HasbrouckInformationShare

Each venue's contribution to price discovery — the share of total return variance carried by the first of two synchronised price series.

Quick reference

Field	Value
Family	Microstructure
Input type	(f64, f64) (two venue prices)
Output type	f64
Output range	[0, 1] (share of venue x)
Default parameters	(period = 20) (Python)
Warmup period	period + 1
Interpretation	> 0.5 venue x leads price discovery; < 0.5 follows.

Formula

rx_t = x_t − x_{t−1},  ry_t = y_t − y_{t−1}
IS_x = var(rx) / ( var(rx) + var(ry) )      over the window, ∈ [0, 1]

When the same instrument trades on multiple venues, Hasbrouck's information share measures how much each contributes to the common efficient price; the venue whose innovations carry more variance leads. This streaming form is the variance-ratio proxy — the fraction of total return variance from series x. Above 0.5 = x leads. The full measure fits a VECM and reports Cholesky-ordering bounds; this proxy captures the leading idea without the VECM. Source: crates/wickra-core/src/indicators/hasbrouck_information_share.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	20 (Python)	>= 2	hasbrouck_information_share.rs:55	Rolling window of return pairs. < 2 errors with Error::InvalidPeriod.

The period getter returns the window.

Inputs / Outputs

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

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

A (f64, f64) price pair in, an Option<f64> out. The Python binding takes update(x, y) and batch(x[], y[]) (NaN warmup); Node mirrors update(x, y) / batch(...).

Warmup

warmup_period() == period + 1. One pair seeds the prior level; period returns fill the variance window (warmup_needs_period_plus_one pins this).

Edge cases

• Loud venue leads. A far more volatile x holds nearly all the share (loud_venue_leads pins this).
• Bounded. The reading stays in [0, 1] (equal_venues_split_evenly pins this).
• Flat series → 0.5. Zero variance on both reports the neutral 0.5 (flat_series_is_half pins this).
• Reset. h.reset() clears the prior level, the window and the running sums (reset_clears_state).

Examples

Rust

use wickra::{BatchExt, Indicator, HasbrouckInformationShare};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut h = HasbrouckInformationShare::new(20)?;
    let pairs: Vec<(f64, f64)> = (0..40)
        .map(|i| ((f64::from(i) * 0.5).sin() * 10.0, (f64::from(i) * 0.5).sin() * 1.0))
        .collect();
    println!("x share > 0.8: {}", h.batch(&pairs).last().unwrap().unwrap() > 0.8);
    Ok(())
}

Output:

x share > 0.8: true

Python

import numpy as np
import wickra as ta

h = ta.HasbrouckInformationShare(20)
x = np.sin(np.arange(40) * 0.5) * 10
y = np.sin(np.arange(40) * 0.5) * 1
print(h.batch(x, y)[-1])  # near 1.0

Node

const ta = require('wickra');
const h = new ta.HasbrouckInformationShare(20);
console.log('warmupPeriod:', h.warmupPeriod()); // 21

Streaming

use wickra::{Indicator, HasbrouckInformationShare};

let mut h = HasbrouckInformationShare::new(20).unwrap();
let price_feed: Vec<(f64, f64)> = Vec::new(); // your live stream
for (venue_a, venue_b) in price_feed {
    if let Some(share) = h.update((venue_a, venue_b)) {
        // share > 0.5 -> venue_a is leading price discovery
    }
}

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

Interpretation

1. Lead/lag venue. A persistent share above 0.5 identifies the price-leading market; route or hedge accordingly.
2. Fragmentation monitoring. Shifts in the share track changes in where price discovery happens (e.g. liquidity migrating venues).
3. Spot vs. derivative. Apply to a spot/futures pair to see which leads.

Common pitfalls

• Proxy, not full Hasbrouck. This is the variance-ratio approximation; it omits the VECM cointegration step and the upper/lower bounds.
• Synchronisation. The two series must be aligned in time; stale quotes bias the share.
• Same asset. It assumes the two prices track one efficient price; unrelated series make the share meaningless.

References

Hasbrouck, J. (1995), "One Security, Many Markets: Determining the Contributions to Price Discovery", Journal of Finance.

See also

• Indicator-LeadLagCrossCorrelation — cross-correlation lead/lag.
• Indicator-Cointegration — long-run price linkage.
• Indicator-RollingCorrelation — rolling return correlation.
• Indicators-Overview — the full taxonomy.