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

865,713 valid triggers on 3,716 distinct tickers between 2015-02-24 and 2026-04-22. Universe: us_only · mcap ≥ $100,000,000 · price ≥ $1 (3,716 tickers). Entry at open T+1. 1d = intraday T+1; 20d = open T+1 to close T+20.

Benchmarks: spxew (S&P 500 Equal Weight — the primary benchmark here; a median-stock view that avoids the 2020+ megacap-concentration distortion), spx (S&P 500, cap-weighted), and msci (MSCI World USD). Per-stock regime: trending = ADX(14) ≥ 25, high vol = 20d ann. vol ≥ 20%.

At a glance (20d alpha vs S&P 500 Equal Weight, US-only)

Bullish
+0.02%
vs random-date null: worse than random (pperm=1.000)
Bearish (negative alpha = signal right)
-0.01%
vs random-date null: beats random (pperm=0.005)

Reading this: the random-date null is: for each ticker, sample N random dates and compute the same alpha — what alpha does a signal with no information produce? If the signal's observed alpha beats the null (pperm≤0.05), it's adding real information. If it's inside or worse than the null, the signal doesn't add value over random firing — any observed alpha is either noise or a universe artifact.

How often does WILLIAMS_R fire in each regime?

The signal's bucket distribution is itself informative. If 50%+ of all WILLIAMS_R triggers fire in the "non-trending + high vol" quadrant, the signal is structurally a chop-market event — regardless of what its textbook definition claims. Bullish and bearish are shown separately; counts are across the full US-only sample after the mcap and price floor.

Williams %R (williams_r) — trigger count distribution by per-stock regime quadrant (trending/non-trending × high/low realized volatility) for , US-only universe

Per-stock regime quadrant — 20d alpha

Each trigger is tagged with the host stock's own technical regime on the trigger date: is the stock itself in a trend (ADX(14) ≥ 25) or ranging? And is its realized 20-day volatility high (≥ 20% annualized) or low? This is the textbook conditioning variable — "does this signal work better in trending stocks?" — answered at the level of the individual stock, not the market. Positive bars are good for the signal; negative bars mean alpha vanishes into the benchmark or worse.

Williams %R (williams_r) — mean 20-day alpha versus S&P 500 Equal Weight by per-stock regime quadrant,  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.

Sub-period check — does the signal work in every era?

A multi-year average can hide major instability. We split the sample into three non-overlapping windows: 2015–2019 (pre-COVID, normalized monetary policy), 2020–2022 (pandemic crash + recovery + rate-shock bear), and 2023+ (post-ZIRP, AI megacap rally). If a signal's alpha is positive overall but comes entirely from one era, that's a red flag — the conditions that produced it may not repeat. A robust signal shows a consistent sign across all non-empty buckets.

