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 8 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 Christo¤ersen
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 di¤erence 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
1 Introduction
1.1
1.2
1.3
1.4
1.5

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Problem statements . . . . . .
Research objectives . . . . . .
Research questions . . . . . .

Subject and scope of research
Structure of the thesis . . . .

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2 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 . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 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 . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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3.3 Backtesting Methodology . . . . . . .
3.3.1 Kupiec’s Test . . . . . . . . .
3.3.2 Christo¤ersen’s Tests . . . . .
3.3.3 Hypothesis testing procedure

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4 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 . . . . . . . .
5 Conclusion

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5.1 Main …ndings . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2 Implications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
5.3 Limitation and further studies . . . . . . . . . . . . . . . . . . 79

2


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 5 percentage from GARCH(1,1) model
54
4.10 Parameters estimation of generalized Pareto distribution (GDP),
threshold exceedances of 5 percentage from GJR - GARCH
(1,1) model. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.11 Expected and actual number of VaR violations at threshold 5
percentage. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.12 Violation ratio and Kupiec’s test p - value at 5 percent significance level. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.13 Independence test and Christo¤ersen’s test at 5 percent signi…cance level. . . . . . . . . . . . . . . . . . . . . . . . . . .
4.14 Expected and actual number of VaR violations at threshold
2.5 percentage. . . . . . . . . . . . . . . . . . . . . . . . . . .

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4.15 Violation ratio and Kupiec’s test p - value at 2.5 percent signi…cance level. . . . . . . . . . . . . . . . . . . . . . . . . .
4.16 Independence test and Christo¤ersen’s test at 2.5 pecent signi…cance level. . . . . . . . . . . . . . . . . . . . . . . . . .
4.17 Expected and actual number of VaR violations at threshold 1
percentage. . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.18 Violation ratio and Kupiec’s test p - value at 1 percent significance level. . . . . . . . . . . . . . . . . . . . . . . . . . .
4.19 Independence test and Christo¤ersen’s test at 1 pecent significance level. . . . . . . . . . . . . . . . . . . . . . . . . . .
4.20 Best forecasting VaR model according to Christo¤ersen’s test
at 5, 2.5 and 1 percentage of signi…cance level. . . . . . . .

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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 . . . . . . . . . .

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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,
sta¤s 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.

6


Chapter 1
Introduction
1.1

Problem statements

In recent years, …nancial market in the world have faced the collapse of many
major institutions as well as organizations, such as the stock market crisis
- Black Monday (1987), the bond market crisis in U.S. (1990), the …nancial
crisis in Asia (1997),... and the …nancial crisis in Europe (2007), bankrupt
or bailed by governments of Lehman Brothers, AIG (2008) and then it led to
global …nancial crisis and economy recession all over the world (2008). These
events seem to be rare but now they happen frequently and have a negative
impact to …nancial market on both size and loss. Beside on objective causes,
such as war, calamity, terrorism,... one of main important factors impacting
to …nancial market is a weakness of risk management system. Therefore, a
challenge has been raised is how to identify and measure the risk in order to
minimize the loss as well as ensure the safe environment for …nancial market
and economy system.

In modern risk management, it is not su¢ cient if only simply focus on
quality policy. Risk is actually the expected loss of outcome in future, so it is
often measured by probability distribution. One of the important stages in
…nancial risk management process is build up models to measure and evaluate
the risks. However, a di¢ cult process might be raised when applying them
into actual condition of market because every model is associated with some
de…ned assumptions, hypotheses and sometimes these assumptions are not
satis…ed in particular conditions of market. Therefore, some new approaches
should be studied in these models in order to choose and apply the best one
with actual conditions in various markets.
Financial risk management in the world has attained some improvement
process when changing the mind set from passive to active in risk manage7


ment and applied these risk measure methods into business process evaluation, allocation assets, portfolios management with e¢ ciency result.
Vietnam stock market born in July 2000 is an important step to indicate
an improvement in the country’s economy. Vietnam stock market is relative young when compared to others development stock market in the world
and then it has attained new opportunities as well as faced with many new
challenges. In recent years, although Vietnam stock market has many ‡uctuations but it is still an attractive environment for many foreign investors
as well as local ones. All investors, de…nitely, would like their investments
produce a highest pro…t with lowest risk and they are also two main factors
that in‡uence all their business activities. According 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 should be studied and built up in active and
e¤ective way.
One of the most known risk measurement applied in risk management
is Value at Risk (VaR) and it becomes a popular risk management tool
for …nancial regulations and …nancial institutions to evaluate possible losses
that they can incur. The VaR estimation was required by Basel Committee
on banking supervision to meet the capital required for covering potential

