Mean reversion williams_r

Williams %R

Range: -100 to 0. Bullish: %R crosses above oversold (-80) from below. Bearish: %R crosses below overbought (-20) from above.

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 Lookback period 14 5–50
overbought Overbought level -20 -30–-10
oversold Oversold level -80 -90–-70

Historical context

5,522,997 triggers on 24,258 tickers, 1995-09-06 → 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 -0.07% +0.00%
20-day -0.12% +0.15%
60-day +0.17% +0.40%
1-year +1.54% +2.40%
Random-date null check (20-day): Bullish: worse than random (p=1.000).
Bearish: worse than random (p=1.000).

Where does WILLIAMS_R 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.

Williams %R (williams_r) — 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.

Williams %R (williams_r) — 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.

Williams %R (williams_r) — 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 % -0.01% +0.16% +0.96% +2.94% +12.11%
Bench % +0.04% +0.21% +1.09% +2.76% +10.48%
Alpha % -0.06% -0.07% -0.12% +0.17% +1.54%
Median alpha -0.12% -0.30% -0.94% -1.99% -6.89%
Hit rate (α>0) 47.0% 46.8% 45.3% 44.4% 41.5%
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 2,662,708 2,572,563 2,546,037 2,483,251 2,239,567
spx Stock % -0.01% +0.16% +0.96% +2.94% +12.11%
Bench % +0.01% +0.24% +1.30% +3.33% +14.24%
Alpha % -0.04% -0.11% -0.33% -0.41% -2.17%
Median alpha -0.11% -0.35% -1.19% -2.63% -10.71%
Hit rate (α>0) 47.3% 46.2% 44.1% 42.8% 37.5%
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 2,679,499 2,593,038 2,581,973 2,510,619 2,269,996
msci Stock % -0.01% +0.16% +0.96% +2.94% +12.11%
Bench % +0.06% +0.26% +1.14% +2.97% +11.85%
Alpha % -0.07% -0.11% -0.20% -0.01% -0.07%
Median alpha -0.14% -0.37% -1.07% -2.28% -8.51%
Hit rate (α>0) 46.4% 46.0% 44.6% 43.7% 39.8%
p (naive) <0.001 <0.001 <0.001 0.2549 0.0273
p (HAC) <0.001 <0.001 <0.001 0.5771 0.5800
N 2,662,426 2,572,370 2,548,646 2,491,323 2,244,934
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.
Williams %R (williams_r) — 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 +0.08% +0.08% [+0.08%, +0.08%] 0.005
1d spx +0.08% +0.09% [+0.08%, +0.09%] 1.000
1d msci +0.08% +0.09% [+0.09%, +0.09%] 1.000
5d spxew +0.33% +0.36% [+0.35%, +0.36%] 1.000
5d spx +0.33% +0.37% [+0.36%, +0.38%] 1.000
5d msci +0.32% +0.38% [+0.37%, +0.38%] 1.000
20d spxew +1.01% +1.16% [+1.14%, +1.17%] 1.000
20d spx +1.03% +1.19% [+1.17%, +1.20%] 1.000
20d msci +1.04% +1.20% [+1.19%, +1.22%] 1.000
60d spxew +2.49% +2.48% [+2.46%, +2.51%] 0.174
60d spx +2.66% +2.55% [+2.52%, +2.57%] 0.005
60d msci +2.64% +2.57% [+2.54%, +2.60%] 0.005
252d spxew +4.97% +4.82% [+4.77%, +4.86%] 0.005
252d spx +5.32% +5.16% [+5.11%, +5.21%] 0.005
252d msci +5.15% +5.11% [+5.06%, +5.15%] 0.050

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

Six recent bullish WILLIAMS_R 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
Williams %R (williams_r) — 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 Williams %R (williams_r) — 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 Williams %R (williams_r) — 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
Williams %R (williams_r) — weakest bullish trigger #1 on a US mega-cap, showing the 20-day forward window where the signal failed Williams %R (williams_r) — weakest bullish trigger #2 on a US mega-cap, showing the 20-day forward window where the signal failed Williams %R (williams_r) — 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 168,188 +0.26% +0.78% -0.47% <0.001 +0.26% +1.05% -0.77% <0.001 +0.26% +0.90% -0.61% <0.001
Trending + High vol Crisis selloff or parabolic rally 912,248 +1.45% +1.18% +0.19% <0.001 +1.45% +1.48% -0.05% 0.0017 +1.45% +1.26% +0.12% <0.001
Non-trending + Low vol Quiet chop, summer doldrums 331,385 +0.27% +0.76% -0.47% <0.001 +0.27% +1.02% -0.75% <0.001 +0.27% +0.90% -0.62% <0.001
Non-trending + High vol Classical "whipsaw zone" for momentum 1,347,279 +0.91% +1.10% -0.18% <0.001 +0.91% +1.28% -0.34% <0.001 +0.91% +1.15% -0.25% <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 → 2020-01-01 824,394 -0.34% <0.001 -0.45% <0.001 -0.27% <0.001
2020-2022 2020-01-01 → 2023-01-01 835,687 -0.36% <0.001 -0.14% <0.001 +0.01% 0.5361
2023-2026 2023-01-01 → 2099-01-01 1,098,355 +0.26% <0.001 -0.38% <0.001 -0.31% <0.001