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
spx Stock % -0.04% +0.11% +1.00% +3.06% +12.48%
Bench % -0.01% +0.25% +1.19% +3.37% +13.91%
Alpha % -0.03% -0.13% -0.17% -0.29% -1.41%
Median alpha -0.05% -0.24% -0.63% -1.77% -8.76%
Hit rate (α>0) 48.6% 47.3% 46.9% 45.1% 39.6%
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 415,865 415,358 411,916 402,106 367,283
msci Stock % -0.04% +0.11% +1.00% +3.06% +12.48%
Bench % +0.07% +0.28% +1.14% +3.01% +11.75%
Alpha % -0.09% -0.18% -0.10% +0.06% +0.71%
Median alpha -0.12% -0.30% -0.57% -1.40% -6.53%
Hit rate (α>0) 47.0% 46.7% 47.1% 46.1% 42.1%
p (naive) <0.001 <0.001 <0.001 0.0798 <0.001
p (HAC) <0.001 <0.001 0.0001 0.4089 0.0300
N 414,609 411,616 408,448 400,162 365,683
spxew Stock % -0.04% +0.11% +1.00% +3.06% +12.48%
Bench % +0.01% +0.18% +1.06% +2.79% +10.48%
Alpha % -0.04% -0.07% +0.02% +0.28% +2.20%
Median alpha -0.07% -0.18% -0.42% -1.14% -5.27%
Hit rate (α>0) 48.0% 48.0% 47.8% 46.7% 43.4%
p (naive) <0.001 <0.001 0.3444 <0.001 <0.001
p (HAC) <0.001 <0.001 0.5208 0.0001 <0.001
N 414,132 412,136 408,408 399,229 362,559
Distribution of all 20d alpha outcomes for this direction. Median and winsorized mean shown.
Williams %R (williams_r) — bullish 20-day alpha histogram showing distribution of per-trigger returns
Observed 20d alpha (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 a tail, the signal is doing real work in that direction.
Williams %R (williams_r) — bullish 20-day observed alpha versus random-date permutation null (200 iterations)
Permutation null detail — all horizons × both benchmarks
200-iteration null: for each ticker, sample N random dates from its history (matching observed trigger count) and compute the same alpha. The null distribution's 95% CI is where a signal with no information would land. pperm = one-sided fraction of null iters with mean ≥ observed.
Horizon Bench Observed α Null mean Null 95% CI pperm
1d spx -0.03% -0.00% [-0.03%, +0.19%] 0.811
1d msci -0.09% -0.03% [-0.05%, +0.16%] 1.000
1d spxew -0.04% -0.03% [-0.05%, +0.16%] 0.279
5d spx -0.13% +0.12% [-0.01%, +0.39%] 1.000
5d msci -0.18% +0.13% [-0.01%, +0.40%] 1.000
5d spxew -0.07% +0.15% [+0.02%, +0.42%] 1.000
20d spx -0.17% +0.21% [+0.05%, +0.46%] 1.000
20d msci -0.10% +0.33% [+0.18%, +0.59%] 1.000
20d spxew +0.02% +0.40% [+0.25%, +0.65%] 1.000
60d spx -0.29% +0.40% [+0.20%, +0.71%] 1.000
60d msci +0.06% +0.85% [+0.64%, +1.15%] 1.000
60d spxew +0.28% +1.07% [+0.86%, +1.38%] 1.000
252d spx -1.41% +0.90% [+0.55%, +1.32%] 1.000
252d msci +0.71% +3.21% [+2.85%, +3.65%] 1.000
252d spxew +2.20% +4.58% [+4.25%, +5.01%] 1.000

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

Six recent bullish WILLIAMS_R triggers on US mega-caps, filtered to |alpha| ≤ 25% to exclude catalyst-driven outliers (earnings surprises, M&A, binary events). The first three are the strongest outcomes — what the signal looks like when it works. The last three are the weakest — what the signal looks like when it fails. Each chart shows the stock's price with signal-appropriate technical overlays (e.g. MACD subpanel on MACD pages, Bollinger Bands on Bollinger pages, the 52-week trailing max line on 52w-high pages), a dot marking the trigger date, and the forward window shaded (green when the signal was right, red when it wasn't). Click any chart to open full-size.

Strongest outcomes (what WILLIAMS_R looks like when it works)
Weakest outcomes (what WILLIAMS_R looks like when it fails)
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 % (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 24,209 +0.23% +0.69% -0.45% <0.001 +0.23% +0.55% -0.30% <0.001 +0.23% +0.43% -0.14% 0.0047
Trending + High vol Crisis selloff or parabolic rally 138,953 +1.04% +1.38% -0.33% <0.001 +1.04% +1.24% -0.22% <0.001 +1.04% +1.12% -0.06% 0.2084
Non-trending + Low vol Quiet chop, summer doldrums 42,864 +0.27% +0.80% -0.49% <0.001 +0.27% +0.64% -0.34% <0.001 +0.27% +0.48% -0.17% <0.001
Non-trending + High vol Classical "whipsaw zone" for momentum 210,015 +1.25% +1.21% +0.07% 0.0891 +1.25% +1.21% +0.07% 0.0723 +1.25% +1.15% +0.15% <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 % (spx) p (HAC) Alpha % (msci) p (HAC) Alpha % (spxew) p (HAC)
2015-2019 2015-01-01 → 2020-01-01 118,517 +0.05% 0.2147 +0.18% <0.001 +0.14% 0.0008
2020-2022 2020-01-01 → 2023-01-01 135,952 -0.05% 0.3033 +0.06% 0.2253 -0.23% <0.001
2023-2026 2023-01-01 → 2099-01-01 161,576 -0.43% <0.001 -0.45% <0.001 +0.16% 0.0005

