Bankruptcy Risk Model and Empirical Tests

PNAS, Vol. 107, No. 43, 2010

8 Pages Posted: 11 Nov 2010 Last revised: 19 Nov 2010

See all articles by Boris Podobnik

Boris Podobnik

Boston University; University of Rijeka

Davor Horvatic

Theoretical Physics Department, University of Zagreb

Alexander Michael Petersen

University of California Merced, Ernest and Julio Gallo Management Program

Branko Urosevic

affiliation not provided to SSRN

H. Eugene Stanley

Boston University - Center for Polymer Studies

Date Written: October 26, 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’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 non-bankrupt 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.

Keywords: economic sciences, econophysics, finance, bankruptcy risk, debt-to-asset ratio

Suggested Citation

Podobnik, Boris and Horvatic, Davor and Petersen, Alexander Michael and Urosevic, Branko and Stanley, H. Eugene, Bankruptcy Risk Model and Empirical Tests (October 26, 2010). PNAS, Vol. 107, No. 43, 2010, Available at SSRN: https://ssrn.com/abstract=1706278

Boris Podobnik (Contact Author)

Boston University ( email )

University of Rijeka ( email )

Rijeka, 51000
Croatia

Davor Horvatic

Theoretical Physics Department, University of Zagreb ( email )

Trg maršala Tita 14
Zagreb
Croatia

Alexander Michael Petersen

University of California Merced, Ernest and Julio Gallo Management Program ( email )

School of Engineering
Science & Engineering 2, Suite 315
Merced, CA 95343
United States

Branko Urosevic

affiliation not provided to SSRN ( email )

H. Eugene Stanley

Boston University - Center for Polymer Studies ( email )

Boston, MA 02215
United States

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