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Calculating VaR in EU Candidate States

Calculating VaR in EU Candidate States This paper examines whether VaR models that are created and suited for developed and liquid markets apply to the volatile and shallow financial markets of EU candidate states. To this end, several VaR models are tested on five official stock indexes from EU candidate states over a period of 500 trading days. The tested VaR models are: a historical simulation with rolling windows of 50, 100, 250 and 500 days, a parametric variance-covariance approach, a BRW historical simulation, a RiskMetrics system and a variance-covariance approach using GARCH forecasts. Based on the backtesting results it can be concluded that VaR models that are commonly used in developed financial market are not well-suited to measuring market risk in EU candidate states. Using some of the most widespread VaR models in these circumstances may result in serious problems for both banks and regulators. Keywords: Abbreviations: EU, VaR, VCV, EWMA, Historical simulation, BRW, ARCH, GARCH JEL: C22, C53, G15, G18 DOI: 10.2478/v10033-008-0003-y 1. Introduction The impact of allowing banks to calculate their capital requirement for market risk based on their internal VaR models, as well as the impact of regulation changes on banks in less developed countries, has not been well studied. Even in the European Union, not all of the EU-15 member countries have systematically conducted research on the consequences and impact of these changes on their banking sectors. New EU member states and EU candidate states are even further behind in these issues. The group of EU candidate states is comprised of the following countries: Bulgaria, Romania, Croatia and Turkey. Bulgaria started its accession negotiations with the EU in February 2000, and closed the accession negotiations in June 2004. Romania, like Bulgaria, started its accession negotiations in February 2000, and closed the accession negotiations in December 2004. Both countries will become full EU members in January 2007. Croatia and Turkey started the accession negotiations on the same date, 03.10.2005. Croatia is expected to become a full EU member in 2009. This is not the case with Turkey, which still has a long journey ahead of it. Although very different and unique in their own ways, when looking through a financial prism, these countries are similar in certain respects. The EU candidate states are all significantly lagging behind the most developed EU countries in many fields, but especially in matters of financial legislation, market discipline, insider trading, disclosure of information (financial and other), embezzlement, knowledge of financial instruments, markets and associated risks. When investing in these financial markets, banks and investmend funds employ the same risk measurement models for measuring market * Zikovi: Faculty of Economics, University of Rijeka, Ivana Filipovia 4, Rijeka, Croatia, e-mail: sasa.zikovic@efri.hr SEE booklet CC.indd 23 risk and forming provision as they do in developed markets. This means that risk managers presume equal or similar characteristics and behaviour in these markets to developed markets. Using VaR models that are created and suited for developed and liquid markets in developing markets raises concerns whether VaR models developed and tested in these financial markets apply to the volatile and shallow financial markets of EU candidate states. This paper therefore attempts to provide an answer to the question whether commonly used VaR models adequately capture market risk in the financial markets of EU candidate states. Employing VaR models in forming a bank's provisions that are not suited to developing markets can have serious consequences, resulting in big losses to banks' portfolios that could be undetected by the employed risk measurement models. Banks could also be penalized by the regulators via higher scaling factors when forming their market risk provisions due to the use of a faulty risk measurement model. To this end, variance-covariance methods and historical simulation approaches are used to estimate VaR for official stock indexes from each of the EU candidate states over a period of 500 trading days. In the next step, the performance of the various models is compared over the simulation period with the help of a range of backtesting procedures to determine how accurately the models match the specified confidence intervals. The paper is structured as follows: Section 2 briefly outlines the VaR approaches on which the calculations in this paper are based. Section 3 provides a brief description of the data used. Section 4 presents and explains the results. Section 5 offers a few concluding remarks. of a portfolio. Thus, losses greater than the estimated VaR should only occur with the probability 1-C, i.e. the "tail events", should on average, occur C*N times in every N trading days. The variance-covariance approach assumes that the risk factors that determine the value of the portfolio are multivariate normally distributed, which implies that changes in the value of a portfolio are normally distributed. Since the normal distribution is fully described by its first two moments, the VaR of a portfolio is essentially a multiple of the standard deviation. VaR under the variancecovariance approach is given by: (2) where w is a vector of absolute portfolio weights, w' is its transpose, denotes a variance-covariance matrix and is a scaling factor. The variances and covariances are usually estimated from a daily historical time series of the returns of the relevant risk factors using equally weighted moving averages: (3) is where the mean is often assumed to be zero, variance (or covariance) at time T, ri,t and rj,t are returns and n is the number of observations, i.e. the window length, used to calculate the variances and