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

Bench Metric 1d 5d 20d 60d 252d
spx Stock % -0.02% +0.19% +0.70% +2.34% +11.18%
Bench % +0.01% +0.22% +0.97% +2.94% +13.29%
Alpha % -0.03% -0.02% -0.22% -0.58% -2.10%
Median alpha -0.02% -0.15% -0.72% -1.90% -8.33%
Hit rate (α>0) 49.3% 48.3% 46.2% 44.6% 39.5%
p (naive) <0.001 0.0086 <0.001 <0.001 <0.001
p (HAC) <0.001 0.0156 <0.001 <0.001 <0.001
N 449,514 447,880 444,600 437,099 391,254
msci Stock % -0.02% +0.19% +0.70% +2.34% +11.18%
Bench % +0.01% +0.18% +0.82% +2.46% +10.74%
Alpha % -0.03% +0.02% -0.06% -0.07% +0.45%
Median alpha -0.03% -0.11% -0.55% -1.37% -5.70%
Hit rate (α>0) 49.3% 48.8% 47.0% 46.0% 42.7%
p (naive) <0.001 0.0416 0.0004 0.0193 <0.001
p (HAC) <0.001 0.0603 0.0219 0.2914 0.1395
N 448,141 446,064 442,737 434,282 389,070
spxew Stock % -0.02% +0.19% +0.70% +2.34% +11.18%
Bench % +0.03% +0.21% +0.79% +2.21% +9.67%
Alpha % -0.05% -0.02% -0.01% +0.17% +1.67%
Median alpha -0.04% -0.12% -0.46% -1.12% -4.68%
Hit rate (α>0) 49.0% 48.6% 47.4% 46.7% 43.7%
p (naive) <0.001 0.0313 0.4383 <0.001 <0.001
p (HAC) <0.001 0.0477 0.6137 0.0102 <0.001
N 447,600 443,877 441,386 433,885 387,212
Distribution of all 20d alpha outcomes for this direction. Median and winsorized mean shown.
Williams %R (williams_r) — bearish 20-day alpha histogram showing distribution of per-trigger returns
Observed 20d alpha (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 a tail, the signal is doing real work in that direction.
Williams %R (williams_r) — bearish 20-day observed alpha versus random-date permutation null (200 iterations)
Permutation null detail — all horizons × both benchmarks
200-iteration null: for each ticker, sample N random dates from its history (matching observed trigger count) and compute the same alpha. The null distribution's 95% CI is where a signal with no information would land. pperm = one-sided fraction of null iters with mean ≥ observed.
Horizon Bench Observed α Null mean Null 95% CI pperm
1d spx -0.03% -0.00% [-0.02%, +0.17%] 0.005
1d msci -0.03% -0.03% [-0.04%, +0.15%] 0.935
1d spxew -0.05% -0.03% [-0.04%, +0.15%] 0.005
5d spx -0.02% +0.11% [+0.01%, +0.36%] 0.005
5d msci +0.02% +0.11% [+0.01%, +0.37%] 0.035
5d spxew -0.02% +0.13% [+0.04%, +0.39%] 0.005
20d spx -0.22% +0.24% [+0.12%, +0.50%] 0.005
20d msci -0.06% +0.37% [+0.24%, +0.62%] 0.005
20d spxew -0.01% +0.44% [+0.31%, +0.69%] 0.005
60d spx -0.58% +0.54% [+0.37%, +0.86%] 0.005
60d msci -0.07% +0.98% [+0.81%, +1.30%] 0.005
60d spxew +0.17% +1.21% [+1.04%, +1.53%] 0.005
252d spx -2.10% +1.53% [+1.21%, +1.86%] 0.005
252d msci +0.45% +3.85% [+3.55%, +4.20%] 0.005
252d spxew +1.67% +5.20% [+4.87%, +5.54%] 0.005

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

Six recent bearish WILLIAMS_R triggers on US mega-caps, filtered to |alpha| ≤ 25% to exclude catalyst-driven outliers (earnings surprises, M&A, binary events). The first three are the strongest outcomes — what the signal looks like when it works. The last three are the weakest — what the signal looks like when it fails. Each chart shows the stock's price with signal-appropriate technical overlays (e.g. MACD subpanel on MACD pages, Bollinger Bands on Bollinger pages, the 52-week trailing max line on 52w-high pages), a dot marking the trigger date, and the forward window shaded (green when the signal was right, red when it wasn't). Click any chart to open full-size.

