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Systemic risk in Taiwan stock market
Her-Jiun Sheu a & Chien-Ling Cheng ba
Department of Banking and Finance , National Chi Nan University , No. 1, University Road, Puli , Nantou County , 54561 , Taiwan
b
Institute of Business and Management , National Chiao Tung University , No. 118 Chung-Hsiao W. Rd., Sec. 1, Chung-Cheng District, Taipei , 100 , Taiwan
Published online: 04 Oct 2012.
To cite this article: Her-Jiun Sheu & Chien-Ling Cheng (2012) Systemic risk in Taiwan stock market, Journal of Business Economics and Management, 13:5, 895-914, DOI: 10.3846/16111699.2011.620168
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ISSN 1611-1699 print / ISSN 2029-4433 online 2012 Volume 13(5): 895–914 doi:10.3846/16111699.2011.620168
SYSTEMIC RISK IN TAIWAN STOCK MARKET
Her-Jiun Sheu1, Chien-Ling Cheng21Department of Banking and Finance, National Chi Nan University, No. 1, University Road, Puli, Nantou County 54561, Taiwan
2Institute of Business and Management, National Chiao Tung University, No. 118 Chung-Hsiao W. Rd., Sec. 1, Chung-Cheng District, Taipei 100, Taiwan E-mails: 1hjsheu@ncnu.edu.tw; 2marscheng@scsb.com.tw (corresponding author)
Received 02 May 2011; accepted 17 August 2011
Abstract. Recent fi nancial crises resulted from systemic risk caused by idiosyncratic distress. In this research, taking Taiwan stock market as an example and collecting data from 2000 to 2010 which contained the 2001 dot-com bubble and the 2007–2009 fi nancial crisis, we adopt the CoVaR model to empirically explore the impact of sector-specifi c idiosyncratic risk on the systemic risk of the system and attempt to investigate the links between fi nancial crises, systemic risk and the idiosyncratic risk of a sector-specifi c anom-aly. The result showed sector-specifi c marginal CoVaR, i.e., CoVaR, perfectly explained Taiwan stock market disturbance during the 2001 dot-com bubble and 2007–2008 fi nan-cial crisis. Thus, by identifying the larger CoVaR sectors, i.e. the systemic importance sectors, and by exploring the risk indicators, independent variables, of these systemic im-portance sectors, investors could practically employ the sector-specifi c CoVaR measure to deepen the systemic risk scrutiny from a macro into a micro prudential perspective. Keywords: value at risk, Conditional VaR, systemic risk, idiosyncratic risk, fi nancial crisis, spill over, systemic importance.
Reference to this paper should be made as follows: Sheu, H.-J.; Cheng, C.-L. 2012. Systemic risk in Taiwan stock market, Journal of Business Economics and Management 13(5): 895–914.
JEL Classifi cation: F47, G01, G10, G15, G21.
1. Introduction
Many fi nancial crises have resulted from systemic risk which is caused by idiosyncratic distress, leading to the crunch of the whole system. The interaction between fi nancial distress and systemic risk due to the effect of idiosyncratic distress has been discussed recently (Fu 2009; Campbell et al. 2008; Ang et al. 2006). Amongst the idiosyncratic distress, sector-specifi c risk, which is caused by a group of interconnected institutions, has been given as the main reason for sudden increases in systemic risk, leading to the formalization of fi nancial crises. In this research, taking Taiwan stock market as an example and collecting data from 2000 to 2010 which contained the 2001 dot-com bubble and the 2007–2009 fi nancial crisis, we adopted the CoVaR model to empirically
explore the impact of sector-specifi c idiosyncratic risk on the systemic risk of the whole fi nancial system and attempt to investigate the links between fi nancial crises, systemic risk, and the idiosyncratic risk of a sector-specifi c anomaly.
International stock market transmission across different markets has been comprehen-sively studied. Many recent studies have discussed the volatility spillover effect of stock market returns. These papers have shown some typical characteristics of the volatil-ity spillover effect among different stock markets (Martens, Poon 2001; Goetzmann et al. 2001; Worthington, Higgs 2004; Michelfelder RA 2005; Scheicher 2001; Bekaert, Harvey 1997; Gokcan 2000; Sheu, Cheng 2011). In addition, within a stock market, during times of fi nancial crisis, losses tend to spread from a single sector across other sectors, leading to increased system-wide risk and probable deterioration of the whole stock market system. This fi nancial system instability or potential catastrophe, caused by idiosyncratic events and resulting in risk to the entire fi nancial system, is defi ned as systemic risk. Many fi nancial crises are initially caused by a “sector-specifi c” idi-osyncratic distress of a country, then spill over across other sectors to increase systemic risk, consequently leading to worldwide crashes. These crises result from systemic risk, caused by idiosyncratic distress, which cannot be reduced through portfolio diversifi ca-tion. Several reasons might lead to systemic risk and there are two commonly used as-sessments for measuring systemic risk, i.e. the “too big to fail” and “too interconnected to fail” test. The “too big to fail” test considers an asset size relative to the marketplace, i.e. market share concentration and the “too interconnected to fail” measures the likeli-hood and extent of negative impact to the overall economic system from the failure of a group of correlated institutions.
