Substantial academic research explains why firms should hedge, but little work has addressed how firms should hedge. We assume that firms can experience costly states of nature and derive optimal hedging strategies using vanilla derivatives (e.g., forwards and options) and custom "exotic" derivative contracts for a value-maximizing firm facing both hedgable (price) and unhedgable (quantity) risks. Customized exotic derivatives are typically better than vanilla contracts when correlations between prices and quantities are large in magnitude and when quantity risks are substantially greater than price risks. Finally, we discuss how our model may be applied in practice.

Substantial academic research explains why firms should hedge, but little work has addressed how firms should hedge. We assume that firms can experience costly states of nature and derive optimal hedging strategies using vanilla derivatives (e.g., forwards and options) and custom “exotic” derivative contracts for a value-maximizing firm facing both hedgable (price) and unhedgable (quantity) risks. Customized exotic derivatives are typically better than vanilla contracts when correlations between prices and quantities are large in magnitude and when quantity risks are substantially greater than price risks. Finally, we discuss how our model may be applied in practice.

This article provides a comprehensive study of survivorship issues using the mutual fund data of Carhart (1997). We demonstrate theoretically that when survival depends on multiperiod performance, the survivorship bias in average performance typically increases with the sample length. This is empirically relevant because evidence suggests a multiyear survival rule for U.S. mutual funds. In the data we find the annual bias increases from 0.07% for 1-year samples to 1% for samples longer than 15 years. We find that survivor conditioning weakens evidence of performance persistence. Finally, we explain how survivor conditioning affects the relation between performance and fund characteristics.

This article provides a comprehensive study of survivorship issues using the mutual fund data of Carhart (1997). We demonstrate theoretically that when survival depends on multiperiod performance, the survivorship bias in average performance typically increases with the sample length. This is empirically relevant because evidence suggests a multiyear survival rule for U.S. mutual funds. In the data we find the annual bias increases from 0.07% for 1-year samples to 1% for samples longer than 15 years. We find that survivor conditioning weakens evidence of performance persistence. Finally, we explain how survivor conditioning affects the relation between performance and fund characteristics.