losses and VaR …gures considered as additional information to shareholders
have disclosed by many of …nancial institutions. VaR can answer well a
question what is a maximum …nancial amount possible to loose with given
time horizon under given con…dence level or signi…cance level. An overview
of VaR is reviewed by Du¢ e and Pan (1997).
Many methodologies are using to estimate VaR only based on simple
assumption that all …nancial returns follows Gaussian normal distribution.
However, estimating VaR by using normal distribution for each asset has
raised an inaccuracy result because non - normality of …nancial returns.
Therefore, various advanced VaR measurement techniques are used to estimate VaR of daily returns of stock index and then the performance of these
models are evaluated in order to …nd out the best ones which could be used
by …nancial institutions to manage market risk.

1.2

Research objectives

1. To suggest suitable risk measurement VaR models for portfolio in Vietnam stock market.

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1.3

Research questions

1. Does the forecasting VaR performance improve from unconditional to
conditional volatility models?
2. Does the forecasting VaR performance unchange with respect to di¤erent signi…cance level?
3. Is it possible to …nd out one VaR model which has best forecasting

performance for Vietnam stock market?

1.4

Subject and scope of research

This thesis studies risk measurement VaR with various models as well as
methodologies in advanced and applies these models into risk measure for
Vietnam stock market.
The purpose of this thesis is to identify a best appropriate VaR method
including unconditional VaR models such as Historical simulation, normality VaR, Student’s - t VaR, skewed Student’s - t VaR and conditional VaR
models where volatility is forecasted by using Exponential Weighted Moving
Average (EWMA), Generalized Autoregressive Conditional Heteroscedastic
(GARCH) and GJR - GARCH in risk measurement through measuring potential losses of daily return of VNINDEX as well a group of 8 banking stock
indexes with di¤erent time period for each stock index. The longest time period is in VNINDEX which is studied from year 2002 to the end of November
2015. Stock indexes historical return data is assumed to provide su¢ cient
information for model evaluation and predicting one - day return forecasts
under 95%, 97.5% and 99% con…dence level. In order to evaluate quality of
forecasting, some backtesting models including violation ratio, Kupiec’s test,
independence test and Christo¤ersen’s test are performed.
Findings of this study might be useful for …nancial institutions or …nancial
regulatory, particularly risk managers in Vietnam stock markets.
All data used in analysis are calculated by programming and statistical
software called R.

1.5

Structure of the thesis

Thesis contains 6 chapters. First chapter introduces concept of risk and risk

measurement through some tools such as Value at Risk (VaR), Extreme Value
Theory (EVT). Second chapter summarizes literature review and empirical
9


researches on VaR, EVT modeling. Third chapter presents data and methodology of VaR estimation as well as performance comparison through several
backtesting models. Fourth chapter discusses empirical results, analysis and
backtesting. Finally, conclusions and implications as well as further studies
are last part of this thesis.

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Chapter 2
Literature review
This literature review includes 3 parts. The …rst part describes some de…nitions of concepts used in this thesis. The second part is theoretical review
containing some models used to study risk management. And the last part
mentions empirical studies.

2.1
2.1.1

De…nitions
Financial return data

Because stock indexes are mostly not stationary and often integrated at order
1 so it is modeled to changes of prices or log - return series of prices. Daily
…nancial return data have some characteristics which are known as stylized
facts. According to McNeil et al. (2005), these properties can be extended
to scope of time interval including shorter such as intra - day and longer such

as weekly, monthly.
In theory, …nancial returns are often assumed to independent and identical distribution (i.i.d.) but not in reality which often exhibit dependence
in second moment causing time - varying volatility and volatility clustering.
Clustering means that large returns tend to be followed by another large
return and small returns tend to be followed by small returns (Campbell et
al., 1997; McNeil et al., 2005). It can be understood that the probability of
getting large returns are higher than small returns. Black (1976) founded an
asymmetric of volatility phenomenon meaning that negative returns tend to
increase volatility in future more than positive impact which has known as
leverage e¤ects. In addition, Mandelbrot (1963) addressed that …nancial returns are not normal distribution and otherwise, distributions usually follow
to a fat - tails or leptokurtic. Compared to normal distribution, leptokur-

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tic distribution has an excess kurtosis indicating that the tail is fatter than
predicted by the normal distribution.