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

Bench Metric 1d 5d 20d 60d 252d
spxew Stock % +0.03% +0.21% +0.83% +2.62% +12.31%
Bench % +0.04% +0.22% +0.74% +2.26% +10.00%
Alpha % -0.02% +0.00% +0.15% +0.40% +2.40%
Median alpha -0.07% -0.26% -0.73% -1.78% -5.87%
Hit rate (α>0) 48.2% 47.2% 46.3% 45.0% 42.5%
p (naive) <0.001 0.3638 <0.001 <0.001 <0.001
p (HAC) <0.001 0.3999 <0.001 <0.001 <0.001
N 2,655,513 2,557,182 2,544,325 2,485,306 2,196,052
spx Stock % +0.03% +0.21% +0.83% +2.62% +12.31%
Bench % +0.02% +0.23% +0.92% +3.02% +13.74%
Alpha % +0.00% -0.01% -0.05% -0.39% -1.46%
Median alpha -0.06% -0.29% -0.97% -2.60% -9.87%
Hit rate (α>0) 48.3% 46.8% 45.1% 42.8% 38.2%
p (naive) 0.0037 0.0035 <0.001 <0.001 <0.001
p (HAC) 0.0038 0.0069 <0.001 <0.001 <0.001
N 2,682,061 2,597,938 2,569,361 2,516,507 2,223,847
msci Stock % +0.03% +0.21% +0.83% +2.62% +12.31%
Bench % +0.04% +0.21% +0.80% +2.59% +11.32%
Alpha % -0.01% +0.02% +0.07% +0.06% +0.90%
Median alpha -0.08% -0.27% -0.85% -2.18% -7.49%
Hit rate (α>0) 48.0% 47.1% 45.7% 43.9% 40.8%
p (naive) <0.001 <0.001 <0.001 <0.001 <0.001
p (HAC) <0.001 <0.001 <0.001 0.0388 <0.001
N 2,663,410 2,579,722 2,562,480 2,500,319 2,213,542
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.
Williams %R (williams_r) — 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 +0.11% +0.07% [+0.07%, +0.08%] 1.000
1d spx +0.11% +0.08% [+0.08%, +0.08%] 1.000
1d msci +0.13% +0.09% [+0.08%, +0.09%] 1.000
5d spxew +0.35% +0.32% [+0.31%, +0.33%] 1.000
5d spx +0.37% +0.34% [+0.33%, +0.34%] 1.000
5d msci +0.40% +0.34% [+0.33%, +0.35%] 1.000
20d spxew +1.10% +1.05% [+1.03%, +1.06%] 1.000
20d spx +1.13% +1.08% [+1.06%, +1.09%] 1.000
20d msci +1.14% +1.09% [+1.08%, +1.10%] 1.000
60d spxew +2.20% +2.27% [+2.25%, +2.30%] 0.005
60d spx +2.17% +2.34% [+2.32%, +2.37%] 0.005
60d msci +2.19% +2.36% [+2.34%, +2.39%] 0.005
252d spxew +4.25% +4.44% [+4.38%, +4.49%] 0.005
252d spx +4.47% +4.79% [+4.73%, +4.84%] 0.005
252d msci +4.50% +4.74% [+4.68%, +4.79%] 0.005

