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Market risk versus credit risk of the selected countries in the trans pacific partnership agreement

UNIVERSITY OF ECONOMICS
HO CHI MINH CITY
VIETNAM

INSTITUTE OF SOCIAL STUDIES
THE HAGUE
THE NETHERLANDS

VIETNAM – THE NETHERLANDS
PROGRAMME FOR M.A. IN DEVELOPMENT ECONOMICS

MARKET RISK VERSUS CREDIT RISK OF SELECTED
COUNTRIES IN THE TRANS-PACIFIC PARTNERSHIP
AGREEMENT

BY

QUANG VAN TUAN

MASTER OF ARTS IN DEVELOPMENT ECONOMICS


HO CHI MINH CITY
December 2017


UNIVERSITY OF ECONOMICS INSTITUTE OF SOCIAL STUDIES
HO CHI MINH CITY
THE HAGUE
VIETNAM
THE NETHERLANDS

VIETNAM – THE NETHERLANDS
PROGRAMME FOR M.A. IN DEVELOPMENT ECONOMICS

MARKET RISK VERSUS CREDIT RISK OF SELECTED
COUNTRIES IN THE TRANS-PACIFIC PARTNERSHIP
AGREEMENT
A thesis submitted in partial fulfilment of the requirements for the degree of
MASTER OF ARTS IN DEVELOPMENT ECONOMICS

BY
QUANG VAN TUAN

Academic Supervisor
Dr. VO HONG DUC

HO CHI MINH CITY
December 201


ABSTRACT
At the time this study is finalized, the future of the so-called Trans-Pacific
Partnership Agreement (TPP) is still uncertain after the US Present Donald Trump walked
away from his predecessor Barack Obama’s commitment. A different version of TPP, or
to be called the Comprehensive and Progressive Agreement for Trans-Pacific Partnership
(CPTPP), may be formed without the US presence. Among these member countries,
Vietnam and Malaysia (in the ASEAN), together with Australia and New Zealand, in the
Pacific Ocean, are generally considered closely competitive nations for various industries,
in particular for Agriculture; Food and Beverage and Tourism.
This study is conducted to measure and rank the market risk level of 10
industries/sectors for selected courtiers in the Asia Pacific region: Vietnam, Malaysia,


Australia and New Zealand. Two periods are considered in market risk, including: (i) the
GFC period (2007-2009); and (ii) the post-GFC period (2010-2016). The market risk level
is measured using the parametric approach and the historical approach for both Value at
Risk (VaR), the potential losses in the future over the given time period (day or month) at
a given confidential level, and Conditional Value at Risk (CVaR), which is designed to
estimate the risk of extreme loss.
Findings from this study confirm that Vietnamese sectors are relatively riskier than
their counterparts in Malaysia, Australia and New Zealand. In addition, market risk level
across sectors in all countries has substantially reduced in the post-GFC period. Financials
including Banks, Diversified Financials, and Insurance have been largely ignored from the
Vietnamese Government’s focus. Interestingly, IT industry is considered very low risk in
Vietnam whereas this sector belongs to a group of high market risk in Malaysia, Australia,
and New Zealand.
This study is then extended to measure and rank the credit risk level for all industries
for Vietnam as the case study. Credit risk is generally defined as the risk that is determined
on a credit requirement from the default. Findings from this empirical study indicate that
Industrials, Energy and Consumer Discretionary sectors have had the worst ranking
performance in relation to their credit risk. Utilities, Financials and IT have achieved a
substantial improvement in the post-post GFC periods. In addition, this study also
i


demonstrated an important link between market risk and credit risk, which can provide an
important insight to develop for further issues integrating these aspects.
With the ambition to be a financial hub in the Asia Pacific region in the regional
integration and a modern industrial economy, a shift of the attention to this particular and
important sector in Vietnam is the near future is strongly recommended.

