Maximum Drawdown

Abstract

A drawdown is defined as the accumulated percentage loss due to a sequence of drops in the price of an investment. It is collected over non-fixed time intervals and its duration is also a random variable. The maximum drawdown occurring over a fixed investment horizon is a flexible measure that provides a different perception of the risk and price flow of this investment. In this article a new modeling strategy for maximum drawdown that separates its duration and severity along with suggestions of a flexible distribution from the extreme value theory for modeling the losses is proposed. Applications for the fitted distribution, which include the computation of risk measures, classification and selection of investments, as well as its use in optimal portfolio allocation, are discussed. The properties of the model-based maximum drawdown-at-risk are then analyzed and a new risk measure, the conditional maximum drawdown-at-risk, is presented. Illustrations using stock market indexes as well as insights on the connection of the fluctuations of the maximum drawdown and the volatility of the underlying return series are provided. This methodology is applicable to various alternative investment strategies as well.