BetaNeutralSpread

The beta-neutral spread between two assets — the residual of a rolling OLS regression of a on b, in price units.

Quick reference

Field	Value
Family	Price Statistics
Input type	(f64, f64) (a pair of prices a, b)
Output type	f64 (price units)
Output range	unbounded; 0 when a sits exactly on its hedge
Default parameters	period is required (>= 2)
Warmup period	period
Interpretation	Positive → a rich vs. its hedge; negative → a cheap; 0 → fairly priced.

Formula

Each update takes one (a, b) price pair. Over the trailing window of period pairs the indicator fits the hedge ratio β (and intercept α) by OLS and reports the current residual:

β      = cov(a, b) / var(b)        α = ā − β · b̄
spread = a_now − (α + β · b_now)

Subtracting β · b removes a's exposure to b, so the spread is market- (beta-)neutral: it is what is left after the common factor is hedged out. Positive means a is rich relative to its hedge, negative means cheap — the raw signal a pairs trade fades. Where PairSpreadZScore standardises this residual into a z-score and Cointegration bundles it with an ADF test, this indicator returns the residual itself, in price units. If b is flat over the window (var(b) = 0) there is no defined slope and it falls back to β = 0, so the spread becomes a_now − ā.

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

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	none	>= 2	beta_neutral_spread.rs:63	Look-back window of pairs for the OLS fit. < 2 errors with Error::InvalidPeriod.

Inputs / Outputs

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

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

Python streams as update(a, b) -> float | None and batches over two equal-length arrays. Node streams as update(a, b) and batches over a[], b[].

Warmup

warmup_period() == period. The unit test accessors_and_metadata pins warmup_period() == 20 for period = 20; warmup_returns_none pins the first Some at the period-th pair.

Edge cases

• Perfect linear relationship. When a = α + β·b exactly, the residual is zero; pinned by perfect_linear_relationship_has_zero_spread.
• Dislocation. A departure from the fitted line produces a nonzero spread; pinned by dislocation_produces_nonzero_spread.
• Flat b. Zero variance in b collapses the slope to β = 0, so the spread reduces to a_now − ā.
• Reset. reset() clears the regression window.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut s = BetaNeutralSpread::new(20)?;
    // a = 2*b exactly -> residual is zero.
    let pairs: Vec<(f64, f64)> =
        (0..40).map(|t| (2.0 * f64::from(t), f64::from(t))).collect();
    let last = s.batch(&pairs).into_iter().flatten().last().unwrap();
    println!("{last:.6}");
    Ok(())
}

Output:

0.000000

Python

import numpy as np
import wickra as ta

t = np.arange(40, dtype=float)
a = 2.0 * t
b = t
print(round(ta.BetaNeutralSpread(20).batch(a, b)[-1], 6))

Output:

0.0

Node

const ta = require('wickra');
const a = Array.from({ length: 40 }, (_, t) => 2 * t);
const b = Array.from({ length: 40 }, (_, t) => t);
console.log(new ta.BetaNeutralSpread(20).batch(a, b).at(-1).toFixed(6));

Output:

0.000000

Interpretation

BetaNeutralSpread is the dollar-value dislocation of a hedged pair: long a, short β units of b, and the spread is your mark-to-market deviation from fair. Fade extremes — short the spread when it is large and positive, long when large and negative — and exit near zero. Because the output is in price units it is not directly comparable across pairs with different volatilities; standardise with PairSpreadZScore when ranking signals across pairs.

Common pitfalls

• Leg order matters. The regression is asymmetric: regressing a on b gives a different hedge ratio than b on a. Fix the dependent leg and keep it consistent.
• Rolling β drifts. The hedge ratio is refit every bar, so a structural break shows up as both a moving β and a spread that does not revert. Confirm the relationship is stable with Cointegration.

References

Engle, R. F. & Granger, C. W. J. (1987), cointegration and error correction; the OLS-residual spread is the Engle–Granger first-stage residual.

See also

• Indicator-PairSpreadZScore — standardised entry/exit timing.
• Indicator-Cointegration — hedge ratio + ADF stationarity test.
• Indicators-Overview — the full taxonomy.