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 INSTITUTE OF SOCIAL STUDIES CHI MINH CITY VIETNAM 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 ØUANTITATIVE ỈISK ANALVSIS: AN APPỈOACH F VIETNAM STOCK MKET Nguyen Nam Khanh January fi†, £0fi6 Abstract Value at Risk (VaR) is widely used in risk measurement It is defined as the worst expected loss of a portfolio under a given time horixon at a given confidence level The aim of the thesis is to evaluate performance of fi6 VaR models in forecasting one - day ahead VaR for daily return of VNIN- DEX and a group banking stock indexes including AGB, BVH, GTG, EIB, MBB, SHB, STB, VGB to find 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 GARGH, GJR - GARGH with three return distributions normal, Student‘s - t and skewed Student‘s - t and associated Extreme Value Theory (EVT) models are performed at †%, £.†% and fi% of significance level Violation ration, Kupiec‘s unconditional coverage test, independence test and Ghristoffersen 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 difference 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 financial market situation Ke4mords: Value at Risk, Extreme Value Theory, financial risk manage- ment, conditional volatility model, backtesting, stock index Comtemts Imtroductiom fi.fi fi.£ fi.3 fi.4 fi.† Problem statements t Research objectives Research questions Subject and scope of research Structure of the thesis .9 Literature review 11 £.fi Definitions fifi £.fi.fi Financial return data fifi £.fi.£ Goncept of Risk fi£ £.fi.3 Glassification of Risk fi3 £.fi.4 Risk measurement and Goherence fi3 £.£ Theoretical review fi4 £.£.fi Value at Risk fi4 £.£.£ GARGH fit £.£.3 Extreme Value Theory fit £.3 Empirical studies review fi8 £.3.fi Empirical research on modeling and measuring VaR fi8 £.3.£ Empirical research on Extreme Value Theory (EVT) VaR £0 Æesearch Methodology 22 3.fi Data selection ££ 3.£ Methodology ££ 3.£.fi Unconditional VaR models £3 3.£.£ Gonditional VaR models - Volatility model using EWMA, GARGH, GJR - GARGH model £6 3.£.3 Extreme value theory (EVT) distribution in VaR modeling 30 fi 3.3 Backtesting Methodology 3† 3.3.fi Kupiec‘s Test 3t 3.3.£ Ghristoffersen‘s Tests 39 3.3.3 Hypothesis testing procedure 40 Empirical Æesults 41 4.fi Descriptive statistics 4fi 4.£ GARGH, GJR - GARGH and EVT model estimation 49 4.3 Models forecasting performance analysis †6 4.4 Graphical analysis of model forecasting t£ Comclusiom †.fi †.£ †.3 56 Main findings t6 Implications t8 Limitation and further studies t9 £ List of Tables 4.fi Descriptive of data sample .43 4.£ Descriptive statistics of daily stock index returns .44 4.3 Parameters estimation of GARGH(fi,fi) model with normal distributed innovation for daily stock index returns †0 4.4 Parameters estimation of GARGH(fi,fi) model with Student‘s - t distributed innovation for daily stock index returns †0 4.† Parameters estimation of GARGH(fi,fi) model with skewed Student‘s - t distributed innovation for daily stock index returns †fi 4.6 Parameters estimation of GJR - GARGH(fi,fi) model with normal distributed innovation for daily stock index returns †£ 4.t Parameters estimation of GRJ - GARGH(fi,fi) model with Student‘s - t distributed innovation for daily stock index returns †£ 4.8 Parameters estimation of GRJ - GARGH(fi,fi) model with skewed Student‘s - t distributed innovation for daily stock index returns †3 4.9 Parameters estimation of generalixed Pareto distribution (GPD), threshold exceedances of † percentage from GARGH(fi,fi) model †4 4.fi0 Parameters estimation of generalixed Pareto distribution (GDP), threshold exceedances of † percentage from GJR - GARGH (fi,fi) model †† 4.fifi Expected and actual number of VaR violations at threshold † percentage †6 4.fi£ Violation ratio and Kupiec‘s test p - value at † percent significance level †t 4.fi3 Independence test and Ghristoffersen‘s test at † percent significance level .63 4.fi4 Expected and actual number of VaR violations at threshold £.† percentage 64 4.fi† Violation ratio and Kupiec‘s test p - value at £.† percent significance level 6† 4.fi6 Independence test and Ghristoffersen‘s test at £.† pecent significance level 66 4.fit Expected and actual number of VaR violations at threshold fi percentage 6t 4.fi8 Violation ratio and Kupiec‘s test p - value at fi percent significance level .68 4.fi9 Independence test and Ghristoffersen‘s test at fi pecent significance level .69 4.£0 Best forecasting VaR model according to Ghristoffersen‘s test at †, £.† and fi percentage of significance level tfi List of Figures 4.fi 4.£ 4.3 4.4 4.