Conditional drawdown at risk (CDaR): the drawdown counterpart to CVaR

Conditional drawdown at risk (CDaR) is the average depth of the worst drawdowns in a return series, conditional on those drawdowns exceeding a chosen threshold. It is the drawdown analogue of expected shortfall (CVaR) on the return distribution: a tail-risk measure that summarises the severity of the worst observations rather than treating only the single worst as informative.

What CDaR is

CDaR was introduced by Chekhlov, Uryasev, and Zabarankin (2003) as part of a framework for portfolio optimisation against drawdown-based risk measures. The metric is defined as the average of the largest α% of drawdown observations in a portfolio's drawdown time series, where α is typically chosen as 5% or 10%—analogous to the conventional 95% or 90% CVaR confidence level.

For a portfolio's drawdown series, CDaR at the 5% level is computed by sorting the drawdown observations from largest (most negative) to smallest, taking the largest 5% of values, and averaging them. The result is a single number that summarises how deep the portfolio has typically been in its worst-case episodes, without being dominated by the single worst observation.

How it works

For a return series of 1,000 daily observations, CDaR at the 5% level uses the 50 deepest drawdown observations. If the worst observation in the series was −38% and the 50 deepest observations average −32%, the CDaR(5%) for the period is 32%. The same series might have a maximum drawdown (the single deepest observation) of 38% and a value at risk on returns at the 5% level of −2.5%—each metric describing a different aspect of the tail.

The metric has two desirable mathematical properties. It is a coherent risk measure (it satisfies sub-additivity, monotonicity, positive homogeneity, and translation invariance), which makes it well-behaved in optimisation contexts: combining two assets cannot produce a portfolio whose CDaR is greater than the sum of the individual CDaRs. And it is convex in portfolio weights, which means it can be used as the objective in tractable optimisation problems—the basis for the original Chekhlov-Uryasev-Zabarankin work.

As α approaches 0, CDaR approaches maximum drawdown (the single worst observation). As α approaches 100%, CDaR approaches the average drawdown across the entire series (the pain index). The metric therefore generalises the maximum-drawdown and pain-index measures into a single parameterised family.

What the evidence shows

For diversified equity indices over multi-decade windows, CDaR at the 5% level typically lies in the 30–45% range, reflecting the depth of major-market drawdowns in 1929–1932, 2000–2002, and 2007–2009. CDaR at the 10% level is typically 5–10 percentage points smaller, reflecting the dilution from including drawdowns just outside the worst tail.

The Chekhlov-Uryasev-Zabarankin framework also supports portfolio optimisation against CDaR as the risk measure, replacing volatility in the standard mean-variance setup. Empirically, portfolios optimised against CDaR tend to allocate differently from mean-variance-optimised portfolios with similar return targets: the CDaR-optimised portfolios reduce exposure to assets with deep, persistent drawdowns (e.g., highly leveraged or single-asset-class exposures) and tilt toward more diversified combinations.

CDaR-based optimisation has been more common in institutional and CTA contexts than in retail portfolio construction, where Sharpe-based optimisation remains the dominant convention. The concept is straightforward and well-supported in the literature; adoption has been gradual.

Limitations and trade-offs

CDaR depends on the choice of α. Different conventions produce different numbers, and comparisons across portfolios should use a consistent confidence level. CDaR(5%) is the most common, but CDaR(1%) and CDaR(10%) are also used—particularly in CTA performance reporting.

Like all drawdown-based metrics, CDaR is sensitive to the evaluation window. A short window may exclude the portfolio's worst drawdown entirely; a long window may include drawdowns from regimes that are no longer relevant to forward-looking analysis. The metric is also sensitive to the sampling frequency: a daily series produces different CDaR values from a monthly series for the same underlying portfolio, because the daily series captures intraday and short-horizon drawdowns that the monthly series smooths over.

CDaR is informative as a backward-looking summary but should not be used as a forward-looking estimate without acknowledgment of its sample dependence. The historical CDaR is the realised tail experience over the sample, not a guarantee about future tail behaviour. Forward-looking applications typically combine the historical estimate with stress-testing or scenario analysis.

CDaR in pfolio

CDaR is not currently displayed in pfolio Insights. The drawdown time series, maximum drawdown, and value at risk and expected shortfall on the return distribution are all available; CDaR can be derived externally from the drawdown time series.

Related articles

• Expected shortfall (CVaR): a more complete measure of tail risk than VaR
• Value at risk (VaR) explained: understanding tail risk in your portfolio
• Maximum drawdown: the essential measure of portfolio risk and loss
• Drawdown explained: measuring and understanding portfolio losses
• Mean-CVaR optimisation: portfolio construction against expected shortfall