Emprical evaluation of Value at Risk(VaR) model using the Lusaka stock Dissertation

Emprical evaluation of Value at Risk(VaR) model using the Lusaka stock exchange - Dissertation Example Abstract This study develops an evaluation of Value at Risk measure for a portfolio consisting of three stocks traded at the Lusaka stock Exchange. The analysis set out from 1-day, 1% VaR and take a two dimension approach: the volatility models and the distributions are used when computing VaR. Consequently, the historical volatility, the EWMA volatility model, GARCH-type models for the volatility of the stocks and of the portfolio and a dynamic conditional correlation (DCC) model were considered. VaR was computed using standard normal distribution, and other different methodologies of taking into account the non-normality of the returns (the Cornish-Fisher approximation, the modeling of the empirical distribution of the standardized returns and the Extreme Value Theory approach). The objective was to evaluate the Value at Risk model using the Lusaka stock exchange return. The results suggest that using conditional volatility models and distributional tools that account for the non-n ormality of the returns leads to a better VaR-based risk management. ... ACKNOWLEDGEMENT 2 DECLARATION 3 BACKGROUND TO THE STUDY 7 1.1 INTRODUCTION 7 1.2 Overview of Lusaka Stock Index 9 1.3 Problem statement 12 1.2.2 Research Questions 13 1.2.1 Objectives 14 1.2.3 The Hypothesis: 14 1.2.4The organization of the rest of the chapters 14 LITERATURE REVIEW 15 Theoretical and Conceptual Framework 27 3.1 Introduction 27 3.2.2 Discussion of the Model 30 3.2.3Advantages of GARCH 31 3.3 Other Models 31 3.3.1 GARCH DCC 31 3.3.2 Historical volatility 33 3.3.3 EWMA Volatility Model 33 3.4 Distributions 34 3.4.1 The standard normal distribution 34 3.4.2 The historical quantiles 35 3.4.3 the t-Student, Normal Inverse Gaussian (NIG) and Generalized Hyperbolic (GH) distributions 35 3.4.4 The Cornish-Fisher (CF) approximation 36 3.4.5 Extreme Value Theory(EVT) 36 Methodology 39 4.1 Introduction 39 4.2 Research Design 39 4.3 Sources of Data 40 4.5 Data Collection Methods 40 4.6 Data Reliability 40 4.6 Data Analysis 41 4.7 Limitations to the Study 41 4.8 Summary 41 5.0 DAT A ANALYSIS , FINDINGS AND DISCUSION 42 5.1 The Data 42 5.2 VaR using the Historical Volatility 47 5.3 VaR using the EWMA volatility model 58 5.4 VaR using a GARCH volatility model for portfolio returns 66 5.5 VaR using GARCH volatility models for the stock returns 77 6.0 CONCLUSIONS 98 BACKGROUND TO THE STUDY 1.1 INTRODUCTION In the financial literature, three types of risk are distinguished; these are business risk, strategic risk and financial risk. Business risk pertains to the risks a firm faces exclusively on account of their presence in some product market. This type of risk stems from uncertainty in such activities as technological innovations, product