Traditionally, value-at-risk (VaR) is widely used to access the risk of loss of specifi c fi nancial assets and provides a measure to manage the market risk of assets. However, VaR focuses on these assets in isolation and does not consider external impacts. Using value-at-risk (VaR) to access assets, it seems negligible to capture the systemic risk and the true risk is often underestimated when other assets come under stress. For investors to control the risk for underlying assets, the appropriate risk measure could not only access the risk of a sector’s economic activities itself, but also consider the impact to systemic risk from the idiosyncratic distress. Thus, to supplement the drawback of VaR for estimating market risk, it is necessary to employ more interdependent and comprehensive measures that could consider the interconnected nature of the fi nancial system and gauge the increased systemic risk due to the distress of other fi nancial as-sets. However, it was not until the fi nancial crisis of 1998 that some researches begun to discuss systemic risk and develop approaches to measure it. Among these approaches, the “CoVaR” method, proposed by Adrian and Brummermeier (2008), is a more inter-dependent and comprehensive method and has been successfully employed to capture systemic risk.
Following this CoVaR method, the Taiwan stock market during periods of 2000–2010 was taken as an example to explore systemic risk caused by “sector-specifi c” distress for some reason. First, Taiwan rose to second in the world for global IT competitiveness through its strengths in R&D and nurturing technology talent (Business Software
ance 2008). Second, given the economic success of Taiwan in the last several decades, many global investors have taken an active interest and hold an index investment posi-tion in this stock market. Finally, the technology industry and fi nancial industry rank as the top two important industries in Taiwan stock market. Thus, it is an appropriate objective to measure and backtest the systemic risk during the 2001 dot-com bubble and the 2007–2009 fi nancial crisis.
The purpose of this paper is to empirically explore the impact of “sector-specifi c” idi-osyncratic risk on the systemic risk of the whole fi nancial system. First, this paper examines the magnitude of systemic risk and the marginal risk contribution caused by sectors to the overall systemic risk on the Taiwan stock market. Further, the differences, between VaR of sectors and sector-specifi c marginal systemic risks, were also compared. Finally, we endeavored to investigate the links between marginal systemic risk caused by a sector-specifi c anomaly and the impact of global fi nancial crises on Taiwan stock market. It is hoped the results of this study will be a useful tool for those stock investors to accurately identify the true systemic risk of Taiwan stock market and to properly allo-cate their investment portfolios across sectors according to their true risk contributions. The structure of this paper is as follows. Section II discusses risk contagion theory. Sec-tion III describes the methodology used to measure the systemic risk of Taiwan stock market and the implementation of the model, which is designed to solve the research problems. Section IV demonstrates the results of the research and other computation analysis. Finally, section V summarizes some fi ndings and conclusions.
2. Risk contagion theory and literature regarding sector contribution to the whole system
2.1. Drawbacks of VaR
Value-at-risk (VaR) converts the downside risk of a portfolio into a single number, making it an easy to understand and widely used measure of the risk of fi nancial assets. However, it has been challenged by many recent literatures. Artzner et al. (1999) sug-gested because VaR was not sub-additive1, meaning the VaR of a combined portfolio can
be larger than the sum of the VaRs of its components, it was not only incompatible with Markowitz portfolio theory (Markowitz 1952), but also did not suggest diversifi cation reduces risk. Besides, Wong and Fong (2010) proposed since VaR focused on the asset itself in isolation, the real risk of this asset might be underestimated, especially when other assets came under stress. Moreover, Brunnermeier, Crocket, Goodhart, Perssaud, and Shin (2009) suggested because VaR measured a single asset’s risk in isolation and did not consider the interconnected effect among assets, it might not necessarily refl ect systemic risk, which is the risk when the stability of the whole fi nancial system is threatened. Based on these criticisms, it is doubtful whether VaR is a good risk measure. Nowadays, many international investors have major stakes in overseas markets to pur-sue higher profi t opportunities. Given the economic success in the last two decades,
1 A risk measure ρ ( ) is subadditive, if, for any two fi nancial assets A and B, ρ (A + B) is no greater than ρ (A) + ρ (B). Sub-additivity: ρ(X + Y) ≤ ρ(X) + ρ(Y), for any risks X, Y , lack of sub–additiv-ity (Artzner et al. (1999), Mathematical Finance)
Taiwan stock market has attracted considerable global investments and the most used instrument is investment in Taiwan stock index, such as the MSCI Taiwan Index. Meas-uring and monitoring the true risk of Taiwan stock market has become a critical issue for investors. VaR, focusing on the risk of an individual exposure in isolation, is the most commonly used measure of risk. However, it does not necessarily refl ect how much risk a single exposure contributes to the whole system, i.e. systemic risk, when the stability of the whole system is destroyed. It is necessary to employ more interdependent and comprehensive risk measures to capture the true risk of assets, including systemic risk, which is the main cause of fi nancial crises.
2.2. Risk contagion during the crisis
Groups of interdependent institutions, defi ned as sectors, can contribute to systemic risk in two ways, the common exposure effects, and inter-linkages effects. First, a shock from a sector could become systemic because of direct common exposure, meaning a downward shock could affect most of the institutions within the sector simultaneously and thus trigger a systemic crisis in the sector (De Nicolò, Kwast 2002; Hawkesby et al. 2007). Financial globalization assists the capital and fi nancial assets to fl ow across various markets, which increases systemic risk and links all markets together expos-ing them to common risk. Second, due to the markedly increased industry integration nowadays, a more and more complicated web of economy activities and transactions implies this integration enhances the inter-linkage effects and exposes the entities of the web to the same risk factors, and that a shock hitting one institution could spread to the others connected to it.
