The financial crisis and, more recently, the European sovereign crisis, have led to a growing research literature on systemic risk, with different definitions and measurement models. According to the ECB (2009), "systemic risk is the risk of experiencing a strong systemic event, which adversely affects a number of systemically important intermediaries or markets". This broad view of systemic risk, which considers the system as a whole rather than individual institutions in isolation, is shared by many other definitions. However, systemic risk measurement models still differ in many details, such as the involved agents, the nature of the shocks and the economic perspective.
The main distinction between measurement models derives from the use of a cross-sectional, rather than a time-dynamic perspective. While the former mostly concentrates on the relationships between agents operating in the market (e.g. Lorenz et al. 2009, Battiston et al. 2012, Billio et al. 2012, Diebold and Yilmaz 2014, Barigozzi and Brownlees 2013, Ahelegbey et al. 2015, Das 2015, and Giudici and Spelta 2016), the latter focuses on cause-and-effect relationships over time (among others, Chong et al. 2006, Longstaff 2010, Shleifer and Vishny 2010, Duffie and Lando 2001, Lando and Nielsen 2010, Koopman et al. 2012, Betz et al. 2014, Duprey et al. 2015, Acharya et al. 2010, Adrian and Brunnermeier 2011, Brownlees and Engle 2012, Acharya et al. 2012, Dumitrescu and Banulescu 2014, Hautsch et al. 2015). Consequently, we can distinguish between models centred on contagion between institutions, and models that aim to predict what will happen in the nearby future, with an early-warning perspective. Contagion models can identify transmission channels, but are descriptive rather than predictive. Time-dependent models are predictive but, focusing on single institutions, they do not capture contagion mechanisms.
A new combined approach
While time dynamic models explain whether the risk of a bank, a company, or of a country, is affected by an endogenous market crisis event, or by a set of exogenous risk factors, cross-sectional models explain whether the same risk depends on contagion effects. In Giudici and Parisi (2016a), we have improved these two classes of models, introducing multivariate time-dependent stochastic processes, combined with correlation network models. Our model has been applied in a macroeconomic context to measure the systemic risk of the aggregate sovereign, corporate and bank sectors in different countries.
In new work, we extend the previous approach at the microeconomic level (Giudici and Parisi 2016b). In particular, we combine time-dependent default probabilities of financial institutions with correlation network models, thereby deriving a time-dependent total probability of default, which corrects the baseline probability of default with a probabilistic ‘add-on’ that depends on contagion effects deriving from interconnections with all the other institutions.
Bail-in or bail-out?
The methodology proposed in Giudici and Parisi (2016b) has been employed to analyse the main differences between bail-in and bail-out scenarios, which may occur in case a financial institution is close to its default point. More precisely, two alternatives have been compared: either the ‘troubled’ institution defaults, thus affecting its neighbours (the other banks in the system) through contagion propagation; or the troubled institution is helped by the other banks in the system through a capital lending operation (see Figure 1).
In the first situation, which we call the bail-in scenario, the troubled bank's default affects its neighbours through a shock in their default probabilities derived from contagion effects. However, after a while, the bank system reaches a new equilibrium without the defaulted bank and, thus, is affected by less contagion risk. In the second situation, which we call the bail-out scenario, the troubled bank does not default and, thus, does not affect its neighbours through a shock in their default probabilities. However, it continues to be part of the system, so that all the other banks in the network will still be affected by the high contagion risk derived from its presence. A comparison of the total default probabilities under these two scenarios will allow us to establish which banks in the system would benefit from a bail-out, rather than a bail-in scenario.
Application: Atlante and the Italian banking system
The above-described research design has first been applied to a stylised banking system, composed by three banks. Afterwards, it has been applied to the Italian banking system. This is a particularly interesting case study, as in April 2016 Italian banks organised themselves in the joint capitalisation of an equity fund, called Atlante, whose two main aims are the recapitalisation of ‘troubled’ financial institutions and the creation of an industrial non-performing loan asset disposal vehicle. Each bank decided, on a voluntary basis, whether to allocate capital to the Atlante fund, and to what degree, as shown in Table 1 below. Following this intervention, a medium-size lender, Banca Popolare di Vicenza (POPVI), found to be strongly under-capitalised by the ECB, has been recapitalised by the Atlante fund, which has fully subscribed a €1.75 billion capital increase. A similar intervention is foreseen for a similar lender (Veneto Banca).
Table 1. Largest Italian banks in terms of capitalisation, capital transferred to the Atlante fund (in million euros) and its impact on their capitalisation (expressed in percentage points)
The actual choice of each bank (to take part in the Atlante fund or not) can be evaluated from a systemic risk perspective. In particular, it can be done by examining how and how much the advantage of choosing a bail-out rather than a bail-in scenario depends on the default probability of the troubled bank (see Figure 2), on the partial correlations with it, and between safe banks (see Figure 3).
Figure 2 Italian banking system: Simulation
Figure 3 Bank correlations
The results of the research can be summarised as follows.
- First, it indicates that the smaller and safer a bank is, the larger the advantage of choosing the bail-out scenario. Such advantage is negatively associated with the default probability of the troubled bank, positively associated with the partial correlation with the troubled bank and, finally, negatively associated with the correlations between the safe banks.
