Eur. Phys. J. B (2012) 85: 102
https://doi.org/10.1140/epjb/e2012-20781-3

Regular Article

A simple analytical model for dynamics of time-varying target leverage ratios

¹ Institute of Theoretical Physics and Department of Physics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong SAR, P.R. China
² Research Department, Hong Kong Monetary Authority and Hong Kong Institute for Monetary Research, 55/F, Two International Finance Centre, 8 Finance Street, Central, Hong Kong SAR, P.R. China

^a e-mail: edcflo@gmail.com

Received: 21 September 2011
Published online: 26 March 2012

Abstract

In this paper we have formulated a simple theoretical model for the dynamics of the time-varying target leverage ratio of a firm under some assumptions based upon empirical observations. In our theoretical model the time evolution of the target leverage ratio of a firm can be derived self-consistently from a set of coupled Ito’s stochastic differential equations governing the leverage ratios of an ensemble of firms by the nonlinear Fokker-Planck equation approach. The theoretically derived time paths of the target leverage ratio bear great resemblance to those used in the time-dependent stationary-leverage (TDSL) model [Hui et al., Int. Rev. Financ. Analy. 15, 220 (2006)]. Thus, our simple model is able to provide a theoretical foundation for the selected time paths of the target leverage ratio in the TDSL model. We also examine how the pace of the adjustment of a firm’s target ratio, the volatility of the leverage ratio and the current leverage ratio affect the dynamics of the time-varying target leverage ratio. Hence, with the proposed dynamics of the time-dependent target leverage ratio, the TDSL model can be readily applied to generate the default probabilities of individual firms and to assess the default risk of the firms.