[We provide fully analytical, optimal dynamic hedges in incomplete markets by employing the traditional minimum-variance criterion. Our hedges are in terms of generalized "Greeks" and naturally extend no-arbitrage-based risk management in complete markets to incomplete markets. Whereas the literature characterizes either minimum-variance static, myopic, or dynamic hedges from which a hedger may deviate unless able to precommit, our hedges are time-consistent. We apply our results to derivatives replication with infrequent trading and determine hedges and replication values, which reduce to generalized Black-Scholes expressions in specific settings. We also investigate dynamic hedging with jumps, stochastic correlation, and portfolio management with benchmarking.]

We provide fully analytical, optimal dynamic hedges in incomplete markets by employing the traditional minimum-variance criterion. Our hedges are in terms of generalized “Greeks” and naturally extend no-arbitrage–based risk management in complete markets to incomplete markets. Whereas the literature characterizes either minimum-variance static, myopic, or dynamic hedges from which a hedger may deviate unless able to precommit, our hedges are time-consistent. We apply our results to derivatives replication with infrequent trading and determine hedges and replication values, which reduce to generalized Black-Scholes expressions in specific settings. We also investigate dynamic hedging with jumps, stochastic correlation, and portfolio management with benchmarking.

Absent much theory, empirical works often rely on the following informal reasoning when looking for evidence of a mutual fund tournament: If there is a tournament, interim winners have incentives to decrease their portfolio volatility as they attempt to protect their lead, while interim losers are expected to increase their volatility so as to catch up with winners. We consider a rational model of a mutual fund tournament in the presence of short-sale constraints and find the opposite: Interim winners choose more volatile portfolios in equilibrium than interim losers. Several empirical works present evidence consistent with our model. However, based on the above informal argument, they appear to conclude against the tournament behavior. We argue that this conclusion is unwarranted. We also demonstrate that tournament incentives lead to differences in interim performance for otherwise identical managers and that mid-year trading volume is inversely related to mid-year stock return.