1. Introduction

Due to its computational and numerical intensity coupled with limited availability of data, a few adjustments will be made in testing Izhar’s proposed theoretical model. Firstly, the process through which VaR is generated will undergo a slight modification since the variables in the analysis do not reflect non-linearity relationships. Nonlinearity might arise from derivative products such as options. As will be shown in the later section, none of the variables in the model are categorised as one, hence the issue of non-linearity is irrelevant since a quadratic relationship among variables does not exist. As a result, the issue of first and second derivative relationships, namely delta-gamma cannot be analysed. The analysis, therefore, shall focus on the issue of normality vis–a-vis non-normality of the distribution density functions of the analysed variables.

In analysing VaR, this study does not simply use the data and follow a prescribed assumption to produce VaR. Rather, it will carefully analyse the behaviour of the data by taking into account volatility, skewness and kurtosis of identified variables. As will be shown in the later section, volatility analysis employs two models, constantvariance model and exponential weighted moving average (EWMA) model.

This approach has been adopted by Li (1999), Hull and White (1998), and RiskMetrics (1996). The organisation of this paper is as follows; first, an introduction; second, a revisit on the theoretical background of value at risk (VaR); third, an explanation on the methodology used in the study; fourth, discussions on the empirical findings; and fifth the conclusion.

2. What is Value at Risk (VaR)?

Formally the Value at Risk (VaR) can be defined as the maximum loss that could occur in a given level of confidence within a certain period of time. If τ is denoted as the investor’s temporal horizon, with Rt(τ ) the series data realised in the interval (t, t+ τ ) and with θ the level of confidence, the VaR given by the loss such that,

P(Rt(τ ) ≤ -VaR) = 1- θ (1)

Thus, the VaR is the percentile at the (1-θ )% of the variables under analysis in the interval (t, t+ τ ). The temporal horizon τ and the level of confidence θ are parameter schosen by the investor. The choice of τ depends on the frequency with which the investor wishes to control his/her investment.