Ulcer Index: Comparing Full-Period and Rolling Measures

Summary

The document raises a methodological question about two ways of calculating the Ulcer Index, a drawdown-based measure of downside risk. One definition takes the root mean square of drawdowns across a sample, producing a single value for that sample. The other calculates percentage drawdowns from a rolling high close and averages their squares over a chosen lookback, producing a time series. The author asks why the measures differ, which reflects the original measure and common practice, and which version belongs in the Martin ratio.

No answers or evidence resolving these questions are included in the document. Its useful contribution is to identify that the formulas use different sampling windows and output formats, so their values may not be directly comparable. It does not establish a preferred definition, specify implementation details beyond the quoted procedures, or explain the implications for performance evaluation. Readers would need to consult the cited book, original research, or a documented implementation to settle those choices.

Key ideas

• A full-sample Ulcer Index summarizes drawdowns over an entire observation set as one value.
• A rolling calculation uses a selected lookback and produces a series of values.
• Different windows and sampling conventions can explain discrepancies between implementations.
• The document asks which form is appropriate for the Martin ratio but does not answer it.
• The definitions should not be treated as interchangeable without clarifying their calculation windows.

Tags

# Difference between the two definitions of Ulcer Index


# Difference between the two definitions of Ulcer Index












The Ulcer Index (UI) is defined as follows on page 89 of the book "Practical Portfolio Performance Measurement and Attribution, 2E" by Carl Bacon:

$$ UI= \sqrt{\sum_{i=1}^{i=n} \frac{D_{i}^{'2}}{n}} $$

where $D^{'}_i$ is the drawdown since the previous peak in period i.

Investopedia on the other hand defines it procedurally as:

> The indicator is calculated in three steps: Percentage Drawdown = [(Close - 14-period High Close)/14-period High Close] x 100 Squared Average = (14-period Sum of Percentage Drawdown Squared)/14 Ulcer Index = Square Root of Squared Average

Evidently, the Bacon version results in a number without any parameters, while Investopedia's calculates it as a series given a number of periods taken into consideration as a parameter. So,

- Why is the number of periods not needed for Bacon's version?

- Why does the most recent value (and every other value, as I can notice) of Investopedia series differ from the number calculated by Bacon's formula?

- Which of these definitions is a) correct (as per the original paper) and b) most commonly used?

- When we are calculating Martin ratio, should we use Ulcer Index a) as per Bacon formula or b) the most recent value in the Investopedia's series?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.