Risk contagion theory and literature with regarding to sector contribution to the whole system

3.2.1 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 financial assets. However, it has been challenged by many recent literatures.

Artzner et al. (1999) suggested 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 diversification reduces risk. Besides, Wong and Fong (2010) proposed since VaR focused on the asset itself on 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

1 A risk measure ρ ( ) is subadditive, if, for any two financial 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–additivity [Artzner et al. (1999, Mathematical Finance)]

risk in isolation and did not consider the interconnected effect among assets, it might not necessarily reflect systemic risk, which is the risk when the stability of the whole financial 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 pursue higher profit opportunities. Given the economic success in the last two decades, Taiwan’s stock market has attracted considerable global investments and the most used instrument is investment in Taiwan’s stock index, such as the MSCI Taiwan Index. Measuring and monitoring the true risk of Taiwan’s 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 reflect 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 financial crises.

3.2.2 Risk contagion during the crisis

Groups of interdependent institutions, defined 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 and Kwast, 2002; Hawkesby, Marsh, and Stevens, 2007).

Financial globalization assists the capital and financial assets to flow across

various markets, which increases systemic risk and links all markets together exposing 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 financial crises begin with sector-specific distress that then spills over into other sectors. These “sector-specific” 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 financial bubble centered on internet-based companies, the so-called burst of the dot-com companies, and finally affecting most markets in the world, and (2) the 2007-09 financial crisis, which spread from failures of financial 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, Greenspan, Levitt, and Born, 1999; Brunnermeier, 2009; Adrian and Shin, 2010a,b; Junior et al., 2010; Allen, Babus and Carletti, 2009; Embrechts, 2000).

Apparently, these cases resulted from a “sector-specific” anomaly and then this

“sector-specific” anomaly transmitted to increase systemic risk, which not only led to the crisis of the local financial system, but also spilled over across most financial markets and harmed the worldwide financial system. Further, as these global financial crises have shown, common exposure effects and inter-linkages effects have played an important role in international systemic risk that could not be diversified away. It highlights the interconnectedness of financial markets

nowadays and demonstrates the importance to employ more interdependent and holistic measures that can take into account the interconnected nature of the financial system and evaluate how much the risk of the asset may deteriorate when other related assets become distressed.

3.2.3 CoVaR model

Systemic risk, as defined, 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 opposed 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 financial crises, it was not until the financial 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 find total systemic risk (Tarashev, Borio and Tsatsaronis, 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 and Stoker, 2002; Kurth and Tasche, 2003; Glasserman, 2005;

Acharya et al, 2009; Huang et al, 2009; Tarashev, Borio, and Tsatsaronis, 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 fixed set of failure events. Conquering the disadvantage of the top-down approach, few researches have recently begun to employ the bottom-up approach to measure systemic risk. Adrian and Brummermeier (2008) proposed the concept of “CoVaR”, defined 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-specific or a sector-specific 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 financial institutions in the US, Europe and Japan. Fong, et al. (2009) estimated CoVaRs to evaluate the interdependence of financial institutions in Hong Kong. However, these papers emphasized measuring the systemic risk caused by individual institution’s anomaly, i.e. “institution-specific”

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 definition and the classification 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-specific”

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-specific” distress, would bring down more severely negative effects on the whole system and would be the primary risk contributor of financial crises. However, there is a lack of research discussing the systemic risk caused by the “sector-specific” disaster. This paper focuses on the Taiwan stock market’s systemic risk, conditional on “sector-specific” idiosyncratic risk.