A Dynamic Model of Risk-Shifting Incentives with Convertible Debt

43 Pages Posted: 21 Feb 2006 Last revised: 17 Aug 2009

See all articles by Pascal Francois

Pascal Francois

HEC Montreal - Department of Finance

Georges Hübner

HEC Liège

Nicolas A. Papageorgiou

HEC Montreal - Department of Finance

Date Written: July 31, 2009

Abstract

Green (1984) demonstrates in a one-period setting that convertible debt can eliminate the asset substitution problem. However, in a multi-period setting the terms of the convertible issue will in general be set before the specific asset substitution opportunity presents itself. This leaves room for a strategic non-cooperative game between shareholders and convertible debtholders. We show that two risk-shifting scenarios arise as attainable Nash equilibria. Pure asset substitution occurs when, despite convertible debtholders not exercising their conversion option, shareholders still find it profitable to shift risk. Strategic conversion occurs when, despite convertible debtholders giving up the conversion option value, they are better off receiving their share of the wealth expropriation from straight debtholders. We use contingent claims analysis and the Black and Scholes (1973) setup to characterize the equilibria. Even when initial convertible debt is endogenously designed so as to minimize the likelihood of risk-shifting equilibria, we show that asset substitution cannot be completely eliminated. Our overall conclusion is that -- in contrast to agency theory's claim -- convertible debt is an imperfect instrument for mitigating shareholders' incentive to increase risk.

Keywords: Convertible debt, Risk shifting, Non-cooperative game

JEL Classification: C72, G32

Suggested Citation

Francois, Pascal and Hübner, Georges and Papageorgiou, Nicolas A., A Dynamic Model of Risk-Shifting Incentives with Convertible Debt (July 31, 2009). Available at SSRN: https://ssrn.com/abstract=884180 or http://dx.doi.org/10.2139/ssrn.884180

Pascal Francois (Contact Author)

HEC Montreal - Department of Finance ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada
514-340-7743 (Phone)
514-340-5632 (Fax)

Georges Hübner

HEC Liège ( email )

Rue Louvrex 14, Bldg. N1
Liege, 4000
Belgium
+32 42327428 (Phone)

Nicolas A. Papageorgiou

HEC Montreal - Department of Finance ( email )

3000 Chemin de la Cote-Sainte-Catherine
Montreal, Quebec H3T 2A7
Canada

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