2.1.2

Concept of Risk

Risk can be understood as unexpected outcome which might be happened
in future. In …nance, risk is a di¤erence between return which is achieved
from an investment and expected outcome or the volatility of unexpected
outcomes which can represent the value of equity, assets, or earnings. Risk
is uncertainty outcome and often developed by probability distribution. According to Basel Accords de…nition, …nancial risk can be divided into three
types including credit risk, operational risk and market risk. Liquidity risk
could be considered as an additional category if necessary.
Credit risk, or default risk is de…ned as risk of loss due to payment default

of borrower including concentration risk, consumer credit risk, securitization
and credit derivatives. Credit risk has been less researched due to limit data
available which mainly only belongs to large rating agencies. But in recent
years, it has become attractive due to the failure of several large …nancial
institutions in the U.S., for example Merry Lynch, Lehman Brothers (2008).
Operational risk indicates the risk of internal processes failure, systems
and people. Fraud, legal and political risk are examples of operational risk.
Market risk can be understood as a changes the prices of …nancial assets such as stock prices, exchange rates, interest rates and commodity risk.
Interest rate risk, currency risk, volatility risk, equity risk are included in
market risk. Because interest rates and equity prices are available widely
and high quality, so market risk can be understood as …nancial risk studies
which is highly concentrated in this thesis.
Following to development of information technology, …nancial products
become more and more sophisticated and …nancial markets around the worlds
become more integrated, so understand well …nancial risk becomes more
important. More and more researches on various features of …nancial series
have been studied.
In this thesis, market risk mentioning the uncertainty of pro…ts or losses
causing of the changes in market condition will be studied because only this
type have enough data.
Firms disclose various types of risks but in general, it can be classi…ed
into 2 types including systematic and unsystematic risks.

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2.1.3

Classi…cation of Risk

Systematic risk
Systematic risk is risk e¤ecting to all or almost stocks. Unstable of economy
environment such as interest rate movement, volatile exchange rates and high
in‡ation... are elements of systematic risk.
One of the key element should be shown up is market risk. Market risk
happened due to reaction from investors at phenomenon happens in market.
Unsystematic risk
Unsystematic risk is risk e¤ecting to one asset or a group of assets or it only
impacts to a speci…c security. Unsystematic risk includes business risk and
…nancial risk.
Business risk includes business decisions and business environment. Business decision includes corporation structure choices, investment decision,
product development choices and marketing strategies implementation. Business environment includes competition and macroeconomic risks.
Financial risk is possible losses of some or all of the original investments.
For example, losses can happen caused of interest rate movement or volatile
exchange rate.
Therefore, all investors can face many types of risk when they invest in
stock market and this is the most important element where they concentrate
on. However, in this research, only …nancial risk is studied especially at risk
models to measure and assess the stock price return.

2.1.4

Risk measurement and Coherence

In modern …nancial risk management, only rely on qualitative methods are
not enough and not e¢ ciency, the more important thing is build up and
development methods which can quantify the level of risk and …nancial losses.
And based on this, …nancial institutions, …nancial regulators and investors
have a reliable source to determine decision making. Loss of a …nancial
position can be represented by a random variable and then all characteristic

losses of …nancial position are expressed through distribution of loss random
variables. Because the loss distribution is unknown and hard to estimate
then some summary statistics are employed to quantify the distributions loss
in reality and a risk measure is one of these ones. Risk measure provides a
potential risk estimation and di¤erent chosen risk measure leads to di¤erent
a¤ects to quality of predicting the losses of …nancial position so the choice

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of a suitable risk measure becomes a crucial task towards building a realistic
picture of risk.
Coherence
Risk measure is a tool to estimate the potential loss of …nancial position
so it should be consistent with the basis theory in …nance called coherence.
Let be a risk measure and is a coherence if four following conditions are
satis…ed for any two loss random variables X and Y (Artzner et al., 1999):
1. Subadditive: (X + Y )
(X) + (Y )
2. Monotonicity: If X Y then (X)
(Y )
3. Positive homogeneity: (cX) = c (X), for any positive constant c
4. Transition invariance: (X + c) = (X) + c, for any positive constant
c:
The subadditive property indicates that a combine of two positions is
less risky than separate them individually. This property relating to diversi…cation mentions that a diversi…ed portfolio should not be greater than
individual components in level of risk. The monotonicity mentions that a
lower loss asset will generate a lower risk measure. The positive homogeneity
expresses that doubling an asset should lead to double its risk. The transition invariance property shows that if one additional risk is added, it will
generate more risky and adding one more constant to a random variable leads

to unchanged in its variability which is one of statistics properties.