covariances. Another frequently used estimator is the exponentially weighted moving average (EWMA), which is used in RiskMetrics methodology. In contrast to equally weighted moving averages, the exponentially weighted moving average weights current observations more than past observations in calculating conditional variances (covariances). The EWMA estimator in its recursive form is given by: 2. Analyzed VaR Models The VaR approach is attractive to practitioners and regulators because it is easy to understand and it provides an estimate of the amount of capital that is needed to support a certain level of risk. Another advantage of this measure is the ability to incorporate the effects of portfolio diversification. Many banks and other financial institutions now base their assessment of financial risk and risk management practices on VaR or plan to do so in the future. VaR reduces the risk associated with any portfolio to just one number, the expected loss associated with a given probability over a defined holding period. VaR for a given probability C can be expressed as: VaRc = F-1(C) (1) where F­1(C) denotes the inverse of cumulative probability distribution of the changes in the market value (4) Parameter determines the exponentially declining weighting scheme of the observations. One difference between the two estimators is that the equally weighted moving average does not account for time-dependent variances, whereas the exponentially weighted moving average does. A more sophisticated parametric estimator of volatility is a GARCH process: (5) SEE booklet CC.indd 24 where t ~ IID N(0,1) In a GARCH model t denotes a real-valued discretetime stochastic process whose conditional distribution is assumed to follow a specific probability distribution (Gaussian, Student's T, etc.). The sizes of the parameters and determine the short-run dynamics of the resulting volatility time series. Large GARCH lag coefficients i indicate that shocks to conditional variance take a long time to die out, so volatility is persistent. Large GARCH error coefficients mean that volatility reacts intensely to market movements, meaning that if alpha is relatively high and beta is relatively low, volatilities tend to be spiky. The second approach used in this paper is historical simulation. In contrast to parametric methods, no specific distributional assumptions about the individual market risk factors, i.e. returns, are made, and no variances or covariances have to be estimated. Instead, it is only assumed that the distribution of the relevant market returns is constant over the sample period. Historical simulation VaR can be expressed as: where are the weights associated with return ri and I(·) is the indicator function. If BRW quantile estimator equals the historical simulation estimator. Boudoukh, Richardson and Whitelaw in their paper set equal to 0,97 and 0,99, the same coefficients used in this paper. 3. Data and Methodology For transitional economies such as those of EU candidate states, a significant problem for a serious and statistically significant analysis is the short histories of their market economies and active trading in financial markets. Because of the short time series of returns of individual stocks and their highly variable liquidity, it is practical to analyze the stock indexes of these countries. A stock index can be viewed as a portfolio of selected securities from an individual country. In this paper, the performance of selected VaR models is tested on stock indexes from Croatia (Zagreb stock exchange (CROBEX) and Varazdin stock exchange (VIN)), Bulgaria (SOFIX), Romania (BBETINRM) and Turkey (XU100). To answer which VaR models adequately capture the market risk in the stock markets of the EU candidate states, nine VaR models are tested on the stock indexes of EU candidate states. The tested VaR models are: a historical simulation with rolling windows of 50, 100, 250 and 500 days, a parametric variance-covariance approach, a BRW historical simulation, a RiskMetrics system and a variancecovariance approach using GARCH forecasts. VaR models are calculated for a one-day holding period at 95% and 99% coverage of the market risk. To secure the same outof-the-sample VaR backtesting period for all of the tested indexes, the out-of-the-sample data sets are formed by taking out 500 of the latest observations from each index. The rest of the observations are used as pre-sample observations needed for VaR starting values and volatility model calibration. When employing the ARMA-GARCH VCV model the goal, is to capture the dynamic of the data generating process of the return series so that the standardised innovations are independently and identically distributed (IID). The ACF, PACF and Ljung-Box Q-statistic test the presumption of IID in standardized innovations. If the tests do not discover autocorrelation in the standardized innovations employed, the ARMA model can be considered adequate. Squared standardized innovations are tested for autocorrelation and ARCH effects through ACF, PACF and Ljung-Box Qstatistic. The most parsimonious GARCH model based on the Akaike and Schwartz information criterion that passes the tests of autocorrelation and ARCH effects in the squared standardized innovations is chosen to describe the volatility dynamics of the return series. The validity of the analyzed VaR models in EU candidate states is tested by the Kupiec test, the Christoffersen independence test, (6) where returns is taken from the set of ordered . The BRW approach developed by Boudoukh, Richardson and Whitelaw (1998), combines RiskMetrics and historical simulation methodologies, by applying exponentially declining weights to past returns of the portfolio. Each of the most recent N returns of the portfolio, rt, rt-1, ..., rt-N+1, is associated a weight, respectively. The role of the term is simply to ensure that the weights sum to 1, provided . After the