Key words:

Market risk; Credit risk; Sectors; VaR; CVaR; DD; Vietnam; Malaysia,
Australia, New Zealand

ii


DECLARATION

I hereby declare that the thesis entitled “Market risk versus credit risk of selected
countries in the Trans-Pacific Partnership Agreement” written and submitted by me in
fulfillment of the requirements for the degree of Master of Art in Development Economics
to the Vietnam – Netherlands Programme. This is also my original work and conclusions
drawn are based on the material collected by me.
I further declare that this work has not been submitted to any other university for the
award of any other degree, diploma or equivalent course.

HCMC, December 2017

Quang Van Tuan

ii


ACKNOWLEDGEMENTS

First of all, I would like to express my gratitude to my supervisor Dr. Vo Hong Duc,
for his knowledge, motivation, support and for providing me enormous, valuable
opportunities. His guidance helped me at all the time of research and writing of this thesis,
without him, this thesis would have never been completed.
In addition, I would like to thank Prof. Nguyen Trong Hoai, Dr. Pham Khanh Nam,
Dr. Truong Dang Thuy who have provided me the valuable knowledge in the first step of
research.
Furthermore, I would also like to thank all lecturers, staff and Mr. Pham Ngoc Thach
at the Vietnam Netherlands Programme.
Finally, I wish to express my greatest gratitude to my parents, my aunt and my
younger sister for their unconditional encouragement, support and love on the way I have
chosen.

Quang Van Tuan
Ho Chi Minh City, Vietnam

iii


CONTENTS

ACKNOWLEDGEMENTS ............................................................................................... iii
CONTENTS ....................................................................................................................... iv
LIST OF TABLES ............................................................................................................. vi
LIST OF FIGURES ........................................................................................................... vi
ABBREVIATIONS .......................................................................................................... vii
CHAPTER 1 ....................................................................................................................... 8
INTRODUCTION .............................................................................................................. 8
1.1.

Problem statement ................................................................................................ 8

1.2.

The research objectives ...................................................................................... 11

1.3.

Research questions ............................................................................................. 11

1.4.

A choice of the countries in the Asia Pacific Region in this study .................... 12

CHAPTER 2 ..................................................................................................................... 13
LITERATURE REVIEW ................................................................................................. 13
2.1.

Theoretical review .............................................................................................. 13

2.1.1.

Basel II ........................................................................................................ 13

2.1.1.1.
2.1.2.

Categories of risk ................................................................................. 15

Value at Risk ............................................................................................... 16

2.1.2.1.

Introduction ......................................................................................... 16

2.1.2.2.

The Historical method ......................................................................... 16

2.1.2.3.

The Monte Carlo simulation ................................................................ 17

2.1.2.4.

The Variance-Covariance method ....................................................... 18

2.1.2.5.

Comparison of VaR Methodologies .................................................... 20

2.1.2.6.

Limitations of VaR .............................................................................. 21

2.1.3.

Conditional Value at Risk ........................................................................... 22

2.1.4.

Correlation .................................................................................................. 23

2.1.5.

Distance to Default ..................................................................................... 25

2.1.5.1.

KMV-Morton Model ........................................................................... 25
iv


2.1.5.2.
2.2.

Steps in the KMV-Merton model ........................................................ 27

Empirical literature ............................................................................................. 28

2.2.1.

Empirical evidences on the market risk ...................................................... 28

2.2.2.

Empirical evidences on credit risk .............................................................. 29

CHAPTER 3 ..................................................................................................................... 31
METHEDOLOGY AND DATA ...................................................................................... 31
3.1.

Methodology ...................................................................................................... 31

Value at Risk ............................................................................................................. 31
Conditional Value at Risk ......................................................................................... 31
Equity model ............................................................................................................. 32
Distance to Default ................................................................................................... 33
Hypothesis Testing.................................................................................................... 34
Test selection ........................................................................................................ 34
Spearman Rank Correlation Test .......................................................................... 34
3.2.

Data .................................................................................................................... 36

CHAPTER 4 ..................................................................................................................... 38
EMPIRICAL RESULTS ................................................................................................... 38
4.1.

Data descriptions ................................................................................................ 38

4.2.

Market Risk by VaR and CVaR Results ............................................................ 41

4.2.1.

In the GFC period (2007 - 2009) ................................................................ 41

4.2.2.

In the post-GFC (2010 – 2016) ................................................................... 44

4.2.3.

