bollinger
Bollinger Bands
Bullish: Price crosses above upper Bollinger Band. Bearish: Price crosses below lower Bollinger Band. 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: US large-cap (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, US-only
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% |
Sign flip across horizons. Bearish triggers go from -0.06% (5d) to +3.51% (1y) — short-term works as a sell signal but at 1-year horizon stocks mean-revert and outperform.
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.
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. The 20d alpha you'd actually capture if you took the trade. Bars matching your direction's "right" sign (green) = the signal worked in that regime; opposite sign = avoid it there. A signal with one strong-positive bar and three flat ones isn't a "20d alpha" signal — it's a "20d alpha when the stock is X" signal.
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 matching your direction's "right" sign = the signal is durable. One era doing all the work = a regime-specific edge that may not repeat. The bigger the variance across eras, the smaller the position you should run.
↑ Bullish triggers
| Bench | Metric | 1d | 5d | 20d | 60d | 252d |
|---|---|---|---|---|---|---|
| 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 | |
| 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 |
Permutation null detail — all horizons × both benchmarks
| Horizon | Bench | Observed lift | Null mean | Null 95% CI | pperm |
|---|---|---|---|---|---|
| 1d | spx | +0.08% | +0.09% | [+0.08%, +0.09%] | 0.557 |
| 1d | msci | +0.12% | +0.09% | [+0.08%, +0.09%] | 0.005 |
| 1d | spxew | +0.11% | +0.08% | [+0.07%, +0.08%] | 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 |
| 5d | spxew | +0.51% | +0.34% | [+0.33%, +0.36%] | 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 |
| 20d | spxew | +1.20% | +1.12% | [+1.10%, +1.14%] | 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 |
| 60d | spxew | +2.67% | +2.41% | [+2.36%, +2.44%] | 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 |
| 252d | spxew | +5.42% | +4.76% | [+4.68%, +4.84%] | 0.005 |
Example triggers on US large-caps (2023+, mcap ≥ $30B)
Six recent bullish BOLLINGER triggers on US mega-caps. Top three: the signal's best outcomes. Bottom three: the worst. Catalyst-driven outliers (|α| > 25%) excluded so what's left is the signal's own typical good and bad days, not earnings shocks.
Strongest outcomes (what BOLLINGER looks like when it works)
Weakest outcomes (what BOLLINGER looks like when it fails)
Stock-regime quadrants (2×2 per-stock, 20d alpha detail table)
| Quadrant | N | Stock % (spx) | Bench % (spx) | Alpha % (spx) | p (HAC) | Stock % (msci) | Bench % (msci) | Alpha % (msci) | p (HAC) | Stock % (spxew) | Bench % (spxew) | Alpha % (spxew) | p (HAC) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Trending + Low vol Clean directional grind, low whipsaw | 90,593 | +0.19% | +1.16% | -0.96% | <0.001 | +0.19% | +1.00% | -0.80% | <0.001 | +0.19% | +0.91% | -0.67% | <0.001 |
| Trending + High vol Crisis selloff or parabolic rally | 401,207 | +2.26% | +1.79% | +0.41% | <0.001 | +2.26% | +1.52% | +0.63% | <0.001 | +2.26% | +1.39% | +0.75% | <0.001 |
| Non-trending + Low vol Quiet chop, summer doldrums | 140,021 | +0.20% | +1.17% | -0.95% | <0.001 | +0.20% | +1.05% | -0.82% | <0.001 | +0.20% | +0.92% | -0.68% | <0.001 |
| Non-trending + High vol Classical "whipsaw zone" for momentum | 509,367 | +1.21% | +1.52% | -0.27% | <0.001 | +1.21% | +1.36% | -0.17% | <0.001 | +1.21% | +1.30% | -0.07% | 0.0001 |
Sub-period breakdown table (20d alpha)
| Period | N | Alpha % (spx) | p (HAC) | Alpha % (msci) | p (HAC) | Alpha % (spxew) | p (HAC) |
