Applications of Value-at-Risk Models for Risk Management

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Acknowledgement

I would take this opportunity to thank my research supervisor, family and friends for their support and guidance without which this research would not have been possible.

DECLARATION

I, [type your full first names and surname here], declare that the contents of this dissertation/thesis represent my own unaided work, and that the dissertation/thesis has not previously been submitted for academic examination towards any qualification. Furthermore, it represents my own opinions and not necessarily those of the University.

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Abstract

The main aim of the study is to calculate the value at risk (VaR) for the following for ?ve equity indices (CAC40, DAX30, FTSE100, NIKKEI225 and S&P500), obtained from DataStream for the period of July 9th, 1987 to October 18th, 2002. For all indices, we compute daily log returns. However, the research focuses on the calculation of the VaR using 2 sets of data, one containing all the observations in the last 5 years and another one containing only the observations in the last 2 years.

Table of Contents

CHAPTER 1 INTRODUCTION6

Background of the Study6

Problem Statement7

Research Aims and Objectives7

Significance of the Study8

CHAPTER 2 LITERATURE REVIEW11

Defining VAR13

A Short History of VaR14

The Development of VAR15

Case Study Example- Procter & Gamble17

The decision problem: active risk management18

VaR diagnostics for individual models21

VaR Basics22

Different Approaches to VaR22

Variance-covariance Approach23

Historical Simulation24

Monte Carlo Simulation26

Comparing the Methods27

CHAPTER 3 RESEARCH METHODOLOGY30

Analytical VaR30

Historical Simulation Approach31

Data31

CHAPTER 4 RESULTS AND FINDINGS33

Data and Results33

Normal Distribution37

Leptokurtic Distributions40

Model Selection43

Monthly Volitality Analysis44

CHAPTER 5 CONCLUSION47

REFERENCES49

CHAPTER 1 INTRODUCTION

Background of the Study

The dissertation is devoted to study of risk management techniques for decision making in highly uncertain environments. The traditional framework of decision making under the presence of uncertainties relies on stochastic programming (Birge and Louveaux, 1997; Pr´ekopa, 1995) or simulation (Ripley, 1987) approaches to surpass simpler quasi-deterministic techniques, where the uncertainty is modeled by relevant statistics of the stochastic parameters, such as expectation or variance. One method of limiting an institution's risks in derivatives trading is to place a limit on the amount it can lose with a given probability over a specified period of time. For instance, one might consider the losses at a 1% level over ten days or at a 5% level over one day. This value is called Value-at-Risk or VAR.

Often a financial institution's portfolio consists of many underlying instruments, such as equities, fixed-income securities, commodities and so on. All these instruments depend hundreds of market variable, and many different types of risk measures are produced daily to capture the performance of portfolio. However, this does not give the senior manager much better understanding of the current performance of the portfolio or the portfolio value forecast under the volatile future market conditions. Hence, the value at risk (VaR) measure is soon introduced, which compresses the Greek letters for all market variables into one single number and makes comparison between performances of different portfolios much simpler.

Problem Statement

Value-at-Risk (VaR) has been widely promoted by regulatory groups and embraced by financial institutions as a way of monitoring and managing market risk - the risk of loss due to ...