A levered investor is liable to get caught in a liquidity trap. Unable to secure funding after an abrupt market decline, he may be forced to sell valuable securities at depressed prices. This experience was commonplace during the 2007–2009 financial crisis, and it has refocused the attention of levered investors on an important liquidity trap trigger, a drawdown, which is maximum decline in portfolio value over a fixed horizon. The following figure shows how a severe drawdown can have a disruptive effect on an investment process.

In the event of a large drawdown, common risk diagnostics, such as volatility, Value-at-Risk, and Expected Shortfall, at the end of the intended investment horizon are irrelevant. Indeed, within the universe of hedge funds and commodity trading advisors (CTAs), one of the most widely quoted measures of risk is maximum drawdown.

**Drawdown: From Practice to Theory and Back Again [linked pdf]
**The paper will appear in Mathematics and Financial Economics

CDAR Co-Director Lisa Goldberg and co-author Ola Mahmoud, a postdoctoral fellow and lecturer at the University of St Gallen and Affiliated Researcher at UC Berkeley’s Center for Risk Management Research, have developed a mathematically and economically sound path dependent risk measure capturing drawdown: Conditional Expected Drawdown (CED). In the context of risk measures, CED is convex with respect to portfolio weights, which means that it promotes diversification and can be used in an optimizer. It is also homogenous of degree one, so that it supports linear risk attribution.

By focusing on the maximum of all drawdowns within a path of fixed length T, the authors address a highly relevant risk management concern affecting fund managers on a daily basis, who ask themselves: what is the expected maximum possible cumulative drop in net asset value within the investment horizon T? If this loss exceeds a certain threshold, the investor may be forced to liquidate. For a given investment horizon T , Conditional Expected Drawdown indicates this expected cumulative loss in excess of a threshold, and it can be measured for various confidence levels.

The authors also show that drawdown is inherently path dependent and accounts for serial correlation, whereas traditional single-period risk measures do not account for consecutive losses.

**The Temporal Dimension of Risk [linked pdf]**

Since drawdown inherently accounts for the path over a given time period, it comes equipped with two dimensions: a spatial dimension (drawdown magnitude) and a temporal dimension (drawdown duration). While the magnitude component of drawdown has been extensively studied in the academic literature and is regularly used by the investment community, the temporal dimension, its duration, which measures the length of excursions below a running maximum, has not received the same kind of attention.

UC Berkeley’s Affiliated Researcher Ola Mahmoud introduces the notion of temporal path-dependent risk measure to capture the risk associated with the temporal dimension of an investment path. In particular, the author studies the temporal dimension of investment drawdown. Two temporal dimensions considered are drawdown duration, which measures the time it takes a process to reach a previous running maximum, and liquidation stopping time, which captures a subjectively set time threshold beyond which an investor liquidates if the drawdown exceeds this threshold.