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 UNIVERSITY OF ECONOMICS HO CHI MINH CITY VIETNAM INSTITUTE OF SOCIAL STUDIES THE HAGUE THE NETHERLANDS 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 VNINDEX 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, Kupiec’s 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 Backtesting indicates that there is no best model for all cases because of characteristic 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 management, 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 De…nitions 2.1.1 Financial return data 2.1.2 Concept of Risk 2.1.3 Classi…cation of Risk 2.1.4 Risk measurement and Coherence 2.2 Theoretical review 2.2.1 Value at Risk 2.2.2 GARCH 2.2.3 Extreme Value Theory 2.3 Empirical studies review 2.3.1 Empirical research on modeling and measuring VaR 2.3.2 Empirical research on Extreme Value Theory (EVT) VaR 9 11 11 11 12 13 13 14 14 17 17 18 18 20 Research Methodology 3.1 Data selection 3.2 Methodology 3.2.1 Unconditional VaR models 3.2.2 Conditional VaR models - Volatility model using EWMA, GARCH, GJR - GARCH model 3.2.3 Extreme value theory (EVT) distribution in VaR modeling 22 22 22 23 26 30 3.3 Backtesting Methodology 3.3.1 Kupiec’s Test 3.3.2 ChristoÔersens Tests 3.3.3 Hypothesis testing procedure Empirical Results 4.1 Descriptive statistics 4.2 GARCH, GJR - GARCH and EVT model estimation 4.3 Models forecasting performance analysis 4.4 Graphical analysis of model forecasting Conclusion 35 37 39 40 41 41 49 56 72 76 5.1 Main …ndings 76 5.2 Implications 78 5.3 Limitation and further studies 79 List of Tables 4.1 Descriptive of data sample 4.2 Descriptive statistics of daily stock index returns 4.3 Parameters estimation of GARCH(1,1) model with normal distributed innovation for daily stock index returns 4.4 Parameters estimation of GARCH(1,1) model with Student’s - t distributed innovation for daily stock index returns 4.5 Parameters estimation of GARCH(1,1) model with skewed Student’s - t distributed innovation for daily stock index returns 4.6 Parameters estimation of GJR - GARCH(1,1) model with normal distributed innovation for daily stock index returns 4.7 Parameters estimation of GRJ - GARCH(1,1) model with Student’s - t distributed innovation for daily stock index returns 4.8 Parameters estimation of GRJ - GARCH(1,1) model with skewed Student’s - t distributed innovation for daily stock index returns 4.9 Parameters estimation of generalized Pareto distribution (GPD), threshold exceedances of percentage from GARCH(1,1) model 54 4.10 Parameters estimation of generalized Pareto distribution (GDP), threshold exceedances of percentage from GJR - GARCH (1,1) model 4.11 Expected and actual number of VaR violations at threshold percentage 4.12 Violation ratio and Kupiec’s test p - value at percent significance level 4.13 Independence test and ChristoÔersens test at percent signicance level 4.14 Expected and actual number of VaR violations at threshold 2.5 percentage 43 44 50 50 51 52 52 53 55 56 57 63 64 4.15 Violation ratio and Kupiec’s test p - value at 2.5 percent signi…cance level 4.16 Independence test and ChristoÔersens test at 2.5 pecent signicance level 4.17 Expected and actual number of VaR violations at threshold percentage 4.18 Violation ratio and Kupiec’s test p - value at percent significance level 4.19 Independence test and ChristoÔersens test at pecent significance level 4.20 Best forecasting VaR model according to ChristoÔersens test at 5, 2.5 and percentage of signi…cance level 65 66 67 68 69 71 List of Figures 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 4.10 4.11 4.12 4.13 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 performance for daily return of EIB at 5% signi…cance level GARCH VaR model forecasting performance for daily return of ACB at 5% signi…cance level GJR - GARCH VaR model forecasting performance for daily return of MBB at 5% signi…cance level EVT GARCH VaR model forecasting performance for daily return of CTG at 5% signi…cance level EVT GJR - GARCH VaR model forecasting performance for daily return of BVH at 5% signi…cance level 42 45 46 46 47 47 48 48 72 73 74 74 75 ACKNOWLEDGEMENTS I would like to send special thanks to my academic supervisor Dr Truong Dang Thuy, for his patience guidance, enthusiasm and support during my thesis writing process I would also like to thank Dr Pham Khanh Nam who also gave me valuable advices for my thesis A special thank goes out to all lecturers, staÔs of the Vietnam - Netherlands Program as well as my classmates for all their helps and supports I am most grateful to my family Thank you for always being there for me, thank you for inspiring me, supporting me and making me appreciate the value of education Last but not least, I would like to thank my wife and my daughter Thank you for your patience, deep understanding and encouragement I am grateful to you 4.4 Graphical analysis of model forecasting In order to understand more advanced empirical results presented in previous section through visual, graphical analysis are presented in this part A group of models having similar characteristics are only presented because of many VaR models produced Conditional EWMA volatility model is put into group of unconditional models to see the trend of them All graphical analysis backtesting for each index can be seen in separated Appendix Figure 4.9 presents