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Taking the Twists into Account: Predicting Firm Bankruptcy Risk with Splines of Financial Ratios

Author

Listed:
  • Giordani, Paolo
  • Jacobson, Tor
  • Schedvin, Erik von
  • Villani, Mattias

Abstract

We demonstrate improvements in predictive power when introducing spline functions to take account of highly nonlinear relationships between firm failure and leverage, earnings, and liquidity in a logistic bankruptcy model. Our results show that modeling excessive nonlinearities yields substantially improved bankruptcy predictions, on the order of 70%–90%, compared with a standard logistic model. The spline model provides several important and surprising insights into nonmonotonic bankruptcy relationships. We find that low-leveraged as well as highly profitable firms are riskier than those given by a standard model, possibly a manifestation of credit rationing and excess cash-flow volatility.

Suggested Citation

  • Giordani, Paolo & Jacobson, Tor & Schedvin, Erik von & Villani, Mattias, 2014. "Taking the Twists into Account: Predicting Firm Bankruptcy Risk with Splines of Financial Ratios," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 49(4), pages 1071-1099, August.
    • Handle: RePEc:cup:jfinqa:v:49:y:2014:i:04:p:1071-1099_00
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    Cited by:

    1. Cathcart, Lara & Dufour, Alfonso & Rossi, Ludovico & Varotto, Simone, 2020. "The differential impact of leverage on the default risk of small and large firms," Journal of Corporate Finance, Elsevier, vol. 60(C).
    2. Gunawan, David & Dang, Khue-Dung & Quiroz, Matias & Kohn, Robert & Tran, Minh-Ngoc, 2019. "Subsampling Sequential Monte Carlo for Static Bayesian Models," Working Paper Series 371, Sveriges Riksbank (Central Bank of Sweden).
    3. Xueyan Dong & Kam C. Chan & Yujia Cui & Jenny Xinjiao Guan, 2021. "Strategic deviance and cash holdings," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 48(3-4), pages 742-782, March.
    4. Muhammad Zubair Mumtaz & Zachary Alexander Smith, 2018. "IPOs in the U.S. from 2005 to 2015: Using the Spline Regression Technique to Estimate Aggregate Issuance and Performance," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 68(2), pages 165-199, April.
    5. Lee, Kangbok & Joo, Sunghoon & Baik, Hyeoncheol & Han, Sumin & In, Joonhwan, 2020. "Unbalanced data, type II error, and nonlinearity in predicting M&A failure," Journal of Business Research, Elsevier, vol. 109(C), pages 271-287.
    6. Villani, Mattias & Kohn, Robert & Nott, David J., 2012. "Generalized smooth finite mixtures," Journal of Econometrics, Elsevier, vol. 171(2), pages 121-133.
    7. Ida Nervik Hjelseth & Arvid Raknerud & Bjørn H. Vatne, 2022. "A bankruptcy probability model for assessing credit risk on corporate loans with automated variable selection," Working Paper 2022/7, Norges Bank.
    8. Michel Alexandre & Gilberto Tadeu Lima & Luca Riccetti & Alberto Russo, 2023. "The financial network channel of monetary policy transmission: an agent-based model," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(3), pages 533-571, July.
    9. Taoushianis, Zenon, 2025. "Bankruptcy prediction with fractional polynomial transformation of financial ratios," European Journal of Operational Research, Elsevier, vol. 327(2), pages 690-702.
    10. Péter Bauer & Marianna Endrész, 2016. "Modelling Bankruptcy Using Hungarian Firm-Level Data," MNB Occasional Papers 2016/122, Magyar Nemzeti Bank (Central Bank of Hungary).
    11. Ken Li, 2024. "Liquidity ratios and corporate failures," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 64(1), pages 1111-1134, March.
    12. Matias Quiroz & Robert Kohn & Mattias Villani & Minh-Ngoc Tran, 2019. "Speeding Up MCMC by Efficient Data Subsampling," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 831-843, April.
    13. Dang, Khue-Dung & Quiroz, Matias & Kohn, Robert & Tran, Minh-Ngoc & Villani, Mattias, 2019. "Hamiltonian Monte Carlo with Energy Conserving Subsampling," Working Paper Series 372, Sveriges Riksbank (Central Bank of Sweden).
    14. Niklas Amberg & Tor Jacobson & Erik von Schedvin & Robert Townsend, 2021. "Curbing Shocks to Corporate Liquidity: The Role of Trade Credit," Journal of Political Economy, University of Chicago Press, vol. 129(1), pages 182-242.
    15. Koresh Galil & Neta Gilat, 2019. "Predicting Default More Accurately: To Proxy or Not to Proxy for Default?," International Review of Finance, International Review of Finance Ltd., vol. 19(4), pages 731-758, December.
    16. Feng Li & Mattias Villani, 2013. "Efficient Bayesian Multivariate Surface Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 706-723, December.
    17. Quiroz, Matias & Villani, Mattias, 2013. "Dynamic mixture-of-experts models for longitudinal and discrete-time survival data," Working Paper Series 268, Sveriges Riksbank (Central Bank of Sweden).
    18. Georgios Sermpinis & Serafeim Tsoukas & Ping Zhang, 2019. "What influences a bank's decision to go public?," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 24(4), pages 1464-1485, October.
    19. Flavio de Carolis & Vinzenz Peters, 2025. "European SMEs, Corporate Finance and Economic Resilience to Floods," Working Papers 832, DNB.

    More about this item

    JEL classification:

    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation
    • G38 - Financial Economics - - Corporate Finance and Governance - - - Government Policy and Regulation

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