RollMeasure

The effective bid-ask spread implied by the negative first-order serial covariance of trade-price changes (Roll, 1984).

Quick reference

Field	Value
Family	Microstructure
Input type	Trade (price is used)
Output type	f64
Output range	>= 0
Default parameters	period is required (>= 3)
Warmup period	period + 1
Interpretation	Larger = wider implied spread; 0 on a trending / frictionless tape.

Formula

Δpₜ    = priceₜ − priceₜ₋₁
γ      = sample lag-1 autocovariance of Δp over the last `period` changes
spread = 2 · √(−γ)   if γ < 0,   else 0

Roll's insight: in a frictionless market price changes are serially uncorrelated, but the bid-ask bounce — trades alternating between buying at the ask and selling at the bid — induces a negative autocovariance whose magnitude pins the spread. The measure recovers an effective spread from trade prices alone, with no quote data. When the serial covariance is non-negative the model implies no spread and the indicator returns 0.

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

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	none	>= 3	roll_measure.rs:56	Window of price changes. < 3 errors with Error::InvalidPeriod.

Inputs / Outputs

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

use wickra::{Indicator, RollMeasure, Trade};
// RollMeasure: Input = Trade, Output = f64
const _: fn(&mut RollMeasure, Trade) -> Option<f64> = <RollMeasure 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. (Size and side are accepted for a uniform trade API but only the price is used.)

Warmup

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

Edge cases

• Bid-ask bounce. Prices bouncing 100/101 give Δp alternating +1/−1, autocovariance −1, so spread 2; pinned by bid_ask_bounce_implies_spread.
• Trending prices. Monotone prices give constant Δp (non-negative covariance) → spread 0; pinned by trending_prices_imply_no_spread.
• Non-negativity. Output is >= 0; pinned by output_is_non_negative.
• Reset. reset() clears the price reference and the change window.

Examples

Rust

use wickra::{BatchExt, Indicator, RollMeasure, Side, Trade};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut roll = RollMeasure::new(6)?;
    let prices: Vec<Trade> = (0..20)
        .map(|i| Trade::new(if i % 2 == 0 { 100.0 } else { 101.0 }, 1.0, Side::Buy, 0).unwrap())
        .collect();
    println!("{:?}", roll.batch(&prices).into_iter().flatten().last());
    Ok(())
}

Output:

Some(2.0)

Python

import wickra as ta

roll = ta.RollMeasure(6)
last = None
for i in range(20):
    last = roll.update(100.0 if i % 2 == 0 else 101.0, 1.0, True)
print(last)

Output:

2.0

Node

const ta = require('wickra');
const roll = new ta.RollMeasure(6);
let last = null;
for (let i = 0; i < 20; i++) last = roll.update(i % 2 === 0 ? 100 : 101, 1, true);
console.log(last);

Output:

2

Interpretation

RollMeasure recovers a transaction-cost proxy from trade prices when you have no quotes: a wider implied spread means higher round-trip cost and a bouncier tape. It is 0 for trending or frictionless series (no bid-ask bounce to detect). Use it alongside quote-based spreads (QuotedSpread, EffectiveSpread) when only the tape is available, and with AmihudIlliquidity for the price-impact side.

Common pitfalls

• Zero is informative. A 0 reading is not a failure: it means the recent serial covariance is non-negative (trending tape), so Roll's model implies no spread.
• Needs a bouncing tape. On strongly trending data the measure under-reports the true spread — that is a known limitation of the estimator, not a bug.

References

Roll, "A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market" (1984).

See also

• Indicator-QuotedSpread — quote-based spread.
• Indicator-EffectiveSpread — trade-vs-mid spread.
• Indicator-AmihudIlliquidity — price-impact liquidity.
• Indicators-Overview — the full taxonomy.