Ranking Shifts in Vietnam .......................................................................... 40

4.3.

Credit Risk by Distance to Default Results for Vietnam ................................... 44

4.4.

Market risk versus Credit risk outcomes ............................................................ 45

CHAPTER 5 ..................................................................................................................... 48
CONCLUDING REMARKS AND POLICY IMPLICATIONS ..................................... 48
5.1.

Concluding remarks ........................................................................................... 48

5.2.

Policy implications ............................................................................................. 49

5.2.1.

The implications for practitioners and investors ......................................... 50

5.2.2.

The implications for Vietnamese government ............................................ 50

5.3.

The limitations and further research................................................................... 51

Reference .......................................................................................................................... 52
v


LIST OF TABLES

Table 1

Comparison of VaR methods ........................................................................... 20

Table 2

Matrix Variance-Covariance Calculation for a Two-Asset Portfoli ................ 33

Table 3

Spearman Rank Correlation Test ..................................................................... 35

Table 4

Sector Breakdown ............................................................................................ 37

Table 5

Daily commodity market price movements in Vietnam and Malaysia (2007–
2016) ................................................................................................................. 39

Table 6

Daily commodity market price movements in Australia and New Zealand
(2007–2016) ..................................................................................................... 40

Table 7

The level of market risk proxied by VaR using Parametric and Historical
approaches for Vietnam, Malaysia, Australia and New Zealand in the GFC
period (2007-2009) ........................................................................................... 42

Table 8

The level of market risk proxied by CVaR using Parametric and Historical
approaches for Vietnam, Malaysia, Australia and New Zealand in the GFC
period (2007-2009) ........................................................................................... 43

Table 9

The level of market risk proxied by VaR using Parametric and Historical
approaches for Vietnam, Malaysia, Australia and New Zealand in the GFC
period (2010-2016) ........................................................................................... 38

Table 10 The level of market risk proxied by CVaR using Parametric and Historical
approaches for Vietnam, Malaysia, Australia and New Zealand in the GFC
period (2010-20016) ......................................................................................... 39
Table 11 VaR Ranking Shifts in Vietnam ...................................................................... 41
Table 12 CVaR Ranking Shifts in Vietnam ................................................................... 43
Table 13 DD Ranking Shifts in Vietnam ....................................................................... 44
Table 14 Market Risk proxied by Parametric and Credit Risk proxied by DD
Comparison in post-GFC (2010 – 2016) .......................................................... 46
Table 15 Market Risk proxied by Historical and Credit Risk proxied by DD Comparison
in post-GFC (2010 – 2016) .............................................................................. 47

vi


LIST OF FIGURES

Figure 1

Distribution of daily returns of NASDAQ 100 – Ticker: QQQ ..................... 17

Figure 2

Monte Carlo simulation 100 random trials ..................................................... 18

Figure 3

Distribution of daily returns of NASDAQ 100 – Ticker: QQQ ..................... 19

Figure 4

VaR, CVaR, Deviations.................................................................................. 22

Figure 5

VaR Values Changes in Vietnam ................................................................... 41

Figure 6

CVaR Values Changes in Vietnam ................................................................ 43

vi


ABBREVIATIONS

Basel II

Basel II Accord 2004: BIS revised capital adequacy framework

CVaR

Conditional Value at Risk: Value at risk on condition.

