KRatio

Kestner's consistency score — the slope of the cumulative-return curve divided by the standard error of that slope.

Quick reference

Field	Value
Family	Risk / Performance
Input type	f64 (per-period returns)
Output type	f64
Output range	unbounded (sign follows the equity-curve slope)
Default parameters	(period = 30) (Python)
Warmup period	period
Interpretation	Higher = steadier upward equity curve.

Formula

equity_t   = Σ_{i<=t} return_i            (cumulative curve, t = 1..period)
slope, b0  = OLS(equity_t ~ t)
SE(slope)  = sqrt( (Σ residual² / (period − 2)) / Σ(t − t̄)² )
K-Ratio    = slope / SE(slope)

The K-Ratio fits a least-squares trend line through the cumulative-return curve and reports the trend's t-statistic. A steep slope with little scatter (a smooth, straight climb) scores high; the same total return earned in a few lucky jumps scatters the residuals, inflates the standard error, and scores lower. This is Kestner's original 1996 form. Later revisions scale by the period count (slope / (SE · period) in 2003, slope / (SE · √period) in 2013) — apply that downstream when comparing across window lengths. A perfectly linear window has zero residual scatter, so the slope's standard error is zero and the ratio is undefined; the indicator reports 0.0. Source: crates/wickra-core/src/indicators/k_ratio.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	30 (Python)	>= 3	k_ratio.rs:66	Window of returns. < 3 errors with Error::InvalidPeriod (the SE divides by period − 2).

The period getter returns the window.

Inputs / Outputs

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

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

An f64 return in, an Option<f64> out. Python update(ret) / batch(returns) (NaN warmup); Node update(ret) / batch(returns[]) (null warmup).

Warmup

warmup_period() == period. The first value lands once period returns are seen (reference_value exercises the emission at index period − 1).

Edge cases

• Reference value. [0.01, 0.02, 0.03] → equity [0.01, 0.03, 0.06], slope 0.025, K-Ratio 5√3 ≈ 8.660254 (reference_value pins this).
• Constant returns. A perfectly linear curve is degenerate and reports 0.0 (constant_returns_are_degenerate_zero pins this).
• Rising curve. A noisy but upward window reports > 0 (rising_curve_is_positive).
• Non-finite input. A NaN/∞ return is skipped (ignores_non_finite_input).
• Reset. kr.reset() clears the window (reset_clears_state).

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut kr = KRatio::new(3)?;
    let out = kr.batch(&[0.01, 0.02, 0.03]);
    println!("{:?}", out[2]); // Some(8.660254...)
    Ok(())
}

Output:

Some(8.660254037844387)

Python

import numpy as np
import wickra as ta

kr = ta.KRatio(30)
returns = 0.001 + np.random.randn(60) * 0.01
print(kr.batch(returns)[-1])

Node

const ta = require('wickra');
const kr = new ta.KRatio(3);
console.log(kr.batch([0.01, 0.02, 0.03]).at(-1)); // ~8.66

Streaming

use wickra::{Indicator, KRatio};

let mut kr = KRatio::new(30).unwrap();
let daily_returns: Vec<f64> = Vec::new(); // your live stream
for r in daily_returns {
    if let Some(k) = kr.update(r) {
        // larger k -> straighter, steadier equity growth
    }
}

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

Interpretation

1. Consistency, not magnitude. Two strategies with the same return rank by smoothness — the K-Ratio rewards the one whose curve hugs its trend line.
2. Drawdown early-warning. A falling K-Ratio while the equity still rises means the climb is getting choppier — often a precursor to a drawdown.
3. Cross-window comparison. Because the raw 1996 form grows with the window, apply the period scaling before comparing 30-bar and 250-bar K-Ratios.

Common pitfalls

• Needs dispersion. Constant or near-constant returns make the curve linear and the ratio degenerate (0.0) — feed real, noisy returns.
• Version confusion. This is the 1996 slope / SE form; cite the variant when comparing against other libraries.
• Sign. The K-Ratio is negative for a declining equity curve — read the sign, not just the magnitude.

References

Kestner, L. N. (1996), Getting a Handle on True Performance — the K-Ratio; revised in Quantitative Trading Strategies (2003) and a 2013 errata.

See also

• Indicator-SharpeRatio — mean over total volatility.
• Indicator-LinearRegression — the underlying OLS trend fit.
• Indicators-Overview — the full taxonomy.