probability weights are assigned, VaR is calculated based on the empirical cumulative distribution function of returns with the modified probability weights. To better understand the assumptions behind the BRW approach and its connection to historical simulation, BRW quantile estimator can be expressed as: (7) SEE booklet CC.indd 25 the Blanco-Ihle test, the Lopez test, and the RMSE and MAPE measures. Although there is an abundance of research papers dealing with VaR and market risk measurement and management, all of the existing VaR models have been developed and tested in mature, developed and liquid markets. Testing of VaR models in other, less developed or developing financial market is at best scarce. Zikovi, Bezi (2006) investigated the performance of historical simulation VaR models on stock indexes of the EU candidate states. CROBEX (Croatia), SOFIX (Bulgaria), BBETINRM (Romania) and XU100 (Turkey) indexes all show clear positive trends over a longer time period. With the exception of the XU100 index, all of other indexes analyzed exhibit asymmetry and leptokurtosis. Based on performed tests of normality, it can be said with great certainty that these returns are not normally distributed. The tests employed show significant autocorrelation and ARCH effects in the squared returns of all the analyzed indexes. These phenomena violate normality assumption, as well as the IID assumption, which is a necessary requirement for the proper implementation of historical simulation. Results point to the conclusion that even though historical simulation provided correct unconditional coverage for the indexes tested at most of the confidence levels, use of historical simulation (especially based on shorter observation periods) is not recommendable in these markets. on normality assumption, as well as for the nonparametric and semi-parametric approaches that are based on the IID assumption, such as historical simulation and the BRW approach. This is very indicative for risk managers, because the elementary assumptions of many VaR models are not satisfied, meaning that VaR figures obtained for such models cannot be completely trusted. An ARMAGARCH model performs a transformation of original return data to obtain independently and identically distributed observations. The ARMA-GARCH model successfully captured the dynamics of stock indexes from EU candidate states and produced standardized innovations that proved to be independently and identically distributed. In modelling conditional volatility, a basic GARCH (1,1) model was sufficient for all stock indexes. Estimated ARMA-GARCH parameters for stock indexes of EU candidate states are presented in Table I. As can be seen from Table I, some of the tested indexes, such as VIN and BBETINRM, show unusually low persistence in volatility but are very reactive to volatility, which will make VaR forecasts based on GARCH volatility spiky. The majority of stock indexes are not even closely integrated, as is presumed by the EWMA volatility modelling that underlies the RiskMetrics model. The estimated GARCH parameters of stock indexes from EU candidate states point to the conclusion that VaR models based on simpler conditional volatility models, such as MA or EWMA, will underestimate or overestimate the true level of risk. The Kupiec test and Christoffersen independence test are usually used to identify VaR models that are acceptable to the regulators, and provide the desired level of safety to individual banks and, due to the contagion effect, to the entire banking sector. The results of the overall acceptance, according to the Kupiec and Christoffersen independence tests, of tested VaR models at 95% and 99% confidence levels and 10% significance level are presented in Tables II and III. 4. Backtesting Results Based on the ACF, PACF and Ljung-Box Q statistics of the returns and squared returns of analyzed stock indexes from EU candidate states given in tables V ­ IX, the presence of autocorrelation and heteroskedasticity in the data is obvious. All of the analysed indexes exhibit heteroskedasticity, with VIN, BBETINRM and SOFIX exhibiting autocorrelation in their returns. This finding is troubling for VaR models based Table I - Estimated ARMA-GARCH parameters for stock indexes from EU candidate states SEE booklet CC.indd 26 3/31/2008 15:09:35 Table II - Number of VaR model failures according to Kupiec test and Christoffersen independence test, tested on five EU candidate states' stock indexes, 500 observations, at 95% confidence level Table III - Number of VaR model failures according to Kupiec test and Christoffersen independence test, tested on five EU candidate states' stock indexes, 500 observations, at 99% confidence level From the data in Table II, it is clear that at a 95% confidence level, the tested VaR models perform very differently, with a majority of VaR models failing the Kupiec test and Christoffersen independence test for at least one stock index. VaR models that passed the Kupiec test across all the analyzed stock indexes are the GARCH VCV model, RiskMetrics system and both BRW models with = 0.97 and 0.99. According to the Kupiec test, the worst performer out of all the tested VaR models is the HS 50 model, which failed the Kupiec test for four out of five stock indexes. The HS 50 model is followed by HS 500 with three failures. According to the Christoffersen independence test, the best performers are the HS 250 and both BRW models with = 0.97 and 0.99. The worst performers are HS 50 and GARCH VCV. Overall, the best performers according to the Kupiec test and Christoffersen independence test at a 95% confidence level across stock indexes of EU candidate states are the BRW models with = 0.97 and 0.99. The worst performers are the HS 50 and HS 500 models. Although it is very informative to look at VaR model performance at different confidence levels, the true test of VaR model