Calmar Ratio and Ulcer Index

Why the Calmar Ratio and Ulcer Index matter

The Calmar Ratio and the Ulcer Index were created to help investors decide whether portfolio returns truly compensate for stressful periods. The Calmar Ratio links compounded growth to the worst historical drawdown; the Ulcer Index shows how deep and persistent price declines have been below their highs.

What is the Calmar Ratio?

The Calmar Ratio compares a strategy’s compound annual growth rate (CAGR) with its maximum percentage drop from a peak (Maximum Drawdown). Higher values signal a more efficient balance between return and downside risk over the long run.

$Calmar\ Ratio = \frac{CAGR}{|MDD|}$

Where:

• $CAGR$ is the annualised growth rate of capital;
• $MDD$ is the maximum drawdown expressed as an absolute value.

How to compute it step by step

1. Compute total performance over your analysis window (e.g. the last 3 years) and convert it into CAGR.
2. Identify the maximum drawdown in the same window.
3. Divide the CAGR by the absolute drawdown.

A Calmar Ratio above 3 is often deemed excellent for hedge funds or systematic strategies; values under 1 warn that growth is not offsetting the pain inflicted by losses.

Numerical example

Assume a strategy compounds at 12% per year across three years and endures a maximum drawdown of -20%. The Calmar Ratio is:

$Calmar = \frac{0.12}{0.20} = 0.6$

Returns are not high enough to compensate for the depth of the setback, highlighting the need for better risk controls.

Strengths and weaknesses of the Calmar Ratio

• Captures medium-to-long term performance, filtering daily noise.
• Easy to communicate and benchmark across managers.
• Highly sensitive to the chosen window: older drawdowns may no longer reflect current risk.
• Ignores loss frequency, focusing only on the single worst drop.

What is the Ulcer Index?

The Ulcer Index (UI) measures both the intensity and the duration of drawdowns. Unlike standard deviation, it concentrates solely on negative deviations, making it valuable for investors concerned with prolonged underwater periods.

$UI = \sqrt{\frac{1}{N} \sum_{i=1}^{N} D_i^2}$

Where $D_i$ is the percentage drawdown from the previous peak on day $i$ within the observation window.

Ulcer Index in four steps

1. Build the running series of portfolio highs.
2. Compute the percentage loss from the last high for each day (drawdown).
3. Square every drawdown and average the results.
4. Take the square root of that average.

Worked example

Consider the weekly equity line below:

The Ulcer Index over five observations is:

$UI = \sqrt{\frac{0^2 + 0^2 + (-2.88)^2 + (-5.77)^2 + (-1.92)^2}{5}} \approx 3.10$

Values above 2–3 suggest frequent or deep drawdowns; strategies with UI below 1 are usually considered very stable.

Using Calmar Ratio and Ulcer Index together

• The Calmar Ratio summarises how well growth compensates for the single worst loss, ideal for comparing funds or portfolios.
• The Ulcer Index reveals whether losses are concentrated or stretched over time.
• Combined they offer a richer picture: a high Calmar paired with a high UI can hide lengthy pullbacks, while a modest Calmar and a low UI describe a patient yet resilient approach.

Practical tips

• Refresh the metrics on rolling windows aligned with the investor’s horizon.
• Cross-check results with liquidity and leverage indicators to avoid partial conclusions.
• Feature both metrics in periodic reports to maintain a transparent dialogue with clients and stakeholders.

Key takeaways

• The Calmar Ratio highlights a strategy’s ability to recover from its worst losses.
• The Ulcer Index measures the average “pain” endured by staying invested.
• No single indicator is sufficient: combine them with qualitative assessments and scenario analysis.