DD

Distance to Default: approach developed by KMV – Merton

GICS

Global Industry Classification Standard

VaR

Value at Risk

vii


CHAPTER 1
INTRODUCTION
1.1. Problem statement
In recent years, the global financial market has undergone a huge change. At the early
stage of the 2000s, the European Union indicated an important inclination of the European
financial markets. Moreover, the international crisis of 2007 - 2008, which was originated
from the US, caused the negative effect on the global system. In addition, Duffie & Pan
(1997) presented the idea to minimalize the loss by recognizing and calculating the risk,
and certify the financial market and economy system securely.
Vietnam has emerged as a new economic engine for the Southeast Asian region with
many important industries. The three pillars contributing the most value to the Vietnamese
economy over the last decade or so are agriculture, manufacturing, and food & beverage.
Among these key pillars, for example, agriculture is a key industry, which has consistently
contributed 20 percent to the national GDP in 2015.1 In addition, Vietnam becomes an
official member of The Trans-Pacific Partnership (TPP) with 11 other countries including
Australia, Brunei, Canada, Chile, Japan, Malaysia, Mexico, Peru, New Zealand, Singapore,
and the United States. According to statistics,2 total gross domestic product (GDP) of the
current TPP parties is approximately $28 trillion, comprises 40 percent of global GDP and
one third of world trade. TPP members account for 11.3 percent of world population and
25.9 per cent world trade.
Even though the full TPP Agreement is dead under the water after the US Present
Donald Trump walked away from his predecessor Barack Obama’s commitment. A
different version of TPP, or to be called the Comprehensive and Progressive Agreement
for Trans-Pacific Partnership (CPTPP), may be formed without the US presence. This new
CPTPP agreement will bring both opportunities and challenges for Vietnam in the future.
In order to maximize the potential benefits from this new partnership, it is time to recognize
the important role of sectorial risk, in particular, for key sectors (industries) relatively to
1
2

https://www.gso.gov.vn/default.aspx?tabid=621&ItemID=15507
http://www.nytimes.com/interactive/2016/business/tpp-explained-what-is-trans-pacific-partnership.html

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similar sectors from other members.
In addition, the so-called Asia-Pacific region has emerged as the economic and
political powerhouse for the last decade or so. It is time for Vietnam to go beyond the
borders of the ASEAN. The common market has been getting larger and larger and
competition has been becoming more challenging. Malaysia and Thailand are no longer
the only competitors for certain sectors in Vietnam. It is time for Vietnam, as well as other
identical ASEAN nations including Thailand and Malaysia, to recognize and prepare a
response for competition from other countries, who are not the members of the ASEAN,
from the Asia-Pacific region, in particular for Australia and New Zealand.
Risks may subsist in every movement of life and risk estimation is the essential
activity. Moreover, this movement may support the lenders forecasting and avoiding bad
debts. In business activities, risk may arise from various sources: the volatility of the
business environment; business cycle, changes in government policies and especially in
the financial markets. In the event, a number of companies passively accept the risk.
However, others attempt to manage risk by utilizing the proactive methods. Either of
circumstances, risk should be carefully monitored because of its potentially harmful effects
Jorion (2007).
According to Basel II Accord (Bank for International Settlements, 2004), risk may
be split into three groups including credit risk, operational risk, and market risk. First,
credit risk is generally defined as risk of loss because of the payment default of borrower.
Second, operational risk presents the risk due to internal process failures, systems and
people. Third, market risk is considered as a change in the price of financial assets due to
the changes in interest rates, stock prices, exchange rates and commodity risk.
To be more precise, one of the most effective techniques to estimate the market risk
is Value at Risk (VaR). In 1995, The Basel Accord recommended banks to calculate the
capital requirements for market risk by employing certain parameters with value at risk
model. VaR laid the groundwork for resolving a numerous aspect of financial risk. Jorion
(1996) and Pritsker (1997) indicated that VaR, as a risk management method, can estimate
the maximum expected loss that may occur over a given period, at a given confidence level.
In addition, VaR is an uncomplicated risk management and 𝛼-percentile of a distribution
9


