Peak-to-valley drawdowns: insights into extreme path-dependent market risk

Abstract

In this paper, we study risk from the perspective of peak-to-valley market drawdowns. The objective is to gain empirical insights into the drawdown behavior of various asset classes during several time intervals. While the existing literature on drawdown distributions has primarily focused on local drawdowns or consecutive daily drops in various asset classes, this paper focuses on extreme (cumulative) losses occurring over a daily, biweekly, monthly, quarterly and yearly period. The typical investor is mainly concerned with significant negative downward movements, especially when several of these movements happen within a specific time frame. The drawdown measure studied herein embodies this path-dependent risk better than a typical daily standard deviation or value-at-risk estimate due to its cumulative and path-dependent nature. The drawdowns over different periods are analyzed for 25 assets linked to equity indexes, commodities and foreign exchange rates. The tail observations of these drawdowns are fitted to the power law (Pareto distribution) and the stretched exponential (Weibull distribution). We find that the bulk of these observations are well fitted by both distributions. In addition, our analysis shows that the most extreme observations tend to fall between the Weibull and Pareto fits, suggesting that these can be used to define a lower and upper boundary for modeling future drawdowns.