wickra/docs/wiki/indicators/volatility/Indicator-UlcerIndex.md

UlcerIndex

Ulcer Index — Peter Martin's downside-only risk measure: the root-mean-square of recent drawdowns.

Quick reference

Field	Value
Family	Volatility
Sub-category	Downside risk
Input type	f64 (single close)
Output type	f64
Output range	[0, ∞) (percent)
Default parameters	period = 14 (Python)
Warmup period	2·period − 1
Interpretation	Depth and duration of drawdowns; 0 means no drawdown at all.

Formula

max_t       = highest price over the trailing `period` bars
drawdown_t  = 100 · (price_t − max_t) / max_t
UlcerIndex  = √( mean( drawdown² over period ) )

Standard deviation treats an up-move and a down-move as equally "volatile". The Ulcer Index measures only the pain of being underwater: for each bar it takes the percentage drop from the trailing high, squares it, and reports the root-mean-square. A market that only rises has no drawdown and an Ulcer Index of 0; the deeper and longer the drawdowns, the higher the reading. It is the volatility term in the Martin ratio (Ulcer Performance Index).

Parameters

Name	Type	Default	Valid range	Description
period	usize	14 (Python)	>= 1	Look-back for both the trailing high and the RMS window. 0 errors with Error::PeriodZero.

The Python binding defaults period to 14.

Inputs / Outputs

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

impl Indicator for UlcerIndex {
    type Input = f64;
    type Output = f64;
    // update(&mut self, input: f64) -> Option<f64>
}

A single f64 close in, an Option<f64> out. Python maps this to float | None / numpy.ndarray (NaN warmup); Node to number | null / Array<number> (NaN warmup).

Warmup

UlcerIndex::new(period).warmup_period() == 2·period − 1. The first period prices fill the trailing-maximum window; the per-bar squared drawdown then needs another period − 1 bars to fill the RMS window.

Edge cases

• Pure up-trend. Price never trades below its own running high, so every drawdown — and the Ulcer Index — is 0 (pure_uptrend_yields_zero pins this).
• Constant series. A flat series has no drawdown; the output is 0.0 (constant_series_yields_zero pins this).
• Non-negative. The Ulcer Index is an RMS of real numbers and is never negative (output_is_non_negative pins this).
• NaN / infinity inputs. Non-finite inputs are silently dropped.
• Reset. ui.reset() clears both rolling windows and the sum.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut ui = UlcerIndex::new(2)?;
    let out: Vec<Option<f64>> = ui.batch(&[10.0, 8.0, 12.0, 9.0]);
    println!("{:?}", out);
    Ok(())
}

Output:

[None, None, Some(14.142135623730951), Some(17.67766952966369)]

UlcerIndex(2) warms up after 3 bars. At bar 3 the squared drawdowns in the window are [400, 0], so the index is √(400/2) = √200. At bar 4 they are [0, 625], giving √(625/2) = √312.5. This matches the reference_values test in crates/wickra-core/src/indicators/ulcer_index.rs.

Python

import numpy as np
import wickra as ta

ui = ta.UlcerIndex(2)
print(ui.batch(np.array([10.0, 8.0, 12.0, 9.0])))

Output:

[       nan        nan 14.1421356 17.6776695]

Node

const ta = require('wickra');
const ui = new ta.UlcerIndex(2);
console.log(ui.batch([10, 8, 12, 9]));

Output:

[ NaN, NaN, 14.142135623730951, 17.67766952966369 ]

Interpretation

UlcerIndex answers "how uncomfortable has holding this been?" — a high reading means deep or prolonged drawdowns, a low reading means a smooth ride up. It is most useful for comparing instruments or strategies on a downside-risk basis, and as the denominator of the Ulcer Performance Index ((return − risk-free) / UlcerIndex), a Sharpe-ratio analogue that penalises only downside volatility.

Common pitfalls

• Reading it as two-sided volatility. The Ulcer Index ignores upside entirely — a wildly choppy up-trend can still score near 0. Use StdDev for two-sided dispersion.
• Forgetting the doubled warmup. Warmup is 2·period − 1, not period.

References

Peter Martin and Byron McCann, The Investor's Guide to Fidelity Funds (1989); the index is also documented at StockCharts. The trailing-high drawdown RMS here follows that definition.

See also

• Indicator-StdDev.md — two-sided dispersion.
• Indicator-Atr.md — per-bar range volatility.
• Indicators-Overview.md — the full taxonomy.