Minimum EDaR
Minimise Entropic Drawdown-at-Risk — the entropic analogue of CDaR. Designed for investors who care about the magnitude and probability of sustained drawdowns rather than single-period losses.
Overview
Entropic Drawdown-at-Risk (EDaR) extends the entropic risk-measure framework to drawdowns. Where EVaR bounds CVaR on single-period returns, EDaR bounds CDaR on the drawdown process. It is coherent, tighter than CDaR, and strictly more conservative.
EDaR is well-suited to capital-preservation mandates where the magnitude of peak-to-trough losses, not just point-in-time variance, is the primary concern.
Mathematical Formulation
Let be the drawdown process of the portfolio value . EDaR at confidence level is:
The optimisation problem is:
Folio Lab uses skfolio's MeanRisk with RiskMeasure.EDAR at by default, solved with exponential-cone capable solvers (CLARABEL, SCS).
EDaR vs CDaR
EDaR satisfies and so is always at least as conservative as CDaR. In regimes with heavy-tailed drawdowns (e.g. equity crises), EDaR forces the optimiser to take less drawdown risk than the CDaR-optimal portfolio would.
Advantages & Limitations
Advantages
- Coherent: Has all the desirable properties for risk control.
- Drawdown-aware: Captures path dependence, not just point-in-time variance.
- Strict bound: Always at least as conservative as CDaR.
Limitations
- Data hungry: Drawdown estimation needs sufficient history.
- Conservative: Can sit out otherwise productive risk.
- Solver requirements: Exponential-cone formulation.
References
- Chekhlov, A., Uryasev, S., & Zabarankin, M. (2005). "Drawdown measure in portfolio optimization." International Journal of Theoretical and Applied Finance, 8(1), 13-58.
- Ahmadi-Javid, A. (2012). "Entropic value-at-risk: A new coherent risk measure." Journal of Optimization Theory and Applications, 155(3), 1105-1123.
- skfolio documentation —
skfolio.RiskMeasure.EDAR.