There are two tax incentives for corporations to hedge: to increase debt capacity and interest tax deductions, and to reduce expected tax liability if the tax function is convex. We test whether these incentives affect the extent of corporate hedging with derivatives. Using an explicit measure of tax function convexity, we find no evidence that firms hedge in response to tax convexity. Our analysis does, however, indicate that firms hedge to increase debt capacity, with increased tax benefits averaging 1.1 percent of firm value. Our results also indicate that firms hedge because of expected financial distress costs and firm size.

Previous research offers little large-sample evidence on the magnitude of non-financial firms ' risk exposure hedged by financial derivatives. In a sample of 234 large non-financial corporations that use derivatives, we find that if the median firm simultaneously experiences a three standard deviation change in interest rates, currency exchange rates, and commodity prices, it will collect $15 million of cash from its entire derivatives portfolio and that the entire derivatives portfolio will rise in value by $31 million. These dollar amounts are modest relative to firm size, operating cash flows, investing cash flows and other firm benchmarks. The findings raise questions about the role of derivatives securities held by non-financial firms.

Substantial academic research has explained why ¯rms should hedge, but little work has addressed how ¯rms should hedge. We assume that ¯rms face 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 ¯rm that faces both hedgable (price) and unhedgable (quantity) risks. Optimal hedges depend critically on price and quantity volatilities, the correlation between price and quantity, and pro¯t margin. A close relationship exists between the optimal number of forward contracts and the optimal custom hedge: At the forward price of the traded good, the optimal forward hedge and the optimal exotic hedge have identical \deltas. " At prices di®erent from the forward price, the exotic contract ¯ne-tunes the ¯rm's exposure by including a non-linear payo ® component. We also determine the bene¯ts from choosing customized exotic derivatives over vanilla contracts for di®erent types of ¯rms. 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