INTRODUCTION
Problem statement
The Association of Southeast Asian Nations (ASEAN) is a regional organization founded on August 8, 1967, by Indonesia, Malaysia, the Philippines, Singapore, and Thailand, and has since expanded to include Brunei, Cambodia, Laos, Myanmar, and Vietnam ASEAN aims to promote inter-governmental cooperation, economic integration, and social progress among its ten member nations while ensuring regional stability and peaceful conflict resolution Over the years, ASEAN has deepened its integration, particularly in economic aspects, by removing most tariffs to facilitate the flow of goods and services among its members.
The establishment of the ASEAN Economic Community (AEC) in December 2015 marked a significant milestone in regional economic integration, creating a vast market valued at $2.6 trillion and encompassing over 622 million people By adopting a 'smallest common denominator' approach that prioritizes harmonious relations and national sovereignty, ASEAN countries have fostered trade through ambitious economic treaties and free-trade agreements As of 2014, the AEC emerged as the third largest economy in Asia and the seventh largest globally, highlighting its growing importance in the world economy.
Economic integration within ASEAN presents both opportunities and challenges for its member countries While it can foster growth and collaboration, the diverse economic and cultural backgrounds of these nations may lead to increased implementation costs Balancing these factors is essential for the success of the organization.
The ASEAN region exhibits varied patterns of economic growth, with most countries classified as low-middle income, while Singapore and Brunei enjoy stronger economic positions Post-AEC integration, existing income inequality may widen, exacerbated by high inflation rates in certain nations This disparity can lead to differing price levels and purchasing power among member states, enabling some countries to acquire more goods from others Additionally, varying inflation rates may influence investment levels, as different monetary policy responses could adversely affect certain sectors and industries Consequently, workers from less economically stable countries might seek opportunities in more prosperous ASEAN members.
ASEAN economies exhibit significant disparities in development, with high-saving nations like Brunei, Malaysia, and Singapore contrasting sharply with low-saving countries such as Cambodia, Laos, and the Philippines A December 2015 survey by the American Chamber of Commerce in Singapore revealed that multinational companies are motivated to expand in the ASEAN region due to various "pull factors," including the market's attractiveness and a relatively low level of political, corruption, and security risks (Asian Development Bank, 2016).
Vietnam is poised to become a young Tiger in Asia over the next decade, thanks to its stable economic development alongside other member countries This growth has led to a significant increase in foreign individual investors and multinational corporations entering the Vietnamese market over the past two decades The rising foreign capital inflow signals the attractiveness of the Vietnamese economy and its financial market For new investors, obtaining information to guide their investment decisions is crucial, as assessing risk in relation to expected returns is essential for successful investing.
In the context of the Vietnamese financial market, all industries are relevant for investment considerations, highlighting the need for effective risk measurement to guide investors.
The establishment of the ASEAN Economic Community (AEC) poses a significant threat to various industries in Vietnam, as the country and its ASEAN counterparts exhibit comparable strengths in certain sectors Therefore, it is crucial to assess and evaluate the risks faced by key industries in Vietnam to offer timely recommendations for policymakers.
In light of the opportunities and challenges presented by the establishment of the ASEAN Economic Community (AEC) in December 2015, as well as potential economic agreements like the Trans-Pacific Partnership (TPP) under the new U.S administration, this study titled "Measuring Market Risk for ASEAN: A Value-at-Risk Approach" aims to assess market risks in the region.
Research objectives
This study is conducted in order to achieve the following two key objectives:
This study aims to assess the relative market risk levels across various industries in selected ASEAN countries, specifically Vietnam, Thailand, Singapore, and Malaysia Utilizing advanced techniques such as Value at Risk (VaR) and Conditional Value at Risk (CVaR), the analysis focuses on publicly available data spanning approximately 10 years to provide a comprehensive understanding of market dynamics in the international financial landscape.
In the capital asset pricing model, conventional market risk, referred to as Beta, is estimated through quantile regression These estimates are subsequently analyzed alongside the relative risk levels of key industries, which are derived from Value at Risk (VaR) and Conditional Value at Risk (CVaR) techniques.
Research questions
In order to achieve the above mentioned objectives, the following research questions have been raised:
How substantial does the level of the market risk change between the periods of pre-crisis and post-crisis in the 2008/2009 global financial crisis using VaR and CVaR?
What are the currently prevailing levels of the market risk for all industries in selected countries in the ASEAN, being Vietnam, Thailand, Singapore, and Malaysia?
Whether or not the market risk level of all industries obtained from the VaR and CVaR techniques and the conventional Beta are consistent?
Contribution of thesis
Since the 1950s, when Harry Markowitz pioneered risk management, the field has evolved significantly, now recognized as a distinct subfield of finance Effective risk management emphasizes qualitative and organizational aspects, including sound judgment and an understanding of potential pitfalls and market history This study aims to measure market risks using innovative approaches like Value at Risk (VaR) and Conditional Value at Risk (CVaR), which offer key contributions to the discipline.
