Drawdown: From Practice to Theory and Back Again

TL;DR

This paper introduces Conditional Expected Drawdown (CED) as a formal risk measure for maximum drawdown, demonstrating its mathematical properties and empirical advantages over traditional risk metrics like ES and volatility.

Contribution

It formalizes drawdown risk as CED, a convex and positively homogeneous measure, and explores its properties and empirical relevance in risk attribution and modeling.

Findings

CED is more sensitive to serial correlation than ES or volatility.

Empirical analysis shows higher correlation between CED and AR(1) parameters.

CED can be used effectively in quantitative risk optimization.

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.