Quantitative risk analysis, an approach for vietnam stock market

UNIVERSITY OF ECONOMICS HO CHI MINH CITY VIETNAM ERASMUS UNVERSITY ROTTERDAM INSTITUTE OF SOCIAL STUDIES THE NETHERLANDS VIETNAM – THE NETHERLANDS PROGRAMME FOR M.A IN DEVELOPMENT ECONOMICS QUANTITATIVE RISK ANALYSIS: AN APPROACH FOR VIETNAM STOCK MARKET BY NGUYEN NAM KHANH MASTER OF ARTS IN DEVELOPMENT ECONOMICS HO CHI MINH CITY, January 2016 VIETNAM VIETNAM – NETHERLANDS PROGRAM FOR M.A IN DEVELOPMENT ECONOMICS QUANTITATIVE RISK ANALYSIS: AN APPROACH FOR VIETNAM STOCK MARKET A thesis submitted in partial fulfillment of the requirements for the degree of MASTER OF ARTS IN DEVELOPMENT ECONOMICS By NGUYEN NAM KHANH Academic Supervisor Dr TRUONG DANG THUY Ho Chi Minh City, January 2016 QUANTITATIVE RISK ANALYSIS: AN APPROACH FOR VIETNAM STOCK MARKET Nguyen Nam Khanh January 15, 2016 Abstract Value at Risk (VaR) is widely used in risk measurement It is de…ned as the worst expected loss of a portfolio under a given time horizon at a given con… dence level The aim of the thesis is to evaluate performance of 16 VaR models in forecasting one - day ahead VaR for daily return of VNIN-DEX and a group banking stock indexes including ACB, BVH, CTG, EIB, MBB, SHB, STB, VCB to …nd out the most appropriate model for each stock index Three unconditional volatility models including historical, normal and Student’s - t as well as EWMA and two volatility models including GARCH, GJR - GARCH with three return distributions normal, Student’s - t and skewed Student’s - t and associated Extreme Value Theory (EVT) models are performed at 5%, 2.5% and 1% of signi…cance level Violation ration, Kupiecs unconditional coverage test, independence test and ChristoÔersen conditional coverage test are used to backtested performance of all models Besides statistical analysis, graphical analysis is also incorporated Backtest-ing indicates that there is no best model for all cases because of character-istic diÔerence from particular stock index Implication of this thesis is that a suitable VaR forecasting model is only chosen after backtesting frequently performance of various models in order to ensure that most relevant and most accurate models are suited for current …nancial market situation Keywords: Value at Risk, Extreme Value Theory, …nancial risk manage-ment, conditional volatility model, backtesting, stock index Contents Introduction 1.1 1.2 1.3 1.4 1.5 Problem statements Research objectives Research questions Subject and scope of research Structure of the thesis Literature review 2.1 2.2 2.3 Research Methodology 3.1 3.2 De…nitions 2.1.1 2.1.2 2.1.3 2.1.4 Theoretical review 2.2.1 2.2.2 2.2.3 Empirical studies review 2.3.1 2.3.2 Data selection Methodology 3.2.1 3.2.2 3.2.3 3.3 Backtesting Methodology 3.3.1 3.3.2 3.3.3 Empirical Results 4.1 4.2 4.3 4.4 Descriptive statistics GARCH, GJR - GARCH and EV Models forecasting performance Graphical analysis of model fore Conclusion 5.1 5.2 5.3 Main …ndings Implications Limitation and further studies List of Tables 4.1 4.2 4.3 Descriptive of data sample Descriptive statistics of daily stock index returns Parameters estimation of GARCH(1,1) model with tributed innovation for daily stock index returns Parameters estimation of GARCH(1,1) model with - t distributed innovation for daily stock index retur Parameters estimation of GARCH(1,1) model with Student’s - t distributed innovation for daily stock i turns Parameters estimation of GJR - GARCH(1,1) mod mal distributed innovation for daily stock index ret Parameters estimation of GRJ - GARCH(1,1) mod dent’s - t distributed innovation for daily stock inde Parameters estimation of GRJ - GARCH(1,1) model Student’s - t distributed innovation for daily stock i turns Parameters estimation of generalized Pareto distrib threshold exceedances of percentage from GARC 54 Parameters estimation of generalized Pareto distrib threshold exceedances of percentage from GJR (1,1) model Expected and actual number of VaR violations at percentage Violation ratio and Kupiec’s test p - value at perc icance level Independence test and ChristoÔersen test at pe ni…cance level Expected and actual number of VaR violations at 2.5 percentage 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 4.14 4.15 Violation ratio and Kupiec’s test p - value at 2.5 percent sig-ni… cance level 65 4.16 Independence test and ChristoÔersen test at 2.5 pecent sig-ni cance level 66 4.17 Expected and actual number of VaR violations at threshold percentage 67 4.18 Violation ratio and Kupiec’s test p - value at percent significance level 68 4.19 Independence test and ChristoÔersen test at pecent significance level 69 4.20 Best forecasting VaR model according to ChristoÔersen test at 5, 2.5 and percentage of signi…cance level 71 List of Figures 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 Daily value of stock index Daily return of stock index Histograms of daily stock index returns Qnorm - QQ plot of daily stock index returns ACF for daily stock index returns PACF for daily stock index returns ACF for squared of daily stock index returns PACF for squared of daily stock index returns EWMA and unconditional VaR models forecasting p for daily return of EIB at 5% signi…cance level GARCH VaR model forecasting performance for d of ACB at 5% signi…cance level GJR - GARCH VaR model forecasting performanc return of MBB at 5% signi…cance level EVT GARCH VaR model forecasting performance return of CTG at 5% signi…cance level EVT GJR - GARCH VaR model forecasting perfor daily return of BVH at 