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Bankruptcy risk model and empirical tests

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  • Boris Podobnik
  • Davor Horvatic
  • Alexander M. Petersen
  • Branko Urov{s}evi'c
  • H. Eugene Stanley

Abstract

We analyze the size dependence and temporal stability of firm bankruptcy risk in the US economy by applying Zipf scaling techniques. We focus on a single risk factor-the debt-to-asset ratio R-in order to study the stability of the Zipf distribution of R over time. We find that the Zipf exponent increases during market crashes, implying that firms go bankrupt with larger values of R. Based on the Zipf analysis, we employ Bayes's theorem and relate the conditional probability that a bankrupt firm has a ratio R with the conditional probability of bankruptcy for a firm with a given R value. For 2,737 bankrupt firms, we demonstrate size dependence in assets change during the bankruptcy proceedings. Prepetition firm assets and petition firm assets follow Zipf distributions but with different exponents, meaning that firms with smaller assets adjust their assets more than firms with larger assets during the bankruptcy process. We compare bankrupt firms with nonbankrupt firms by analyzing the assets and liabilities of two large subsets of the US economy: 2,545 Nasdaq members and 1,680 New York Stock Exchange (NYSE) members. We find that both assets and liabilities follow a Pareto distribution. The finding is not a trivial consequence of the Zipf scaling relationship of firm size quantified by employees-although the market capitalization of Nasdaq stocks follows a Pareto distribution, the same distribution does not describe NYSE stocks. We propose a coupled Simon model that simultaneously evolves both assets and debt with the possibility of bankruptcy, and we also consider the possibility of firm mergers.

Suggested Citation

  • Boris Podobnik & Davor Horvatic & Alexander M. Petersen & Branko Urov{s}evi'c & H. Eugene Stanley, 2010. "Bankruptcy risk model and empirical tests," Papers 1011.2670, arXiv.org.
  • Handle: RePEc:arx:papers:1011.2670
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    References listed on IDEAS

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    Cited by:

    1. Einar Erlingsson & Simone Alfarano & Marco Raberto & Hlynur Stefánsson, 2013. "On the distributional properties of size, profit and growth of Icelandic firms," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 8(1), pages 57-74, April.
    2. Li, Jianjun & Hsu, Sara & Qin, Yanzhi, 2014. "Shadow banking in China: Institutional risks," China Economic Review, Elsevier, vol. 31(C), pages 119-129.
    3. Chen, Yanguang, 2012. "The rank-size scaling law and entropy-maximizing principle," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 767-778.
    4. Kaldasch, Joachim, 2012. "Evolutionary model of the growth and size of firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(14), pages 3751-3769.
    5. Chen, Yanguang & Wang, Jiejing, 2014. "Recursive subdivision of urban space and Zipf’s law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 392-404.
    6. Chen, Yanguang, 2012. "The mathematical relationship between Zipf’s law and the hierarchical scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3285-3299.
    7. Xiao, Weilin & Zhang, Weiguo & Zhang, Xili & Chen, Xiaoyan, 2014. "The valuation of equity warrants under the fractional Vasicek process of the short-term interest rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 320-337.
    8. Cristescu, Constantin P. & Stan, Cristina & Scarlat, Eugen I. & Minea, Teofil & Cristescu, Cristina M., 2012. "Parameter motivated mutual correlation analysis: Application to the study of currency exchange rates based on intermittency parameter and Hurst exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2623-2635.
    9. Giulio Bottazzi & Davide Pirino & Federico Tamagni, 2015. "Zipf law and the firm size distribution: a critical discussion of popular estimators," Journal of Evolutionary Economics, Springer, vol. 25(3), pages 585-610, July.
    10. Anindya S. Chakrabarti, 2013. "Bimodality in the firm size distributions: a kinetic exchange model approach," Papers 1302.3818, arXiv.org, revised May 2013.
    11. Hu, Lunchao & Tian, Kailan & Wang, Xin & Zhang, Jiang, 2012. "The “S” curve relationship between export diversity and economic size of countries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 731-739.
    12. Chakrabarti, Anindya S., 2012. "Effects of the turnover rate on the size distribution of firms: An application of the kinetic exchange models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6039-6050.
    13. Xiao, Weilin & Zhang, Xili, 2016. "Pricing equity warrants with a promised lowest price in Merton’s jump–diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 219-238.
    14. Lee, Sangwook & Kim, Min Jae & Lee, Sun Young & Kim, Soo Yong & Ban, Joon Hwa, 2013. "The effect of the subprime crisis on the credit risk in global scale," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2060-2071.
    15. Liu, Yufang & Zhang, Weiguo & Fu, Junhui, 2016. "Binomial Markov-Switching Multifractal model with Skewed t innovations and applications to Chinese SSEC Index," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 56-66.
    16. Morales, Raffaello & Di Matteo, T. & Gramatica, Ruggero & Aste, Tomaso, 2012. "Dynamical generalized Hurst exponent as a tool to monitor unstable periods in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3180-3189.
    17. Wu, Yajing & Guo, Jinzhong & Chen, Qinghua & Wang, Yougui, 2011. "Socioeconomic implications of donation distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4325-4331.

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