MartinRatio

The Ulcer Performance Index — mean return over the Ulcer Index (the RMS of percentage drawdowns).

Quick reference

Field	Value
Family	Risk / Performance
Input type	f64 (per-period returns)
Output type	f64
Output range	unbounded (negative for net-losing windows)
Default parameters	(period = 14) (Python)
Warmup period	period
Interpretation	Higher = more return per unit of underwater stress.

Formula

equity_t = Π_{i<=t} (1 + return_i)               (compounded curve)
peak_t   = max_{s<=t} equity_s
dd_t%    = 100 · (peak_t − equity_t) / peak_t      (percentage drawdown)
UlcerIdx = sqrt( mean( dd_t%² ) )
Martin   = mean(returns) / UlcerIdx

The Martin Ratio (a.k.a. Ulcer Performance Index, UPI) divides the average per-period return by the Ulcer Index — the root-mean-square of the percentage drawdowns. The Ulcer Index captures both the depth and the duration of time spent underwater, so a long shallow slump and a short deep one can score alike. Versus Wickra's other drawdown ratios, Martin uses the RMS (not the plain average of the SterlingRatio, nor the un-normalised sum-norm of the BurkeRatio) and expresses drawdowns in percent, so its denominator lives on a 0..100 scale and its output is numerically smaller than the fractional-drawdown ratios. A window that never draws down has an Ulcer Index of zero and reports 0.0. Source: crates/wickra-core/src/indicators/martin_ratio.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	14 (Python)	>= 2	martin_ratio.rs:50	Window of returns (14 is the classic Ulcer Index window). < 2 errors with Error::InvalidPeriod.

The period getter returns the window.

Inputs / Outputs

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

use wickra::{Indicator, MartinRatio};
// MartinRatio: Input = f64, Output = f64
const _: fn(&mut MartinRatio, f64) -> Option<f64> = <MartinRatio 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. [0.1, −0.1, 0.1] → drawdowns% [0, 10, 1], Ulcer Index sqrt(101/3), Martin (0.1/3) / sqrt(101/3) (reference_value pins this).
• No drawdown. A monotonically rising window has a zero Ulcer Index and reports 0.0 (no_drawdown_is_zero pins this).
• Losing window. A net-losing window gives a negative ratio (losing_window_is_negative pins this).
• Non-finite input. A NaN/∞ return is skipped (ignores_non_finite_input).
• Reset. mr.reset() clears the window (reset_clears_state pins this).

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut mr = MartinRatio::new(3)?;
    let out = mr.batch(&[0.1, -0.1, 0.1]);
    println!("{:?}", out[2]); // Some(0.00574...)
    Ok(())
}

Output:

Some(0.005744817400227442)

Python

import numpy as np
import wickra as ta

mr = ta.MartinRatio(14)
returns = np.random.randn(60) * 0.05
print(mr.batch(returns)[-1])

Node

const ta = require('wickra');
const mr = new ta.MartinRatio(3);
console.log(mr.batch([0.1, -0.1, 0.1]).at(-1)); // ~0.00574

Streaming

use wickra::{Indicator, MartinRatio};

let mut mr = MartinRatio::new(14).unwrap();
let daily_returns: Vec<f64> = Vec::new(); // your live stream
for r in daily_returns {
    if let Some(upi) = mr.update(r) {
        // a falling UPI means rising underwater stress
    }
}

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

Interpretation

1. Stress-adjusted return. The Ulcer Index penalises time underwater, so the Martin Ratio rewards strategies that recover quickly from drawdowns.
2. Scale awareness. Because drawdowns are in percent, Martin Ratios are an order of magnitude smaller than the fractional Sterling/Burke ratios — never compare raw values across the three.
3. Family triangulation. A high Martin but low BurkeRatio says the underwater periods are shallow on average even if one is deep.

Common pitfalls

• No-drawdown anomaly. A window that only rises reports 0.0 (undefined), not infinity.
• Percent scale. Do not mix Martin values with Sterling/Burke values — the denominator units differ (percent vs fraction).
• Risk-free omitted. This rolling form uses the raw mean return; subtract the risk-free rate from your inputs first if you want an excess-return Martin Ratio.

References

Martin, P. G., & McCann, B. B. (1989), The Investor's Guide to Fidelity Funds — the Ulcer Index and the Ulcer Performance Index (Martin Ratio).

See also

• Indicator-SterlingRatio — average drawdown.
• Indicator-BurkeRatio — sum of squared drawdowns.
• Indicator-SharpeRatio — mean over total volatility.
• Indicators-Overview — the full taxonomy.