2.2
2.2.1

Theoretical review
Value at Risk

Financial institutions can be lost billions of dollars due to a poor …nancial
risk management which are experienced in …nance crisis period. In order to
have a quantitative …gures of risk, Value at Risk (VaR) was developed and
now it becomes a popular tool in risk management because this approach
summaries overall market risk through a single quantity, easy to understand
and does not depend on a speci…c kind of distribution. VaR can be used by
…nancial institutions to measure their risks as well as by a regulatory to setup
requirement. VaR summarizes the worst expected loss of assets or portfolio
over a target holding period with a given level of con…dence in normal market
condition (Jorion, 1997, 2007). It could be estimated through the predictive
distribution in econometric modeling of the loss random variable.
Let Vt ; Vt+l be the value of a …nancial position at time t and t + l,
respectively. Let Lt (l) is the loss random variable of …nancial position for
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the next l periods from the time index t and the cumulative distribution
function of Lt (l) is denoted by Fl (xt ) or Fl (x). For short expression, the time
index t will be drop but it is understood that Fl (x) is a function depending
on the time index t. Then, Lt (l) is either a negative or positive function of
Vt+l Vt .
Because big loss is less frequently happened so small probability denoted

by p is used, for example, 5% or 1% or 0.1% to assess the loss. After that,
with a given time horizon l under probability p, VaR of the …nancial position
is de…ned as
V aR1 p = inffxjFl (x) 1 pg
(2.1)
From the de…nition, Fl (V aR1 p )
1 p is absolutely satis…ed, which
says
P r(Lt (l) V aR1 p ) 1 p or P r(Lt (l) > V aR1 p ) p
(2.2)
indicating with the probability 1 p, the potential loss of …nancial position
over the time period from t to t + l is less than or equal to V aR1 p or the
probability that the potential loss of …nancial position greater than V aR1 p
over the same time period is at most p.
If VaR is a continuous loss random variable then it can be shown as
V
Z+1
ZaR
f (x)dx = p or equivalent f (x)dx = 1

p

(2.3)

1

V aR

where p is the signi…cant level, f (x) is a probability distribution function
(pdf) of portfolio or assets values, x stands for the return in the market value

of a given asset or portfolio over a given time horizon. It says that VaR is
(1 p)th quantile of a distribution which is also referred to as the 100(1 p)th
percentile of the loss variable X.
Given a probability density function of standardize return, VaR can be
calculated by combination of volatilities and residual of distribution function
as:
V aR1

p

1

=

(1

p)^ t

(2.4)

1
where ^ t is the conditional standard deviation at time t.
( ) is the
quantile of a standardized normal variable, such at normal distribution, Student’s - t distribution, skew Student’s - t distribution or any assumed distributions. VaR is a coherent risk measure if the loss random variables are
normal distribution.
Volatility, time horizon and con…dence level or signi…cance level are factors determining VaR for portfolio or a certain asset. The volatility is estimated through statistical models. Depend on speci…c …nancial activity type,