acceptability for regulators is its performance at a 99% confidence level, as prescribed by the Basel Committee. According to the results obtained at a 99% confidence level, which are presented in Table III, all of the VaR models failed the Kupiec test for at least one stock index. The situation is somewhat better with the Christoffersen independence test, where HS 250 and BRW model with = 0.99 both passed the test. The best performers according to the Kupiec test are the HS 500 model (one failure), the BRW model with = 0.99 and the GARCH VCV model (two failures). The worst performers according to the Kupiec test are the HS 50 model (five failures), followed by the HS 100, Normal VCV and RiskMetrics models, all of which failed the Kupiec test for four out of the five tested indexes. Overall, the best performer according to the Kupiec and Christoffersen independence tests at a 99% confidence level across stock indexes of EU candidate states is the HS 500 model, followed by the BRW model with = 0.99 and the GARCH VCV model. The superior performance of the HS 500 model at a 99% confidence level can be attributed to a presumed high volatility, which is a consequence of the long observation period of this model and the occurrence of extreme events in the observation period. The worst performer is the HS 50, followed by the HS 100 and RiskMetrics system. When evaluating the VaR models analyzed according to other criteria, such as the Lopez test, Blanco-Ihle test, RMSE and MAPE, the situation is somewhat different. The best performing VaR models according to these criteria are presented in Table IV. Table IV ­ Best performing VaR model for EU candidate states' stock indexes according to different criteria based on 500 trading days observation period SEE booklet CC.indd 27 3/31/2008 15:09:35 Rankings from Table IV show that different models are predominant depending on the confidence level used for the analysis. According to the Lopez and BlancoIhle tests, the BRW models and GARCH VCV model are constantly among the best performing VaR models for both confidence levels. The HS models and RiskMetrics system are often among the best performers according to the RMSE measure. 5. Conclusion Based on the backtesting results, it can be concluded that the VaR models that are commonly used in developed financial market are not well suited for measuring market risk in EU candidate states. Tested at a 99% confidence level, the best performers for these markets are the HS 500 model, BRW model and GARCH VCV model. At the same time, HS 500, which was the best VaR model at a 99% confidence level, was among the worst rated VaR models at a 95% confidence level. These findings bear very important implications that must be addressed by regulators and risk practitioners operating in EU candidate states. Risk managers have to start thinking outside the frames set by their parent companies or else banks investing in these markets may find themselves in serious trouble, dealing with losses that they were not expecting. Contrary to widespread opinion, it is not enough to blindly implement the VaR models offered by various software companies. Every VaR software package that a bank is thinking about implementing should be rigorously tested and analyzed to see if it really provides a correct estimate of the true level of risk to which a bank will be exposed. National regulators have to take into consideration that simplistic VaR models widely used in some developed countries are not well suited for these illiquid and developing financial markets. The results obtained show that returns on indexes from EU candidate states are characterized by autocorrelation and heteroskedasticity, which considerably complicates VaR estimation and requires more complex, computationally and intellectually demanding VaR models. Before allowance is given to banks to use internal VaR models that are either purchased or developed in-house, national regulators should rigorously check and analyze the backtesting performance, as well as the theoretical framework of such models for any inconsistencies or unwanted simplifications. Appendix Table V - ACF, PACF and Ljung-Box Q test for mean adjusted returns and squared returns for CROBEX index in the period 24.10.2000 - 2.1.2007. SEE booklet CC.indd 28 Table VI - ACF, PACF and Ljung-Box Q test for mean adjusted returns and squared returns for VIN index in the period 24.10.2000 - 1.1.2007. Table VII - ACF, PACF and Ljung-Box Q test for mean adjusted returns and squared returns for BBETINRM index in the period 24.10.2000 - 3.1.2007. SEE booklet CC.indd 29 Table VIII - ACF, PACF and Ljung-Box Q test for mean adjusted returns and squared returns for SOFIX index in the period 24.10.2000 - 1.1.2007. Table IX - ACF, PACF and Ljung-Box Q test for mean adjusted returns and squared returns for XU100 index in the period 24.10.2000 - 4.1.2007. SEE booklet CC.indd 30 Table X - Backtesting results and diagnostics of 500 VaR forecasts for CROBEX index daily log returns, 95% and 99% confidence level, period 22.11.2004 - 2.1.2007 Table XI - Backtesting results and diagnostics of 500 VaR forecasts for VIN index daily log returns, 95% and 99% confidence level, period 5.11.2004 - 1.1.2007 SEE booklet CC.indd 31 Table XII - Backtesting results and diagnostics of 500 VaR forecasts for BBETINRM index daily log returns, 95% and 99% confidence level, period 8.12.2004 - 3.1.2007 Table XIII - Backtesting results and diagnostics of 500 VaR forecasts for SOFIX index daily log returns, 95% and 99% confidence level, period 23.12.2004 - 1.1.2007 SEE booklet CC.indd 32 3/31/2008 15:09:37 Table XIV - Backtesting results and diagnostics of 500 VaR forecasts for XU100 index daily log returns, 95% and 99% confidence level, period 7.1.2005 - 4.1.2007 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png South East European Journal of Economics and Business de Gruyter