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

Six recent bearish WILLIAMS_R 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
Williams %R (williams_r) — 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 Williams %R (williams_r) — 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 Williams %R (williams_r) — 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
Williams %R (williams_r) — weakest bearish trigger #1 on a US mega-cap, showing the 20-day forward window where the signal failed Williams %R (williams_r) — weakest bearish trigger #2 on a US mega-cap, showing the 20-day forward window where the signal failed Williams %R (williams_r) — 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 209,277 +0.45% +0.38% +0.11% <0.001 +0.45% +0.69% -0.22% <0.001 +0.45% +0.54% -0.06% 0.0015
Trending + High vol Crisis selloff or parabolic rally 1,042,153 +1.01% +0.76% +0.32% <0.001 +1.01% +0.97% +0.08% <0.001 +1.01% +0.84% +0.23% <0.001
Non-trending + Low vol Quiet chop, summer doldrums 337,323 +0.49% +0.50% +0.01% 0.5731 +0.49% +0.75% -0.25% <0.001 +0.49% +0.60% -0.10% <0.001
Non-trending + High vol Classical "whipsaw zone" for momentum 1,175,111 +0.89% +0.85% +0.08% <0.001 +0.89% +0.97% -0.05% 0.0011 +0.89% +0.88% +0.06% 0.0001
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 → 2020-01-01 832,308 -0.25% <0.001 -0.48% <0.001 -0.28% <0.001
2020-2022 2020-01-01 → 2023-01-01 822,478 +0.14% <0.001 +0.38% <0.001 +0.51% <0.001
2023-2026 2023-01-01 → 2099-01-01 1,108,442 +0.47% <0.001 -0.04% 0.0276 +0.04% 0.0328

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

Not a standalone entry trigger at 20 days. Bullish 20d alpha is -0.12% — worse than random : firing on random dates would have done better. Bearish 20d alpha is +0.15% — 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 +0.19% / 20d on 912,248 historical triggers.
  • Least-bad bearish cell: Non-trending + Low vol — alpha +0.01% / 20d on 337,323 triggers — still wrong-signed; no bearish cell produced negative alpha.
  • Best era for bullish: 2023-2026 — alpha +0.26% / 20d on 1,098,355 triggers.
  • Best era for bearish: 2015-2019 — alpha -0.25% / 20d on 832,308 triggers.

3 · When it fails — common false positives

  • Weakest bullish cell: Trending + Low vol — alpha -0.47% / 20d on 168,188 triggers.
  • Weakest bearish cell: Trending + High vol — alpha +0.32% / 20d on 1,042,153 triggers.
  • Worst era for bullish: 2020-2022 — alpha -0.36% / 20d on 835,687 triggers.
  • Worst era for bearish: 2023-2026 — alpha +0.47% / 20d on 1,108,442 triggers.

Signal-specific failure patterns

Oversold-exit re-arms repeatedly in persistent downtrends
The bullish trigger fires when %R crosses back above −80 from below — a close lifting off the bottom of its 14-day high-low range. In a persistent downtrend the range itself keeps sliding lower, so any modest bounce pushes %R out of the oversold zone, the bounce fades, %R re-enters, and the trigger re-arms. The signal can fire against the trend many times on the way down because nothing in the trigger checks trend direction. Whether those countertrend fires have paid historically is an empirical question — read the at-a-glance table and the permutation-null line above for the current answer rather than assuming the mean-reversion textbook.
Leaving overbought is not the same event as a top
The bearish trigger fires when %R drops back below −20 from above. In a strong uptrend, price hugs the top of its 14-day range and %R can sit above −20 for weeks; the eventual dip below the line is often a routine pullback inside an ongoing advance, not a reversal. Mechanically, the trigger detects 'no longer pressing the top of its two-week range' — a much weaker statement than 'topping out'. Treat the direction label as nominal and let the live tables on this page adjudicate whether the bearish side carries any forward information at your horizon.
Range-width blindness
%R normalises the close inside the 14-day high-low range but is indifferent to how wide that range is: a stock drifting in a 2% band and one swinging through a 40% band produce identical %R readings. Quiet consolidations and violent selloffs are pooled into the same trigger population, which is one structural reason unconditional oscillator triggers are noisy. The volatility-regime split in the tables above is where that pooling gets unpacked — check it, and the sub-period rows, before extrapolating any single era's behaviour.

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.

Oscillator-family redundancy

Williams %R belongs to the momentum-oscillator family alongside RSI, Stochastics, and CCI — each normalises recent price against a short lookback window into a bounded range (Murphy, Technical Analysis of the Financial Markets, 1999; Pring, Technical Analysis Explained, 5th ed. 2014; Kirkpatrick & Dahlquist, Technical Analysis, 3rd ed. 2015). The overlap with Stochastics is exact by construction: %R equals the raw (fast) stochastic %K minus 100 over the same lookback, so the two indicators differ only in trigger logic, not information content. Stacking two or more of these in the same direction within a single Daily Report produces correlated rather than independent evidence.