15

such as measured in one - day ahead VaR, one - year ahead VaR, time horizon
is chosen and a¤ects to volatility measure and then also a¤ect to VaR, where
a longer time period leads to a higher volatility and …nally, a higher VaR.
Con…dence level chosen represents how often a loss on portfolio or speci…c
asset greater than VaR. It can be set lower at 95% for short data period
and in case of very conservative approach in risk management; con…dence
level can be set high as 99.9% or even 99.99%. 95% and 99% are con…dence
intervals which are commonly used in empirical studies (Danielson and de
Vries, 1997).
The oldest de…nition of VaR might be seen from the portfolio optimization
theory by Markowitz (1952). However, it had become unsuitable measurement after stock market crashed in 1987 called Black Monday due to simple
assumptions in this methodology which does not appropriate to actual situations. A new suitable methodology should be studied and then well - known
RiskMetrics were developed and published by J.P. Morgan in 1994, VaR has
become a popular measurement in risk management. Research on VaR was
strongly supported when Basel II Accord (BIS, 2006) (Basel Committee on
Banking Supervision) clearly expressed that VaR is a preferred measurement
for market risk. Since then, more and more studies on VaR have been developed to improve the quality of risk management through providing a better
predicted measure in future loss.
The method to calculation VaR could be split into two groups under parametric and nonparametric approaches. In this study, EVT (Extreme Value
Theory) is a parametric approach focusing on tail distribution where rare
event existed. Parametric methodology includes GARCH, Equally weighted
moving average (EqWMA), Exponential Weighted Moving Average (EWMA).
In the other hand, the Historical simulation belongs to nonparametric methodology.
The choice of risk measure is crucial step in order to build realistic …gures
of risk. However, there is another essential element comes from …nancial returns which impacts to accuracy of risk …gures. Numerous empirical studies
pointed out that asset return exhibit volatility clustering, fat - tails and skewness; therefore these phenomena should be accounted for probabilistic model.
Before EVT, lot of methodology researches in whole distribution mentioning
for entire sample of return of assets (McNeil & Frey, 2000). In this study, 16
di¤erent models will be compared together in order to …nd out which model
is the best. They are the variance - covariance with normal distribution

and Student’s t distribution, historical simulation, EMWA, GARCH, GJR
- GARCH and EVT combining with three distributed innovations normal,
Studen’s - t and skewed Student’s - t; and then residuals extracted from
volatility models GARCH, GJR - GARCH are modeled by Peak - Over 16


Threshold model from Extreme Value Theory which only concentrates on
the tail.

2.2.2

GARCH

In reality, …nancial series always volatile and in order to predict the volatility of these return time series, several forecasting volatility models were
introduced such as ARCH (Engle, 1982), a well - known models GARCH
(Bollerslev, 1986) which is now widely applied in forecasting the volatility
of …nancial return time series. In order to capture volatility clustering feature in …nancial time series, several alternative modes have been developed.
For example, GARCH(1,1) is considered as a successful approach to account
certain features of …nancial returns such as volatility clustering and excess
kurtosis (Hansen & Lunde, 2005). However, GARCH is a model which is
often used to predict in short term and fail to capture asymmetric behavior (Baillie, Bollerslev & Mikkelsen, 1996; Davidson, 2004; Ding & Granger,
1996). Therefore, several advanced models applied to particular condition
of market have been produced such as Asymmetric Power Autoregressive
Conditional Heteroscedastic (APARCH) (Ding, Granger and Engle, 1993),
EGARCH (Nelson, 1991), GJR - GARCH (Glosten et. al, 1993) ...

2.2.3

Extreme Value Theory

VaR is a well - known parametric methodology in risk measurement but
combining with a simple normal distribution assumption will raise an inaccuracy result. According to this approximation, all risk measurement results
of high quantiles are underestimated, especially in fat - tails …nancial series
happened frequently in empirical studies mentioned by Mandelbrot (1963)
and Fama (1965). In order to cover this limitation, some studies have used
more appropriate fat - tails distributions such as Student - t distribution or
normal distribution mixture but VaR actually only concentrate on central of
observation which is also mean that they are studied under normal market
conditions. In another side, nonparametric methods based on no assumption
of speci…c empirical distribution have been also given to pass this problem,
they, however, are still faced with some limitation. For example, non - parametric method produces a problem on assuming all observations having the
same weight as well as it cannot be applied in out - of - sample quantiles.
In contrast of forcing the entire return series in VaR, Extreme Value
Theory (EVT) only focus on tail areas of distributions where extreme or rare
events are taken into account. Extreme value theory (EVT) is a useful tool
to support risk measurement because it could take over a better approach
17


to …t extreme rare events which are limited by mentioned simple assumption
before. In a di¤erent way compared to VaR, EVT has no assumptions about
the original distribution of all the empirical observations. It is a powerful
and robust framework in study of the tail behavior of distribution, especially
in fat - tails and it can be used to handle for a very high quantiles in predicting an extreme loss or crashes situations. Although EVT is a popular
methodology which has been applied in climatology and hydrology long time
ago, it has been only introduced comprehensive in …nance and insurance in
recent year by Embrechts et al. (1997). Since its introduction to …nance,
there are a signi…cant number of …nancial studies relating to extreme values
have discovered in recent years and a comparison between their results with
other VaR models are reviewed. De Haan, Jansen, Koedijk, and de Vries

