VolatilityRatio

Schwager's Volatility Ratio — today's true range divided by the EMA of the prior true ranges; a reading above 2.0 marks a wide-ranging day.

Quick reference

Field	Value
Family	Volatility & Bands
Input type	Candle (high / low / close)
Output type	f64
Output range	[0, ∞) (1.0 = today's range equals its typical level)
Default parameters	(period = 14) (Python)
Warmup period	period + 2
Interpretation	> 2.0 = wide-ranging day; < 1 = inside/quiet day.

Formula

TR_t = max(high − low, |high − prev_close|, |low − prev_close|)
VR_t = TR_t / EMA_n(TR through bar t−1)

Jack Schwager's volatility ratio compares today's true range to its recent typical level. A value above 2.0 is a wide-ranging day — today's range is more than twice the smoothed average — which often precedes or accompanies a reversal. The denominator is the exponential moving average of true range excluding the current bar (smoothing 2 / (period + 1), seeded with the simple average of the first period true ranges), so a single large bar stands out instead of inflating its own benchmark. Using a standard EMA — rather than the Wilder smoothing of Atr — keeps the ratio distinct from a plain TR / ATR. Source: crates/wickra-core/src/indicators/volatility_ratio.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	14 (Python)	>= 1	volatility_ratio.rs:60	Number of true ranges seeding and smoothing the denominator EMA. 0 errors with Error::PeriodZero.

The period getter returns the window length; value returns the current output if ready.

Inputs / Outputs

From crates/wickra-core/src/indicators/volatility_ratio.rs:

use wickra::{Candle, Indicator, VolatilityRatio};
// VolatilityRatio: Input = Candle, Output = f64
const _: fn(&mut VolatilityRatio, Candle) -> Option<f64> = <VolatilityRatio as Indicator>::update;

A Candle in, an Option<f64> out. The Python binding takes a candle for update and three numpy columns (high, low, close) for batch; Node takes update(high, low, close) and batch(high[], low[], close[]) (NaN warmup).

Warmup

warmup_period() == period + 2. Bar 1 sets the previous close; bars 2..=period+1 seed the denominator EMA; the first ratio is emitted on bar period + 2 (first_emission_at_warmup_period pins this).

Edge cases

• Steady range → 1.0. A constant true range makes the EMA equal it, so the ratio is exactly 1.0 (steady_range_ratio_is_one pins this).
• Wide-ranging day → > 2.0. A bar whose range is far above the smoothed benchmark pushes the ratio past 2.0 (wide_ranging_day_exceeds_two pins this).
• Flat market. Zero-range candles drive every true range and the EMA to 0; the ratio is guarded to 0.0 rather than 0 / 0 (flat_market_yields_zero pins this).
• Non-negative. True range and its EMA are non-negative, so VR >= 0 (output_is_non_negative pins this).
• Finiteness. Candle::new rejects non-finite fields, so no in-method guard is needed.
• Reset. vr.reset() clears the previous close, the seed accumulator, the EMA and the last value (reset_clears_state).

Examples

Rust

use wickra::{BatchExt, Candle, Indicator, VolatilityRatio};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut vr = VolatilityRatio::new(3)?;
    // Eight candles each with a constant true range of 2.0.
    let candles: Vec<Candle> = (0..8)
        .map(|i| {
            let base = 100.0 + f64::from(i);
            Candle::new(base - 1.0, base + 1.0, base - 1.0, base, 1_000.0, 0).unwrap()
        })
        .collect();
    let out = vr.batch(&candles);
    println!("warmup_period = {}", vr.warmup_period());
    println!("last = {:?}", out.last().unwrap());
    Ok(())
}

Output:

warmup_period = 5
last = Some(1.0)

A steady range makes the EMA equal today's true range, so the ratio settles at 1.0.

Python

import numpy as np
import wickra as ta

vr = ta.VolatilityRatio(3)
high  = np.array([101, 102, 103, 104, 105, 106, 110], dtype=float)
low   = np.array([ 99, 100, 101, 102, 103, 104, 100], dtype=float)
close = np.array([100, 101, 102, 103, 104, 105, 105], dtype=float)
print(vr.batch(high, low, close))

Output:

[ nan  nan  nan  nan  1.   1.  ~5.]

The first five bars warm up / hold at 1.0; the final wide bar (range 10 versus a typical 2) prints a ratio well above 2.0.

Node

const ta = require('wickra');

const vr = new ta.VolatilityRatio(14);
console.log('warmupPeriod:', vr.warmupPeriod()); // 16
const high  = Array.from({ length: 40 }, (_, i) => 100 + i + 1);
const low   = Array.from({ length: 40 }, (_, i) => 100 + i - 1);
const close = Array.from({ length: 40 }, (_, i) => 100 + i);
console.log(vr.batch(high, low, close).at(-1)); // ~1.0 (steady range)

Streaming

use wickra::{Candle, Indicator, VolatilityRatio};

let mut vr = VolatilityRatio::new(14).unwrap();
let mut last = None;
for i in 0..40 {
    let base = 100.0 + f64::from(i);
    let c = Candle::new(base, base + 2.0, base - 1.0, base + 0.5, 1_000.0, 0).unwrap();
    last = vr.update(c);
}
println!("{last:?}");

Streaming update and batch are equivalent tick-for-tick (batch_equals_streaming pins this).

Interpretation

The volatility ratio is a range-expansion filter. Schwager used it to flag days whose range breaks decisively out of the recent norm:

1. Wide-ranging-day signal. VR > 2.0 marks a bar more than twice the typical range — a climactic move that frequently exhausts a trend and precedes a reversal.
2. Breakout confirmation. Pair a directional breakout with a high VR to distinguish a genuine range expansion from drift inside the prior range.
3. Quiet-market detection. Sustained VR < 1 signals contracting ranges — the coiling that often precedes the next expansion.

Because the denominator is the EMA of prior ranges, the ratio reacts to today's bar immediately without that bar diluting its own benchmark.

Common pitfalls

• Two conventions share the name. Some sources define the ratio as today's true range over the N-day high-low span; this implementation uses the widely-charted EMA-of-true-range form (Schwager / IncredibleCharts), where > 2.0 means "twice the typical range".
• It is not TR / ATR. The denominator uses standard EMA smoothing, not Wilder's, and excludes the current bar — so it will not match an ATR-based ratio bar-for-bar.
• Choose period for your timeframe. A short period makes every spike look wide; a long one smooths genuine expansions away.

References

Schwager, J. D. (1996), Schwager on Futures: Technical Analysis, Wiley. See also the IncredibleCharts reference on the Volatility Ratio (EMA-of-true-range form, wide-ranging-day threshold 2.0).

See also

• Indicator-Atr — Wilder-smoothed true range (the absolute level).
• Indicator-Natr — normalized ATR as a percentage of price.
• Indicator-TrueRange — the raw per-bar true range.
• Indicators-Overview — the full taxonomy.