Dynamic Hedging Incentives, Debt, and Warrants

In a static setting, Green (1984) shows that a warrant contract can eliminate the asset substitution problem created by debt. In contrast, we show that when the firm chooses volatility dynamically, no warrant can eliminate asset substitution, as equity is always risk-loving when the firm is near default. The hedging incentive produced by a warrant is weakest when the option is out of the money, precisely when the speculative incentive due to limited liability is strongest. Although warrants mitigate dynamic asset substitution, we show that they exacerbate the agency problem of premature default (underinvestment). Indeed, unless a firm has sufficient volatility discretion, the costs of premature default dominate. For firms with sufficient volatility discretion, where warrants potentially increase value, they do so only if they grant large equity stakes. The optimal warrant contract entails "maximum deterrence," fully diluting existing shareholders upon conversion.