The Performance of Value-At-Risk in Perspective of the Financial Crisis

The Performance of Value-at-Risk in Perspective of the

Financial Crisis

Abstract

The period leading to the beginning of the nancial crisis in 2008 is the event of interest in

this paper. A mix of a quantitative, empirical performance research of Value-at-Risk (VaR)

and a qualitative based investigation leads to the conclusion that the parametric and the

nonparametric Value-at-Risk approaches underperform. They are one of the (many) codetermining

factors that indirectly led to the collapse of the nancial system. In combination

with the presence of bad incentives at risk management departments of nancial enterprises,

Value-at-Risk lead to a large contagion on a macroeconomic scale. The popularized standalone

RiskMetricsTM methodology, which was introduced around 1995, concerns a simplied

parametric approach. The assumption is made that this method was broadly implemented

next to the popular nonparametric approach called Historical Simulation (Pérignon & Smith,

2010). The empirical research conducted in this paper focuses on the performance of the parametric

VaR calculation by using the RiskMetricsTM methodology, which includes a Gaussian

ARMA(0,0)-IGARCH(1,1) model without drift for the conditional heteroscedastic volatility

equation.

Contents

1 Introduction 3

2 Theory 4

2.1 Value-at-Risk Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2.2 Value-at-Risk In Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2.1 RiskMetricsTM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

3 Research Methods 10

4 Results 12

4.1 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

4.2 Eects on Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.3 Macro Eects of Value-at-Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

5 Conclusion 19

5.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

References 21

Acknowledgements

The authors would like to thank Dr. A.H. Siegmann for the help on obtaining the data through

DataStream. In addition, as many lines of programming had to be written, the authors hereby

would like to thank Dr. C.S. Bos for his help with the Ox language.

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1 Introduction

With the collapse of the collateralized debt securities market in 2008 and as more trading scandals

have uncovered, the issue of how banks manage their risk has gained more notoriety. Risk management

has always been a big obstacle for banks and other nancial institutions. The trade-o

between return and risk is something that has always been a big issue for these nancial rms

and institutions. Not only does the return have to be as high as possible, without risking a major

trading loss that could cause a default, but the returns also have to be sustainable. An important

tool that nancial and nonnancial enterprises have been using to manage their risk is the Valueat-

Risk method, commonly referred to as VaR. This risk management tool calculates the amount

of money invested that can be lost with some condence level for an individual asset or portfolio.

This means that if a nancial institution is interested in the absolute amount of money that it

can lose on its investment, given an alpha of ve percent, within a one day period, the forecast

of one day Value-at-Risk (95%) has to be calculated. That is, within 5% of the cases these losses

will exceed the Value-at-Risk. The previous example for a condence level of 95% would hold if

the VaR is calculated correctly, which requires that the rights assumptions are made, and if it is

able to forecast the VaR within a certain condence interval. However, the calculation of the VaR

can be quite complex as this paper will show. Regarding the section discussing several popular

VaR approaches, the objective is to merely give the reader a comprehensive overview of the main

models. No empirical evidence is given unless stated otherwise.

In practice, the commonly used VaR approaches are generally acclaimed for their simplicity, as

risk managing institutions care about the interpretation and the clarity of the models entertained.

The question that remains, however, is: are these simplied models that are used in practice

the best way to measure and manage risk? And what is the eect on nancial markets once

most nancial rms have adopted this method? In this paper, the assumptions of the general

Value-at-Risk tool and its eects on the internal environment of enterprises, as well as on the

external environment of nancial enterprises, the (nancial) security markets, will be analyzed.

The limitations of the model will be put into perspective and will be specically looked at with

reference to the nancial crisis of 2008. The thesis statement of this paper is:

What are the eects of the Value-at-Risk methods on the risk management practice

of nancial enterprises and nancial markets and what are the limitations and shortcomings

of the model, as it was used previous, during and after the nancial crisis of

2008?

The subsections that will be discussed are:

1. What is the eect of Value-at-Risk on the risk management of nancial enterprises?

2. What is the macro eect of Value-at-Risk on nancial markets?

The results obtained will be enforced with an empirical research on the 1995 RiskMetricsTM

methodology, which has been the benchmark for parametric VaR approach in the nancial industry.

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2 Theory

In this section, the most common Value-at-Risk methods are touched upon. Their underlying

structures are discussed in detail, with the focus on the modeling of the volatility of a specic asset

or portfolio. Besides the modeling of the volatility, the use of VaR in practice will be discussed,

with a particular focus on the standalone RiskMetrics methodology, which was originally developed

by J.P. Morgan Chase & Co.

2.1 Value-at-Risk Models

There are three main methods for calculating the Value-at-Risk of a certain asset or portfolio.

These methods can be categorized as either a parametric or a nonparametric approach. This

paper discusses the use and eects of the VaR models in practice, although the focus is mainly

on the parametric approach.