The adoption of Value at Risk (VaR) globally has led to its application in Vietnam's securities market, where it is calculated for ten industries over a decade Additionally, Conditional Value at Risk (CVaR), an extension of VaR, is also computed for these industries The findings from this study will provide empirical evidence to assist the Vietnamese Government in optimizing privatization and equitization efforts Furthermore, these results offer historical insights that can aid investors in making informed investment decisions.
Second, this study use conventional Beta as a critical factor The values of
The comparison of Value at Risk (VaR) and Conditional Value at Risk (CVaR) with Betas will determine their consistency, providing valuable insights for investors This analysis serves as a guide for utilizing risk measurement techniques effectively, aiding investors in making informed investment decisions.
This study highlights the need for new risk measurement approaches in Vietnam, as traditional methods may not capture all significant factors By addressing this gap, the research opens avenues for further investigation in the field.
Structure of thesis
This study is constructed as follows The first chapter is Introduction Chapter
This article summarizes existing literature on risk measurement, focusing on Value at Risk (VaR) and Conditional Value at Risk (CVaR), while also reviewing relevant empirical studies Chapter 3 details the data description, research methods, and models used in the analysis Chapter 4 presents the empirical results, and Chapter 5 concludes with a summary of the main findings and discusses implications derived from the results.
LITERATURE REVIEW
Theoretical
This elective section addresses a fundamental aspect of finance: risk management In various activities, risk is an inherent factor due to uncertain outcomes Consequently, a significant part of finance involves the responsibilities of financial specialists and the operations within financial departments, focusing on effectively managing, controlling, and capitalizing on risk.
The term "risk" is complex and encompasses various interpretations related to financial outcomes, often associated with uncertainty, randomness, and probability While it can refer to both positive and negative outcomes, there is no universally accepted definition of risk that fits all contexts As highlighted by Apostolik (2015), common definitions of risk include the likelihood of an undesirable event occurring, the potential loss from an unexpected incident, the probability of unfavorable results, and the impact of adverse outcomes.
Jordio (2007) defined risk can be as the volatility of unexpected outcomes, generally the value of assets or liabilities of interest
Firms face various risks, categorized as business and nonbusiness risks Business risks are voluntarily undertaken by corporations to gain competitive advantages and enhance shareholder value These risks encompass factors related to the product market, including technological innovations, product design, and marketing strategies Additionally, firms are exposed to macroeconomic risks stemming from economic cycles and fluctuations in income and monetary policies Conversely, nonbusiness risks are those beyond a firm's control.
Nonbusiness risks encompass various challenges, including strategic risk stemming from significant changes in the economy or political landscape, which are hard to mitigate without diversifying across different business sectors and countries Additionally, financial risks involve potential losses in financial markets, such as those caused by fluctuating interest rates or defaults on financial commitments By carefully optimizing their exposure to financial risks, firms can focus on effectively managing their business-related risks.
This study focuses on measuring market risk, which refers to the potential for loss or gain due to unexpected changes in market prices or rates Market risk encompasses various types, including interest rate risk, equity risk, exchange rate risk, and commodity price risk, each defined by specific risk factors Additionally, market risk is distinct from other financial risks, such as credit risk and operational risk.
There are several techniques of market risk measurement have developed over years However, this study delineate three objective tools that are used
Value at Risk is probably the most widely used risk measure in finance It has become the classic measurement that financial executives use to quantify market risk
In 1988, the Basel I Capital Accord marked a significant advancement in establishing risk-based capital adequacy requirements, focusing on minimum regulatory capital for credit risk among members of the Basel Committee on Banking Supervision (BCBS) Credit risk entails the potential loss when borrowers fail to meet their financial obligations to banks Regulatory capital, as defined by the Capital Accord, serves to ensure that banks maintain sufficient resources to absorb unexpected losses across their operations, thereby enhancing financial stability.
In January 2001, the Basel Committee on Banking Supervision (BCBS) introduced the Basel II Capital Accord, which succeeded the original Basel I Capital Accord Basel II enhances its predecessor by allowing banks greater flexibility in determining the necessary capital reserves based on their specific risk exposures Additionally, it emphasizes the stability and reliability of the international financial system and promotes advancements in risk management practices.
The Basel I Capital Accord primarily emphasized minimum regulatory capital requirements, while the Basel II Capital Accord expands this scope by introducing a comprehensive supervisory framework known as the "three pillars."
- Pillar 1 - Minimal regulatory capital requirements;
- Pillar 2 - Supervisory review of capital adequacy;
- Pillar 3 - Market discipline and disclosure;
This paper primarily examines the measurement of credit risk, as detailed in Pillar 1 The section on credit risk measurement provides a concise overview of the key concepts outlined within the various Pillars.
Source: Bank of International Settlement
Figure 2.1 Three pillars of Basel II
Pillar 1 - Minimum Regulatory Capital Requirements
For the first pillar of the Basel II Capital Accord the Basel Committee proposed capital requirements associated with three categories of risk:
Market risk refers to the potential decline in the value of an investment caused by fluctuations in market factors Under the Basel II Capital Accord, market risk can be assessed using two primary methods: the Standardized Approach and the Internal Models Approach.