Many fi nancial crises begin with sector-specifi c distress that then spills over into other sectors. These “sector-specifi c” caused crises comprise those before 2000, such as the 1987 Black Monday stock market crash and the 1998 Russian crisis, as well as those after 2000 of (1) the 2001 dot-com bubble, resulting in a fi nancial bubble centered on internet-based companies, the so-called burst of the dot-com companies, and fi nally af-fecting most markets in the world, and (2) the 2007–2009 fi nancial crisis, which spread from failures of fi nancial institutions in the United States, due primarily to exposure to subprime securities and credit default swaps(CDS), rapidly devolving into a global crisis which led to many bank failures in Europe and sharp value reductions in equities and commodities worldwide (Brady 1988; Rubin et al. 1999; Brunnermeier 2009; Adrian, Shin 2010a, b; Junior et al. 2010; Allen et al. 2009; Embrechts 2000).
Apparently, these cases resulted from a specifi c” anomaly and then this “sector-specifi c” anomaly transmitted to increase systemic risk, which not only led to the crisis of the local fi nancial system, but also spilled over across most fi nancial markets and harmed the worldwide fi nancial system. Further, as these global fi nancial crises have shown, common exposure effects and inter-linkages effects have played an important role in international systemic risk that could not be diversifi ed away. It highlights the interconnectedness of fi nancial markets nowadays and demonstrates the importance to employ more interdependent and holistic measures that can take into account the inter-connected nature of the fi nancial system and evaluate how much the risk of the asset may deteriorate when other related assets become distressed.
2.3. CoVaR model
Systemic risk, as defi ned, is the risk of collapse of a whole market where the failure of an idiosyncratic distress could cause a cascading failure of the entire system, as op-posed to risk only associated with any one individual entity, a group of entities, or a component of the system. Although systemic risk is the most important formal reason for fi nancial crises, it was not until the fi nancial crisis of 1998 that a few studies began to discuss the measures of systemic risk. These studies can be divided into two types, one adopts a top-down approach exploring systemic risk by attributing it to individual contributors, and the other adopts a bottom-up approach gauging marginal systemic risk that an individual entity contributes to the whole system, not decomposing systemic risk into individual contributors and not attempting to add components up to fi nd total systemic risk (Tarashev et al. 2010).
Several studies have used the top-down approach, decomposing the aggregate systemic risk and allocating it to individual contributors according to their expected loss in the event of distress (Praschnik et al. 2001; Hallerbach 2002; Koyluoglu, Stoker 2002; Kurth, Tasche 2003; Glasserman 2005; Acharya et al. 2009; Huang et al. 2009; Tarashev et al. 2010). The advantage of this top-down approach is the sum of the risk attributed to individual risk contributors will exactly equal the overall systemic risk. However, the disadvantage of this approach is it cannot be employed for the conditions where systemic risk is not measured by a fi xed set of failure events. Conquering the disad-vantage of the top-down approach, few researches have recently begun to employ the bottom-up approach to measure systemic risk. Adrian and Brummermeier (2008) pro-posed the concept of “CoVaR”, defi ned as the VaR of an asset conditional on some other assets being in distress, to measure the severity of the systemic risk, which is the whole system failure or potential catastrophe conditional on the negative effects caused by an institution-specifi c or a sector-specifi c severe calamity. Acharya, Pedersen, Philippon and Richardson (2009, 2010) measured the contributions of individual banks to systemic risk and proposed a “tax charge” based on the contribution to systemic risk. Chan-Lau (2008) used a similar approach to study the spillover effects of the CDS spreads of fi nancial institutions in the US, Europe and Japan. Fong et al. (2009) estimated Co-VaRs to evaluate the interdependence of fi nancial institutions in Hong Kong. However, these papers emphasized measuring the systemic risk caused by individual institution’s anomaly, i.e. “institution-specifi c” distress, and proposed institutions that were too large to fail were likely to cause risk spillover effects on the system, as well as transmit more systemic risk to the whole system. Nevertheless, according to the defi nition and the clas-sifi cation of Brunnermeier, Crocket, Goodhart, Perssaud, and Shin (2009), systemic risk includes the risk caused not only by “individual institutions”, which are so large (“too big to fail”) that they could negatively affect others, but also by a group of institutions, which are so interdependent (“too interconnected to fail”) that they are “systemic as part of a herd” which possess similar characteristics and could be affected by common risk factors. The previous studies of “institution-specifi c” CoVaR only emphasized the “too big to fail” effect, rather than the “too interconnected to fail” effect. However, due to the above mentioned inter-linkage effect and common exposure effect, the failure of
a group of interconnected institutions, i.e., “sector-specifi c” distress, would bring down more severely negative effects on the whole system and would be the primary risk con-tributor of fi nancial crises. However, there is a lack of research discussing the systemic risk caused by the “sector-specifi c” disaster. This paper focuses on the Taiwan stock market’s systemic risk, conditional on “sector-specifi c” idiosyncratic risk.
3. Properties of the conditional VaR methodology
As indicated in the introduction, there are two types of systemic risk measures, the top-down approach estimates systemic risk by attributing it to individuals, while the bottom-up approach focuses directly on the marginal systemic risk which individual contributors attribute to. Amongst the bottom-up approach, the CoVaR model has been proved by Boyson, Stahel and Stulz (2008) and Jorion and Zhang (2009) to be a good method to measure systemic risk using quantile regressions. There are many advantages of using the CoVaR method. First, it provides a method to explore the comprehensive risk spillovers across the entire fi nancial system. Second, it can decompose the marginal risk, CoVaR, from the total systemic risk. Then, it can help investors pay more atten-tion to the important marginal risk contributory sectors instead of overall systemic risk, i.e., from the macro prudential perspective to micro prudential perspective. Finally, by exploring the risk factors of important marginal contributory sectors on systemic risk, it can help investors monitor the movement of these important risk factors as an early warning signal of overall systemic risk.
