Abstract
Direct contagion has been widely studied in recent years and little evidence has been found to be relevant to the study of systemic risk. However, we argue that this limited contagion effect might be associated with a lack of relevant data. A common assumption for the estimation of the matrices of exposures is to apply the maximum entropy principle to deal with data gaps; such an assumption might lead to an underestimation of contagion risk. In this paper, there are no data gaps and the information set is extended from interbank exposures alone to exposures among most of the financial intermediaries in the Mexican financial system (we even include exposures to some international foreign banks). Naturally, the contagion risk of an extended network of exposures changes with respect to the interbank exposures network, as there are many more institutions which can be the source of contagion and there are more institutions which can fail due to contagion. The most important contribution of this paper is that it provides evidence on financial contagion with an extended exposures network under stressful conditions. The results presented here support the international efforts by the Bank for International Settlements, the International Monetary Fund and the Financial Stability Board to increase the amount of information available which can be used to assess systemic risk and contagion based on exposures and funding data.
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Notes
Stress testing is a technique used to assess how vulnerable a financial system is to exceptional but plausible macroeconomic shocks.
The institutions included in the analysis represent more than 80 % of the Mexican financial system’s assets.
This mechanism is quite convenient as the stressed scenarios are linked to the macroeconomic variables.
The exposure of the i-th institution with the j-th institution, \(\ell _{ij}\), is defined as the total risk that the i-th institution has with the j-th institution. Therefore, if the j-th institution defaults, the i-th institution loses \(\theta _{ij} \ell _{ij}\), where \(\theta _{ij}\in [0,1]\) is the loss given default. The total exposures include: foreign exchange, derivatives, securities and deposits and loans.
The regulatory capital of banks, icap (for its acronym in Spanish), is defined as
$$\begin{aligned} icap=\frac{NC}{RWA} \end{aligned}$$where NC is the net capital and RWA are the risk weighted assets.
The capital consumption index, icc, is defined as
$$\begin{aligned} icc=\frac{R}{GC} \end{aligned}$$where R is the capital requirement and GC the global capital.
For simplicity, it is assumed that the loss given default, \(\theta _{ij}=\theta =100~\%\). It is important to note that, because we are focusing the attention on tail risks, taking the worst case scenario, though unrealistic, is quite useful to measure the resilience of the Mexican financial system, given a systemic crisis.
As stated in the Mexican regulation \(\delta =20~\%\).
\(\Sigma \) was estimated by using univariate autoregressions with four lags.
The traditional approach is to set \(\underline{\alpha }=0_{KM}\) except for the elements corresponding to the first lag of the dependent variable in each equation, which is set to one.
The ridge estimator is defined as the solution of
$$\begin{aligned} \min _{\beta } \sum _{i=1}^n \left( y_i - \beta _0-\sum _{j=1}^p \beta _j x_{ij}\right) ^2+\lambda \sum _{j=1}^p \beta _j^2 \end{aligned}$$where \(\lambda > 0\) is a penalty parameter such that if \(\lambda \) increases \(\beta \) shrinks towards zero.
Changes in macroeconomic variables, the so-called risk factors, affect the market value of instruments because the risk factors were specifically chosen as the undelying rates, stock indexes and FX that affected the valuation of the Mexican instruments the most. The valuation was made using RiskWatch, a software from the Canadian company named Algorithmics.
The Frobenius norm of a correlation matrix R defined as
$$\begin{aligned} ||R||_F=\sqrt{\sum _{i,j} r_{ij}^2} \end{aligned}$$has the property of being bounded, such that
$$\begin{aligned} \sqrt{n} \le ||R||_F \le n . \end{aligned}$$
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Acknowledgments
The authors want to express their gratitude to Juan Pablo Graf Noriega and Pascual O’Dogherty Madrazo for their support for this research. The views expressed here are those of the authors and do not represent the views of Banco de México.
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Solorzano-Margain, J.P., Martinez-Jaramillo, S. & Lopez-Gallo, F. Financial contagion: extending the exposures network of the Mexican financial system. Comput Manag Sci 10, 125–155 (2013). https://doi.org/10.1007/s10287-013-0167-5
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DOI: https://doi.org/10.1007/s10287-013-0167-5