Operational risk, as defined by Basel II, refers to the potential loss arising from insufficient or failed internal processes, personnel, systems, or external events To assess operational risk, three primary methods are employed: the Basic Indicator Approach, the Standardized Approach, and the Advanced Measurement Approach.
Credit risk refers to the potential loss incurred when borrowers fail to meet their financial obligations to a bank To assess credit risk, several methods can be employed, including the Standardized Approach, the Foundation Internal Rating Based Approach, and the Advanced Rating Based Approach The Standardized Approach enhances risk sensitivity compared to the previous Basel I framework, while the two Internal Rating Based (IRB) approaches leverage banks' internal risk ratings, offering a significantly higher level of risk sensitivity.
Pillar 2 - Supervisory review of capital adequacy
The second pillar of Basel II focuses on the supervisory review of capital adequacy, requiring national supervisors to ensure that banks establish an internal capital assessment process aligned with their risk profiles It emphasizes the importance of banks' management in developing effective risk management techniques for capital management Additionally, supervisors are tasked with evaluating the effectiveness of banks' capital adequacy assessments.
In the Netherlands, the Dutch Central Bank (De Nederlandsche Bank or DNB) serves as the supervisor overseeing the internal processes of banks, ensuring they align with necessary risk management standards and are subject to thorough review and intervention.
Pillar 3 - Market discipline and disclosure
The third pillar of the Basel II Capital Accord focuses on market discipline and transparency through enhanced disclosure Its primary objective is to foster improved financial reporting related to risks, enabling market participants to gain a clearer insight into banks' risk profiles and the sufficiency of their capital positions.
Empirical studies
This section will present in turn the empirical studies related to VaR, CVaR and conventional Beta,
In recent decades, risk modeling has become an essential component of global wealth management, with Value at Risk (VaR) emerging as a popular method for assessing portfolio risk (Hsu et al.).
Previous research indicates that correlations in financial markets are asymmetric, differing between downside and upside movements Additionally, the tails of return distributions exhibit fatter characteristics compared to normal distributions, as highlighted by Ang and Chen (2011).
(2002), Boyer et al (1999), Kolari et al (2008), Longin and Solnil (2001)
Recent advancements in trading technology have made high-frequency data widely accessible, leading to the emergence of a new group of active market participants, notably high-frequency traders These traders are characterized by their very short investment horizons and their dependence on tools for measuring market risk High-frequency data, which includes intraday market information such as transaction prices, bid-ask prices, and intraday trading volume, has been the focus of research for over a decade, with early studies primarily examining exchange rates, as seen in the works of Zou (1996), Taylor and Xu (1997), and Beltratti and Morana.
Recent studies on equity data, such as those by Adresen et al (2001a), Giot and Laurent (2004), and Fuertes et al (2009), have primarily focused on calculating daily risk measures with a time horizon of less than one day.
Halleib and Pohleier (2012) conducted an empirical study on the Value at Risk (VaR) method, questioning the significance of market capitalization Their research extends beyond this inquiry, examining the performance of various VaR models and distributional assumptions across different contexts.
22 estimation time windows Although within a complex study, the author found evidence that market capitalization in important for VaR estimation
Hsu et al (2011) conducted a study to evaluate portfolio risk in six Asian markets—Indonesia, Korea, Malaysia, Singapore, Taiwan, and Thailand—by integrating extreme value theory with traditional Monte Carlo Value at Risk (VaR) simulation Their research began by examining the relationship between stock returns and fluctuations in currency value, providing insights into the dynamics of international portfolio investments.
The continuous rate of return of a portfolio at time t, denoted as \( r_{p,t} \), is calculated using the formula \( r_{p,t} = r_{i,t} + r_{e,t} \), where \( r_{i,t} \) represents the stock index return in local currency and \( r_{e,t} \) indicates the change in the American terms foreign currency exchange rate, which is the price of one unit of foreign currency in US dollars This mathematical representation helps in understanding the relationship between portfolio returns, stock index performance, and currency exchange fluctuations, thereby providing insights into Value at Risk (VaR) calculations.
The Value at Risk (VaR) is defined as the infimum of the set of returns \( r \in R \) such that the probability \( P(R_p \geq VaR) = \alpha \), where \( R_p \) represents a sequence of portfolio negative returns over time periods \( t, t-1, t-2, \ldots, t-h \) The analysis indicates that the selected countries exhibit a positive yet weak correlation between stock index returns and fluctuations in currency values Furthermore, variations in foreign exchange rate policies and the extent of government intervention significantly influence the distribution and tail dependence across different nations.
In their 2004 study, Huang and Lin analyzed the forecasting performance of three Value at Risk models, focusing on two potential sources of performance enhancement: asymmetry in conditional variance and fat-tailed distributions They evaluated the models' accuracy and efficiency using various performance measures, utilizing daily SGX-DT and TAIFEX Taiwan stock index futures prices from May 7, 2004.