† 4.6 4.t 4.8 4.9 4.fi0 4.fifi 4.fi£ 4.fi3 Daily value of stock index 4£ Daily return of stock index 4† Histograms of daily stock index returns .46 Ønorm - ØØ plot of daily stock index returns .46 AGF for daily stock index returns 4t PAGF for daily stock index returns 4t AGF for squared of daily stock index returns 48 PAGF for squared of daily stock index returns 48 EWMA and unconditional VaR models forecasting performance for daily return of EIB at †% significance level t£ GARGH VaR model forecasting performance for daily return of AGB at †% significance level t3 GJR - GARGH VaR model forecasting performance for daily return of MBB at †% significance level t4 EVT GARGH VaR model forecasting performance for daily return of GTG at †% significance level t4 EVT GJR - GARGH VaR model forecasting performance for daily return of BVH at †% significance level t† † AGKNOWLEDGEMENTS 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, staffs 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 amalysis of model forecastimg 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 Gonditional 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 †% significance 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 figure, EWMA plot provides total different 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 figures REIB Actual EWMA HS Nor ma 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 †% significance level Figure 4.fi0 shows forecasting performance of three distributed innovat£ RA CB Actual GARCH_Nor GARCH_Std GARCH_Sstd 0.05 0.00 •0.05 •0.10 500 1000 1500 Figure 4.fi0: GARGH VaR model forecasting performance for daily return of AGB at †% significance level tions normal, Student‘s - t and skewed Student‘s - t used in GARGH model for AGB Student‘s - t is account for fat - tails in case of AGB here, so Stu- dent‘s - t GARGH model produces more negative forecast when high negative losses occur compared to normal GARGH model and has the same behavior as Skewed Student‘s - t GARGH model According to Table 4.fi3 and Table 4.fi4, Student‘s - t GARGH model is the best model proved by Kupiec‘s test and Ghristoffersen‘s test in forecasting performance for daily return of AGB stock index at †% significance level Figure 4.fifi presents forecasting quality of GJR - GARGH model for MBB In this comparison, GJR - GARGH with distributed skewed Studen‘ts - t provide best result that can be seen in Table 4.fi3 and Table 4.fi4 When using Extreme Value Theory to model only tail distribution by Peak - over - Threshold (POT) methodology, GTG has best result in EVT GARGH with skewed Student‘s - t distributed innovations which is drawn in Figure 4.fi£ Figure 4.fi3 presents forecasting performance of EVT GJR GARGH 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 findings to identify what missing t3 RMBB 0.06 Actual 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.fifi: GJR - GARGH VaR model forecasting performance for daily return of MBB at †% significance level RCTG Actual EVT_G_Nor EVT_G_Std EVT_G_Sstd 0.06 0.04 0.02 0.00 •0.02 •0.04 •0.06 200 400 600 800 1000 Figure 4.fi£: EVT GARGH VaR model forecasting performance for daily return of GTG at †% significance level t4 RBVH Actual EVT_GJR_Nor EVT_GJR_Std EVT_GJR_Sstd 0.05 0.00 •0.05 •0.10 200 400 600 800 1000 Figure 4.fi3: EVT GJR - GARGH VaR model forecasting performance for daily return of BVH at †% significance 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 reflect 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 t† Chapter Comclusiom This section includes three parts First part is main finding of this thesis Implication is present in second part And the last part is discussion of limitation and further studies 5.1 Maim fimdimgs This section summaries main finding 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 first 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 – xero skewness excepting only BVH has excess kurtosis nearly xero These features and Jarque - Bera statistical normality test indicate strongly that the daily returns are not normally distribution AGF and PAGF figures are used to visualixe 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 finding is a good proxy for volatility and GARGH model could be a suitable choice Ø – Ø plot once again presents fat - tails and non – normality for all daily returns of stock indexes Previous findings are confirmed through estimated parameters analysis of volatility models which are fitted 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 t6 returns occur more frequently than negative returns In order to take account leverage effects feature, GJR - GARGH(fi,fi) conditional volatility model is suitable choice Most of estimated parameters of volatility models are highly statistically significant In order to evaluate performance of fi6 fitted