is easily figured out. The tempting simplicity of the VaR concept can conduct its
implementation as an ordinary risk measure for financial actualities entailed in not only
operations, banks, insurances, but also an institutional investment, and nonfinancial
enterprises. As such, VaR tends to become the prevailing method for measuring risk in
majority of the industries and countries.
Despite its popularity, VaR remains unsatisfactory mathematical properties. Artzner
et al (1999) analyzed risk measures and concluded that an arrangement of axioms that
should be suitable for any risk measures, which persuades these axioms, is considered to
be “coherent”. The four axioms are Monotonicity, Translation Equivariance, Subadditivity,
and Positive Homogeneity. However, there is no precise quantity of VaR and each measure
stretch with its limitations and VaR is not able to catch the subadditivity axiom. Therefore,
VaR is not recognized for a coherent risk measure. This makes VaR optimization a
challenging computational problem.
Acerbi and Tasche (2002) demonstrated that Condition Value at Risk (CVaR) could
convince all the above axioms and especially subadditivity axiom. As such, CVaR is a
coherent risk measure. CVaR is considered as a good measurement of the extreme losses
in the tail of the distribution as it is conditioned on the returns exceeding VaR. First, CVaR
is usually measured as a percentage. If VaR is measured at a 95% confidence level, CVaR
will be the average of the worst 5% of observations. Second, CVaR has been related to
sector risk and economic periods to measure modifications in risk for extensive product
categories by Powell, Vo, and Pham (2016c); Pflug (2000) presented that CVaR is a
rational measure, not containing the disadvantageous properties of VaR such as
subadditivity. Third, CVaR does measure tail risk as it appraises those returns beyond VaR.
This research aims to emphasize on market risk and credit risk, which have attracted
great attention from academia, investment bankers, and policymakers. Although numerous
studies such as Allen at el (2014); Powell, Vo, and Pham (2016a, 2016b, 2016c)
investigated the market and credit risk for various countries over the world, there has been
no study concerning, comparing Value at Risk (VaR) and Conditional Value at Risk
(CVaR) rankings for various sectors for Vietnam and other members from the Asia-Pacific
region. As a result, this study is conducted to fill this gap. In addition, this study will
10


demonstrate the link, if any, between the market risk estimates when the VaR/CVaR and
the Distance to Default techniques are adopted in the context of selected countries in the
Asia-Pacific region including Vietnam.
A careful examination indicates that Vietnam and Malaysia (the ASEAN members)
and Australia and New Zealand (the non-ASEAN members) are relatively identical in
relation to the key industries that contribute substantially to the national economies.
According to Bloomberg where all the data required for this study are extracted, economic
activities in any economy can be allocated into 11 different sectors. These sectors include
Energy; Materials; Industrials; Consumer Discretionary; Consumer Staples; Healthcare;
Financials; Information Technology; Telecommunication Services; Utilities; and Real
estate. The choice of these four selected countries is arbitrary albeit interesting. While
Vietnam and Malaysia are developing countries, Australia and New Zealand are developed
economies. All these selected countries are members of the Asia-Pacific Economic
Cooperation.

1.2. The research objectives
This study is conducted to achieve the following research objectives:
 First, estimating the market risk for all sectors for Vietnam and selected other
countries in the Asia-Pacific region where data is available. Furthermore, this
study will closely focus on the differences of the estimates between the crisis
and non-crisis periods.
 Second, estimating the credit risk using the Distance to Default (DD) structural
approach and providing the link, if any, between the VaR and the DD model.

1.3. Research questions
The following research questions have been raised in this study:
 What is the currently prevailing market risk level of various sectors from
Vietnam and selected other countries in the Asia-Pacific region using VaR and
CVaR?
 Is there any link between the estimates of the market risk using VaR techniques
11


and the credit risk using the DD model?

1.4. A choice of the countries in the Asia Pacific Region in this study
Due to time constraint, conducting research for all members of the Asia Pacific
Region may become excessive. As such, it is the intention of this study is to focus on the
members in the Australasian region. In this region, members include Malaysia and Viet
Nam (ASEAN) and Australia and New Zealand. A preliminary search provides evidence
to confirm that Brunei may not be on the final list because of its financial market size and
its level of economic development. It is worth noting that, for example, agriculture is one
of the top three industries for Vietnam, Malaysia, Australia and New Zealand. A scrutiny
will be conducted.

12


CHAPTER 2
LITERATURE REVIEW
This chapter is to review the theoretical and empirical literature on both market risk
and credit risk. There are two main parts in this chapter:
i.

The basis theories in market risk and credit risk.

ii.

The empirical evidences on market risk and credit risk.