5% signi…cance level 4.10 4.11 4.12 4.13 RMBB Actual 0.06 GJR_GARCH_Nor GJR_GARCH_Std GJR_GARCH_Sstd 0.04 0.02 0.00 -0.02 -0.04 -0.06 100 200 300 400 500 Figure 4.11: GJR - GARCH VaR model forecasting performance for daily return of MBB at 5% signi…cance level Figure 4.12: EVT GARCH VaR model forecasting performance for daily return of CTG at 5% signi…cance level 74 Figure 4.13: EVT GJR - GARCH VaR model forecasting performance for daily return of BVH at 5% signi…cance level part in statistics only based on numerical For example, HS is best model in some cases, but performance shown in graph is very poor when the HS trend cannot re‡ect what changes in reality and its adjustment is very slow and persistent Therefore, graphical analysis should be incorporated with statistic analysis in order to provide more accuracy in results 75 Chapter Conclusion This section includes three parts First part is main …nding of this thesis Implication is present in second part And the last part is discussion of limitation and further studies 5.1 Main …ndings This section summaries main …nding of empirical research on daily return of stock indexes in Vietnam stock market Moreover, implications and limi-tations of the study are presented Finally, further research with application in practical is discussed In the …rst step of empirical study, a general picture for each stock index is given by descriptive statistics All daily return of stock indexes have fat tailed because of a positive value of excess kurtosis as well as non – zero skewness excepting only BVH has excess kurtosis nearly zero These features and Jarque - Bera statistical normality test indicate strongly that the daily returns are not normally distribution ACF and PACF …gures are used to visualize autocorrelation of daily returns and squared of daily returns It points out that squared of daily return is high autocorrelation which is also supported by Ljung – Box test result This …nding is a good proxy for volatility and GARCH model could be a suitable choice Q – Q plot once again presents fat - tails and non – normality for all daily returns of stock indexes Previous …ndings are con…rmed through estimated parameters analysis of volatility models which are …tted to whole data sample in daily return of each stock index Daily returns is non –normality and might be suitable for Student’s – t distribution because of highly degree of freedom estimations from nearly three to ten Positive value of skewness indicates that positive 76 returns occur more frequently than negative returns In order to take account leverage eÔects feature, GJR - GARCH(1,1) conditional volatility model is suitable choice Most of estimated parameters of volatility models are highly statistically signi…cant In order to evaluate performance of 16 …tted models, log - likelihood test as well as AIC, BIC statistical tests are compared which shows that there is signi…cant improvement when changing distribution assumption of daily returns from normal to Student’s – t in most of stock indexes There is minor improvement when changing distributed innovations assumption of daily return from Student’s - t to skewed Student’s - t distribution Fur-thermore, according to the tests, GJR - GARCH(1,1) model is better …tting data than GARCH(1,1) model Therefore, by combining these …ndings, GJR - GARCH(1,1) model with skewed Student’s - t distributed innovations might be considered as the best …tted model in most of cases In order to model extreme losses returns concentrated in the left tail of daily return distributions of each stock index, Peak - over - Threshold (POT) model from Extreme Value Theory are also …tted to residuals for daily return of each index In this thesis, we convert residuals into standardized residuals because generalized Pareto distributions (GPD) assume that data series follow independent and identical distribution (i.i.d.) Then an integrate them in VaR model could account extreme returns during …nancial turmoil and other extreme events Performance of 16 forecasting VaR models is evaluated by backtesting procedure A rolling window of 1000 observations in VNINDEX and 500 observations in the rest of stock indexes are used to estimate model and one - day ahead VaR forecasts were computed for the rest of data sample at diÔerent signicance of levels by 5%, 2.5% and 1% After that, forecasted VaRs and actual losses are compared through violation rate at three given signi…cance levels In order check violation ratio in statistical point of view, Kupiec’s p – value is used However, Kupiec’s test does not take into account independence or clustering feature which occur frequently in … nancial series Therefore, independence test and ChristoÔersen test are performed Independence test is used to check forecasted VaRs clustering and Christof-fersen’ test is a combination of Kupiec’s test and independence test Based on these tests, best forecasting VaR models for each stock index are chosen by comparing their performance Many unconditional volatility models easily pass violation rate and Kupiec’s test, however, only few of them are able to pass ChristoÔersen test However, graphical analysis shows poor results for these ones and they are not coincidence together because of unable to capture volatility clustering in daily return series Additionally, these models produce over - estimated 77 result in case of taken into account extreme daily returns for estimation By combining statistics analysis and graphical analysis, unconditional is not a suitable choice in forecasting VaR