Risk Shifting, Conversion Rules, and Optional Payment Schedules

Prior theories of convertible debt have showed that this instrument can mitigate the risk-shifting problem arising when managers substitute risky projects for safer ones, since the attribution to debt investors of a contingent equity claim can deconvexify the shape of levered equity. However, existing risk-shifting theories of convertibles omit to fully consider that these instruments must be designed so to leave investors a large part of project rents – to specify high conversion ratios – to provide effective deterrence against risk-shifting incentives.My first contribution to the literature on convertible debt and risk shifting is to show that, given a specific cash flow distribution, it is possible to design conversion features so to create an upward jump discontinuity in investors' payoff function. By making the firm's payment schedule non-monotonic, this jump discontinuity implicitly raises the leverage of the conversion option, without, however, increasing the project rents investors can capture. My second contribution is to show that when the level of fixed claims is exogenously, rather than endogenously determined, the optimal convertible debt contract is implemented by granting debt investors two options. At an interim date, investors can choose one between two alternative conversion plans: a debt-like and an equity-like conversion plan. Once payoff are realized, investors can then choose whether to convert or not. Finally, policy considerations are extensively discussed