Comparison of VaR Models to the Brazilian Stock Market Under the Hypothesis of Serial Independence in Higher Orders: Are Garch Models Really Indispensable?

Luiz Maluf,Jéssica Asano

doi:10.15728/bbr.2019.16.6.6

Abstract

Our objective in this article was to verify which models for the Value at Risk (VaR), among those that do not consider conditional volatility (Extreme Values Theory and the traditional Historical Simulation), and those that do consider it (GARCH and IGARCH), are adequate for the main index of the Brazilian stock market, the IBOVESPA. For this purpose, backtesting of adherence and the independence of first and higher orders were implemented for the four models mentioned, over forecast horizons of 1 and 10 days. The contribution is based on a the more rigorous criteria than those used in the literature for validating VaR models, as we performed backtesting for violation independence of higher orders on forecast horizons of 10 days. The results show that only GARCH family models were adequate. Thus, it is recommended to entities of the National Financial System that keep relevant positions in the Brazilian stock market, the utilization of internal risk models based on conditional volatility, in order to minimize the occurrence of violation clusters.

Highlights

The objective of this article was to verify which models for Value at Risk (VaR), among those that consider and do not consider the conditional volatility of returns, are suitable for the main index of the Brazilian stock market, the IBOVESPA
The VaR of 1 and 10 days was calculated, by means of the models IGARCH(1,1), Historical Simulation, GARCH(m,n), and Extreme Values Theory (EVT), all considering the investment of a monetary unit of capital (C=1), and it was implemented the backtesting for adherence and independence of the violations of Kupiec (1995), Christoffersen (1998) and LB proposed by Berkowitz et al
Were estimated for the daily log-returns series of the IBOVESPA and the VaR measure was extracted from each model, with the objective of verifying which of them are suitable for the Brazilian stock market, in investment horizons of 1 and 10 days

Summary

Introduction

The objective of this article was to verify which models for Value at Risk (VaR), among those that consider and do not consider the conditional volatility of returns, are suitable for the main index of the Brazilian stock market, the IBOVESPA. VaR, considering in addition to the adherence (unconditional coverage), the independence of their violations (conditional coverage). The latter has become an important concern for managers of financial institutions, and for regulatory bodies in the international environment, since the occurrence of clusters of violations (large unprovisioned losses occurred in succession) can lead to the bankruptcy of these institutions and the risk of a systemic financial market crisis (Christtoffersen & Pelletier, 2004). For other entities of the National Financial System, such as investment funds, pension funds and insurance companies, which have significant portions of the investments of their funds in the stock market, the use of internal stock risk assessment models is important to ensure solvency, the competitiveness and sustainability of their business, as demonstrated by Chan (2010), in a study on internal risk models and regulatory capital in the context of the Brazilian insurance market

Objectives

Methods

Results

Conclusion