A Simple Analytical Model for Dynamics of Time-Varying Target Leverage Ratios

European Physical Journal B, Vol. 85, No 3, Article Number 102, 2012

7 Pages Posted: 3 Sep 2009 Last revised: 27 Mar 2012

See all articles by Chi-Fai Lo

Chi-Fai Lo

The Chinese University of Hong Kong

Cho-Hoi Hui

Hong Kong Monetary Authority - Research Department

Date Written: September 20, 2011

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 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., International Review of Financial Analysis 15:220-36 (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 firm value (leverage) volatility 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.

Keywords: Target leverage ratios, Fokker-Planck equation, Mean-reverting dynamics

JEL Classification: C60, G13, G32

Suggested Citation

Lo, Chi-Fai and Hui, Cho-Hoi, A Simple Analytical Model for Dynamics of Time-Varying Target Leverage Ratios (September 20, 2011). European Physical Journal B, Vol. 85, No 3, Article Number 102, 2012. Available at SSRN: https://ssrn.com/abstract=1467385 or http://dx.doi.org/10.2139/ssrn.1467385

Chi-Fai Lo (Contact Author)

The Chinese University of Hong Kong ( email )

Department of Physics
Shatin, N.T., Hong Kong
China

Cho-Hoi Hui

Hong Kong Monetary Authority - Research Department ( email )

Hong Kong
China

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