INTRODUCTION

The importance of systemic risk is hardly disput­able. Furthermore, it is at the heart of intense discussions for all regulators and financial au­thorities. Despite the relevance of systemic risk for the maintenance of financial stability and its recent popularity, it is still work in progress as we lack a universal definition and tools to measure it.

Having defined systemic risk, we can now focus on ways to measure it in order to manage it. In most standard risk models, there are risk measures such as expected loss, VaR, CVaR, etc. These risk measures can provide us with an idea of the size of the loss and its likelihood in a systemic crisis. Having said so, in our opinion it is very important to estimate, in the best possible and accurate form, the distribution of losses for the system as a whole, instead of adding up individual risk measures for each bank.

Financial contagion is one of the key ele­ments on the definition of systemic risk; in fact, both terms were used in an interchangeable way in the past. Nowadays, it is clear that it is just one of the components of systemic risk, a very important one though. However, it is not easy to model or quantify financial contagion especially in the presence of indirect contagion or contagion through indirect links.

As in the case of systemic risk, there are many definitions for financial contagion due to the complex way in which financial institutions are related today. Additionally, it is difficult to verify empirically if financial difficulties are transmit­ted between financial institutions or whether the cause of financial distress is something different, like common exposures. Furthermore, it is neces­sary to distinguish between two different types of contagion: direct and indirect contagion. While direct financial contagion³ has been studied widely by several central banks⁴, indirect contagion⁵ is in contrast difficult to estimate due to the inher­ent information problems faced by the financial authorities and researchers.

More recently, there has been a furor to study systemic risk by means of network theory to the point that the term “too interconnected to fail” is widely known by international regulators. Even though, we believe that such approaches (graph theory and network models) are very useful in un­derstanding the relevance of particular institutions due to their connections in the financial system, and to model the transmission of shocks they are not enough to model adequately systemic risk. The studies on payments systems and network theory are the perfect example of a successful application of such approach in the arena of systemic risk but they can only provide a limited view of the problem. The topology of the network of funds flows on the payment systems is very useful to identify some banks, which are relevant players in such a system, banks that can be considered of systemic relevance because of the role they play.

In this chapter, two institutions are said to be connected if there is an exposure between them in any direction. We have already expressed that Complex Derivatives (CDS) exposures and indi­rect connections may be problematic. Additionally we think it is important to mention that from our experience problematic connections in banking systems are those:

• That for the bank which is lending, such connection represents an important per­centage of its Tier1 Capital.

• When “overexposed”⁶ banks have their lending highly concentrated (something that could be easily measured by using the Herfindahl-Hirschman Index).

Regarding indirect connections, it is difficult to avoid being exposed to the same types of shocks, because many institutions have similar business models, and all strive to invest in those areas with the best returns. The extent to which a certain type of shock can hit the banking sector could be limited by a high degree of diversification of each financial institution, which would limit the extent to which it suffers from a shock.

Regulation could be enhanced to ensure a “higher degree” of diversification in the financial sector. However, even this type of regulation may fall short form obtaining the desired results. For example, several very diverse companies may have foreign exchange debt and fail when the exchange rate changes abruptly rendering diversification regulation useless. Moreover, certain aspects of financial connections must be taken into account:

• Some activities are necessary and difficult to change. Banks which act like “hubs” in any network of the financial system are particularly important, as a failure or dis­ruption of any of such banks could threaten the stability of the system.

• Banks’ connectedness may depend on as­pects such as: Preference, peer monitoring costs and Too-Big-To-Fail (TBTF) moral hazard driven choices.

• It is commonly accepted that in normal times strong interbank linkages are funda­mental for the functioning of the interbank market, for it is through these connections that liquidity travels across banking insti­tutions. It is also accepted that in times of crisis these connections tend to dry up. There is a danger that any regulation that limits interbank connections may be costly in good times and not applicable in bad times.

In addition to the approaches on systemic risk measurement, contagion analysis and network models to study financial stability, there is another tool, which is becoming increasingly important for the financial authorities: Stress testing. Stress tests have become very relevant in recent times and can be considered as an almost standard tool in risk management. Many commercial and central banks, insurers and regulators perform stress tests as part of the risk management strategy of their respective institutions.

Stress testing can have several definitions but in Borio et al. (2012) the authors provide a simple yet useful one: “In its broadest sense, stress testing is a technique to test the stability of an entity or system under adverse conditions” (p. 2).

From the perspective of global financial regu­lators as well as from the perspective of central banks, stress tests are now an unavoidable tool for designing policies to preserve financial stability. Moreover, stress testing is a common part of the financial stability reports elaborated by central banks. However, stress tests face some criti­cisms, as in the cases of Iceland and Europe the responsible of performing such tests have failed to identify serious weaknesses in the banking system.

It is important to note that from the financial stability perspective, stress testing have evolved from individual tests to system wide macroeco­nomic stress tests.

From a financial authority point of view, the methodologies for the design of stress tests can be divided in two approaches: the bottom-up ap­proach and the top-down approach explained in Sorge (2004) and Cihak (2007). The top-down approach is commonly used by central banks. In this approach, the purpose is to evaluate the impact of a scenario using aggregated data. Nevertheless, by using such an approach some relevant aspects could be ignored; for example, the interconnections between banks and the inherent contagion. On the other hand, under the bottom-up approach the objective is to evaluate the impact of a particular scenario by using data from the individual portfolios of the relevant institutions. The bottom-up approach should deliver more precise results; unfortunately, such an approach is limited by the lack of data and the complexity of the financial system.

In this work we employ the bottom-up ap­proach as we possess relatively good information on the individual banks, the interbank market and the size of the Mexican banking system permits to perform computer simulations to estimate the distribution of losses for the banking system as a whole. It is important from our point of view the relevance of performing coherent system wide stress test as it has been pointed out in Sorge and Virolainen (2006).

The design of scenarios is a relevant aspect in stress testing. It is important to point out that the result of the stress tests depends heavily on the design of such macroeconomic scenarios. The real objective to design a stress scenario is that it must satisfy the conditions of being a severe event and its probability of occurrence is not zero. To this end, the aspects that generate the most vulner­ability to the financial system must be identified and should be incorporated on the design of the stress scenario.

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