This paper adopts the CoVaR method to gauge systemic risk, both CoVaR and CoVaR, of Taiwan stock market. For the purpose of this study, VaR and CoVaR were generated from functions of a vector of macroeconomic state variables and were estimated by quan-tile regressions. To clarify, the framework of this study is depicted as following Fig. 1.
3.1. VaR, CoVaR and ΔCoVaR model
For a given probability and time horizon, VaR is defi ned as a threshold value such that the probability that the market loss on the portfolio over the given time horizon exceeds this value is exactly the given probability level (Jin, Jorion 2006; Suhobokov 2007). The fi rst step of this paper is to measure the VaRs of the whole Taiwan stock market (de-noted as “system VaR”) and its component sectors (de(de-noted as “sector VaR”) using the historical simulation method because this method provides a simple and straightforward implementation of valuation, as well as no distribution assumption and no complicated
Fig. 1. Study framework Quantile Regression Macroeconomic State Variables Sector VaR System VaR CoVar DCoVar
calculations being required (Suhobokov 2007). In the second step, following the study of Adrian and Brunnermeier (2009), the CoVaR method is employed to evaluate the systemic risk of Taiwan stock market conditional on sector-specifi c distress. In the fol-lowing section, CoVaRi is defi ned as the system (whole Taiwan stock market, hereafter) VaR conditional on specifi c sector i being in distress and CoVaRi was defi ned as the marginal contribution of sector i to the overall systemic risk which is generated from the difference between the CoVaRi and the VaR of the whole system.
The distinction between CoVaRi and CoVaRi is the former allows us to study how
much the systemic risk will be when conditional on sector-specifi c’s distress, while the latter quantifi es how much marginal risk a sector contributes to overall systemic risk. Both VaR and CoVaR measures were computed using the Quantile Regression approach, which was suggested by Koenker and Bassett (1978) to estimate the coef-fi cients. This approach could estimate a specicoef-fi c quantile under a conditional distribu-tion and recently has been successfully used in the analysis of VaR and CoVaR (Chen 2002; Gaglianone et al. 2009; Schaumburg 2010; Coroneo, Veredas 2008; Ou, Yi 2010; Chernozhukov, Umantsev 2001; Chernozhukov, Du 2008).
3.2. Estimation CoVaR with macroeconomic state variables
Three steps were used to estimate CoVaR with macroeconomic state variables. First, to capture time variation in the joint distribution of a sector’s return (X i) and the whole
Taiwan stock market index return ( system t
X ), the conditional distribution as a function of
state variables is estimated. Subscripted with t, the time-varying i t
X and system t
X were
estimated by conditioning on a vector of 1-month lagged time series for macroeconomic state variables Mt–1. The following regressions (1) and (2) were run in the monthly data (where “i” denotes a specifi c sector and “system” denotes the whole system):
1 ,
i i i i
t t t
X M (1)
1 .
system system system system
t t t
X M (2)
In addition, to generate the CoVaR conditional on an individual sector, the whole Tai-wan stock market index return ( system
t
X ), regressed as a function of its lag 1 return
( system1 t
X ), an individual sector’s return ( i) t
X and a vector of 1-month lagged time series
for macroeconomic state variables Mt–1, was also estimated in the monthly data:
| | | | |
1
0 1 1 2 3
system system i system i system system i i system i system i
t t t t t
X X X M . (3)
Second, using the coeffi cients of the quantile approach from the fi rst step, the predicted values, VaRt and CoVaRt, were generated from the regressions (4), (5), and (6):
1
VaRi i i
,
t Mt (4)
1
VaRsystem system system
,
t Mt (5)
1 1
| | | |
0 1 2 3
CoVaRit system i system iVaRtsystem system iVaRti system iMt . (6)
Finally, a panel of monthly CoVaRi t
, conditional on a sector “i”, was obtained by subtracting VaRtsystem fromCoVaRit:
CoVaRi CoVaRi VaRsystem
.
t t t
(7)
When estimating the above-mentioned time-varying CoVaRt and VaRt, the set of lagged macroeconomic state variables Mt–1 was used as controlling variables to remove varia-tion which was not directly related to the risk of the fi nancial system (Aktan et al. 2010). These macroeconomic state variables were usually used to describe the “state” of the dynamic system and to forecast the future behavior of the system. Many stud-ies have suggested the aggregate stock market return predictability is highly related to macroeconomic state variables that could refl ect the business cycle (Chen et al. 1986; Fama, French 1993; Vassalou 2003; Petkova 2006; Ludvigson, Ng 2007; Birz, Lott 2008; Cenesizoglu, Timmermann 2008; Li, Liu 2010; Festic et al. 2009). In reference to these researches, the selected macroeconomic state variables and reasons to be chosen are listed as below:
1) Short term “Credit spread”: which was defi ned as the difference between the rate of a government bond and the rate of commercial paper in Taiwan money market. 2) Monetary Aggregate M1B: which equalled M1A plus Passbook savings deposits
of Individuals and non-profi t organizations in banks and community fi nancial in-stitutions.
3) Unemployment rate: the unemployment rate and Taiwan stock return were found to be stable time series after difference and to have a long-term equilibrium. 4) The GDP leading index: which is composed of seven sub-indicators and is widely
used in the fi nancial fi eld, because it is a signifi cant indicator of Taiwan stock market returns.