1998 to January 31, 2002 Overall, the findings had implications for investors, financial institutions, and futures exchanges
In the financial sector, Value-at-Risk (VaR) is the leading risk measure employed by institutions to assess and manage market risk, a primary focus for regulators and internal risk controllers Despite its popularity, VaR faces criticism for its inconsistencies and lack of coherence, as highlighted by Artzner et al (1999) and Acerbi and Tasche (2002) Additionally, VaR fails to account for the statistical properties of significant losses beyond its threshold, known as tail risk To address these limitations, Conditional Value-at-Risk (CVaR) has emerged as a more robust alternative risk measure.
Conditional Value-at-Risk (CVaR), also known as tail conditional expectation, was introduced by Artzner et al in 1997, with further developments in its coherence by Inui and Kijima in 2005 Research by Yamai and Yoshiba from 2002 to 2005 explored various applications of CVaR Additionally, Pattarathammas et al (2008) focused on estimating both Value-at-Risk (VaR) and CVaR using nine different models applied to ten historical series of Asian Index log returns from November 1, 1996, to December 31, 2007 Furthermore, the relevance of CVaR has been increasing within the insurance industry, as noted by Embrechts et al.
(1997) Bucay and Rosen (1999) used CVaR in credit risk evaluations A case study on application of the CVaR methodology to credit risk was described by Anderson and Urysev (1999)
In his 2015 study, Powell examined the extreme credit and market risk associated with the Australian mining industry, utilizing Value at Risk (VaR) as a key risk measurement tool To effectively assess tail risk, he also incorporated Conditional Value at Risk (CVaR) into his analysis The research compared mining entities to the broader market, including the 500 largest companies by market capitalization, during the global financial crisis from 2007 to 2009 The findings revealed that the market risk for mining shares, as indicated by both VaR and CVaR, was significantly higher than that of the overall market.
Numerous studies have sought to evaluate the implications of the Capital Asset Pricing Model (CAPM) by analyzing historical rates of return on securities alongside the market index Among the most notable research efforts, Lintner's 1965 study stands out, as highlighted by Diacogiannis (1994).
24 whose study was reproduced by Douglas (1968), Jacob (1971), Miller and Scholes
(1972), and Black, Jensen and Scholes (1972), whose methodology has been adopted for the empirical testing of CAPM in ASE, Blume and Friend (1973), and Fama and MacBeth (1973)
Numerous tests of the Capital Asset Pricing Model (CAPM) have focused on the relationship between average asset returns and their betas across various time intervals Initial assessments by Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) utilized a two-stage procedure to analyze this relationship Specifically, Black, Jensen, and Scholes estimated betas from monthly returns of NYSE stocks during the 1926-1930 period, using an equally weighted portfolio of all NYSE stocks Their results indicated that the CAPM did not hold true for the examined period.
Fama and MacBeth (1973) also estimated monthly market returns for all NYSE stocks over 1926-1929, and then they ranked all stocks by beta and formed
In their analysis of 20 portfolios from 1930 to 1934, researchers calculated average returns and betas similarly to Black, Jensen, and Scholes They used these betas to forecast portfolio returns for the period from 1935 to 1938 The findings revealed that the beta coefficient was statistically insignificant and remained low across various sub-periods Additionally, the study indicated that residual risk did not impact security returns, with intercepts significantly exceeding the risk-free rate, suggesting that the Capital Asset Pricing Model (CAPM) was not validated.
Though initial empirical studies support the CAPM (Fama and MacBeth
RESEARCH METHODOLOGY AND DATA
Data
This study analyzes daily data from listed companies in the stock markets of four ASEAN countries—Vietnam, Thailand, Malaysia, and Singapore—over a 16-year period from 2000 to 2015 This timeframe encompasses a variety of economic conditions that are anticipated to influence different industries in unique ways The selection of these countries is based on the availability of relevant data throughout the research period, ensuring comprehensive coverage for the analysis.
Data from Bloomberg indicates that economic activities can be categorized into 11 distinct sectors according to the Global Industry Classification Standard These sectors are Energy, Materials, Industrials, Consumer Discretionary, Consumer Staples, Healthcare, Financials, Information Technology, Telecommunication Services, Utilities, and Real Estate.
Commercial and Professional services Transportation
25 Consumer Discretionary Automobile and Component
Consumer Durables & Apparel Consumer Services
30 Consumer Staples Food & Staples Retailing
Food, Beverage & Tobacco Household & Personal Products
35 Health Care Health Care Equipment & Services
45 Information Technology Technology Hardware & Equipment
The table below summaries the numbers of firms which are selected to measure and estimate the market risk.
Table 3 Daily market price movements in 4 countries (Vietnam, Malaysia, Singapore and Thailand)
No of firms Max (%) Min (%) Aver (%) S.D (%) No of firms Max (%) Min (%) Aver (%) S.D (%)
No of firms Max (%) Min (%) Aver (%) S.D (%) No of firms Max (%) Min (%) Aver (%) S.D (%)
Research methodology – the Models
To address research objectives, following three models/methods are to be considered and proposed to be utilized in this study
This study will utilize the two most popular approaches for estimating Value at Risk (VaR): the Variance-Covariance method and the Historical method.