Measured pairings — Bonferroni survivors

Beyond the literature pairings above, these are the same-day co-fire combinations involving Williams %R 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 — 5 of the 33 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
stochastics bullish + williams_r bullish +0.20% +0.32% 31,815 0.002
bollinger bullish + williams_r bullish +0.24% +0.28% 18,595 0.002

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

Europe — 7 surviving pairs
Pair (same-day co-fire, long) Full α Test α (2023+) Test N p_perm test
rsi bearish + williams_r bearish +0.48% +0.52% 5,802 0.002
bollinger bearish + williams_r bearish +0.40% +0.46% 6,855 0.002
vwap_cross bearish + williams_r bearish +0.36% +0.41% 3,388 0.006
stochastics bearish + williams_r bearish +0.36% +0.39% 11,446 0.002
cci bearish + williams_r bearish +0.33% +0.35% 11,506 0.002
bollinger bullish + williams_r bullish +0.28% +0.18% 5,876 0.086
cci bullish + williams_r bullish +0.35% +0.08% 9,070 0.321

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

Hong Kong — 5 surviving pairs
Pair (same-day co-fire, long) Full α Test α (2023+) Test N p_perm test
rsi bearish + williams_r bearish +1.03% +1.91% 1,981 0.002
bollinger bearish + williams_r bearish +0.82% +1.34% 3,008 0.002
cci bearish + williams_r bearish +0.58% +0.86% 3,398 0.002
weekly_change bullish + williams_r bearish +1.49% +0.77% 1,235 0.106
stochastics bearish + williams_r bearish +0.53% +0.73% 3,861 0.002

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

China A-shares — 19 surviving pairs
Pair (same-day co-fire, long) Full α Test α (2023+) Test N p_perm test
weekly_change bearish + williams_r bullish +5.32% +7.51% 7,294 0.002
volume_breakout bullish + williams_r bullish +0.95% +2.27% 8,927 0.002
bollinger bullish + williams_r bullish +1.71% +1.77% 34,977 0.002
hh_hl_structure bearish + williams_r bearish +0.77% +1.54% 2,711 0.002
hh_hl_streak bullish + williams_r bullish +1.33% +1.27% 1,189 0.002
rsi bullish + williams_r bullish +1.85% +1.18% 19,261 0.002
macd bullish + williams_r bullish +0.50% +1.10% 10,608 0.002
stochastics bearish + williams_r bearish +0.52% +1.01% 57,784 0.002
rsi bearish + williams_r bearish +0.43% +0.99% 27,909 0.002
vwap_cross bullish + williams_r bullish +0.34% +0.71% 18,678 0.002
cci bullish + williams_r bullish +0.48% +0.67% 55,921 0.002
vwap_cross bearish + williams_r bearish +0.25% +0.67% 14,342 0.002
stochastics bullish + williams_r bullish +0.51% +0.67% 65,651 0.002
cci bearish + williams_r bearish +0.35% +0.62% 40,420 0.002
weekly_change bullish + williams_r bearish -0.37% +0.43% 28,381 0.002
volume_breakout bearish + williams_r bearish -0.72% +0.15% 20,640 0.164
new_20d_low bearish + williams_r bullish -0.60% -1.54% 4,763 0.002
hh_hl_structure bullish + williams_r bearish -3.42% -3.45% 134 0.002
cci bullish + williams_r bearish -4.02% — — —

19 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.

  • Pair with a trend filter — The raw trigger ignores trend direction, so conditioning on it is the natural refinement — for example, taking bearish %R fires only below a declining 50DMA, or bullish fires only above it. The filter discards most triggers, which is the point: it separates with-trend from countertrend populations. Testable within the platform's own screens without new data.
  • Let the table pick the holding period — Oscillator exits can behave very differently at 20 versus 60 days, and the relationship is not stable across regimes. Compare the horizon columns in the at-a-glance table before choosing between time stops and price stops — time stops only make sense if the current data shows the effect compounding with horizon.

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

The trigger is a one-day cross event: %R (14-day lookback at default settings) crossing above the −80 line for bullish, below the −20 line for bearish. The backtest behind the tables above measures entry at the open on T+1 after a trigger on the close of T. Treat tradability as an empirical, direction-conditional question: if a side beats the random-date null in the current tables at your horizon, it can serve as a screen tile in that direction; if it does not, treat its fires as context — a note that the stock just left an extreme of its two-week range — rather than an entry. Horizon choice should come from the horizon columns in the live table, not from a remembered number. Everything here describes historical tendency, not a recommendation.

See a live screen of this signal

Curated Daily Reports that screen for this signal, refreshed at the open, midday and close — free to view, no account needed: