A Dynamic Model of Risk-Shifting Incentives with Convertible Debt

Abstract

In a one-period setting Green (1984) demonstrates that convertible debt perfectly mitigates the asset substitution problem by curbing shareholders’ incentive to increase risk. This is because claimholders design the capital structure precisely when the risk-shifting opportunity is available. In practice, firms do not alter their capital structure over the life of the convertible debt. Hence, when the risk-shifting opportunity arises, convertible debt design may no longer match with firm asset value to mitigate the asset substitution problem. 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 convertibles 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.