Folio Lab/Documentation

Minimum Average Drawdown

Minimise the average drawdown: the mean distance of the portfolio below its running peak, over every day of the run window. Every day spent under water counts, in proportion to how far under water it is.

Overview

Average drawdown is the drawdown counterpart of MAD: it uses the whole drawdown path rather than its worst point. Chekhlov, Uryasev and Zabarankin (2005) give its linear-programming form on uncompounded cumulative returns. It is CDaR at confidence level 0.

Because every day counts, it rewards a portfolio that recovers quickly, not only one that falls less.

FolioLab implements this method with skfolio's mean-risk estimator, usingRiskMeasure.AVERAGE_DRAWDOWN with the objective set to minimise risk. The problem is a linear programme, solved by CVXPY with CLARABEL first, then HiGHS, then SCS. Per-name weight bounds, asset exclusions, and group sum limits such as sector caps pass to the estimator and enter the same programme.

Mathematical Formulation

Average drawdown

is the vector of daily asset returns on day, and is the number of days in the run window.

Linear programme

The same running-peak variables as maximum drawdown, with the mean in place of the maximum.

Average vs maximum drawdown

Maximum drawdown keeps one episode. Average drawdown weighs every day, so a long shallow drawdown can cost more than a short deep one.

The measure is less sensitive to a single crash than maximum drawdown, and more sensitive to slow recoveries.

What the result is, and is not

The weights minimise the measure on the returns of the run window, and only on them. They are not a forecast that the measure will be lowest in the future. Like every method on FolioLab, this one is not validated out of sample, and no claim is made that it performs better than any other method.

Before release, FolioLab compared these weights with the weights riskfolio-lib 7.0.1 produces for the same measure on the same returns.

Advantages & Limitations

Advantages

  • Whole path: Uses every day of the drawdown path.
  • Rewards recovery: Time under water is penalised, not only depth.
  • Linear: Solved as a linear programme on uncompounded returns.

Limitations

  • Dilutes the tail: One deep drawdown can be offset by many days at the peak.
  • Uncompounded: Differs slightly from the compounded drawdown in the results.
  • History-bound: The measure is the in-sample average of the run window.

References

  • Chekhlov, A., Uryasev, S., & Zabarankin, M. (2005). "Drawdown Measure in Portfolio Optimization." International Journal of Theoretical and Applied Finance, 8(1), 13-58.
  • Cajas, D. (2021). Riskfolio-Lib documentation - risk measures.
  • skfolio documentation - skfolio.RiskMeasure.AVERAGE_DRAWDOWN.

Not investment advice. Past performance is not indicative of future results.