts are 20-day holds vs S&P 500 Equal Weight. Longer horizons can differ in either direction — check the permutation detail tables below before extrapolating.

2 · When it works — the setups that drive it

  • Best bullish setup: Trending + High vol — alpha +0.75% / 20d on 401,207 historical triggers.
  • Least-bad bearish cell: Non-trending + High vol — alpha +0.02% / 20d on 493,454 triggers — still wrong-signed; no bearish cell produced negative alpha.
  • Best era for bullish: 2023-2026 — alpha +0.36% / 20d on 443,216 triggers.
  • Best era for bearish: 2015-2019 — alpha -0.37% / 20d on 400,529 triggers.

3 · When it fails — common false positives

  • Weakest bullish cell: Non-trending + Low vol — alpha -0.68% / 20d on 140,021 triggers.
  • Weakest bearish cell: Trending + High vol — alpha +0.33% / 20d on 578,778 triggers.
  • Worst era for bullish: 2015-2019 — alpha -0.12% / 20d on 347,704 triggers.
  • Worst era for bearish: 2023-2026 — alpha +0.67% / 20d on 543,666 triggers.

Signal-specific failure patterns

Lower-band re-entries catch informed selling, not statistical noise
The bullish trigger is the close crossing back above the lower band (20-day simple moving average minus 2 standard deviations of the close) after having closed below it. The band-excursion thesis treats a two-sigma stretch as random noise that should revert. In practice a close below the lower band usually has a cause — earnings, guidance, sector news — and the re-entry cross often marks a pause in a continuing decline rather than a completed reversal. Whether the bullish pool is currently earning or losing against the benchmark is shown in the at-a-glance table above; the mechanics only explain why the answer moves with market character.
Band-walking trends generate false bearish fires
In a strong advance price 'walks' the upper band — Bollinger's own observation — repeatedly closing above it and slipping back inside. Every slip back below the upper band prints a bearish fire here, yet during a band walk those crosses mark consolidation inside a working trend, not exhaustion. Expect the bearish side to misfire most often on the strongest names in the screen — exactly the stocks most likely to appear on bullish tiles at the same time. The regime-quadrant charts above show what this currently costs on trending versus non-trending host stocks.
The bands adapt to trailing volatility — trigger meaning shifts with the vol regime
Band width is two standard deviations of the trailing 20 closes, so the envelope tightens after a volatility crush — routine moves start crossing it — and balloons after a vol spike, when only violent moves register. Firing rate and the information content of each fire are therefore regime-dependent by construction, and results should be expected to differ across macro eras. The regime split and sub-period breakdown above are the current read on how much this matters.

4 · Pairing inside a screen

The statements below describe how this signal relates to others by construction — which indicator family it belongs to, and where same-family redundancy might reduce the independence of evidence inside a Daily Report. These are taxonomic classifications drawn from standard technical-analysis texts; they are not pairing backtests. Measured pair results — same-day co-fires put through the pair backtest — follow under “Measured pairings” below.

Volatility-envelope construction

Bollinger Bands are a volatility envelope: a 20-period simple moving average ± 2 standard deviations of price (Bollinger, Bollinger on Bollinger Bands, 2001). This construction is distinct from momentum oscillators (RSI, Stochastics, Williams %R, CCI) and from moving-average crossover signals, so pairing Bollinger with any one of them does not produce same-family redundancy.

Measured pairings — Bonferroni survivors

Beyond the literature pairings above, these are the same-day co-fire combinations involving Bollinger Bands that cleared the pair backtest's Bonferroni cut on the full 2016–2026 sample (549 pairs × 5 horizons = 2,745 hypotheses), on universes filtered to ADV ≥ $5M, price ≥ $5 and market cap ≥ $100M. That cut is two-sided: it asks only whether the co-fire's α is reliably different from zero, in either direction, so a pair can survive by reliably underperforming — 6 of the 28 rows below do exactly that (negative full-sample α). The same run holds out 2023+: the Test columns are that held-out window, printed for every row with enough held-out co-fires to measure, so a survivor that did not repeat out of sample is visible rather than hidden. All α figures here are for holding the stock long after the co-fire — no shorting assumed, and no sign flip for bearish legs. So positive α means the co-fire was followed by outperformance and negative α by underperformance, whichever way either leg points — a bearish leg does not flip the reading. Survivors are rare by design — absence of a pair here means it did not clear the cut, not that it was untested. Ranked by held-out (2023+) α. Historical tendencies, not recommendations.

US (NYSE / NASDAQ / AMEX)

Pair (same-day co-fire, long) Full α Test α (2023+) Test N p_perm test
bollinger bullish + stochastics bullish +0.43% +0.47% 13,468 0.002
bollinger bullish + new_20d_low bearish +0.73% +0.46% 4,001 0.010
bollinger bullish + weekly_change bearish +0.97% +0.45% 6,480 0.010
bollinger bullish + williams_r bullish +0.24% +0.28% 18,595 0.002
bollinger bearish + double_bottom_breakdown bearish -3.89% — — —

5 of this universe's 18 surviving pairs involve this signal · α vs ^SPXEW.

Europe — 3 surviving pairs
Pair (same-day co-fire, long) Full α Test α (2023+) Test N p_perm test
bollinger bearish + williams_r bearish +0.40% +0.46% 6,855 0.002
bollinger bullish + stochastics bullish +0.46% +0.24% 3,957 0.066
bollinger bullish + williams_r bullish +0.28% +0.18% 5,876 0.086

3 of this universe's 20 surviving pairs involve this signal · α vs ^STOXX.