Calculating VaR in EU Candidate States

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10.2478/v10033-008-0003-y
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Abstract

This paper examines whether VaR models that are created and suited for developed and liquid markets apply to the volatile and shallow financial markets of EU candidate states. To this end, several VaR models are tested on five official stock indexes from EU candidate states over a period of 500 trading days. The tested VaR models are: a historical simulation with rolling windows of 50, 100, 250 and 500 days, a parametric variance-covariance approach, a BRW historical simulation, a RiskMetrics system and a variance-covariance approach using GARCH forecasts. Based on the backtesting results it can be concluded that VaR models that are commonly used in developed financial market are not well-suited to measuring market risk in EU candidate states. Using some of the most widespread VaR models in these circumstances may result in serious problems for both banks and regulators. Keywords: Abbreviations: EU, VaR, VCV, EWMA, Historical simulation, BRW, ARCH, GARCH JEL: C22, C53, G15, G18 DOI: 10.2478/v10033-008-0003-y 1. Introduction The impact of allowing banks to calculate their capital requirement for market risk based on their internal VaR models, as well as the impact of regulation changes on banks in less developed countries, has not been well studied. Even in the European Union, not all of the EU-15 member countries have systematically conducted research on the consequences and impact of these changes on their banking sectors. New EU member states and EU candidate states are even further behind in these issues. The group of EU candidate states is comprised of the following countries: Bulgaria, Romania, Croatia and Turkey. Bulgaria started its accession negotiations with the EU in February 2000, and closed the accession negotiations in June 2004. Romania, like Bulgaria, started its accession negotiations in February 2000, and closed the accession negotiations in December 2004. Both countries will become full EU members in January 2007. Croatia and Turkey started the accession negotiations on the same date, 03.10.2005. Croatia is expected to become a full EU member in 2009. This is not the case with Turkey, which still has a long journey ahead of it. Although very different and unique in their own ways, when looking through a financial prism, these countries are similar in certain respects. The EU candidate states are all significantly lagging behind the most developed EU countries in many fields, but especially in matters of financial legislation, market discipline, insider trading, disclosure of information (financial and other), embezzlement, knowledge of financial instruments, markets and associated risks. When investing in these financial markets, banks and investmend funds employ the same risk measurement models for measuring market * Zikovi: Faculty of Economics, University of Rijeka, Ivana Filipovia 4, Rijeka, Croatia, e-mail: sasa.zikovic@efri.hr SEE booklet CC.indd 23 risk and forming provision as they do in developed markets. This means that risk managers presume equal or similar characteristics and behaviour in these markets to developed markets. Using VaR models that are created and suited for developed and liquid markets in developing markets raises concerns whether VaR models developed and tested in these financial markets apply to the volatile and shallow financial markets of EU candidate states. This paper therefore attempts to provide an answer to the question whether commonly used VaR models adequately capture market risk in the financial markets of EU candidate states. Employing VaR models in forming a bank's provisions that are not suited to developing markets can have serious consequences, resulting in big losses to banks' portfolios that could be undetected by the employed risk measurement models. Banks could also be penalized by the regulators via higher scaling factors when forming their market risk provisions due to the use of a faulty risk measurement model. To this end, variance-covariance methods and historical simulation approaches are used to estimate VaR for official stock indexes from each of the EU candidate states over a period of 500 trading days. In the next step, the performance of the various models is compared over the simulation period with the help of a range of backtesting procedures to determine how accurately the models match the specified confidence intervals. The paper is structured as follows: Section 2 briefly outlines the VaR approaches on which the calculations in this paper are based. Section 3 provides a brief description of the data used. Section 4 presents and explains the results. Section 5 offers a few concluding remarks. of a portfolio. Thus, losses greater than the estimated VaR should only occur with the probability 1-C, i.e. the "tail events", should on average, occur C*N times in every N trading days. The variance-covariance approach assumes that the risk factors that determine the value of the portfolio are multivariate normally distributed, which implies that changes in the value of a portfolio are normally distributed. Since the normal distribution is fully described by its first two moments, the VaR of a portfolio is essentially a multiple of the standard deviation. VaR under the variancecovariance approach is given by: (2) where w is a vector of absolute portfolio weights, w' is its transpose, denotes a variance-covariance matrix and is a scaling factor. The variances and covariances are usually estimated from a daily historical time series of the returns of the relevant risk factors using equally weighted moving averages: (3) is where the mean is often assumed to be zero, variance (or covariance) at time T, ri,t and rj,t are returns and n is the number of observations, i.e. the window length, used to calculate