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Drawdown Measure in Portfolio Optimization

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What they found

The authors propose conditional drawdown at risk (CDaR), the average of the worst fraction of drawdowns over a sample path, as a risk measure that better matches how fund managers and their investors actually experience risk than variance does. They show CDaR is a coherent risk measure, that portfolio optimization with a CDaR constraint reduces to a linear program, and apply it to a portfolio of futures strategies, showing how the efficient frontier changes when drawdown, rather than volatility, is the risk being controlled.

See it drawn

Original diagrams for the ideas on this page. Illustrative, not real market data.

An equity curve and its drawdownAn account balance rising over a year, falling from a peak to a trough, then climbing back to the old peak.ACCOUNT EQUITY$20k$12k$8k024681012TIME (MONTHS)PEAK $16,000TROUGH $12,000DRAWDOWN−25%RECOVERY
Equity curve and drawdown. An account balance plotted month by month. The fall from the $16,000 peak to the $12,000 trough is a 25% drawdown, and the shaded area lasts until the balance climbs back to the old peak.

What you can use

  • Drawdown is the risk traders and allocators actually feel; optimizing for volatility alone can produce portfolios with unacceptable drawdowns.
  • Averaging the worst drawdowns (not just the single maximum) is a more stable target than maximum drawdown, which is dominated by one event.
  • Drawdown-constrained optimization is practical and is the basis for many allocators' risk limits.

Caveats

Optimization over historical paths overfits to the specific drawdowns in the sample. Technical, aimed at quantitative practitioners.

Tags: risk, drawdown, portfolio-optimization, cdar

Summaries are our own reading of the paper, not the authors' words. Educational only, not advice. Discuss it in Book Club.