|---|---|---|---|---|---|---|---|
| 2015-2019 2015-01-01 → 2020-01-01 | 347,704 | -0.19% | <0.001 | +0.02% | 0.3053 | -0.12% | <0.001 |
| 2020-2022 2020-01-01 → 2023-01-01 | 349,798 | -0.02% | 0.5113 | +0.24% | <0.001 | -0.04% | 0.0657 |
| 2023-2026 2023-01-01 → 2099-01-01 | 443,216 | -0.29% | <0.001 | -0.28% | <0.001 | +0.36% | <0.001 |
↓ Bearish triggers negative alpha = signal was right (stock underperformed market)
| Bench | Metric | 1d | 5d | 20d | 60d | 252d |
|---|---|---|---|---|---|---|
| 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 | |
| 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 |
Permutation null detail — all horizons × both benchmarks
| Horizon | Bench | Observed lift | Null mean | Null 95% CI | pperm |
|---|---|---|---|---|---|
| 1d | spx | +0.09% | +0.09% | [+0.08%, +0.09%] | 1.000 |
| 1d | msci | +0.10% | +0.09% | [+0.08%, +0.10%] | 1.000 |
| 1d | spxew | +0.09% | +0.08% | [+0.07%, +0.08%] | 1.000 |
| 5d | spx | +0.34% | +0.36% | [+0.35%, +0.37%] | 0.005 |
| 5d | msci | +0.35% | +0.36% | [+0.35%, +0.37%] | 0.015 |
| 5d | spxew | +0.31% | +0.34% | [+0.33%, +0.36%] | 0.005 |
| 20d | spx | +1.17% | +1.14% | [+1.12%, +1.16%] | 0.990 |
| 20d | msci | +1.18% | +1.15% | [+1.13%, +1.18%] | 0.970 |
| 20d | spxew | +1.14% | +1.11% | [+1.09%, +1.13%] | 0.995 |
| 60d | spx | +2.23% | +2.48% | [+2.44%, +2.52%] | 0.005 |
| 60d | msci | +2.26% | +2.50% | [+2.46%, +2.54%] | 0.005 |
| 60d | spxew | +2.33% | +2.41% | [+2.37%, +2.45%] | 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 |
| 252d | spxew | +4.43% | +4.59% | [+4.51%, +4.65%] | 0.005 |
Example triggers on US large-caps (2023+, mcap ≥ $30B)
Six recent bearish BOLLINGER triggers on US mega-caps. Top three: the signal's best outcomes. Bottom three: the worst. Catalyst-driven outliers (|α| > 25%) excluded so what's left is the signal's own typical good and bad days, not earnings shocks.
Strongest outcomes (what BOLLINGER looks like when it works)
Weakest outcomes (what BOLLINGER looks like when it fails)
Stock-regime quadrants (2×2 per-stock, 20d alpha detail table)
| Quadrant | N | Stock % (spx) | Bench % (spx) | Alpha % (spx) | p (HAC) | Stock % (msci) | Bench % (msci) | Alpha % (msci) | p (HAC) | Stock % (spxew) | Bench % (spxew) | Alpha % (spxew) | p (HAC) |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Trending + Low vol Clean directional grind, low whipsaw | 116,618 | +0.59% | +0.64% | -0.04% | 0.1562 | +0.59% | +0.50% | +0.12% | <0.001 | +0.59% | +0.35% | +0.28% | <0.001 |
| Trending + High vol Crisis selloff or parabolic rally | 578,778 | +0.97% | +0.94% | +0.09% | 0.0004 | +0.97% | +0.81% | +0.22% | <0.001 | +0.97% | +0.72% | +0.33% | <0.001 |
| Non-trending + Low vol Quiet chop, summer doldrums | 151,671 | +0.53% | +0.68% | -0.16% | <0.001 | +0.53% | +0.54% | -0.01% | 0.6075 | +0.53% | +0.42% | +0.11% | <0.001 |
| Non-trending + High vol Classical "whipsaw zone" for momentum | 493,454 | +0.83% | +0.96% | -0.11% | <0.001 | +0.83% | +0.88% | -0.01% | 0.6020 | +0.83% | +0.82% | +0.02% | 0.2677 |
Sub-period breakdown table (20d alpha)
| Period | N | Alpha % (spx) | p (HAC) | Alpha % (msci) | p (HAC) | Alpha % (spxew) | p (HAC) |
|---|---|---|---|---|---|---|---|
| 2015-2019 2015-01-01 → 2020-01-01 | 400,529 | -0.65% | <0.001 | -0.43% | <0.001 | -0.37% | <0.001 |
| 2020-2022 2020-01-01 → 2023-01-01 | 395,813 | +0.28% | <0.001 | +0.40% | <0.001 | +0.06% | 0.0329 |
| 2023-2026 2023-01-01 → 2099-01-01 | 543,666 | +0.19% | <0.001 | +0.25% | <0.001 | +0.67% | <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: fraction of 200 random-date null iterations with mean ≥ observed. 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 zero edge even if the t-test says "significant."
