We study dynamic equilibrium in a Lucas economy with two stocks, two heterogeneous constant relative risk aversion investors, and portfolio constraints. We focus on margin and leverage constraints, which restrict access to credit. We find a positive relationship between the amount of leverage in the economy and magnitudes of stock return correlations and volatilities. Tighter constraints generate rich patterns in correlations and volatilities, make them less countercyclical, increase risk premia proportionally to assets' margins, and increase prices of low-margin assets more than prices of high-margin assets. We derive closed-form solutions for the unconstrained case and the case of leverage constraints.

We theoretically analyze how index investing affects financial markets using a dynamic exchange economy with heterogeneous investors and two Lucas trees. We identify two effects of indexing: lockstep trading of stocks increases market volatility and stock return correlations but reduction in risk sharing decreases them. Overall, indexing decreases market volatility but has an ambiguous effect on the correlations. Also, index investing decreases an investor’s welfare, but indexing by other investors partially offsets the loss. When the introduction of index trading opens financial markets for new investors, the improved risk sharing makes market returns more volatile and stock returns more correlated.

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.

Toronto and University of Warwick for helpful comments. All errors are our responsibility. Dynamic Mean-Variance Asset Allocation Mean-variance criteria remain prevalent in multi-period problems, and yet not much is known about their dynamically optimal policies. We provide a fully analytical characterization of the optimal dynamic mean-variance portfolios within a general incomplete-market economy, and recover a simple structure that also inherits several conventional properties of static models. We also identify a probability measure that incorporates intertemporal hedging demands and facilitates much tractability in the explicit computation of portfolios. We solve the problem by explicitly recognizing the time-inconsistency of the mean-variance criterion and deriving a recursive representation for it, which makes dynamic programming applicable. We further show that our time-consistent solution is generically different from the pre-commitment solutions in the extant literature, which maximize the mean-variance criterion at an initial date and which the investor commits to follow despite incentives to deviate. We illustrate the usefulness of our analysis by explicitly computing dynamic mean-variance portfolios under various stochastic investment opportunities in a straightforward way, which does not involve solving a Hamilton-Jacobi-Bellman