Williams %R

Classic momentum oscillator overbought oversold classic

A momentum indicator that measures overbought and oversold levels, similar to a stochastic oscillator.

Visual Example

Williams %R — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-06-25 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The Williams %R indicator is a technical analysis tool that a momentum indicator that measures overbought and oversold levels, similar to a stochastic oscillator.

This indicator is primarily used for identifying key market conditions. It provides a robust signal that can be easily integrated into both simple strategies and more complex machine learning feature pipelines. Compared to its alternatives, it offers a distinct balance of responsiveness and stability.

Traders often combine this with other metrics to confirm signals and avoid false positives during sideways market regimes. It remains a standard tool for systematic trading models.

Use to identify entry and exit points in the market. Readings from 0 to -20 are considered overbought, while readings from -80 to -100 are considered oversold.

Developed by Larry Williams, %R compares the closing price of a stock to the high-low range over a specific period, typically 14 days. It is used to determine when a stock might be overbought or oversold and to identify potential trend reversals. — StockCharts ChartSchool

QuantWave implements this indicator via the universal Next<T> trait, guaranteeing bit-identical results between Rust streaming, Python streaming, and Polars batch (.ta() / map_batches) surfaces.

Formula / Specification

Implementation (quantwave-core/src/indicators/momentum.rs):

\[ \%R = \frac{\text{Highest High} - \text{Close}}{\text{Highest High} - \text{Lowest Low}} \times -100 \]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/willr.json.

Parameters

Parameter	Default	Description
`timeperiod`	14	Lookback period

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::WILLR;
use quantwave_core::traits::Next;

let mut ind = WILLR::new(14);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import WILLR

ind = WILLR(14)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_williams_r(series: pl.Series) -> pl.Series:
    ind = qw.WILLR(14)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_williams_r, return_dtype=pl.Float64).alias("williams_r")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

Warm-up: first 14 bars may return NaN or partial state per implementation.
Parameter sensitivity: smaller periods increase noise; larger periods increase lag.
Sudden gaps or bad ticks can distort rolling windows — consider pre-filtering.
Single-series indicators ignore volume unless otherwise documented.
Validated via proptests against gold-standard vectors where available.
No look-ahead bias; streaming and Polars batch paths are bit-identical.

Boundary Behavior

Condition	Behavior
Warm-up	Leading bars return NaN until warmup_bars is satisfied.
period > len	When period exceeds series length, output is all NaN.
NaN inputs	NaN in input propagates to output (NaN out).
Invalid params	Non-positive period or missing required params raise ValueError.
Empty data	Empty input returns an empty result series.

Sources & References

Primary Source: https://www.investopedia.com/terms/w/williamsr.asp

Implementation: quantwave-core/src/indicators/momentum.rs (WILLR / WILLR_METADATA). Parity: quantwave-core/tests/gold_standard/willr.json

Provenance: Standards bulk upgrade 2026-06-25 IST — see docs/DOCUMENTATION_STANDARDS.md.