Modeling drawdowns and drawups in financial markets

Beatriz Vaz de Melo Mendes, Vinicius Ratton Brandi

Abstract

ABSTRACT

Periods of turbulence are often characterized by observed consecutive drops in prices, called “drawdowns”. In such cases, static, one-period measures of risk insufficiently describe downside risk. In this paper, we assess risk by formally modeling these random strings of negative returns. We use long-tailed distributions from extreme value theory to model the severity and duration of the drawdowns. This leads to the concept of drawdown-at-risk (DAR) and conditional DAR. The proposed distributions adjust properly to extreme values previously found to be outliers. The paper illustrates the importance of these concepts with stock market indices.