Wad

Larry Williams' Accumulation/Distribution — a cumulative, volume-free line that adds true-low accumulation on up-closes and true-high distribution on down-closes.

Quick reference

Field	Value
Family	Volume
Input type	Candle (high / low / close)
Output type	f64
Output range	(−∞, +∞) (a cumulative line; only slope/divergence matters)
Default parameters	None (parameter-free)
Warmup period	2
Interpretation	Rising = accumulation; falling = distribution; watch divergence vs price.

Formula

if close > prev_close:  AD =  close − min(low,  prev_close)   (true low)
if close < prev_close:  AD =  close − max(high, prev_close)   (true high)
if close = prev_close:  AD =  0
WAD_t = WAD_{t−1} + AD

Despite living in the Volume family, Williams' A/D uses no volume. On an up-close it credits how far price closed above the true low (the lower of today's low and yesterday's close); on a down-close it debits how far price closed below the true high; an unchanged close contributes nothing. The running total is the line. This is deliberately different from Chaikin's volume-weighted Adl. Source: crates/wickra-core/src/indicators/wad.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
—	—	—	—	None.	The Williams A/D line takes no parameters; Wad::new() is infallible.

The value getter returns the current cumulative total if ready.

Inputs / Outputs

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

use wickra::{Candle, Indicator, Wad};
// Wad: Input = Candle, Output = f64
const _: fn(&mut Wad, Candle) -> Option<f64> = <Wad 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() == 2. The first candle only seeds the reference close and emits nothing; the first cumulative value lands on the second bar (first_bar_seeds_without_output pins this).

Edge cases

• Up-close accumulates. A higher close credits close − true_low (up_close_accumulates pins this).
• Down-close distributes. A lower close debits close − true_high (down_close_distributes pins this).
• Unchanged close. An equal close adds exactly 0, regardless of the bar's range (unchanged_close_adds_nothing pins this).
• Monotone in a trend. A clean uptrend produces a non-decreasing line (pure_uptrend_is_monotone pins this).
• Finiteness. Candle::new rejects non-finite fields, so no in-method guard is needed.
• Reset. wad.reset() clears the reference close, the running total and the last value (reset_clears_state).

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut wad = Wad::new();
    let candles = [
        Candle::new(100.0, 101.0, 99.0, 100.0, 1_000.0, 0)?, // seed
        Candle::new(100.0, 102.0, 100.0, 101.0, 1_000.0, 0)?, // up-close: +1
    ];
    let out = wad.batch(&candles);
    println!("warmup_period = {}", wad.warmup_period());
    println!("last = {:?}", out.last().unwrap());
    Ok(())
}

Output:

warmup_period = 2
last = Some(1.0)

Close rose from 100 to 101; the true low is min(100, 100) = 100, so AD = 101 − 100 = 1.

Python

import numpy as np
import wickra as ta

wad = ta.Wad()
high  = np.array([101, 102, 103], dtype=float)
low   = np.array([ 99, 100, 101], dtype=float)
close = np.array([100, 101, 102], dtype=float)
print(wad.batch(high, low, close))

Output:

[ nan  1.  2.]

Node

const ta = require('wickra');

const wad = new ta.Wad();
console.log('warmupPeriod:', wad.warmupPeriod()); // 2
const high  = [101, 102, 103];
const low   = [ 99, 100, 101];
const close = [100, 101, 102];
console.log(wad.batch(high, low, close)); // [NaN, 1, 2]

Streaming

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

let mut wad = Wad::new();
let mut last = None;
for i in 0..20 {
    let base = 100.0 + f64::from(i);
    let c = Candle::new(base, base + 1.0, base - 1.0, base + 0.5, 1_000.0, 0).unwrap();
    last = wad.update(c);
}
println!("{last:?}");

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

Interpretation

Williams' A/D is a divergence tool, not a level:

1. Bullish divergence. Price makes a lower low while WAD makes a higher low → accumulation under weak price → potential reversal up.
2. Bearish divergence. Price makes a higher high while WAD makes a lower high → distribution into strength → potential reversal down.
3. Trend confirmation. WAD rising with price confirms the advance; the line flattening ahead of price warns the move is running on fumes.

Because no volume enters the formula, WAD works on instruments with unreliable or missing volume (FX, some indices) where Chaikin's line cannot.

Common pitfalls

• Absolute level is arbitrary. The line's value depends on the start point; only its shape carries information.
• It is not Chaikin A/D. Adl weights a money-flow multiplier by volume; WAD uses true-range geometry and no volume — they can diverge sharply.
• Gaps matter. The true-low/true-high construction folds in the prior close, so overnight gaps are captured rather than ignored.

References

Williams, L. R. (1979), How I Made One Million Dollars Last Year Trading Commodities. The accumulation/distribution line described there is the volume-free construction implemented here.

See also

• Indicator-Adl — Chaikin's volume-weighted A/D line.
• Indicator-ChaikinMoneyFlow — the bounded money-flow oscillator.
• Indicator-Obv — cumulative signed volume.
• Indicators-Overview — the full taxonomy.