5) Exchange rate movement: which plays an important role in Taiwan economic performance and in the short run has signifi cantly negative infl uences on Taiwan stock returns.
6) The Crude Oil price movements: which has similar impacts as exchange rate movements and in the short run has a signifi cantly negative infl uence on Taiwan Stock returns.
7) NASDAQ index return: which has been proved to be the most infl uential external source on Taiwan stock market.
Besides, Taiwan is one of the Four Asian Dragons and its stock market has attracted a large number of investors’ attention owing to its rapid economic growth over the past decades. Since it is highly correlated with international capital markets and other Asian stock markets, Taiwan stock market could provide pricing predication or hedging tools for other Asian stock markets (Sheu, Cheng 2011). This analysis, taking Taiwan stock market as example, focused on the VaR and ΔCoVaR of this stock market index and its components of 18 sector indices, which are denoted as following Table 1.
Table 1. Variable defi nition
Whole stock market VaR: Xsystem: Taiwan stock index
Sector VaR:
X1: cement sector X7: medical technique sector X13: electronic sector
X2: food sector X8: ceramic sector X14: building sector
X3: plastic sector X9: papermaking sector X15: shipping sector
X4: textile fi ber sector X10: steel sector X16: sightseeing sector
X5: electrical machinery sector X11: rubber sector X17: banking sector
X6: electric appliance sector X12: automobile sector X18: trade sector
Data was collected from January 2001 through September 2010, covering the dot-com bubble of 2001 as well as the fi nancial crisis of 2007–2009, containing a whole eco-nomic cycle of Taiwan.
4. Empirical results
This section presents the empirical results of applying the CoVaR method using the quantile approach introduced in the previous section to explore the systemic risk mea-sures of Taiwan stock market. First, the results of quantile regressions for sector’s re-turns (X i) and whole system return (X system) on the macroeconomic state variables were
calculated. Second, VaRs of the whole Taiwan stock market (system VaR, VaRsystem)
and individual sectors (sector VaR, VaRi) on isolation were estimated. Third, systemic
CoVaR measures conditional on individual sectors, CoVaRi, were generated. In addition,
two risk measures of unconditional and conditional on sectors’ being in distress, i.e., VaRsystem and CoVaRi, were compared. Further, the difference between these two risk
measures, denoted as CoVaRi, was generated to capture the marginal contribution of
an individual sector to overall systemic risk. Finally, the links between CoVaRiof some
important sectors and the recent global fi nancial crises were also investigated. 4.1. VaR estimation
The coeffi cients of quantile regressions for sector returns (X i) and whole system return
(X system) of Taiwan stock market on macroeconomic state variables were estimated.
Us-ing these equations, the VaR of Taiwan Stock Index (VaRsystem) and VaRs of 18 sector
indices (VaR1 to VaR18), were shown in Table 2, calculated by the Historical Simulation
Method at 1%, 5%, and 10% maximum loss probability and denoted as VaR 1%, VaR 5%, and VaR 10%, respectively.
As seen in Table 2, VaR increased when the maximum loss probability decreased. The trade sector, building sector, electric appliance sector, electronic sector, and electrical machinery sector had the top 5 VaR measures at any confi dence level. For example, at 1% maximum loss probability, the VaR of electronic sector and Taiwan stock index were –0.06697 and –0.06026, respectively, and the sector indices with the largest and smallest VaR were trade sector of –0.11382, and food sector of –0.04110.
Table 2. VaR of stock index & sector index at 1%, 5% and 10% respectively
VaR 1% VaR 5% VaR 10% Whole stock market VaR:
X system: Taiwan stock index –0.06026 –0.05220 –0.04500
Sector VaR:
X1: cement sector –0.04618 –0.04035 –0.03358
X2: food sector –0.04110 –0.03454 –0.02745
X3: plastic sector –0.04990 –0.04423 –0.03759
X4: textile fi ber sector –0.05595 –0.05107 –0.04493
X5: electrical machinery sector –0.06359 –0.05619 –0.04484
X6: electric appliance sector –0.07182 –0.06500 –0.05835
X7: medical technique sector –0.05791 –0.04820 –0.03707
X8: ceramic sector –0.05585 –0.04868 –0.03653 X9: papermaking sector –0.05870 –0.05285 –0.04754 X10: steel sector –0.04850 –0.04401 –0.03587 X11: rubber sector –0.04465 –0.03902 –0.02971 X12: automobile sector –0.04603 –0.04406 –0.03886 X13: electronic sector –0.06697 –0.05941 –0.05006 X14: building sector –0.10082 –0.08487 –0.07066 X15: shipping sector –0.05516 –0.04740 –0.04014 X16: sightseeing sector –0.04912 –0.04529 –0.03626 X17: banking sector –0.05932 –0.05204 –0.04604 X18: trade sector –0.11382 –0.09169 –0.05992
The sector VaR is a risk measure representing the loss due to the sector’s being in distress in isolation. However, the question of whether a sector with bigger VaR could mean it would contribute more marginal risk to the whole system needed to be further investigated and is discussed in the following.
