A comparative study on value at risk and conditional value at risk with an application to the Malaysian financial market

Abstract

Value at risk (VaR) and conditional value at risk (CVaR) are frequently used as risk measures in risk management. VaR estimates the maximum expected loss over a given time period at a given acceptance level, whereas CVaR measures the extreme risk or the risk beyond VaR. This paper aims to perform an empirical study on VaR and CVaR based on the daily returns of the Malaysian stock markets traded in Kuala Lumpur Composite Index (KLCI) over a time period using the RiskMetrics and the peaks over the threshold (POT) methods. In particular, the IGARCH (1, 1) model is applied for the RiskMetrics method, whereas the generalized Pareto distribution (GPD), a distribution based on an extreme value theory, is considered for the POT method. The results show that the GPD, which is considered in the POT method, provides an adequate fit to the data of threshold excesses, and the POT is a more reliable measure of risks compared to the RiskMetrics. Key words: Value at risk, conditional value at risk, RiskMetrics, peaks the over threshold, IGARCH, generalized Pareto.