the variances and covariances. Another frequently used estimator is the exponentially weighted moving average (EWMA), which is used in RiskMetrics methodology. In contrast to equally weighted moving averages, the exponentially weighted moving average weights current observations more than past observations in calculating conditional variances (covariances). The EWMA estimator in its recursive form is given by: 2. Analyzed VaR Models The VaR approach is attractive to practitioners and regulators because it is easy to understand and it provides an estimate of the amount of capital that is needed to support a certain level of risk. Another advantage of this measure is the ability to incorporate the effects of portfolio diversification. Many banks and other financial institutions now base their assessment of financial risk and risk management practices on VaR or plan to do so in the future. VaR reduces the risk associated with any portfolio to just one number, the expected loss associated with a given probability over a defined holding period. VaR for a given probability C can be expressed as: VaRc = F-1(C) (1) where F­1(C) denotes the inverse of cumulative probability distribution of the changes in the market value (4) Parameter determines the exponentially declining weighting scheme of the observations. One difference between the two estimators is that the equally weighted moving average does not account for time-dependent variances, whereas the exponentially weighted moving average does. A more sophisticated parametric estimator of volatility is a GARCH process: (5) SEE booklet CC.indd 24 where t ~ IID N(0,1) In a GARCH model t denotes a real-valued discretetime stochastic process whose conditional distribution is assumed to follow a specific probability distribution (Gaussian, Student's T, etc.). The sizes of the parameters and determine the short-run dynamics of the resulting volatility time series. Large GARCH lag coefficients i indicate that shocks to conditional variance take a long time to die out, so volatility is persistent. Large GARCH error coefficients mean that volatility reacts intensely to market movements, meaning that if alpha is relatively high and beta is relatively low, volatilities tend to be spiky. The second approach used in this paper is historical simulation. In contrast to parametric methods, no specific distributional assumptions about the individual market risk factors, i.e. returns, are made, and no variances or covariances have to be estimated. Instead, it is only assumed that the distribution of the relevant market returns is constant over the sample period. Historical simulation VaR can be expressed as: where are the weights associated with return ri and I(·) is the indicator function. If BRW quantile estimator equals the historical simulation estimator. Boudoukh, Richardson and Whitelaw in their paper set equal to 0,97 and 0,99, the same coefficients used in this paper. 3. Data and Methodology For transitional economies such as those of EU candidate states, a significant problem for a serious and statistically significant analysis is the short histories of their market economies and active trading in financial markets. Because of the short time series of returns of individual stocks and their highly variable liquidity, it is practical to analyze the stock indexes of these countries. A stock index can be viewed as a portfolio of selected securities from an individual country. In this paper, the performance of selected VaR models is tested on stock indexes from Croatia (Zagreb stock exchange (CROBEX) and Varazdin stock exchange (VIN)), Bulgaria (SOFIX), Romania (BBETINRM) and Turkey (XU100). To answer which VaR models adequately capture the market risk in the stock markets of the EU candidate states, nine VaR models are tested on the stock indexes of EU candidate states. The tested VaR models are: a historical simulation with rolling windows of 50, 100, 250 and 500 days, a parametric variance-covariance approach, a BRW historical simulation, a RiskMetrics system and a variancecovariance approach using GARCH forecasts. VaR models are calculated for a one-day holding period at 95% and 99% coverage of the market risk. To secure the same outof-the-sample VaR backtesting period for all of the tested indexes, the out-of-the-sample data sets are formed by taking out 500 of the latest observations from each index. The rest of the observations are used as pre-sample observations needed for VaR starting values and volatility model calibration. When employing the ARMA-GARCH VCV model the goal, is to capture the dynamic of the data generating process of the return series so that the standardised innovations are independently and identically distributed (IID). The ACF, PACF and Ljung-Box Q-statistic test the presumption of IID in standardized innovations. If the tests do not discover autocorrelation in the standardized innovations employed, the ARMA model can be considered adequate. Squared standardized innovations are tested for autocorrelation and ARCH effects through ACF, PACF and Ljung-Box Qstatistic. The most parsimonious GARCH model based on the Akaike and Schwartz information criterion that passes the tests of autocorrelation and ARCH effects in the squared standardized innovations is chosen to describe the volatility dynamics of the return series. The validity of the analyzed VaR models in EU candidate states is tested by the Kupiec test, the Christoffersen independence test, (6) where returns is taken from the set of ordered . The BRW approach developed by Boudoukh, Richardson and Whitelaw (1998), combines RiskMetrics and historical simulation methodologies, by applying exponentially declining weights to past returns of the portfolio. Each of the most recent N returns of the portfolio, rt, rt-1, ..., rt-N+1, is associated a weight, respectively. The role of the term is simply to ensure that the weights