The equation Pr[∆P ∆t ≤ VaR] = π indicates that the probability π represents the likelihood of a portfolio experiencing a market value change (∆P) over a specific time horizon (∆t) that meets or exceeds the defined Value at Risk (VaR) In other words, this equation quantifies the risk of incurring losses that are equal to or greater than the VaR threshold, occurring with the given probability π.
Second, the estimates of the market risk using the CVaR techniques which can be expressed in the following formula:
𝐶𝑉𝑎𝑅 𝛼 = 𝐸(𝛿𝑃|𝛿𝑃 ≥ 𝑉𝑎𝑅 𝛼 ) where α is the left tail percentage of the distribution, δP is the absolute value of negative return of P
Quantile regression, a method introduced by Koenker, will be employed to estimate conventional beta values Additionally, other relevant econometric techniques may be explored and utilized throughout the course of this study, ensuring a comprehensive analysis.
Basset Jr (1978), the estimator can be found with following minimization function:
∀𝜏 ∈ (0,1) where the individual return R it and the market return R mt for t = 1, …,n; and the τ–th quantile regression coefficients, ατ and βτ
Measures of correlation between variables are important to practitioners interested in reducing their risk exposure through diversifying their portfolios
Correlation is a measure of the degree to which a value of one variable is related to
The correlation coefficient is a numerical measure that assesses the strength and direction of the relationship between the values of two instruments It ranges from -1 to +1, with the sign indicating the direction of movement and the absolute value reflecting the strength of that movement For instance, a correlation coefficient of 0.5 suggests that one instrument moves in the same direction as the other, but only by half the magnitude of its movement.
A value of zero means that the instruments are uncorrelated, and their movements are independent of each other
Correlation plays a crucial role in various Value at Risk (VaR) models, particularly in parametric models, as it significantly impacts the measurement of a portfolio's variance and volatility For instance, in a simple two-asset portfolio, the overall volatility can be calculated using the individual volatilities of each asset (x and y) and their correlation The formula is expressed as σ port = √(σ x² + σ y² + 2σ x σ y ρ), where σ x represents the volatility of asset x Understanding this relationship is essential for effective risk management in investment portfolios.
𝜎 𝑦 is the volatility of the asset y
The correlation coefficient between two assets uses the covariance between the assets in its calculation The standard formula for covariance is shown below:
The covariance is calculated by taking the sum of the distances of each return value, x and y, from their mean, and dividing this sum by the number of observations minus one This calculation is essential for determining the correlation coefficient.
𝜎 𝑥 𝜎 𝑦 where σ is the standard deviation of each asset
The correlation equation can be extended to encompass multiple instruments, as correlations are typically derived from historical data This factor is crucial when constructing and analyzing a portfolio, since the risks involved are influenced by the correlations among its components.
A positive correlation among assets in a portfolio heightens risk, as significant movements in one asset are likely mirrored by others, leading to a wider and flatter distribution of returns with increased probabilities of extreme gains or losses Conversely, a negative correlation suggests that assets tend to move in opposite directions, effectively mitigating risk.
In extreme situations like market crashes or significant corrections, asset correlations may lose their relevance as all assets tend to move in the same direction Nevertheless, in typical market conditions, utilizing correlations to mitigate portfolio risk is regarded as a sound strategy, leading to a lower Value at Risk (VaR) for diversified portfolios compared to undiversified ones.
While the concept of Value at Risk (VaR) is straightforward, its implementation can be challenging This section outlines the key steps involved in calculating VaR effectively.
To determine the Value at Risk (VaR) for an individual asset, one can calculate the standard deviation of its returns, utilizing either historical or implied volatility For a 95% confidence level, which corresponds to 5% of observations falling in the left tail of the normal distribution, the relevant data points are situated 1.65 standard deviations from the mean.
Assume that we have two-asset portfolio with some given information as follows:
Current market price per unit $50 $100
Historical volatility 1.00% (daily) 2.00% (daily) And we determine the market risk for above portfolio, using criteria 99% confidence level (or 2.33 as standard deviation for 01 day) and a holding period of
The number 2.33 represents the standard deviation corresponding to a 99% confidence level, while the multiplication factor for a 10-day holding period is √10 For a one-year holding period, the appropriate multiplication factor is √252, reflecting the 252 trading days in a year.
In a two-asset portfolio, we can analyze the relationship that allows us to calculate its volatility, which is essential for determining the Value at Risk (VaR) This calculation is crucial for understanding the potential risk associated with the portfolio's returns.
VaR port = √𝑤 1 2 𝜎 1 2 + 𝑤 2 2 𝜎 2 2 + 2𝑤 1 𝑤 2 𝜎 1 𝜎 2 𝜌 1,2 where w 1 is the weighting of the first asset w 2 is the weighting of the second asset
𝜎 1 is the standard deviation or volatility of the first asset
𝜎 2 is the standard deviation or volatility of the second asset
𝜌 1,2 is the correlation coefficient between the two assets
Value at Risk (VaR) is a straightforward concept that focuses on measuring the volatility of individual assets and the correlation between them using historical data In a portfolio with numerous positions, understanding that the risk of an asset is determined not just by its individual standard deviation but by its contribution to the overall portfolio risk is crucial An asset may appear risky on its own, yet if its returns correlate positively with other assets in the portfolio, it may not increase the overall risk Therefore, the impact of a new asset on portfolio risk is primarily influenced by its correlation or covariance with existing assets.
