The authors analyze the tradeoff between the benefits of hedging in terms of enhanced risk sharing and its costs in terms of financial instability. They model hedging as the design of a contract between a protection buyer, seeking to reduce his risk exposure, and a protection seller. If the latter learns that the hedge is likely to be loss-making for her even though actual losses have not materialized yet, this amounts to an "off-balance sheet" liability. It undermines her incentives to exert monitoring effort to reduce the default risk of her other holdings. In turn, such risk-taking incentives generate counterparty risk. Hence, hedging can create systemic risk by inducing contagion between otherwise independent asset classes. In this context, margins and capital requirements can improve incentives and mitigate risk.