The aim of this paper is to find distributions that adequately describe returns of the Belgrade Stock Exchange index BELEX15. The sample period covers 1067 trading days from 4 October 2005 to 25 December 2009. The obtained models were considered in estimating Value at Risk (VaR) at various confidence levels. Evaluation of VaR model accuracy was based on Kupiec likelihood ratio test. | Yugoslav Journal of Operations Research 21 (2011), Number 1, 103-118 DOI: RETURN DISTRIBUTION AND VALUE AT RISK ESTIMATION FOR BELEX15 Dragan ĐORIĆ Faculty of Organizational Sciences, University of Belgrade, djoricd@ Emilija NIKOLIĆ-ĐORIĆ Faculty of Agriculture, University of Novi Sad, emily@ Received: October 2010 / Accepted: February 2011 Abstract: The aim of this paper is to find distributions that adequately describe returns of the Belgrade Stock Exchange index BELEX15. The sample period covers 1067 trading days from 4 October 2005 to 25 December 2009. The obtained models were considered in estimating Value at Risk ( VaR ) at various confidence levels. Evaluation of VaR model accuracy was based on Kupiec likelihood ratio test. Keywords: Value at risk, return distributions, Kupiec test, BELEX15. MSC: 91B30, 62E99, 60G70. 1. INTRODUCTION Value at Risk ( VaR ) is a commonly used statistic for measuring potential risk of economic losses in financial markets [11, 5, 4, 8]. Using VaR financial institutions can calculate the possible maximum loss over a given time horizon, usually 1-day or 10 days, at a given confidence level. Empirical VaR calculations involve the estimation of lowerorder quantiles, for example 10%, 5% or 1% of the return distribution. While VaR concept is very easy, its measurement is a very challenging statistical problem. Risk analysis can be done in two stages. First, we can express profit-and-loss in terms of returns, and subsequently, model the returns statistically and estimate the VaR of returns by computing appropriate quantile. The main problem is related to the estimation of distribution that adequately describes the returns. The empirical distribution function of the sample of returns is an 104 D. Đorić, E. Nikolić-Đorić / Return Distribution and Value at Risk approximation of the true distribution of returns which is reasonably accurate in the center of the distribution. However, to .
