Ups and (Draw)Downs

Abstract

The concept of drawdown quantifies the potential loss in the value of a financial asset when it deviates from its historical peak. It plays an important role in evaluating market risk, portfolio construction, assessing risk-adjusted performance and trading strategies. This paper introduces a novel measurement framework that produces, along with the drawdown and its dual (the drawup), two Markov chain processes representing the current lead time with respect to the running maximum and minimum, i.e., the number of time units elapsed from the most recent peak and trough. Under relatively unrestrictive assumptions regarding the returns process, the chains are homogeneous and ergodic. We show that, together with the distribution of asset returns, they determine the properties of the drawdown and drawup time series, in terms of size, serial correlation, persistence and duration. Furthermore, they form the foundation of a new algorithm for dating peaks and troughs of the price process delimiting bear and bull market phases. The other contributions of this paper deal with out-of-sample prediction and robust estimation of the drawdown.

Keywords: Financial time series; risk measures; dating bear and bull markets

JEL Classification: C22, C58, E32