4.2. CoVaR estimation
To generate the CoVaR measures, the quantile CoVaR regressions, as shown in equa-tion (6) of secequa-tion 3.2, condiequa-tional on individual sectors were established and the coef-fi cients of regressions were estimated under the OLS method, 10th quantile method,
and 5th quantile method respectively. Under these estimated equations, the CoVaRs for
the whole system conditional on 18 sectors (CoVaR1 to CoVaR18) at 1%, 5%, and 10%
maximum loss probability were then generated independently. To simplify the discus-sion, CoVaR at 5% maximum loss probability was chosen to be shown in Table 3. As indicated in the table, CoVaRs measured using the OLS method were signifi cantly larger
than those estimated by the quantile model and CoVaRs of the quantile method at the 5th quantile were larger than those of the 10th quantile. Besides, regardless of what
model was used, the two highest CoVaRs of Taiwan stock market could occur when it was conditional on the electronic sector and banking sector being at their VaR levels. Combining Table 2 and 3, the top 5 highest VaR sectors (trade sector, building sector, electric appliance sector, electronic sector, and electrical machinery sector) did not com-pletely equal the top 5 highest risk contributory sectors to the system CoVaR (electronic sector, banking sector, electrical machinery sector, electric appliance sector, plastic sec-tor). Amongst these sectors, the electronic sector had the highest sector VaR and the highest systemic CoVaR, however, the banking sector did not have relatively substantial sector VaR, but did have the 2nd highest systemic CoVaR. On the contrary, the trade sector and building sector possessed the two highest sector VaRs, but they did not have relatively high systemic CoVaR. It appears sector VaR is not necessarily correlated with systemic CoVaR, with a Pearson’s correlation of only 0.2715. The reason for this
Table 3. Predicted CoVaR(5%) of Taiwan stock sector index using OLS,
Quantile 5% and Quantile 10% Method
CoVaR (5%) when conditional on: OLS Quantile 10th Quantile 5th
X1: cement sector –0.0324 –0.0697 –0.07347
X2: food sector –0.0307 –0.055 –0.07365
X3: plastic sector –0.0259 –0.0486 –0.07395
X4: textile fi ber sector –0.0318 –0.0532 –0.07313
X5: electrical machinery sector –0.0286 –0.05 –0.07932
X6: electric appliance sector –0.0306 –0.0657 –0.07558
X7: medical technique sector –0.033 –0.0555 –0.06575
X8: ceramic sector –0.0204 –0.0524 –0.0545 X9: papermaking sector –0.0311 –0.0627 –0.07268 X10: steel sector –0.0224 –0.0515 –0.06374 X11: rubber sector –0.0326 –0.0677 –0.0702 X12: automobile sector –0.026 –0.0581 –0.05916 X13: electronic sector –0.035 –0.0629 –0.09508 X14: building sector –0.033 –0.0634 –0.07175 X15: shipping sector –0.0227 –0.0478 –0.06337 X16: sightseeing sector –0.0306 –0.0474 –0.06782 X17: banking sector –0.0316 –0.0623 –0.07999 X18: trade sector –0.0147 –0.0542 –0.06475
mismatch could be the probability sector VaR is not the only risk that transmits to the system and these two risk measures apparently capture different risks of the system. Thus, merely using VaR to measure risk would be insuffi cient and might underestimate its true risk. Up to this point, these results are consistent with those of Adrian, Tobias and Markus Brunnermeier (2008).
Correlation between VaRi and CoVaRi:
VaRi
CoVaRi 0.2715
Fig. 2 depicts the measures of sector VaR(solid line) and systemic CoVaR(dotted line) of all 18 sectors. Clearly, most conditional CoVaRs were larger than the sector’s VaR, except for a few sectors. In addition, it showed a sector with higher VaR did not neces-sarily contribute more systemic risk to the whole system or lead to a higher CoVaR. In addition, as the electronic sector and banking sector rank as the top two CoVaR sec-tors, their time series CoVaRs for the sample period needed to be thoroughly explored, with this being presented in Fig. 3. The CoVaRs of these two sectors was apparently spilt at 2007, matching the time of the global fi nancial crises. Owing to the 2001 dot-com bubble, the electronic sector (as dotted line) had a larger CoVaR than the banking sector (solid line) from 2003 to 2007. On the contrary, for the 2007–2009 fi nancial crisis, the banking sector has had a higher CoVaR measure than electronic sector from 2007 till now, particularly in 2007.
Fig. 2. Sector VaR and CoVaR conditional on 18 sectors
Fig. 3. Sector CoVaR of electronic sector and banking sector during 2003–2010 0.0800 0.0600 0.0400 0.0200 0.0000 VaR CoVaR ×1 ×2 ×3 ×4 ×5 ×6 ×7 ×8 ×9 ×10 ×11 ×12 ×13 ×14 ×15 ×16 ×17 ×18 0.1000
Electronic sector Banking sector
0.1000 0.0800 0.0600 0.0400 0.0200 0.0000 0.1200 0.1400 2003 2004 2005 2006 2007 2008 2009 2010
4.3. Marginal contribution to systemic risk, ΔCoVaR
The difference between CoVaR and VaR measures, denoted as CoVaR, was generated to capture the marginal contribution of an individual sector to overall systemic risk. The CoVaR of Taiwan stock index using OLS, Quantile 5th and Quantile 10th at 1%,
5%, and 10% maximum loss probability were calculated corresponsively and only the CoVaR at 5% maximum loss probability and under the 5th quantile percentile was
listed on Table 4 and depicted in Fig. 4. Similar to the result of CoVaR, ranking as the top 2 largest transaction volume sectors in Taiwan stock market, the electronic sector and banking sector also possessed the top 2 highest marginal risk contribution, CoVaR, for Taiwan stock market, indicating conditional on the crisis of these two sectors, the systemic risk of the whole Taiwan stock market could dramatically increase. This result could simultaneously prove the “too big to fail” and “too interconnected to fail” effects of the fi nancial system characteristics which could not be fully obtained from the result of the VaR measure.
