On a Convex Measure of Drawdown Risk

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 probabilistic risk metrics. 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 attributed to factors; and convex, so that it can be used in quantitative optimization. We provide an efficient linear program for minimum CED optimization and 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. Key terms: leverage; drawdown; maximum drawdown distribution; Conditional Expected Drawdown; volatility; Expected Shortfall; tail mean; liquidity trap; illiquidity; coherent risk measure; deviation measure; risk attribution; risk contribution; risk concentration; generalized correlation; marginal contribution to risk; optimization; portfolio construction; serial correla-