Convex costs and the hedging paradox

Financial theory suggests that hedging can increase shareholder value in the presence of capital market imperfections, including direct and indirect costs of financial distress, costly external financing, and convex tax exposure. The influence of these costs, which are high when profits are low and low or negligible when profits are large, on the extent of firm hedging has not been consistently addressed in the finance literature. In Brown and Toft's (2002) model, more convex costs imply that a firm will decrease the extent of hedging. At the same time, one version of Smith and Stulz's (1985) tax hypothesis implies that a given firm is expected to increase the extent of hedging under a more convex tax exposure. I address this ambiguity in the literature by showing that, in incomplete markets, value-maximizing firms that stand to gain the most from hedging may in fact hedge less than otherwise identical firms with less to gain from hedging. This hedging paradox can partly account for the lack of conclusive evidence to suggest that convex costs can influence both a firm's decision to hedge and the extent of the firm's hedging. Finally, I introduce a new interpretation of empirical relations between potential hedging gains and the extent of hedging.