AmihudIlliquidity

The average absolute log return per unit of traded value over the last period trades — the classic price-impact liquidity proxy (Amihud, 2002).

Quick reference

Field	Value
Family	Microstructure
Input type	Trade
Output type	f64
Output range	>= 0
Default parameters	period is required
Warmup period	period + 1
Interpretation	High = illiquid (small volume moves price a lot); low = deep / liquid.

Formula

rₜ      = ln(priceₜ / priceₜ₋₁)
ILLIQₜ  = |rₜ| / (priceₜ · sizeₜ)        (return per unit of traded value)
Amihud  = mean of ILLIQ over the last `period` trades

Amihud's measure captures how much the price moves for a given amount of traded value: a high reading means small volume already shifts the price a lot (an illiquid, easily-moved market), a low reading means it takes large volume to move the price (a deep, liquid market).

Source: crates/wickra-core/src/indicators/amihud_illiquidity.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	none	>= 1	amihud_illiquidity.rs:50	Window of trades. 0 errors with Error::PeriodZero.

Inputs / Outputs

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

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

Node update(price, size, isBuy) and batch(price[], size[], isBuy[]); Python update(price, size, is_buy) and batch(price, size, is_buy) → 1-D ndarray. (The aggressor side is accepted for a uniform trade API but does not affect the value.)

Warmup

warmup_period() == period + 1: one trade seeds the previous-price reference, then period ratios fill the window. The unit test accessors_and_metadata pins warmup_period() == 21 for period = 20.

Edge cases

• Reference value. For a 100 → 101 move on size 10: |ln(101/100)| / (101 · 10); pinned by known_value.
• Liquidity monotonicity. The same price move on smaller volume gives a larger reading; pinned by higher_for_thinner_volume.
• Flat price. Zero return → zero illiquidity; pinned by flat_price_is_zero.
• Zero-size trades. Skipped (no traded value); the reference price is kept; pinned by skips_zero_size_trades.
• Non-negativity. Output is >= 0; pinned by output_is_non_negative.

Examples

Rust

use wickra::{AmihudIlliquidity, Indicator, Side, Trade};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut a = AmihudIlliquidity::new(1)?;
    a.update(Trade::new(100.0, 10.0, Side::Buy, 0)?); // None (seeds reference)
    println!("{:?}", a.update(Trade::new(101.0, 10.0, Side::Buy, 0)?));
    Ok(())
}

Output:

Some(0.000009851812725909002)

|ln(101/100)| / (101 · 10) ≈ 9.85e-6.

Python

import wickra as ta

a = ta.AmihudIlliquidity(1)
print(a.update(100.0, 10.0, True))   # None
print(a.update(101.0, 10.0, True))   # ~9.85e-6

Output:

None
9.851812725909002e-06

Node

const ta = require('wickra');
const a = new ta.AmihudIlliquidity(1);
a.update(100, 10, true); // null
console.log(a.update(101, 10, true));

Output:

0.000009851812725909002

Interpretation

AmihudIlliquidity is the workhorse cross-sectional liquidity proxy: it rises when price impact per traded value rises (thin, easily-moved markets) and falls in deep markets. Use it to rank instruments by liquidity or to gate position size (scale down as illiquidity climbs). Complements the spread-based measures (RollMeasure, QuotedSpread) and flow toxicity (Vpin).

Common pitfalls

• Scale. Raw Amihud values are tiny (return over dollar-volume); researchers often report ILLIQ × 1e6. Scale yourself for readability.
• Per-trade vs daily. The classic Amihud measure aggregates daily; this is a per-trade streaming version — compare like with like.

References

Amihud, "Illiquidity and Stock Returns: Cross-Section and Time-Series Effects" (2002).

See also

• Indicator-RollMeasure — spread from price-change covariance.
• Indicator-Vpin — flow toxicity.
• Indicators-Overview — the full taxonomy.