| | **Bankruptcy Risk Model and Empirical Tests**
by Boris Podobnik of the Boston University & the University of Rijeka & the University of Ljubljana, Davor Horvatic of the University of Zagreb, Alexander M. Petersen of the Boston University, Branko Urošević of the University of Belgrade, and H. Eugene Stanley of the Boston University November 12, 2010 **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' 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. Pre-petition 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 non-bankrupt firms by analyzing the assets and liabilities of two large subsets of the US economy: 2,545 Nasdaq members and 1,680 NYSE members. We find that both assets and liabilities follow a Pareto distribution. This is not a trivial consequence of the Zipf scaling relationship of firm size quantified by employees -- while the market capitalization of Nasdaq stocks follows a Pareto distribution, this is not true for 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.
**Published in:** *Proceedings of the National Academy of Sciences*, Vol. 107, No. 43, (October 26, 2010), pp. 18325-18330.
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