Skip to main content

Atheoretical Regression Trees for classifying risky financial institutions


We propose a recursive partitioning approach to identify groups of risky financial institutions using a synthetic indicator built on the information arising from a sample of pooled systemic risk measures. The composition and amplitude of the risky groups change over time, emphasizing the periods of high systemic risk stress. We also calculate the probability that a financial institution can change risk group over the next month and show that a firm belonging to the lowest or highest risk group has in general a high probability to remain in that group.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8


  1. We thank Federico Nucera for sharing with us the original dataset on which the paper Nucera et al. (2016) is based. We restrict our sample to include only EU institutions and we exclude real estate and other non financial corporation.




  • Acharya, V., Engle, R., & Richardson, M. (2012). Capital shortfall: A new approach to ranking and regulating systemic risks. American Economic Review Papers and Proceedings, 102(3), 59–64.

    Article  Google Scholar 

  • Acharya, V., & Steffen, S. (2015). The ‘greatest’ carry trade ever? Understanding eurozone bank risks. Journal of Financial Economics, 115(2), 215–236.

    Article  Google Scholar 

  • Acharya, V. V., Pedersen, L. H., Philippon, T., & Richardson, M. P. (2017). Measuring systemic risk. The Review of Financial Studies, 30(1), 2–47.

    Article  Google Scholar 

  • Adrian, T., & Brunnermeier, M. (2016). CoVaR. American Economic Review, 106(7), 1705–1741.

    Article  Google Scholar 

  • Adrian, T., & Shin, H. (2010). Liquidity and leverage. Journal of Financial Intermediation, 19(3), 418–437.

    Article  Google Scholar 

  • Benoit, S., Colletaz, G., Hurlin, C., & Pérignon, C. (2013). A theoretical and empirical comparison of systemic risk measures. HEC Paris Research Papers, No. FIN-2014-1030.

  • Billio, M., Getmansky, M., Lo, A. W., & Pelizzon, L. (2012). Econometric measures of systemic risk in the finance and insurance sectors. Journal of Financial Economics, 104(2), 535–559.

    Article  Google Scholar 

  • Breiman, L., Friedman, J., Stone, C., & Olshen, R. (1984). Classification and regression trees. Boca Raton: CRC Press.

    Google Scholar 

  • Brownlees, C. T., & Engle, R. (2017). SRISK: A conditional capital shortfall measure of systemic risk. The Review of Financial Studies, 30(1), 48–79.

    Article  Google Scholar 

  • Cappelli, C., & Di Iorio, F. (2010). Detecting contemporaneous mean co-breaking via ART and PCA. Quaderni di Statistica, 12, 175–190.

    Google Scholar 

  • Cappelli, C., D’Urso, P., & Di Iorio, F. (2013). Change point analysis of imprecise time series. Fuzzy Sets and Systems, 225, 23–38.

    Article  Google Scholar 

  • Cappelli, C., D’Urso, P., & Di Iorio, F. (2015). Regime change analysis of interval-valued time series with an application to PM10. Chemometrics and Intelligent Laboratory System, 146, 337–346.

    Article  Google Scholar 

  • Cappelli, C., Mola, F., & Siciliano, R. (2002). A statistical approach to growing a reliable honest tree. Computational Statistics and Data Analysis, 38, 285–299.

    Article  Google Scholar 

  • Cappelli, C., Penny, R., Rea, W., & Reale, M. (2008). Detecting multiple mean breaks at unknown points in official time series. Mathematics and Computers in Simulation, 78(2), 351–356.

    Article  Google Scholar 

  • Cappelli, C., & Reale, M. (2005). Detecting changes in mean levels with atheoretical regression tree. In S.Co.2005: Modelli Complessi e Metodi Computazionali Intensivi per la Stima e la Previsione (pp. 479–484). Cleup, Padova.

  • ECB. (2009). The concept of systemic risk. Special Feature in Financial Stability Review, December.

  • ECB. (2010). Analytical models and tools for the identification and assessment of systemic risks. Special Feature in Financial Stability Review, June.

  • ECB. (2011). Systemic risk methodologies. Special Feature in Financial Stability Review, June.

  • Engle, R. (2015). Dynamic conditional beta. Available at SSRN 2404020.

  • Engle, R., Jondeau, E., & Rockinger, M. (2015). Systemic risk in Europe. Review of Finance, 19(1), 145–190.

    Article  Google Scholar 

  • Everitt, B. S., Landau, S., & Leese, M. (2001). Cluster analysis. London: Arnold.

    Google Scholar 

  • Fisher, W. (1958). On grouping for maximum homogeneity. Journal of the American Statistical Association, 53(284), 789–798.

    Article  Google Scholar 

  • Fostel, A., & Geanakoplos, J. (2008). Leverage cycles and the anxious economy. The American Economic Review, 98(4), 1211–1244.

    Article  Google Scholar 

  • Geanakoplos, J., & Pedersen, L. H. (2012). Monitoring leverage. In M. Brunnermeier & A. Krishnamurthy (Eds.), Risk topography: Systemic risk and macro modeling (pp. 113–127). Chicago: University of Chicago Press.

    Google Scholar 

  • Giglio, S., Kelly, B., & Pruitt, S. (2016). Systemic risk and the macroeconomy: An empirical evaluation. Journal of Financial Economics, 119(3), 457–471.

    Article  Google Scholar 

  • Jones, M. (2005). Estimating Markov transition matrices using proportions data: An application to credit risk. IMF working paper, n.05/219.

  • Loh, W.-Y. (2011). Classification and regression trees. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 1(1), 14–23.

    Google Scholar 

  • Nucera, F., Schwaab, B., Koopman, S., & Lucas, A. (2016). The information in systemic risk rankings. Journal of Empirical Finance, 38, 461–475.

    Article  Google Scholar 

  • Rea, W., Reale, M., Cappelli, C., & Brown, J. (2010). Identification of changes in mean with regression trees: An application to market research. Econometric Reviews, 29, 754–777.

    Article  Google Scholar 

  • Rodríguez-Moreno, M., & Peña, J. (2013). Systemic risk measures: The simpler the better? Journal of Banking and Finance, 37(6), 1817–1831.

    Article  Google Scholar 

  • Zhou, C., & Tarashev, N. (2013). Looking at the tail: Price-based measures of systemic importance. BIS Quarterly Review.

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Carmela Cappelli.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This paper should not be reported as representing the views of the European Central Bank (ECB). The views expressed here are those of the authors and do not necessarily reflect those of the ECB or the Eurosystem.



Table 3 collects the descriptive statistics of the risk indicators. Table 4 refers to the mean and the standard error of the principal component scores for each risk group and month. Figure 9 describes the characteristics of the class size distribution for each year, while the behavior of the cut-off points over the time period are reported in Fig. 10 (Table 5).

Table 3 Systemic risk indicators descriptive statistics
Table 4 Mean value in recursive partition (standard error in italic)
Fig. 9
figure 9

Box plots of monthly risk class sizes by year

Fig. 10
figure 10

Monthly cut-off points, 2010–2015

Table 5 Outliers by year in brackets the number of months out of range

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Cappelli, C., Di Iorio, F., Maddaloni, A. et al. Atheoretical Regression Trees for classifying risky financial institutions. Ann Oper Res 299, 1357–1377 (2021).

Download citation

  • Published:

  • Issue Date:

  • DOI:


  • Systemic risk
  • Financial stress
  • Atheoretical Regression Trees
  • Factor analysis