2.1. Theoretical review
The literature review re-examines the Basel Accords II, Value at Risk methodologies,
Conditional Value at Risk methodology and correlation techniques.
 The Basel II framework establishes the minimum standards for management
on a sensitive risk: Market Risk, Operational Risk and Credit Risk
 Value at Risk is one of the most effective techniques to estimate maximum
expected loss on the market risk. In addition, there are three main methods to
calculate VaR. First, the historical method is relied on the actual historical data.
Second, the Monte Carlo method simulation that randomly creates multiple
scenarios. Third, the Variance-Covariance (parametric) method estimates VaR
on the assumption of a normal distribution.
 Conditional value at Risk is a coherent risk approach and satisfies the desirable
characteristics that are the shortcomings of Value at Risk.
 Correlation is an estimate the level of one variable’s value is related to the value
of another. It is particularly important for practitioners interested in minimize
risk to measure the correlation between variables.
2.1.1. Basel II
Basel Capital Accord (Basel I) initially indicated by the Group of Ten (G10)
countries in 1988, to retain the adequate capital that provide a support against unexpected
losses. Therefore, Value at Risk (VaR) was selected as a method proposed to predict the
maximum expected loss over a given period time and confidence level. Moreover, Basel
13


Accord stipulated a standardized approach, which is utilized to calculate the capital for
credit risk and market risk, for all institutions. However, this method may contain several
adequacies, the most important of which were its traditionalism and its failure to
remunerate organizations with higher risk administration.
The Basel Accord was enhanced in April 1995. Basel II permitted associations to
utilize internal models to specify their VaR and the required capital expenses. Nevertheless,
organizations desire to use their internal models, which were originated from regulator, to
employ back-testing method. Following the Australian Prudential Regulatory Authority
(APRA), Basel Accord was chosen as the national mechanism of financial markets. The
normalized procedure is built on ratings from qualified external rating operation.
The Basel II structure entails of three Pillars:
 Pillar 1: Capital Requirements. This Pillar recommends minimum capital
obligations for market risk, operation risk and credit risk. The value of total
capital ratio to risk weighted is determined to 8%. In addition, this ratio has the
same result with the Basel Accord I, but the only difference is the modified
alternatives for measuring risk-weighted assets.
 Pillar 2: Supervisory Review. Managers are involved to certify that all the
capital essential requirements, standard procedures and schemes are similarly
structured in banks to determine the capital requirements. Moreover, the
supervisor in Australian Prudential Regulatory Authority (APRA) initiates
general discussion with bank manager, and confirms that systems are utilized
in practice.
 Pillar 3: Market Discipline. Those achieves the possibility to highlight capital
regulation and alternative endeavors, delivers relative safety to financial
systems and banks. In addition, banks are required to expose their risks and
systems specifically
The Basel II gratefully acknowledges the outstanding position of Value at Risk as a
standard risk measurement and capital estimation. In particular, with the appearance of
Basel II, VaR approach can clearly distinguish the different of the market risk from the
14


credit and other risks. Moreover, market VaR methodology has become very meaningful
to banks to estimate the daily basis with the Basel requirement. This considerable benefit
banks can clarify a reduced capital requirement.
2.1.1.1. Categories of risk
Total capital requirements contain the sum of the capital that is required for the
following risks:
Market Risk, also known of as “systematic risk” that is originated from elements
influencing a large indefinite number of assets in the entire market. Besides, the risk of loss
initiated from the opposite trend in market factors there are four different kinds of market
risk: foreign exchange risk, interest rate risk, equity price risk and commodity price risk.
The value of market risk for capital charge can be measured by utilizing the Regulator’s
standard method or employing the internal model method. Hogan et al (2004) demonstrated
the great advantage of utilizing internal models as the standard method to produce extra
outstanding qualities for the capital charge. Moreover, market risk is also measured by
using the Value at Risk (VaR) method.
Operational Risk is not the formal section of Basel I. This encloses processing risks,
procedural risks and transactional risks. In addition, Banks may deal with these future
scenarios by utilizing either standardized method or Internal Ratings Based (IRB) method.
Moreover, the standardized method includes segmentation of the common enterprise along
typical lines of business after that determining beta for each line, regulator measures the
beta and that beta function is represented for whole industry. By contrast, with IRB method
that bank with highly complex and advanced systems may be obtainable. In addition,
Operational risk can be estimated based on past plans and experience by bank.
Credit Risk refers to the risk that is determined on a credit requirement from the
default. It naturally arises due to the expectation of the borrowers, who desire to pay current
debt by utilizing future cash flow. It is completely impossible to certify that borrowers will
reimburse their debts. A reward of investor, which is originated from the interest payments
for debt obligation of borrower, is assuming credit risk. In addition, this research aims to
emphasize on credit risk, which has attracted great attention from academia, investment
bankers, and policymakers.
15


2.1.2. Value at Risk
2.1.2.1. Introduction
Following

the

introduction

of

RiskMetrics

Technical

paper

by

J.P.

