Maximum drawdown: models and applications

Abstract

Financial series may possess fractal dimensions which would induce cycles of many different durations. This inherent characteristic would explain the turbulent cascades in stock markets when strong local dependence is observed. A drawdown is defined as the percentual accumulated 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 occuring during a fixed investment horizon is a flexible measure that may provide a different perception of the risk and price flow of an investment. In this paper we propose statistical models from the extreme value theory for the severity and duration of the maximum drawdown. Our empirical results indicate that there may exist a relation between the pattern of the GARCH volatility of an investment and the fluctuations of the severity of the maximum drawdown and that, typically, extreme (but not outlying) maximum drawdowns occur during stress periods of high volatility. We suggest applications for the maximum drawdown, including the computation of the Maximum Drawdown-at-Risk with exceedance probability α, and the classification of investments according to their performance when controlling losses via the maximum drawdown.