Matrices Variance-Covariance Value at Risk
In the previous section, how VaR could be calculated for a two-asseet portfolio Here, the illustration of how this is done using matrices
Consider the following hypothetical portfolio, invested in two assets, as shown as below
The standard deviation of each asset is determined through historical observations of asset returns, calculated by taking the ratio of closing prices Using standard statistical formulas, both the mean and standard deviation of these returns are derived, providing essential insights into asset performance.
Hypothesis
In consistence with the research objectives and questions which have previously been discussed, the following research hypotheses have been developed:
H1: Similar levels of market risk exhibited by key industries in selected
ASEAN countries during the research period using VaR rankings of each model
H2: There is an association between undiversified VaR and diversified
H3: There is an association between VaR and CVaR rankings within each model
H4: There is an association between historical and parametric CVaR rankings at industry level
H5: There is an association between undiversified CVaR and diversified
Parametric tests are utilized primarily for large datasets, focusing on statistical measures like means and standard deviation, and are based on the assumption that the observations come from a normally distributed population.
Nonparametric tests are ideal for smaller datasets as they do not rely on assumptions about data distribution These tests focus on rankings instead of specific statistics like means and standard deviations, making them a suitable choice for analyzing non-normally distributed data.
In this study, nonparametric tests are used for two main reasons discussed below:
The data size is relatively small, as we have only 11 data points for each model, representing the Value at Risk (VaR) for 11 different industries, which facilitates the comparison of industry VaRs across various models.
Secondly, this study is more concerned with rankings rather than actual data Different models yield very different actual levels of risk and are calculated on a different basis
Siegel and Castellan (1988), Lee et al (2000) showed a range of parametric tests which are considered suitable for the purposes:
The Spearman Ranking Correlation Test is an effective method for comparing two samples using pure rankings, making it ideal for model comparisons This test is applicable for assessing both diversified and undiversified rankings, as well as parametric and nonparametric rankings.
The rank correlation coefficient \( r_s \) quantifies the relationship between two sets of ranked data, with a value of \( r_s = 1 \) indicating perfect correlation and \( r_s = -1 \) representing perfect inverse correlation The formula for calculating \( r_s \) is given by \( r_s = 1 - \frac{6 \sum d^2}{n(n^2 - 1)} \), where \( d \) is the difference in ranks and \( n \) is the number of observations.
To determine the significance of differences in ranks among various industries, the formula 𝑛(𝑛 2 −1) is utilized, where d represents the rank differences and n indicates the number of industries Statisticians, such as Lee et al (2000), employ the Spearman Rank Correlation Test along with a t-test for analysis While Siegal and Castellan (1988) suggest that the t-test may offer slight advantages, they recommend using the more straightforward z-test for ease of interpretation.
√(1−𝑟 𝑠 2 )/(𝑛−2) which has a t distribution with (n-2) degree(s) of freedom
The Krustal-Wallis Test tests variance of rankings where more than 2 populations are involved This is considered for comparison between the 3 rolling window periods
Using the methodology outlined by Lee et al (2000) and Siegel and Castellan
(1988), the test statistic K compares variations in ranking means:
𝑐 𝑖=1 ) − 3(𝑛 + 1) where ni = the number of observation in the ith sample n = n1+n2+n…+nc = total number of observations in the c samples
Ri = sum of the ranks for ith sample
RESEARCH RESULTS AND DICUSSION
VaR and CVaR
The results are presented in the tables below, illustrating both diversified and undiversified approaches The undiversified method calculates the weighted average of the Value at Risk (VaR) for each individual company, while the diversified approach accounts for the correlations among all entities within the industry.
This article provides a comprehensive overview of the study period in Vietnam, summarizing the outcomes through average results displayed in Table 5 It will present both historical and parametric approaches to illustrate the findings effectively.
Table 5 VaR and CVaR summary over 10-year period in Vietnam
Period (2007-2016) VaR and CVaR 95 percent summary over 10 year
Historical Parametric Historical Parametric Historical Parametric Historical Parametric
Note: Rankings are from 10 (lowest risk) to 1 (highest risk) Source: Author’s calculation
The daily Value at Risk (VaR) values for the historical method range from 2.8% to 3.7%, while the parametric method shows a wider range of 2.7% to 5.8% Notably, the variation in historical VaR is less pronounced than that of the parametric method In the historical assessment, Finance and Real Estate exhibit the same risk level, whereas the parametric method indicates a 0.6% difference between these sectors, both categorized as the highest risk industries Interestingly, the historical method ranks Utilities as the highest risk (3.7%), in stark contrast to the parametric method, which places Utilities at the lowest risk level Overall, the absolute value differences between the two methods are relatively minor, with historical VaR at 2.8% and parametric VaR at 2.7%.
