CDaR: Average of the Worst Portfolio Drawdowns

Key Takeaways

• CDaR averages the worst (1 minus confidence) share of a portfolio's drawdowns over time.
• It contains average drawdown and maximum drawdown as the two extremes of its confidence range.
• A common mistake is judging strategies by maximum drawdown alone, which one freak event can distort.
• CDaR can be minimized directly in portfolio optimization through linear programming.

What It Is

A drawdown is the percentage decline of a portfolio from its running peak. The drawdown curve, sometimes called the underwater curve, tracks how far below the prior high the portfolio sits at every point in time. CDaR summarizes the tail of that curve.

Chekhlov, Uryasev, and Zabarankin introduced CDaR as a one-parameter family of drawdown measures. For a confidence level, CDaR is the average of the worst drawdowns in that tail. It is the drawdown analogue of conditional value at risk, which averages the worst portfolio losses. By design it sits between two familiar bookends, average drawdown and maximum drawdown.

The Intuition

Maximum drawdown reports a single number, the deepest peak-to-trough fall ever recorded. That is useful but fragile. One unusual event can set the maximum, and it tells you nothing about how often deep drawdowns occur or how the rest of the bad cases looked.

Average drawdown has the opposite problem. It blends every dip, including the shallow ones, so it understates the pain of the genuinely bad episodes. CDaR sits between them. By averaging only the worst slice of drawdowns, it captures the severity of serious declines without resting on a single extreme point. Adjusting the confidence parameter slides the measure from average drawdown toward maximum drawdown.

How It Works

CDaR builds on the drawdown curve. The steps are:

1. Build the drawdown curve: at each point, the decline from the running peak.
2. Choose a confidence level alpha (for example, 90%).
3. Identify the worst (1 - alpha) fraction of drawdown observations.
4. Average those worst drawdowns. That average is CDaR.

The limiting cases reveal its structure:

alpha -> 0    : CDaR approaches the average drawdown
alpha -> 1    : CDaR approaches the maximum drawdown

At 90 percent confidence, CDaR averages the worst 10 percent of drawdown readings. A practical strength shown by Chekhlov, Uryasev, and Zabarankin is that minimizing CDaR can be cast as a linear programming problem, so portfolio weights can be chosen to control sustained losses directly rather than only single-period volatility.

Worked Example

You analyze a strategy with several years of daily values and build its drawdown curve. You choose 90 percent confidence, so CDaR averages the worst 10 percent of the drawdown readings.

Across the period, the drawdown curve spends most of its time shallow, but during two stress episodes it falls steeply. The worst 10 percent of readings come almost entirely from those episodes.

Maximum drawdown            = 32%   (single deepest trough)
Average drawdown            = 6%    (all readings)
90% CDaR (worst 10% average) = 21%

The CDaR of 21 percent is more representative of the strategy's serious downside than either bookend. The maximum of 32 percent is a single worst point. The average of 6 percent is diluted by long calm stretches. CDaR captures the typical depth of the strategy's bad spells.

Common Mistakes

1. Relying on maximum drawdown alone. A single crisis can set the maximum, making two very different strategies look identical. CDaR distinguishes them by averaging the worst cases.
2. Picking confidence levels inconsistently. CDaR at 95 percent and CDaR at 80 percent answer different questions. Compare strategies at the same confidence level.
3. Using too short a history. Drawdown measures need enough time to capture multiple stress episodes. A short sample may contain no serious drawdowns at all.
4. Confusing drawdown with single-period loss. Drawdown tracks the path from a peak over time. A measure like VaR or expected shortfall describes a single-period loss, which is a different exposure.
5. Ignoring time underwater. CDaR captures depth but not directly how long recovery takes. Pair it with recovery time or the ulcer index for a fuller view.

Frequently Asked Questions

What is conditional drawdown at risk CDaR in simple terms? Conditional drawdown at risk, or CDaR, is the average of a portfolio's worst drawdowns at a chosen confidence level. It tells you how deep your bad declines from a peak tend to be, not just the single worst one.

How does conditional drawdown at risk affect investment decisions? It helps managers compare strategies on sustained loss rather than a lone worst event, and it can be minimized directly when building a portfolio. That makes it useful for strategies where staying invested through deep declines is the real test.

What is a real-world example of conditional drawdown at risk? A strategy with a 32 percent maximum drawdown and a 6 percent average drawdown might have a 90 percent CDaR of 21 percent, the average of its worst 10 percent of drawdown readings. That figure better represents its typical bad spell.

How can investors use conditional drawdown at risk effectively? Use a long history with several stress periods, fix the confidence level when comparing strategies, and pair CDaR with a recovery-time or time-underwater measure.

How is conditional drawdown at risk different from maximum drawdown? Maximum drawdown is the single deepest peak-to-trough decline. CDaR averages the worst slice of drawdowns, so it is less sensitive to one freak event and more representative of repeated stress.

Sources

1. Chekhlov, A., Uryasev, S. & Zabarankin, M. Drawdown Measure in Portfolio Optimization. https://www.math.columbia.edu/~chekhlov/ChekhlovUryasevZabarankin--03-2004.pdf
2. Chekhlov, A., Uryasev, S. & Zabarankin, M. Portfolio Optimization with Drawdown Constraints. SSRN. https://papers.ssrn.com/sol3/papers.cfm?abstract_id=223323
3. CFA Institute. Measuring and Managing Market Risk. https://www.cfainstitute.org/insights/professional-learning/refresher-readings/2026/measuring-managing-market-risk
4. Investopedia. Maximum Drawdown (MDD). https://www.investopedia.com/terms/m/maximum-drawdown-mdd.asp

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.