A Dynamic Model of Risk-Shifting Incentives with Convertible Debt

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