forcasting performance of each model at 5% signi…cance level of VNINDEX All unconditional VaR models cannot catch up the actual trend, especially in volatility clustering In case of extreme negative returns occur, adjustment of these ones very slow and very persistent In the same …gure, EWMA plot provides total diÔerent result when its behavior can follow changes of actual time series well instead of stable trend of unconditional models Although it is under - estimate in case of extreme losses, it provides quite good performance Unconditional models provide same behavior in all stock indexes indicating that all results of violation ratio and Kupiec’s p value test are pure coincidence for these models whose forecasted is far from reasonable …gures REIB Actual EWMA HS Nor mal Student 0.06 0.04 0.02 0.00 -0.02 -0.04 -0.06 200 400 600 800 1000 Figure 4.9: EWMA and unconditional VaR models forecasting performance for daily return of EIB at 5% signi…cance level Figure 4.10 shows forecasting performance of three distributed innova72 RA CB Actual GARCH_Nor GARCH_Std GARCH_Sstd mal 0.05 0.00 -0.05 -0.10 500 1000 1500 Figure 4.10: GARCH VaR model forecasting performance for daily return of ACB at 5% signi…cance level tions normal, Student’s - t and skewed Student’s - t used in GARCH model for ACB Student’s - t is account for fat - tails in case of ACB here, so Student’s - t GARCH model produces more negative forecast when high negative losses occur compared to normal GARCH model and has the same behavior as Skewed Student’s - t GARCH model According to Table 4.13 and Table 4.14, Student’s - t GARCH model is the best model proved by Kupiec’s test and ChristoÔersens test in forecasting performance for daily return of ACB stock index at 5% signi…cance level Figure 4.11 presents forecasting quality of GJR - GARCH model for MBB In this comparison, GJR - GARCH with distributed skewed Studen’ts - t provide best result that can be seen in Table 4.13 and Table 4.14 When using Extreme Value Theory to model only tail distribution by Peak - over Threshold (POT) methodology, CTG has best result in EVT GARCH with skewed Student’s - t distributed innovations which is drawn in Figure 4.12 Figure 4.13 presents forecasting performance of EVT GJR - GARCH model for BVH Besides on statistics analysis, graphical analysis helps better understand about empirical results in previous sections Graphical analysis not only presents visual trend but also provides some …ndings to identify what missing 73 RMBB 0.06 Actual GJR_GARCH_Nor GJR_GARCH_Std GJR_GARCH_Sstd mal 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 RCTG Actual EVT_G_Nor EVT_G_Std EVT_G_Sstd 0.06 mal 0.04 0.02 0.00 -0.02 -0.04 -0.06 200 400 600 800 1000 Figure 4.12: EVT GARCH VaR model forecasting performance for daily return of CTG at 5% signi…cance level 74 RBVH Actual EVT_GJR_Nor EVT_GJR_Std EVT_GJR_Sstd mal 0.05 0.00 -0.05 -0.10 200 400 600 800 1000 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 limitations 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 Furthermore, 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 ChristoÔersens test are performed Independence test is used to check forecasted VaRs clustering and Christoffersen’s 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 ChristoÔersens 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 graphical analysis, these models are suitable for forecasting VaR with high performance Table 4.20 summaries a list of best forecasting VaR models for each stock index in Vietnam stock market Second and third best forecasting VaR models are sometimes list here because of not much diÔerent of ChristoÔersens 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 signicance of levels following to summary of best model based on ChristoÔersens test in Table 4.20 Therefore, diÔerent models should be applied and frequently checked their performance through backtesting 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 example, 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 information 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, foreign 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 innovations 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 accounted by advanced model such as GJR - GARCH However, this model only capture leverage eÔect and keep the same power as GARCH model Another advanced model can capture both leverage eÔect and power term is asymmetric power autoregressive conditional heteroscedastic model (APARCH) In GARCH, power term is and this value might be diÔerent for each nancial position So, APARCH model should be studied to improve forecasting performance Furthermore, …xed GARCH parameter at 0.94 in EWMA from RiskMetrics seems not reasonable because of diÔerent characteristics in each nancial assets as well as diÔerent current market condition This gure should be re - 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CITY VIETNAM INSTITUTE OF SOCIAL STUDIES THE HAGUE THE NETHERLANDS VIETNAM – NETHERLANDS PROGRAM FOR M.A IN DEVELOPMENT ECONOMICS QUANTITATIVE RISK ANALYSIS: AN APPROACH FOR VIETNAM STOCK MARKET. .. to risk management in Vietnam, …nancial market in general and Vietnam stock market in particular, it is actual limited in term of both policy and tool Therefore, system of …nancial risk management... 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