due to poor performance In the other hand, forecasting VaR models have good performance when considering volatility model in use Based on statisticsanalysis and graph-ical analysis, these models are suitable for forecasting VaR with high per-formance Table 4.20 summaries a list of best forecasting VaR models for each stock index in Vietnam stock market Second and third best forecast-ing VaR models are sometimes list here because of not much diÔerent of ChristoÔersen p - value compared to the best one In general, there is no particular best model for all stock indexes in all time periods and diÔerent signi…cance of levels following to summary of best model based on ChristoÔersen test in Table 4.20 Therefore, diÔerent mod-els should be applied and frequently checked their performance through back-testing methodology for each stock index in order to ensure that most relevant and most accurate models are suited for current …nancial market situation 5.2 Implications VaR is able to measure risk in various types of …nancial assets such as interest rates, foreign exchange rates, commodity prices, equity indexes and daily return of stock index objective in this thesis is only one of example from them The VaR estimation was required by Basel Committee on banking supervision to meet the capital required for covering potential losses For ex-ample, J.P Morgan, Standard Chartered bank disclose its daily VaR at 95 percentage level, Bankers Trust discloses its daily VaR at 99 percentage level According to particular …nancial positions, VaR measure information can be disclosed on the …rm’s …nancial integrity and risk management to regulators, rating agencies, auditors and investors Based on VaR …gures, regulators can monitor risk; rating agencies can rank more accuracy; investors have more transparency information to make decision In general, VaR informa-tion might be used to improve …rm’s terms of trade as well as regulatory and compliance After …nance crisis in 2008, risk management system in banking and …nance sectors have been considering in Vietnam In recent years, there are improvements in this process, for example, many banking are deploying Basel system to improve risk management ability as well as using quantitative approach to measure risk Therefore, VaR can be applied as risk management tool for banking and …nancial sectors in Vietnam in order to reach risk man78 agement technology in the world as well as might make …nancial system safer However, as this study mention, various models should be applied and frequently check their performance by backtesting methodology in order to …nd out the most suitable models for particular …nancial instruments in each current …nancial market situation 5.3 Limitation and further studies This section presents some limitations and based on this, further studies are also discussed Firstly, in portfolio instruments or data objective, this study only measure VaR and evaluate forecasting performance for individual daily return of each stock index However, risk measure is not mentioned and studied in case of more than one stock index This limitation is also opened when portfolio consist many …nancial instruments such as stock index price, for-eign exchange rate and interest rate and so on Therefore, an advanced VaR risk measurement should be studied for whole portfolio more than one asset In case of measuring many assets, dependence structure methodology should be developed Copulas is a powerful tool with many advantage features can be taken into account Secondly, there is limitation in methodology level VaR is not coherence risk measurement because of violated subadditive properties then it is not satis…ed risk diversi…cation properties in order to reduce the losses VaR is only coherence when distribution of …nancial asset is normal However, in case of coherence risk is satis…ed, VaR only answers well question regarding to maximum expected losses of asset with a given time period under given con-… dence level but cannot answers in small case of VaR violated situations such as 1, percentage To overcome the limited of VaR, advanced methodology Expected Shortfall (ES) is introduced in …nancial theory ES is an expected loss of assets or portfolio after an extreme event which is also called the conditional value at risk (CVAR) focusing mainly on the upper tail characteristics of loss distribution ES provides average losses of assets or portfolio when exceeding VaR value This average leads to a better re‡ect the tail behavior of the loss random variables than VaR In theory, ES is a coherent measure risk Moreover, EVT is power tool in structural breaks of extreme return occur, but it is not shown its advantage much in this study Only VNINDEX have enough time period covers …nancial crisis 2007 - 2008 and this stock index is a good example for EVT study Data sample corresponding to each structural should be spitted to investigate performance forecasting of each model in term of before, during and after …nancial turmoil 79 Finally, in term of model level, changing from normal distributed innova-tions to Student’s - t and skewed Student’s - t distribution that appropriate with …nancial series characteristic, such as fat - tailed is an improvement in this thesis Other stylized facts such as leverage eÔects are 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Does the forecasting VaR performance unchange with respect to diÔer-ent signicance level? Is it possible to …nd out one VaR model which has best forecasting performance for Vietnam stock market?