Morgan in 1994 and updated information by J.P. Morgan & Reuters (1996) reveal that
Value at Risk (VaR) approach is a well-known and widely employed metric for estimating
the risk in recent years. VaR is significantly different to other approaches. Harper (2004)
demonstrated that VaR based on the historical information to calculate the potential losses
in the future over the given time period (day or month) at a given confidential level
(typically 95% or 99%).
For instance, the expectation of a portfolio that may lose no more than $1 million,
with 95% confidence level of the time (30 days) has a Value at Risk of $1 million. The
negative aspect is that 5% of the period time or 1 day out of 30, the portfolio could lose at
least $1 million. VaR is also utilized for estimating the governing capital investment.
Moreover, one of the most great advantages of VaR is it may compile several both related
risks and unrelated risks into general method that is expressed in currency terms of an
enterprise or portfolio.
In particular, VaR may be estimated by three methods: The Historical method, the
Monte Carlo simulation and the Variance-Covariance method (or correlation or parametric
method)
2.1.2.2. The Historical method
The historical approach that collects actual historical losses in portfolio from top
(best) to bottom (worse) after that estimating the VaR value based on the assumption of
history information tends to be occurred repeatedly. Harper (2004) denotes the QQQ began
to trade in Mar 1990, the big data from QQQ, which is collected and calculated by daily,
will show in bar chart on Figure 1 to compare and analysis.

16


Figure 1

Distribution of daily returns of NASDAQ 100 – Ticker: QQQ

Source: Investopia (2016)
The red bars spreading out, from -4% to -8%. It describes the highest amount of daily
loss will not over 4% with 95% level of confidence. Moreover, if the investors uses $1000
to invest, they expect that their will loss not higher than $40.
VaR may not calculate the absolute value, instead of estimating the probabilistic
value for the portfolio. In addition, when raising the level of confidence to 99%, the interval
from -7% to -8% will be represented for the daily returns at 1%. If the investor uses $1000
to invest, they expect that their will loss not higher than $70 with 99% level of confidence.
2.1.2.3. The Monte Carlo simulation
The Monte Carlo Simulation refers to approach that randomly creates experiments.
In addition, a random number generates the changes of portfolio value to particular
simulation conducting the Monte Carlo simulation. However, the results for particular
conduct will provide the dissimilar value despise of the small differences among values.
The result conducted 100 trials of monthly returns for QQQ that will show into a bar chart.

17


Figure 2

Monte Carlo simulation 100 random trials

Source: Investopia (2016)
According to the statistics on Figure 2, there are two results in the range from -15%
to -20% and three results in the range from -20% to -25%. This outcome reveals the worst
five results (that complies the worst 5%) may be less than -15%. Therefore, the Monte
Carlo tends to provide the VaR-type conclusion: the loss expectation during given month
for the QQQ not excess than 15% with 95% level of confidence.
2.1.2.4. The Variance-Covariance method
The returns, which are normally distributed; the correlations between risk factors are
the essential requirements for assumption of this approach. Specifically, the VarianceCovariance method requires two important factors to calculate the VaR for an asset: the
mean and a standard deviation that allow sketching the distribution curve.