Strongest outcomes (what WILLIAMS_R looks like when it works)
Weakest outcomes (what WILLIAMS_R looks like when it fails)
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 % (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 39,171 +0.17% +0.50% -0.28% <0.001 +0.17% +0.30% -0.07% 0.0843 +0.17% +0.17% +0.07% 0.0661
Trending + High vol Crisis selloff or parabolic rally 146,088 +0.82% +1.09% -0.22% <0.001 +0.82% +0.96% -0.06% 0.2592 +0.82% +0.88% +0.03% 0.6108
Non-trending + Low vol Quiet chop, summer doldrums 52,590 +0.21% +0.66% -0.43% <0.001 +0.21% +0.42% -0.19% <0.001 +0.21% +0.35% -0.10% 0.0025
Non-trending + High vol Classical "whipsaw zone" for momentum 211,810 +0.91% +1.06% -0.10% 0.0079 +0.91% +0.94% +0.04% 0.2876 +0.91% +0.95% +0.03% 0.4190
Sub-period breakdown table (20d alpha)
Historical clustering check. If alpha concentrates in one era, the signal's robustness is questionable.
Period N Alpha % (spx) p (HAC) Alpha % (msci) p (HAC) Alpha % (spxew) p (HAC)
2015-2019 2015-01-01 → 2020-01-01 136,162 -0.36% <0.001 -0.15% <0.001 -0.09% 0.0107
2020-2022 2020-01-01 → 2023-01-01 141,552 +0.13% 0.0072 +0.29% <0.001 -0.10% 0.0397
2023-2026 2023-01-01 → 2099-01-01 171,954 -0.38% <0.001 -0.24% <0.001 +0.16% 0.0006

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. Bullish 20d alpha is -0.17% and worse than random — triggering on random dates would have produced better long-side returns. Either direction fails the "beats random" test. Don't use Williams %R 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: Non-trending + High vol — alpha +0.07% / 20d on 210,015 historical triggers.
  • Best bearish setup: Non-trending + High vol — alpha -0.10% / 20d on 211,810 historical triggers.
  • Best era for bullish: 2015-2019 — alpha +0.05% / 20d.
  • Best era for bearish: 2020-2022 — alpha +0.13% / 20d.

3 · When it fails — common false positives

  • Weakest bullish cell: Non-trending + Low vol — alpha -0.49% / 20d on 42,864 triggers.
  • Weakest bearish cell: Non-trending + Low vol — alpha -0.43% / 20d on 52,590 triggers.
  • Worst era for bullish: 2023-2026 — alpha -0.43% / 20d.
  • Worst era for bearish: 2023-2026 — alpha -0.38% / 20d.

Signal-specific failure patterns

Bullish fails systematically, deepens over horizon
Williams %R bullish (exit of oversold < −80 zone) produces α=−0.17 at 20d (p(HAC)<1e-10, p_perm=1.000), widening to −0.29 at 60d. 416,045 triggers is a very large sample; the failure is statistically robust, not noise. The overbought/oversold framing doesn't map onto directional forward returns in this universe.
evidence: bullish vs SPX: 20d α=−0.17 N=416k p_perm=1.000; 60d α=−0.29 p_perm=1.000
Bearish is the real signal — compounds strongly at 60d
Williams bearish (exit of overbought > −20 zone) at α=−0.22 at 20d (p(HAC)<1e-18) widens to −0.58 at 60d (p<1e-17). Both horizons have p_perm=0.005. The signal isolates a persistent 1-3 month underperformance in stretched-high stocks. Largest N (449k) of any bearish oscillator — reliable because of scale.
evidence: bearish vs SPX: 20d α=−0.22 p_perm=0.005; 60d α=−0.58 p_perm=0.005
2020-2022 was the noise period (like every oscillator)
2015-2019 bearish α=−0.36, 2020-2022 flips to +0.13, 2023-2026 back to −0.38. Same structure as other oscillators — QE/rate-cut driven liquidity rendered overbought signals non-predictive. Bearish Williams should be down-weighted during obvious liquidity surges.
evidence: bearish 20d vs SPX: 2015-19 −0.36, 2020-22 +0.13, 2023-26 −0.38

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.

Oscillator-family redundancy

Williams %R belongs to the momentum-oscillator family alongside RSI, Stochastics, and CCI — each is constructed from closing price over a short lookback, normalised to 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). Stacking two or more of these in the same direction within a single Daily Report produces correlated rather than independent evidence.

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 trend filterWilliams bearish alone has edge; Williams bearish + close below 50DMA (downtrend filter) would likely concentrate the alpha. Testable without new data.
  • Extend holds60d alpha is nearly 3x the 20d alpha. Holding the full signal window captures substantially more. Time stops > price stops.

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

5 · Before you act — 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 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.
  5. 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 is the tradable side. 449k triggers over 2015-2026 — very large dataset. Alpha compounds from 20d to 60d (−0.22 → −0.58). Entry open T+1. Bullish Williams %R has not produced positive alpha in any horizon, any regime, any sub-period — skip.