- Second, the application to the Italian system reveals that some banks (BPM, CVAL, UBI), either small or highly correlated with POPVI, will benefit from the bail-out scenario, while some others (CRG, MPS, BAPO, BPER, CREDEM, POPSO), poorly correlated with POPVI and highly correlated with each other, will be damaged by this choice. Finally, some, including the largest ones (ISP, UCG, MB, MDL) are practically neutral.
- Third, consistently with our findings, CVAL and UBI are the banks that transferred the biggest fractions of their capital amount to Atlante.
- Fourth, again consistently with our findings, CREDEM and MB have not taken part in the fund. The former is indeed disadvantaged by a bail-out – the latter is almost neutral.
- Last, the long-time troubled bank CRG and MPS have decided to invest in the Atlante fund even if our model suggests they would not benefit from it. Their choices can thus be explained not in terms of systemic risk, but by other strategic factors (such as the expectation that Atlante can acquire part of their large stock of non performing loans).
Acharya, V V, L H Pedersen, T Philippon, and M Richardson (2010), “Measuring Systemic Risk”, Technical Report, New York University
Acharya, V V, R Engle, and M Richardson (2012), “Capital Shortfall: A New Approach to Ranking and Regulating Systemic Risks”, American Economic Review Papers and Proceedings, 102(3), 59-64.
Adrian, T, and M K Brunnermeier (2011), “CoVar ”, NBER Working Paper 17454
Ahelegbey, D F, M Billio, and R Casarin (2015), “Bayesian Graphical Models for Structural Vector Autoregressive Processes”, Journal of Applied Econometrics
Barigozzi, M, and C Brownlees (2013), “Nets: Network Estimation for Time Series”, Technical Report
Battiston, S, D Delli Gatti, M Gallegati, and B Greenwald, and J E Stiglitz (2012), “Liaisons dangereuses: Increasing connectivity risk sharing, and systemic risk”, Journal of Economic Dynamics and Control, 36 (8), 1121-1141
Betz, F, S Oprica, T A Peltonen, and P Sarlin (2014), “Predicting Distress in European Banks”, Journal of Banking and Finance, 45 (C), 225-241
Billio, M, M Getmansky, A W Lo, and L Pelizzon (2012), “Econometric measures of connectedness and systemic risk in the finance and insurance sectors”, Journal of Financial Economics, 104, 535-559.
Brownlees, C, and R Engle (2012), “Volatility, Correlation and Tails for Systemic Risk Measurement”, Technical Report, New York University
Chong, B S, M Liu, and K Shrestha (2006), “Monetary transmission via the administered interest rates channel”, Journal of Banking and Finance, 30 (5), 1467-1484
Das, S R (2015), “Matrix Metrics: Network-Based Systemic Risk Scoring”, Technical Report, Santa Clara University
Diebold, F X, and K Yilmaz (2014), “On the network topology of variance decompositions: Measuring the connectedness of financial firms”, Journal of Econometrics, 182, 119-134
Duffie, D, and D Lando (2001), “Term Structures of Credit Spreads with Incomplete Accounting Information”, Econometrica, 69 (3), 633-664
Duffie, D, L Saita, and K Wang (2007), “Multi-Period Corporate Default Prediction with Stochastic Covariates”, Journal of Financial Economics, 88 (3), 635-665
Dumitrescu, E, and D G Banulescu (2014), “Which are the SIFIs? A Component Expected Shortfall (CES) Approach to Systemic Risk”, Journal of Banking and Finance, 50, 575-588.
Duprey, T, B Klaus, and T A Peltonen (2015), “Dating systemic financial stress episodes in the EU countries”, Technical Report, ECB
ECB (2009), “Financial Stability Review”, Technical Report, ECB
Giudici, P, and L Parisi (2016a), “CoRisk: measuring systemic risk through default probability contagion”, Technical Report, University of Pavia
Giudici, P, and L Parisi (2016b), “Bail-in or Bail-out? The Atlante example from a systemic risk perspective”, Technical Report, University of Pavia
Giudici, P, and A Spelta (2015), “Graphical Network Models for International Financial Flows”, Journal of Business and Economic Statistics, forthcoming
Hautsch, N, J Schaumburg, and M Schienle (2015), “Financial Network Systemic Risk Contributions”, Review of Finance, 19 (2), 685-738
Koopman, S J, A Lucas, and B Schwaab (2012), “Dynamic factor models with macro, frailty, and industry effects for U.S. default counts: the credit crisis of 2008”, Journal of Business and Economic Statistics, 30 (4), 521-532
Lando, D, and M S Nielsen (2010), “Correlation in corporate defaults: contagion or conditional independence”, Journal of Financial Intermediation, 19 (3), 355-372
Longstaff, F A (2010), “The subprime credit crisis and contagion in financial markets”, Journal of Financial Economics, 97 (3), 436-450
Lorenz, J, Battiston, S, and F Schweitzer (2009), “Systemic risk in a unifying framework for cascading processes on networks”, The European Physical Journal B - Condensed Matter and Complex Systems, 71 (4), 441-460
Shleifer, A, and R W Vishny (2010), “Unstable banking”, Journal of Financial Economics, 97 (3), 306-318