Drawdown: From Practice to Theory and Back Again

Mathematics and Financial Economics, Forthcoming

28 Pages Posted: 30 Apr 2014 Last revised: 22 Sep 2016

Lisa R. Goldberg

University of California, Berkeley; Aperio Group

Ola Mahmoud

University of St. Gallen; University of California, Berkeley

Date Written: September 21, 2016

Abstract

Maximum drawdown, the largest cumulative loss from peak to trough, is one of the most widely used indicators of risk in the fund management industry, but one of the least developed in the context of measures of risk. We formalize drawdown risk as Conditional Expected Drawdown (CED), which is the tail mean of maximum drawdown distributions. We show that CED is a degree one positive homogenous risk measure, so that it can be linearly attributed to factors; and convex, so that it can be used in quantitative optimization. We empirically explore the differences in risk attributions based on CED, Expected Shortfall (ES) and volatility. An important feature of CED is its sensitivity to serial correlation. In an empirical study that fits AR(1) models to US Equity and US Bonds, we find substantially higher correlation between the autoregressive parameter and CED than with ES or with volatility.

Keywords: drawdown; Conditional Expected Drawdown; deviation measure; risk attribution; convex optimization; serial correlation

Suggested Citation

Goldberg, Lisa R. and Mahmoud, Ola, Drawdown: From Practice to Theory and Back Again (September 21, 2016). Mathematics and Financial Economics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2430918 or http://dx.doi.org/10.2139/ssrn.2430918

Lisa R. Goldberg

University of California, Berkeley ( email )

Department of Statistics
367 Evans Hall
Berkeley, CA 94720-3860
United States

Aperio Group ( email )

3 Harbor Drive
Suite 315
Sausalito, CA 94965
United States

Ola Mahmoud (Contact Author)

University of St. Gallen ( email )

Faculty of Mathematics and Statistics
Bodanstrasse 6
Saint Gallen, St. Gallen CH-9000
Switzerland

University of California, Berkeley ( email )

Center for Risk Management Research
Evans Hall
Berkeley, CA 94720
United States

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