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
Caution recommended. Bearish 20d alpha is -0.04% and worse than random . Either direction fails the "beats random" test. Don't use Bollinger Bands as a standalone entry trigger. It may still be useful as part of a composite (section 4).
2 · When it works — the setups that drive it
- Best bullish setup: Trending + High vol — alpha +0.41% / 20d on 401,207 historical triggers.
- Best bearish setup: Trending + High vol — alpha +0.09% / 20d on 578,778 historical triggers.
- Best era for bullish: 2020-2022 — alpha -0.02% / 20d.
- Best era for bearish: 2020-2022 — alpha +0.28% / 20d.
3 · When it fails — common false positives
- Weakest bullish cell: Trending + Low vol — alpha -0.96% / 20d on 90,593 triggers.
- Weakest bearish cell: Non-trending + Low vol — alpha -0.16% / 20d on 151,671 triggers.
- Worst era for bullish: 2023-2026 — alpha -0.29% / 20d.
- Worst era for bearish: 2015-2019 — alpha -0.65% / 20d.
Signal-specific failure patterns
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. A multi-signal convergence backtest is planned but not yet run.
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.
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 touch on HIGH volume is capitulation; on low volume is drift. A bullish filter requiring volume > 1.5× average + a follow-through close above T+1 open might isolate real reversals from continuing drawdowns. Not currently implemented in the screen filter layer.
- Regime gate the bullish side — Bullish Bollinger worked 2015-2019 and broke 2020+. A filter requiring 'market breadth > 55%' (most stocks above 50DMA) or 'SPX not within 5% of ATH' might carve out the residual mean-reversion regime.
- Hold the bearish trade to 60d — Bearish edge doubles from 20d to 60d (−0.22 → −0.62). Short-horizon exits on Bollinger bearish leave alpha on the table. This argues for a time-stop rather than a profit-target exit — hold the full 60d window absent a structural invalidation (stock taking out its upper-band high by > 2%).
See also Why technical-only signals don't survive on their own for the broader argument.
5 · Before you act — a 5-point checklist
- 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.
- 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.
- 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.
- Is ADV20 enough for your size? If the trigger is on a $500M name and you want to move $1M notional, you're the tape. Consider adv20d ≥ 5% of your intended position.
- What invalidates you? Define a price level (for longs: a close below the trigger-day low; for shorts: close above the trigger-day high) and honor it. The backtest alpha is an average; any one trade can be at either tail.
Execution notes
Bearish upper-band touches are the only tradable direction here. 20d and 60d both deliver real alpha; 60d compounds more but adds event risk. Entry = open T+1. The bullish lower-touch trade is a structural loser — stocks touching their lower band in a bull market are usually breaking down, not pausing. Note: Bollinger Bands period/std-dev parameters matter a lot; this backtest uses 20-period / 2 stdev which is the Lambert default. Tighter parameters (shorter window, lower stdev) would fire more often on smaller deviations — likely noisier.