sum to 1, provided . After the probability weights are assigned, VaR is calculated based on the empirical cumulative distribution function of returns with the modified probability weights. To better understand the assumptions behind the BRW approach and its connection to historical simulation, BRW quantile estimator can be expressed as: (7) SEE booklet CC.indd 25 the Blanco-Ihle test, the Lopez test, and the RMSE and MAPE measures. Although there is an abundance of research papers dealing with VaR and market risk measurement and management, all of the existing VaR models have been developed and tested in mature, developed and liquid markets. Testing of VaR models in other, less developed or developing financial market is at best scarce. Zikovi, Bezi (2006) investigated the performance of historical simulation VaR models on stock indexes of the EU candidate states. CROBEX (Croatia), SOFIX (Bulgaria), BBETINRM (Romania) and XU100 (Turkey) indexes all show clear positive trends over a longer time period. With the exception of the XU100 index, all of other indexes analyzed exhibit asymmetry and leptokurtosis. Based on performed tests of normality, it can be said with great certainty that these returns are not normally distributed. The tests employed show significant autocorrelation and ARCH effects in the squared returns of all the analyzed indexes. These phenomena violate normality assumption, as well as the IID assumption, which is a necessary requirement for the proper implementation of historical simulation. Results point to the conclusion that even though historical simulation provided correct unconditional coverage for the indexes tested at most of the confidence levels, use of historical simulation (especially based on shorter observation periods) is not recommendable in these markets. on normality assumption, as well as for the nonparametric and semi-parametric approaches that are based on the IID assumption, such as historical simulation and the BRW approach. This is very indicative for risk managers, because the elementary assumptions of many VaR models are not satisfied, meaning that VaR figures obtained for such models cannot be completely trusted. An ARMAGARCH model performs a transformation of original return data to obtain independently and identically distributed observations. The ARMA-GARCH model successfully captured the dynamics of stock indexes from EU candidate states and produced standardized innovations that proved to be independently and identically distributed. In modelling conditional volatility, a basic GARCH (1,1) model was sufficient for all stock indexes. Estimated ARMA-GARCH parameters for stock indexes of EU candidate states are presented in Table I. As can be seen from Table I, some of the tested indexes, such as VIN and BBETINRM, show unusually low persistence in volatility but are very reactive to volatility, which will make VaR forecasts based on GARCH volatility spiky. The majority of stock indexes are not even closely integrated, as is presumed by the EWMA volatility modelling that underlies the RiskMetrics model. The estimated GARCH parameters of stock indexes from EU candidate states point to the conclusion that VaR models based on simpler conditional volatility models, such as MA or EWMA, will underestimate or overestimate the true level of risk. The Kupiec test and Christoffersen independence test are usually used to identify VaR models that are acceptable to the regulators, and provide the desired level of safety to individual banks and, due to the contagion effect, to the entire banking sector. The results of the overall acceptance, according to the Kupiec and Christoffersen independence tests, of tested VaR models at 95% and 99% confidence levels and 10% significance level are presented in Tables II and III. 4. Backtesting Results Based on the ACF, PACF and Ljung-Box Q statistics of the returns and squared returns of analyzed stock indexes from EU candidate states given in tables V ­ IX, the presence of autocorrelation and heteroskedasticity in the data is obvious. All of the analysed indexes exhibit heteroskedasticity, with VIN, BBETINRM and SOFIX exhibiting autocorrelation in their returns. This finding is troubling for VaR models based Table I - Estimated ARMA-GARCH parameters for stock indexes from EU candidate states SEE booklet CC.indd 26 3/31/2008 15:09:35 Table II - Number of VaR model failures according to Kupiec test and Christoffersen independence test, tested on five EU candidate states' stock indexes, 500 observations, at 95% confidence level Table III - Number of VaR model failures according to Kupiec test and Christoffersen independence test, tested on five EU candidate states' stock indexes, 500 observations, at 99% confidence level From the data in Table II, it is clear that at a 95% confidence level, the tested VaR models perform very differently, with a majority of VaR models failing the Kupiec test and Christoffersen independence test for at least one stock index. VaR models that passed the Kupiec test across all the analyzed stock indexes are the GARCH VCV model, RiskMetrics system and both BRW models with = 0.97 and 0.99. According to the Kupiec test, the worst performer out of all the tested VaR models is the HS 50 model, which failed the Kupiec test for four out of five stock indexes. The HS 50 model is followed by HS 500 with three failures. According to the Christoffersen independence test, the best performers are the HS 250 and both BRW models with = 0.97 and 0.99. The worst performers are HS 50 and GARCH VCV. Overall, the best performers according to the Kupiec test and Christoffersen independence test at a 95% confidence level across stock indexes of EU candidate states are the BRW models with = 0.97 and 0.99. The worst performers are the HS 50 and HS 500 models. Although it is very informative to look at VaR model performance at different confidence levels, the