When the U.S. Stock Market Becomes Extreme?

Sofiane Aboura

doi:10.3390/risks2020211

Abstract

Over the last three decades, the world economy has been facing stock market crashes, currency crisis, the dot-com and real estate bubble burst, credit crunch and banking panics. As a response, extreme value theory (EVT) provides a set of ready-made approaches to risk management analysis. However, EVT is usually applied to standardized returns to offer more reliable results, but remains difficult to interpret in the real world. This paper proposes a quantile regression to transform standardized returns into theoretical raw returns making them economically interpretable. An empirical test is carried out on the S&P500 stock index from 1950 to 2013. The main results indicate that the U.S stock market becomes extreme from a price variation of ±1.5% and the largest one-day decline of the 2007–2008 period is likely, on average, to be exceeded one every 27 years.

Highlights

The tail behavior of the financial series has been largely examined by many studies1 with various applications
One naive possibility would have been to apply an OLS procedure to study the relationship between a response variable and an explanatory variable, in order to numerically recompute all the raw returns corresponding to the standardized returns derived from the extreme value theory (EVT) analysis and forecasting
Extreme value theory is usually applied on standardized returns to offer more reliable results, but this makes the economic interpretation more complicated in the real world

Summary

Introduction

The tail behavior of the financial series has been largely examined by many studies with various applications. (e.g., [9,10] etc.) in their EVT analysis, since the literature has applied EVT on independent and identically distributed data such as standardized returns (e.g., [13]). The practice is to extract standardized returns by filtering the raw returns with a GARCH family model; run some standard tests to check for the approximate independent and identically distributed nature of the standardized returns and apply EVT on these data. These standardized returns have no economic meaning in the real world. This article proposes an empirical methodology to convert the results into monetary units such as stock index returns

Methods

Results

Conclusion