To clearly compare VaRi with CoVaRi, Table 5 lists the paired value of these two risk
measures for 18 sectors. From the table, while the trade sector, building sector, electrical appliance sector, electronic sector, and electrical machinery sector ranked as the top 5 highest VaR sectors, the electronic sector and banking sector were the 2 most marginal
Fig. 4. CoVaR of 18 sectors
0.045 0.035 0.0.25 0.0.15 0.005 0.005 ×1 ×2 ×3 ×4 ×5 ×6 ×7 ×8 ×9 ×10 ×11 ×12 ×13 ×14 ×15 ×16 ×17 ×18 Table 4. CoVaR(5%) of Taiwan stock index using Quantile 5th
Conditional on: CoVaRi Conditional on: CoVaRi X1: cement sector –0.0213 X10: steel sector –0.0115
X2: food sector –0.0215 X11: rubber sector –0.0180
X3: plastic sector –0.0217 X12: automobile sector –0.0070
X4: textile fi ber sector –0.0209 X13: electronic sector –0.0429
X5: electrical machinery sector –0.0271 X14: building sector –0.0195
X6: electric appliance sector –0.0234 X15: shipping sector –0.0112
X7: medical technique sector –0.0136 X16: sightseeing sector –0.0156
X8: ceramic sector –0.0023 X17: banking sector –0.0278
X9: papermaking sector –0.0205 X18: trade sector –0.0126
risk contributing sectors for Taiwan stock market. The main conclusions here are sec-tors might have a low VaR but a high CoVaR, and CoVaR could capture not only systemic risk but also the individual sector risk.
The fi nancial crises of the 2001 dot-com bubble and 2007–2009 fi nancial crisis resulted from systemic risk which not only led to the crisis of the local fi nancial system, but also damaged the world-wide fi nancial system. Taiwan is a primary electronic product factory of the world and its banking sector plays an important role in Pacifi c Asia. Thus, these two global fi nancial crises might affect the electronic and banking sectors of Taiwan stock market. Is there any link between the global fi nancial crises and Co-VaR? The time series CoVaRi of electronic sector, banking sector and market average
during 2003 to 2010 was showed on Table 6 and depicted as Fig. 5. For the recovery from the 2001 dot-com bubble, the CoVaR of the electronic sector (blue line) is
get-Table 5. Yearly pairs of VaRi and CoVaRi for 18 sectors
sector VaRi CoVaRi sector VaRi CoVaRi X1: cement sector –0.04035 –0.0213 X10: steel sector –0.04401 –0.0115
X2: food sector –0.03454 –0.0215 X11: rubber sector –0.03902 –0.0180
X3: plastic sector –0.04423 –0.0217 X12: automobile sector –0.04406 –0.0070
X4: textile fi ber sector –0.05107 –0.0209 X13: electronic sector –0.05941 –0.0429
X5: electrical machinery sector –0.05619 –0.0271 X 14: building sector –0.08487 –0.0195 X6: electric appliance sector –0.06500 –0.0234 X 15: shipping sector –0.04740 –0.0112 X7: medical technique sector –0.04820 –0.0136 X 16: sightseeing sector –0.04529 –0.0156
X8: ceramic sector –0.04868 –0.0023 X17: banking sector –0.05204 –0.0278
X9: papermaking sector –0.05285 –0.0205 X18: trade sector –0.09169 –0.0126
Table 6. Time series CoVaR of Electronic Sector, Banking Sector, and Market Average during 2003–2010
Electronic Sector Banking Sector Market Average
2003 –0.0475 –0.0141 –0.0372 2004 –0.0451 –0.0174 –0.0325 2005 –0.0425 –0.0216 –0.0297 2006 –0.0405 –0.0284 –0.0253 2007 –0.0319 –0.0331 –0.0309 2008 –0.0233 –0.0303 –0.0235 2009 –0.0155 –0.0199 –0.0177 2010 –0.0125 –0.0170 –0.0154
ting smaller from 2003 to 2010. However, the banking sector was seriously affected by the 2007–2008 fi nancial crisis, and its CoVaR was largest during these periods. The market average CoVaR of the 18 sectors was largest at the beginning of the sample period and 2007, indicating Taiwan stock market deteriorated during the dot-com bub-ble and the 2007–2008 fi nancial crisis, and CoVaR could capture these characteristics. 5. Conclusion
Many fi nancial crises have resulted from systemic risk that was initially brought by id-iosyncratic distress, spilling over across the related entities and fi nally causing a crunch of the entire system. The interaction between fi nancial distress and systemic risk from the effect of idiosyncratic distress has been discussed recently. Amongst the idiosyn-cratic distress, sector-specifi c risk caused by a group of interconnected institutions has been accused of being the main reason for the increase in systemic risk, which led to the formalization of fi nancial crises. As illustrated previously, VaR focuses on the asset itself in isolation, thus it seems negligible to capture the systemic risk especially when other assets come under stress.
In this research, Taiwan stock market was taken as an example and data were collected from 2000 to 2010, which contained the 2001 dot-com bubble and the 2007–2009 fi nancial crisis. Following the CoVaR method of Adrian, Tobias, and Markus Brun-nermeier (2010), this research attempted to empirically explore the impact of sector-specifi c idiosyncratic risk on the systemic risk of the entire fi nancial system and tried to examine the link between fi nancial crises, systemic risk, and the idiosyncratic risk of a sector-specifi c anomaly.
As defi ned, CoVaR is the system VaR conditional on specifi c sector being in distress and CoVaR is the marginal contribution of individual sector to the overall systemic risk. Both CoVaR and CoVaR were used to measure systemic risk in this paper.
