A Brief Review of Catastrophe Theory and a Test in a Corporate Failure Context

Catastrophe theory (CT) is a mathematical theory that attempts to describe a system exhibiting discontinuous behavior under continuous stimuli. Although CT has been used to describe corporate bankruptcy, this is an application that has not been tested. This paper reviews CT and provides such a test. We construct a time series of stock returns on companies that have filed for Chapter 11. Under certain, frequently occurring conditions, CT would predict a structural shift in firm stock returns as the data of filing is approached. Results confirm that such a shift does occur and in a way consistent with the CT prediction. Our findings both support the use of CT to describe corporate bankruptcy and raise questions about some techniques frequently used to study bankruptcies.     

AN EMPIRICAL INVESTIGATION OF BETA STABILITY: PORTFOLIOS VS. INDIVIDUAL SECURITIES

The concept that portfolio betas are more stable than betas for individual securities has become the 'conventional wisdom' in finance; statements to this effect may be found in many popular finance textbooks. The objective of this paper is to challenge the conventional wisdom. A random sample of individual stock returns and portfolio returns is used to compare the empirical distribution of beta shifts for individual firms and portfolios. The number of statistically significant changes in beta are no greater for individual securities than for portfolios.     

The Estimation of Systematic Risk under Differentiated Risk Aversion: A Mean-Extended Gini Approach

This paper examines a mean-Gini model of systematic risk estimation that resolves some econometric problems with mean-variance beta estimation and allows for heterogeneous risk aversion across investors. Using the mean-extended Gini (MEG) model, we estimate systematic risks for different degrees of risk aversion. MEG betas are shown to be instrumental variable estimators that provide econometric solutions to biases generated by the estimation of mean-variance (MV) betas. When security returns are not normally distributed, MEG betas are proved to differ from MV betas. We design an econometric test that assesses whether these differences are significant. As an application using daily returns, we estimate MEG and MV betas for U.S. securities.