Given equity's convex payoff function, shareholders can transfer wealth from bondholders by increasing firm risk. We test the existing hypothesis that convertible debt reduces this classical agency problem of risk-shifting. First, we derive a measure of shareholders' risk incentives induced by convertible debt using a contingent claims framework. We then document that when risk-shifting incentives are high, the propensity to issue convertible (rather than straight) debt increases and the negative stock market reaction following convertible debt issue announcements is amplified. We further highlight that convertible debt is the only type of security that affects business risk durably downwards. Our conclusions support the agency theoretic rationale for convertible debt financing especially for financially distressed firms.