The analysis reveals contrasting risk rankings between two approaches The historical method identifies Energy as the highest risk industry, followed by Information Technology and Utilities, while Health Care and Consumer Discretionary are deemed the lowest risk sectors In contrast, the parametric method ranks Real Estate as the highest risk, followed by Finance and Energy, with Health Care, Materials, and Consumer Discretionary occupying the lowest risk quartile throughout the study period.
CVaR consistently exceeds VaR as it focuses on the worst 5% of returns, revealing a different risk profile for industries While historical VaR indicates that the Consumer Discretionary sector has an average risk level, CVaR identifies it as one of the most risky industries This discrepancy arises from the calculation methods of VaR and CVaR, suggesting that the volatility in the Discretionary sector may include outliers with extreme values, significantly impacting the average CVaR.
The historical Conditional Value at Risk (CVaR) results for the Staples Consumer and Information sectors show slight variations compared to Value at Risk (VaR) The line graph below illustrates only the historical estimates, revealing that the findings align closely with those derived from the parametric approach, with the exception of the Information and Health sectors.
Figure 4.1 Historical VaR and CVaR in Vietnam (2007-2016)
The averaged values of Value at Risk (VaR) and Conditional Value at Risk (CVaR) do not fully capture the nuances of Vietnam's financial landscape; therefore, it is essential to analyze these metrics across specific sub-periods for a more comprehensive understanding.
Next, the in- and post-GFC periods are considered The table shows how the top risk industries change during periods and given methods
Table 6 VaR results over periods: in crisis and post-crisis in Vietnam
Period (2007-2016) VaR 95 per cent in GFC period and post-GFC
In GFC period (2007-2009) In post-GFC period (2010-2016)
Historical Parametric Historical Parametric Historical Parametric Historical Parametric
Note: Rankings are from 10 (lowest risk) to 1 (highest risk) Source: Author’s calculation
From 2007 to 2009, the highest risk sectors based on historical Value at Risk (VaR) were Energy, Information Technology, and Finance However, between 2010 and 2016, Utilities emerged as the highest risk sector, with Energy and Information Technology following closely in second and third place, respectively Throughout both periods, Health Care and Consumer Discretionary consistently occupied the lowest risk positions This indicates that the risk levels across these industries have remained stable over the studied time frames, as evidenced by the unchanged rankings.
The comparison of risk rankings between parametric methods and historical approaches reveals both similarities and differences across various sectors Notably, Energy, Information Technology, and Finance consistently rank high in risk, while Consumer Discretionary remains the lowest throughout the analyzed period However, Utilities, which parametric calculations attribute a moderate ranking, is deemed the most risky sector by historical methods Overall, from 2007 to 2016, the relative risk levels among industries appear to be stable over time.
The analysis reveals a significant decrease in the volatility of Value at Risk (VaR) from the 2007-2009 recession period to the 2010-2016 recovery phase During the recession, the stock market's VaR fluctuated between approximately 3% and 8%, while in the subsequent years, it narrowed to a range of about 2% to 5%.
Now we consider the changes in rankings of industries in Vietnam for the GFC period (2007-2009) and the post-GFC period (2010 -2016) under both historical and parametric approaches
Table 7 VaR rankings changes in Vietnam
GFC Change VaR GFC ranking
VaR post- GFC ranking Diff in rank
The figure below will illustrate actual VaR per table 7 This bar indicates the exactly pattern, illustrating the absolute difference between two studying periods
Figure 4.2 VaR rankings shift in Vietnam
Between 2007 and 2016, all sectors experienced a significant decline in market risk levels, with Utilities standing out as a notable case Despite being perceived as the "safe" sector during the Global Financial Crisis (2007-2009), Utilities unexpectedly emerged as the riskiest sector in the subsequent years.
Vietnam - Changes in VaR between GFC and post-GFC
VaR GFC VaR Post-GFC
The analysis of 48 businesses post-GFC reveals that industry rankings are not stable, emphasizing the fluctuating nature of market risk levels across different sectors This underscores the importance of understanding that an industry's position can change relative to others in the market, with no assurance of maintaining or improving its ranking over time.
Table 8 illustrates the changes in market risk rankings for various businesses in Vietnam from the Global Financial Crisis (GFC) to the post-GFC period The analysis reveals that the Conditional Value at Risk (CVaR) indicates a significant reduction in extreme losses across industries during these two periods, while the relative rankings among the industries have remained stable.
Table 8 CVaR rankings changes in Vietnam
CVaR Post-GFC Change CVaR GFC ranking
CVaR post- GFC ranking Diff in rank
The figure below will illustrate actual CVaR per table 8 This bar indicates the exactly pattern, illustrating the absolute difference between the GFC and the post-GFC
Figure 4.3 CVaR rankings shift in Vietnam
Utilities have maintained a consistent performance in terms of Value at Risk (VaR), reflecting notable fluctuations in their rankings Conversely, the Finance sector, once considered the riskiest during the Global Financial Crisis (GFC), has since transformed into a more stable and "safer" investment option in Vietnam's market post-GFC.