(1994) gave the quantile estimation using Extreme Value Theory. McNeil
(1997, 1998) used the estimation of quantile risk measures and the tail of
loss by applying Extreme Value Theory in …nancial time series studies. Embrecht et al. (1998) discussed a risk management tool through the Extreme
Value Theory. McNeil (1999) provided an overview of Extreme Value Theory
for risk manager. McNeil and Frey (2000) estimated a risk measurement for
heteroscedasticity at tail of …nancial time series.
EVT approach is de…nitely suitable for extreme quantiles than conventional approach in heavy tail data. In principle, there are two most well known of extreme value models: block maxima model (BMM) and Peaks Over - Threshold (POT) model. The …rst one, BMM, requires a large of
observations in sample with identically and independently distributed (i.i.d.)
losses assumptions. The second one, POT, is a more recent and modern
model focusing on all return losses which exceeds some de…ned high threshold. In practical applications, POT model is the most useful and often used
due to its simple assumption and e¢ cient use of return data on extreme values which are very often limited (McNeil, Frey & Embrechts, 2005). In this
study, only POT model is used to support EVT in risk measurement.

2.3
2.3.1

Empirical studies review
Empirical research on modeling and measuring
VaR

Since Basel II Accord (BIS, 2006) mentioned that VaR is preferred measure for market risk, VaR model have been exploded in research and then
many methodologies were built with advantages and disadvantages as well
as many advanced approaches were studied in order to improve quality of
18


predicting of di¤erent VaR models. There are some advanced approaches,
for example, Extreme Value Theory (EVT) or family of ARCH models such
as the autoregressive conditional heteroscedastic (ARCH) model of Engle
(1982), the generalized autoregressive conditional heteroscedastic (GARCH)

model of Bollerslev (1986), the exponential generalized autoregressive conditional heteroscedastic (EGARCH) model of Nelson (1991), the asymmetric
power autoregressive conditional heteroscedastic (APARCH) model of Ding,
Granger and Engle (1993), the GJR - GARCH model of Glosten et. al (1993)
were used to study on various assets. However, these studies provided different results indicating that no existing best model for predicting, so it is
very useful contribution to test various method in particular asset using most
recent data in market including recent …nancial crisis.
Beder (1995) is considered as one of the …rst author studying on measuring VaR accuracy of di¤erent assets including bonds, stock indexes and
options as well as the mix of these ones by using two classical VaR models
which are Historical simulation (HS) and Monte Carlo simulation. Author
mentioned that VaR measures are very impacted by data, di¤erent parameters, assumptions and methodologies as well as provided 14 di¤erent VaR
estimations in this study even though this paper only used two models. So
there are several shortcomings from these approaches. The main advantage
of Historical simulation methods is no parameters requirement. However,
one of the weakness of Historical simulation method is equally weighted assumption applied to all returns showing that very old returns have as same
impact as recent ones to VaR estimation in case of long time period of data
taken. This weakness is mentioned in study of Boudoukh, Richardson and
Whitelaw (1998) and they also provided suggestion about weight return following to time from their sample to VaR estimation. Hull & White (1998)
also addressed the weight returns on volatility in order to account the recent
volatility changes.
Distribution of …nancial returns is one of an important element impacting
strongly to VaR performance. Using normal distribution in VaR estimation
might lead to an inaccuracy result because the …nancial returns are often not
…t with the normal distribution. Mandelbrot (1963) addressed that …nancial
returns are not normal distribution and otherwise, distributions usually follow to a fat - tails or leptokurtic. Bormetti et al. (2007) presented a non
- Gaussian approach to measure market risk as well as discussed both its
advantages and limitations. In this study, author compared new approach to
other well - known approaches in literature including normal VaR, Historical
simulation and Monte Carlo simulation that are often used in …nancial analysis. In order to capture the excess kurtosis, authors used …tted Student’s - t
distribution known as a better modeling for fat - tails characteristic of …nan19