models, log - likelihood test as well as AIG, BIG statistical tests are compared which shows that there is significant 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 - GARGH(fi,fi) model is better fitting data than GARGH(fi,fi) model Therefore, by combining these findings, GJR - GARGH(fi,fi) model with skewed Student‘s - t distributed innovations might be considered as the best fitted 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 fitted to residuals for daily return of each index In this thesis, we convert residuals into standardixed residuals because generalixed 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 financial turmoil and other extreme events Performance of fi6 forecasting VaR models is evaluated by backtesting procedure A rolling window of fi000 observations in VNINDEX and †00 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 different significance of levels by †%, £.†% and fi% After that, forecasted VaRs and actual losses are compared through violation rate at three given significance 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 ac- count independence or clustering feature which occur frequently in financial series Therefore, independence test and Ghristoffersen‘s test are performed Independence test is used to check forecasted VaRs clustering and Ghristof- fersen‘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 Ku- piec‘s test, however, only few of them are able to pass Ghristoffersen‘s 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 tt 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.£0 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 different of Ghristoffersen‘s p - value compared to the best one In general, there is no particular best model for all stock indexes in all time periods and different significance of levels following to summary of best model based on Ghristoffersen‘s test in Table 4.£0 Therefore, different 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 financial market situation 5.2 Implicatioms VaR is able to measure risk in various types of financial 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 Gommittee on banking su- pervision to meet the capital required for covering potential losses For ex- ample, J.P Morgan, Standard Ghartered bank disclose its daily VaR at 9† percentage level, Bankers Trust discloses its daily VaR at 99 percentage level According to particular financial positions, VaR measure information can be disclosed on the firm‘s financial integrity and risk management to regulators, rating agencies, auditors and investors Based on VaR figures, 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 firm‘s terms of trade as well as regulatory and compliance After finance crisis in £008, risk management system in banking and fi- 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 ap- proach to measure risk Therefore, VaR can be applied as risk management tool for banking and financial sectors in Vietnam in order to reach risk mant8 agement technology in the world as well as might make financial system safer However, as this study mention, various models should be applied and frequently check their performance by backtesting methodology in order to find out the most suitable models for particular financial instruments in each current financial market situation 5.3 Limitatiom amd 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 mea- sure 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 financial 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 Gopulas 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 satisfied risk diversification properties in order to reduce the losses VaR is only coherence when distribution of financial asset is normal However, in case of coherence risk is satisfied, VaR only answers well question regarding to maximum expected losses of asset with a given time period under given con- fidence level but cannot answers in small case of VaR violated situations such as fi, † percentage To overcome the limited of VaR, advanced methodology Expected Shortfall (ES) is introduced in financial theory ES is an expected loss of assets or portfolio after an extreme event which is also called the condi- tional value at risk (GVAR) 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 reflect 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 financial crisis £00t - £008 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 financial turmoil t9 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 financial series characteristic, such as fat - tailed is an 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Is it possible to find out one VaR model which has best forecasting performance for Vietnam stock market?