true test of VaR model acceptability for regulators is its performance at a 99% confidence level, as prescribed by the Basel Committee. According to the results obtained at a 99% confidence level, which are presented in Table III, all of the VaR models failed the Kupiec test for at least one stock index. The situation is somewhat better with the Christoffersen independence test, where HS 250 and BRW model with = 0.99 both passed the test. The best performers according to the Kupiec test are the HS 500 model (one failure), the BRW model with = 0.99 and the GARCH VCV model (two failures). The worst performers according to the Kupiec test are the HS 50 model (five failures), followed by the HS 100, Normal VCV and RiskMetrics models, all of which failed the Kupiec test for four out of the five tested indexes. Overall, the best performer according to the Kupiec and Christoffersen independence tests at a 99% confidence level across stock indexes of EU candidate states is the HS 500 model, followed by the BRW model with = 0.99 and the GARCH VCV model. The superior performance of the HS 500 model at a 99% confidence level can be attributed to a presumed high volatility, which is a consequence of the long observation period of this model and the occurrence of extreme events in the observation period. The worst performer is the HS 50, followed by the HS 100 and RiskMetrics system. When evaluating the VaR models analyzed according to other criteria, such as the Lopez test, Blanco-Ihle test, RMSE and MAPE, the situation is somewhat different. The best performing VaR models according to these criteria are presented in Table IV. Table IV ­ Best performing VaR model for EU candidate states' stock indexes according to different criteria based on 500 trading days observation period SEE booklet CC.indd 27 3/31/2008 15:09:35 Rankings from Table IV show that different models are predominant depending on the confidence level used for the analysis. According to the Lopez and BlancoIhle tests, the BRW models and GARCH VCV model are constantly among the best performing VaR models for both confidence levels. The HS models and RiskMetrics system are often among the best performers according to the RMSE measure. 5. Conclusion Based on the backtesting results, it can be concluded that the VaR models that are commonly used in developed financial market are not well suited for measuring market risk in EU candidate states. Tested at a 99% confidence level, the best performers for these markets are the HS 500 model, BRW model and GARCH VCV model. At the same time, HS 500, which was the best VaR model at a 99% confidence level, was among the worst rated VaR models at a 95% confidence level. These findings bear very important implications that must be addressed by regulators and risk practitioners operating in EU candidate states. Risk managers have to start thinking outside the frames set by their parent companies or else banks investing in these markets may find themselves in serious trouble, dealing with losses that they were not expecting. Contrary to widespread opinion, it is not enough to blindly implement the VaR models offered by various software companies. Every VaR software package that a bank is thinking about implementing should be rigorously tested and analyzed to see if it really provides a correct estimate of the true level of risk to which a bank will be exposed. National regulators have to take into consideration that simplistic VaR models widely used in some developed countries are not well suited for these illiquid and developing financial markets. The results obtained show that returns on indexes from EU candidate states are characterized by autocorrelation and heteroskedasticity, which considerably complicates VaR estimation and requires more complex, computationally and intellectually demanding VaR models. Before allowance is given to banks to use internal VaR models that are either purchased or developed in-house, national regulators should rigorously check and analyze the backtesting performance, as well as the theoretical framework of such models for any inconsistencies or unwanted simplifications. Appendix Table V - ACF, PACF and Ljung-Box Q test for mean adjusted returns and squared returns for CROBEX index in the period 24.10.2000 - 2.1.2007. SEE booklet CC.indd 28 Table VI - ACF, PACF and Ljung-Box Q test for mean adjusted returns and squared returns for VIN index in the period 24.10.2000 - 1.1.2007. Table VII - ACF, PACF and Ljung-Box Q test for mean adjusted returns and squared returns for BBETINRM index in the period 24.10.2000 - 3.1.2007. SEE booklet CC.indd 29 Table VIII - ACF, PACF and Ljung-Box Q test for mean adjusted returns and squared returns for SOFIX index in the period 24.10.2000 - 1.1.2007. Table IX - ACF, PACF and Ljung-Box Q test for mean adjusted returns and squared returns for XU100 index in the period 24.10.2000 - 4.1.2007. SEE booklet CC.indd 30 Table X - Backtesting results and diagnostics of 500 VaR forecasts for CROBEX index daily log returns, 95% and 99% confidence level, period 22.11.2004 - 2.1.2007 Table XI - Backtesting results and diagnostics of 500 VaR forecasts for VIN index daily log returns, 95% and 99% confidence level, period 5.11.2004 - 1.1.2007 SEE booklet CC.indd 31 Table XII - Backtesting results and diagnostics of 500 VaR forecasts for BBETINRM index daily log returns, 95% and 99% confidence level, period 8.12.2004 - 3.1.2007 Table XIII - Backtesting results and diagnostics of 500 VaR forecasts for SOFIX index daily log returns, 95% and 99% confidence level, period 23.12.2004 - 1.1.2007 SEE booklet CC.indd 32 3/31/2008 15:09:37 Table XIV - Backtesting results and diagnostics of 500 VaR forecasts for XU100 index daily log returns, 95% and 99% confidence level, period 7.1.2005 - 4.1.2007

Journal

South East European Journal of Economics and Businessde Gruyter

Published: Apr 1, 2008

References