Our empirical results are summarized as following. The results of the present study might be summarized by pointing out the following. First, the top 5 highest VaR sectors did not completely equal the top 5 highest risk contributory sectors to the system Co-VaR. This showed there was no signifi cant relationship between sector VaR and CoVaR, which was supported by a low correlation coeffi cient of 0.2715. The reason is that the sector VaR and CoVaR captured different risk characteristics. The former accessed the Fig. 5. CoVaRi of electronic sector, banking sector and market average during 2003 to 2010
0.0400 0.0300 0.0200 0.0100 0.0000 0.0500 2003 2004 2005 2006 2007 2008 2009 2010 Electronic sector Banking sector Market average
risk of a sector in isolation, however, the latter appraised the systemic risk conditional on a specifi c sector being at its VaR level. Second, ranking as the top 2 largest transac-tion volume sectors in Taiwan stock market, the electronic sector and banking sector also possessed the top 2 highest marginal risk contributions, CoVaR. This result could simultaneously prove the “too big to fail” and “too interconnected to fail” effects of fi nancial system characteristics, which could not be fully obtained from the result of the VaR measure. Finally, linking the CoVaR measure to the global fi nancial crises, CoVaR perfectly explained Taiwan stock market disturbance during the 2001 dot-com bubble and 2007–2008 fi nancial crisis, both of which were resulted from systemic risk initially brought by a sector-specifi c idiosyncratic distress, fi nally causing the crunch of the whole system. It showed the fi nancial crises, systemic risk, and the idiosyncratic risk of sector-specifi c are all linked.
This study has taken a successful step in the direction of measuring the marginal con-tribution risk of sector-specifi c effects on Taiwan stock market. The fi nding is important for investors by suggesting that the marginal risk contribution, CoVaR, is more es-sential as an estimator of the risk of fi nancial assets and is a useful measure to monitor fi nancial risk. When addressing the value of risk of an asset, the investors should focus not only on its own risk but also on the risk propagated from the system. CoVaR could empirically assist investors to identify systemic risk from a macro into a micro prudential perspective. First, by integrating the monitoring of system VaR with sector-specifi c CoVaR, the investors could shift attention from the VaR of overall system risk to the larger marginal risk contribution of the individual sector, which is called “the systemic importance sector” and which is usually resulted from “too big to fail” or “too interconnected to fail” effects. When the systemic importance sector’s CoVaR increases which accompanied with an ascending market average, it provides investors a warning signal that the whole fi nancial system is faced with increasing systemic risk from the systemic importance sector. Moreover, when the sector’s CoVaR increases continuously and is larger than the market average, it is more likely that the systemic importance sector would be in distress and could further lead to a crunch for the entire system. For example, demonstrated on table 5 and Fig. 4, CoVaR of banking sector deteriorated gradually from 2003 of –0.0141, arrived at the peak on 2007 of –0.0331 which exceeded that of market average of –0.0309, and then mitigated from 2007 to 2010 of –0.017. The period of 2003 to 2010 could be divided into 3 sub-periods which contain different information for investors to practically create and manage their portfo-lios. During 2003 to 2006, the ascending CoVaRs of both banking sector and market average could be regarded as warning signals of increasing distress pressure on systemic risk from banking sector. During 2007, the highest CoVaR of banking sector exceeded market average and the 2007–2008 fi nancial crisis exactly broke out at the same time. During 2008 to 2010, the descending CoVaRs of both banking sector and market average could be explained as the marginal contributory risk from banking sector had been gradually fading away. In addition, the descending CoVaRs of electronic sector during 2003 of –0.0475 to 2010 of –0.0125 could also be regarded as the marginal contributory risk had been gradually diminishing. Second, by identifying the infl uential risk indicators of systemic importance sectors, the investors could focus on the
tant sectors and scrutinize their risk indicators, which can be regarded as early warning signals for the systemic importance sectors and for the entire fi nancial system. Taking liquidity of fi nancial assets as well as default ratio of loan assets, the most important infl uential risk indicators on CoVaR of banking sector, as an example, the 2007–2008 fi nancial crisis spread from failures of fi nancial institutions due primarily to the serious rising default ratio of subprime and the collapse of liquidity on fi nancial assets. When any these risk indicators become unfavorable beforehand, CoVaR of banking sector could soar afterward and this increasing systemic risk could even cause a crunch of the entire system. For investors, it is necessary to identify and scrutinize these early warn-ing signals and take appropriate actions, in advance, to avoid or mitigate the potential losses from either the distress of the systemic importance sector or the catastrophe of the whole market system.
It is recommended the approach outlined in this study be replicated in other stock mar-kets or other fi nancial assets. Moreover, it would be increasingly crucial to explore the infl uential indicators of the ΔCoVaR to predict in advance the marginal risk contribution based on the movement of the risk factors. However, because our sample market is very small compared with international stock markets, and the data period is relatively short, it is possible that other stock markets may have different results.
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Her-Jiun SHEU received his PhD from Stern Business School, New York University in 1989. He is currently a professor of fi nance in the Department of Banking and Finance at National Chi Nan Univer-sity, Taiwan. His research and teaching interests lie in fi nancial management, derivatives, mathematical programming as well as management science.
Chien-Ling CHENG is currently studying in the PhD program of Institute of Business and Manage-ment, Management of National Chiao-Tung University, Taiwan. His primary research interests include fi nancial theory, accounting, banking, and risk management. He is also the Senior Vice President of The Shanghai Commercial and Savings Bank Ltd, Taiwan.