cial returns. Research investigated Italian stock market by using 1000 daily
return of two stocks and two indexes as well as con…rmed leptokurtic behavior of distribution returns because tail parameters fell in the range (2.9, 3.5).
This study mentioned that at 95% con…dence level, the performance result of
the Student’- t distribution and normal distribution are almost equivalent,
however at a higher level such as 99%, the Student’s - t distribution outperform the normal one and based on this results, they suggested this approach
might be a useful for practical applications in …nancial risk management.
However, both normal and Student’- t VaR measures are still have limitation at assuming that volatility of …nancial returns is unchanged or constant
instead of clustering mentioned by Brooks (2008). Clustering means that
large returns tend to be followed by another large return and small returns
tend to be followed by small returns. It can be understood that the probability of getting large returns are higher than small returns. Based on ideas
from ARCH models of Engle (1982), Bollerslev (1986) developed generalized
autoregressive conditional hetoroskedastic (GARCH) model which could capture fat - tails and volatility clustering in …nancial returns. Financial returns
distribution are often change over time known as conditional volatility which
could be captured by GARCH models and then VaR estimations can be depended on time or conditional. One of model might be represented success
for this approach is exponential weighted moving average (EWMA) is employed in RiskMetrics which is developed by corporation J.P. Morgan (1994).
However, this approach assumes that distribution of …nancial returns is normal and this is not often happened in reality mentioned before as a weakness
assumption. Furthermore, according to Black (1976), …nancial returns has
leverage e¤ects phenomenon or asymmetric e¤ect of volatility meaning that
negative returns tend to increase volatility in future more than positive returns impact. In order to capture this shortcoming, GJR - GARCH model
was developed by Glosten et. al (1993).

2.3.2

Empirical research on Extreme Value Theory (EVT)
VaR

Because methodologies of VaR estimation above are studied on whole distribution and then it cannot cover well in case of extremely rare events. In order
to capture these situations, Extreme Value Theory (EVT) was developed
and it only focuses on the tail of distribution instead of whole distribution.

As mentioned above, almost distribution of …nancial returns are fat - tails
and asymmetric. So this methodology is suitable in these cases and this
is a good reason to compare it to parametric volatility models. However,

20


EVT has been applied in …nancial sector in recent years after occurring of
extreme event called Black Monday although it was applied widely in other
physical sciences such as engineering, hydrology. And up to now, EVT has
become popular in …nance because it can perform a good result in predicting
worst situations. McNeil (1997, 1998) used extreme value theory to estimate the tail of loss severity distributions and quantile risk measurement
for …nancial time series. Embrechts et al. (1999) demonstrated an overview
picture about extreme value theory which is considered as risk management
tool. Moreover, following to Embrechts et al. (1999), McNeil (1999) gave
an extensive overview of this approach to risk managers. McNeil and Frey
(2000) estimated tail - related risk measurement for …nancial time series with
heteroscedastic characteristic.
Following is several studies using EVT method in VaR evaluation and
compare to other VaR models which will be discussed.
Kuester, Mittik & Paolella (2006) compared out - of - sample performance
between EVT and parametric VaR models using GARCH volatility modeling
through investigating on 30 years of daily returns from time period February
8, 1971 to June 21, 2001 of NASDAQ Composite index. This study used
1000 returns data moving window (in - of - sample) and model parameters in
each window were updated for every day forecast then it produced 6681 one
day VaR estimation which supported for comparing predictive performance
of the models. Through descriptive statistics, it addressed asymmetric and
leptokurtosis phenomena in distribution of returns and in order to account
for this behavior, authors used skewed Student’s - t instead of normal distribution. Authors pointed that Historical simulation fails the independent test

and predictive performance of skew Student’s - t distribution is much better
than normal return distribution. They also found that volatility model has
positive e¤ect to predicting performance and once again, skew Student’s - t
distribution provides superior performance compared to normal and symmetric Student’s - t distribution assumption. They concluded that a combination
between EVT approach and fat - tails GARCH volatility modeling provides
best results at various con…dence levels.
In another study, Ozun, Cifter and Yilmazer (2010) compared performance of eight di¤erent EVT models and GARCH models with normal,
Student’s and skew Student’s - t distribution as well as used backtesting
methods. In this study, they employed not only VaR but also Expected
Shortfall (ES) to estimate portfolio returns. Then they found that …ltered
EVT models provide results better than any VaR models and are able to
account fat - tails phenomenon in distribution of portfolio return.

21