18


Figure 3

Distribution of daily returns of NASDAQ 100 – Ticker: QQQ

Source: Investopia (2016)
The actual daily standard deviation for QQQ is 2.64% based on the blue curve on
Figure 3. After that, using standard distribution tables by Statsoft Inc (2003) to obtain the
value of the “worst” 5% and 1%. Obviously, the results can be achieved by plugging the
standard deviation into the formulas below:
 95% confidence = -1.645 x 𝜎 = -1.645 x 2.64% = 0.043
 99% confidence = -2.326 x 𝜎 = -2.326 x 2.64% = 0.061
If investing $1 million, then VaR at 95% confidential level = $ 0.43m. VaR at 99%
level of confidence = $ 0.061m.
Moreover, J.P. Morgan & Reuters (1996) indicate and popularize the VaR and the
method to estimate VaR by the following function:
𝑃𝑡
ln (
)
𝑃𝑡−1
The logarithm of the proportion of price (current price and previous price) complies
with the normal distribution assumption to deal with the financial time series observations.
On the low side, zero tends to bound in the lognormal distribution. Choudhry (2004)
reveals the appropriateness of lognormal distribution for estimating financial time series
observations including extreme negative values (values that cannot be practically observed
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with share prices).
2.1.2.5. Comparison of VaR Methodologies
Among these methodologies, this is remained the question for VaR methodologies:
“which method is best?” As Linsmeier and Pearson (2000) indicated that it is not easy to
find out a satisfied answer for that complicated question. Each method differs in ability to
measure and capture the risk of different scenarios. The best choice may be determined by
risk managers for their organization and evaluation. Table 1 will discuss how the three
methods differ depending on precise dimensions.
Table 1

Comparison of VaR methods

Attribute

Is it able to measure the

Historical method

Yes

The Variance-

The Monte Carlo

Covariance method

simulation

No, except for short

risk including option in

holding

period

the portfolio?

with limited option in

Yes

time

the portfolio
Is it easy to apply?

Yes if the past data are

Depending

on

the

Extremely difficult to

readily available

complexity

of

the

implement

instruments and data
Are the computations

Yes

Yes

No

Yes

No

No

achieved quickly?
Is it easy to explain with
managers?

In sum, VaR may be estimated by three methods. However, this thesis tends to utilize
two methods: The Historical and Variance-Covariance method. It is because Historical
method has the same characteristics with Monte Carlo simulation, the key difference in the
step of the algorithm 3 (Historical method uses the historical data, Monte Carlo will
generate randomly number to measure). Moreover, Glasserman, Heidelberger and

3

http://financetrain.com/calculating-var-using-monte-carlo-simulation/

20


Shahabuddin (2000) argued that the estimation of VaR for Big Data (huge portfolios) faces
a tradeoff between speed and accuracy. Hence, Monte Carlo simulation spends much time
to operate and too slow to be practical.
2.1.2.6. Limitations of VaR
Although VaR has a number of advantages, this approach remains the majority of
argument and is accused of providing the considerable loss in both the pre- and postfinancial crisis. In addition, Artzner et al. (1999) demonstrated that VaR is not an
appropriate “coherent” approach of risk because it do not satisfy the following axioms:
In specific, the loss is not only represented by random variable X and Y, but also
𝑐 𝜖 ℝ that is a scalar. In addition, 𝜌 is a risk function, i.e. it demonstrates the random
variable X (or Y) to ℝ. Moreover, the risk is associated with X (or Y).
 Monotonicity reveals that a lower loss asset will produce a lower risk measure.
A risk measure 𝜌 is monotone:
𝑋 ≤ 𝑌 ⇒ 𝜌(𝑋) ≤ 𝜌(𝑌)
 Translation Equivariance demonstrates that if adding more one additional risk,
it may generate more risk and more constant to random variable in order to
stability in its variability. A risk is measured by 𝜌:
𝜌(𝑋 + 𝑐) = 𝜌(𝑋) + 𝑐
 Subadditivity shows that combine of two positions, which risk is not equal or
greater than the sum of the individuals. A risk measure 𝜌:
𝜌(𝑋 + 𝑌) ≤ 𝜌(𝑋) + 𝜌(𝑌)
 Positive Homogeneity mentions that doubling an asset should lead to double
risk. A risk measure 𝜌 is positive homogeneous, if for all X, 𝜆 ≥ 0:
𝜌(𝜆𝑋) = 𝜆𝜌(𝑋)
In this respect, VaR is not a subadditive approach. Result of VaR values when
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