The Spearman Rank Correlation test is utilized to assess the correlation between the Global Financial Crisis (GFC) and the subsequent post-GFC period, focusing on the rankings of Value at Risk (VaR) and Conditional Value at Risk (CVaR) The findings of this test will be detailed in section 4.1.4.
In this section, VaR of Malaysia, Singapore and Thailand will be presented as follows
Beta estimation
The tables below present estimated beta values for two study periods From 2007 to 2009, most beta estimates align with the market beta, indicating predominantly positive values This trend is consistent with the findings from the subsequent period of 2010 to 2016, which will be discussed later.
For an overview, most Betas by LAD and OLS estimated are statistically significant and lower than 1 – the market beta When the market return changed by
1 percent, these stock returns would change the same direction with a magnitude of
Energy and Real Estate sectors exhibit betas exceeding 1, indicating that a 1 percent change in market returns results in a more than 1 percent change in their stock returns In contrast, the overall market shows a beta of less than 1 percent.
Among industries, Energy and Real Estate are ranked to be as the highest risky industries, besides Industry This imply is seem to align with conclusion form VaR
In the other hand, Beta estimations show that Consumer Discretionary is one of the
The analysis reveals that industries deemed "safe" exhibit low risk rankings, aligning with the previously discussed Value at Risk (VaR) and Conditional Value at Risk (CVaR) metrics Specifically, the Energy and Real Estate sectors are anticipated to encounter higher levels of risk compared to the overall market.
Finance is often perceived as one of the lowest risk sectors in the market, a viewpoint that contrasts sharply with the findings of Value at Risk (VaR) analysis, which categorizes finance as a high-risk area.
Table 16 Beta estimates Using CAPM (period 2007 – 2009)
Period (2007-2009) Beta estimations in the GFC period
Weighted-Cap Equally-Cap Weighted-Cap Equally-Cap Weighted-Cap Equally-Cap Weighted-Cap Equally-Cap
Note: Rankings are from 10 (lowest risk) to 1 (highest risk) Source: Author’s calculation
Table 17 Beta estimates Using CAPM (period 2010 – 2016)
Period (2010-2016) Beta estimations in the post-GFC period
Weighted-Cap Equally-Cap Weighted-Cap Equally-Cap Weighted-Cap Equally-Cap Weighted-Cap Equally-Cap
Note: Rankings are from 10 (lowest risk) to 1 (highest risk) Source: Author’s calculation
Between 2010 and 2016, equity beta estimates derived from capital-weighted portfolios were significantly higher than those from equally weighted portfolios Energy and Real Estate sectors consistently exhibited the highest beta values, while Utility, Health, and Finance sectors recorded the lowest averages Notably, the negative beta for Utilities indicates that its returns tend to move inversely to market returns.
Comparison in Vietnam
Below is the results obtained by CAPM (quantile regression) and historical VaR in order to compare whether risk level of Vietnamese industries are relatively consistent
Table 18 Comparison between Beta and VaR (period 2007-1016) Comparison between Beta and VaR in the GFC period and the post-GFC period
In the GFC In the post-GFC
Weighted-Cap Equally-Cap Diversified Undiversified Weighted-Cap Equally-Cap Diversified Undiversified
Note: Rankings are from 10 (lowest risk) to 1 (highest risk) Source: Author’s calculation
During the Global Financial Crisis (GFC), both Beta and historical Value at Risk (VaR) identified Consumer Discretionary as one of the least risky sectors Additionally, while Beta indicates Finance as another low-risk industry, VaR categorizes it as highly volatile Conversely, Energy and Real Estate are typically regarded as the highest risk industries.
Between 2010 and 2016, both CAPM and historical VaR indicated that Energy and Real Estate are the highest risk industries, while Health and Consumer Staples rank as the lowest Notably, CAPM classifies Utilities as a low-risk sector, contrasting with its classification as the highest volatility industry by diversified historical VaR and an average risk by the undiversified approach Additionally, Finance is assessed as average risk by VaR, yet CAPM identifies it as low risk Despite these discrepancies, Energy consistently ranks as the highest risk industry in both CAPM and VaR, with Consumer Staples being recognized as the "safest" sector.
The CAPM and VaR methods indicate that the energy sector has the highest risk in the market throughout the study period According to the 2016 Annual Report by Petro Vietnam Group, the industry is grappling with significant challenges, including the impacts of the financial recession on business activities and living standards The sharp rise in essential goods prices, particularly fuel, has led to a decrease in demand as households seek to conserve energy or switch resources Additionally, the entry of new small and medium enterprises has intensified market competition, posing further challenges for retailers aiming to expand nationwide.
In the finance industry, two methods yield contrasting results regarding risk assessment The Capital Asset Pricing Model (CAPM) ranks finance as the lowest sector, while Value at Risk (VaR) indicates that it experienced high risk during the Global Financial Crisis (GFC) but shifted to a "medium" risk classification afterward Conversely, VaR suggests that Consumer Discretionary, Consumer Staples, and Health sectors are relatively "safe" options for risk-averse investors.