Hong Kong — 4 surviving pairs
Pair (same-day co-fire, long) Full α Test α (2023+) Test N p_perm test
bollinger bearish + rsi bearish +1.41% +1.92% 1,280 0.002
bollinger bearish + stochastics bearish +1.13% +1.76% 1,904 0.002
bollinger bearish + williams_r bearish +0.82% +1.34% 3,008 0.002
bollinger bearish + weekly_change bullish +1.23% +1.32% 1,479 0.002

4 of this universe's 23 surviving pairs involve this signal · α vs ^HSI.

China A-shares — 16 surviving pairs
Pair (same-day co-fire, long) Full α Test α (2023+) Test N p_perm test
bollinger bullish + weekly_change bearish +4.57% +6.33% 12,186 0.002
bollinger bullish + volume_breakout bullish +3.08% +5.99% 2,943 0.002
bollinger bullish + ma_crossover bearish +1.64% +3.62% 428 0.002
bollinger bullish + fresh_52w_low bearish +1.51% +2.23% 681 0.002
bollinger bearish + new_20d_low bearish -2.26% +2.00% 147 0.032
bollinger bullish + williams_r bullish +1.71% +1.77% 34,977 0.002
bollinger bullish + stochastics bullish +1.55% +1.44% 29,183 0.002
bollinger bullish + rsi bullish +1.96% +1.38% 13,489 0.002
bollinger bullish + cci bullish +1.24% +1.38% 4,902 0.002
bearish_trend_breakout bullish + bollinger bearish +1.54% +0.90% 672 0.052
bollinger bearish + stochastics bearish +0.25% +0.88% 27,307 0.002
bollinger bearish + volume_breakout bearish -0.87% +0.05% 18,879 0.593
bollinger bullish + new_20d_low bearish +0.58% +0.02% 7,647 0.836
bollinger bearish + hh_hl_structure bullish -3.87% -3.56% 87 0.002
bollinger bearish + bullish_trend_breakdown bearish -6.12% — — —
bollinger bearish + fresh_52w_low bearish -7.10% — — —

16 of this universe's 138 surviving pairs involve this signal · α vs 83188.HK.

China A-share survivor α runs large but skews toward small-caps, where trading costs and thin liquidity claim a large share of any measured edge — screening context, not a capturable spread.

“—” in the test columns means the held-out 2023+ sample fell below the 20-observation minimum this run requires before it computes any statistic, so no out-of-sample figure exists for that pair — not that it never co-fired again. Those pairs rank last.

What would likely rescue this signal

This block calls out the data or conditions that could turn a technically weak signal into a usable one in a composite screen. Based on signal mechanics and the observed failure patterns above; individual combinations are not yet backtested.

  • Volume-filter the bullish side — A lower-band break on heavy volume looks like capitulation; on light volume it is drift. Requiring elevated volume plus a follow-through close is one way to separate completed reversals from continuing declines. Inside a Daily Report this can be approximated today by AND-composing the Bollinger tile with the volume breakout signal (volume above a multiple of its 20-day average on a directional close).
  • Regime-gate the bullish side — Mean-reversion entries off the lower band assume a market where dips get bought broadly. A gate requiring healthy breadth (most stocks above their 50-day average) or the benchmark trading some distance below its all-time high is a testable way to carve out the environments where the bounce thesis holds. Check the sub-period breakdown above for whether the current data motivates the gate before relying on it.
  • Let the table set the bearish hold — If the current tables show the bearish effect growing from the 20d to the 60d column, short-horizon exits leave most of the move on the table and a time-stop beats a profit target — hold the window absent structural invalidation, such as the stock reclaiming and closing back above its upper band. If the columns are flat or reversed, shorten. Re-check after each backtest refresh.

See also Why technical-only signals don't survive on their own for the broader argument.

5 · Before acting — a 5-point checklist

  1. Normal trading day? Rule out earnings (within ±3 days), ex-dividend, or known corporate-action dates — the signal is almost certainly reading noise, not momentum, in those windows.
  2. Where is price vs its own 50 / 200 DMA? A mean-reversion signal firing against the long-term trend (e.g. oversold in a clean uptrend) is much more reliable than one firing with it.
  3. What's the sector breadth doing? An isolated signal in a broadly down-trending sector is a lower-confidence setup than one firing with the rest of its peer group.
  4. Is ADV20 enough for the intended size? A $1M notional order in a $500M name moves the tape by itself. A useful floor is adv20d ≥ 5% of the intended position.
  5. What invalidates the trade? Define a price level in advance (for longs: a close below the trigger-day low; for shorts: a close above the trigger-day high) and honour it. The backtest alpha is an average; any single trade can land at either tail.

Execution notes

Entry convention in the tables above is next-day open (open T+1). Parameters are the 20-period / 2-standard-deviation defaults from Bollinger's own work; shorter windows or tighter multiples fire more often on smaller excursions and are noisier by construction. Read direction from the live data: under the single-sided long convention used here, a bearish fire 'works' when post-trigger alpha is negative — the stock lags the benchmark after firing. If a side clears the random-date permutation null in the current tables, it can serve as a screen tile in that direction; otherwise treat its fires as context rather than a trade prompt. Historical tendency, not a recommendation.