Dynamic equilibrium with two stocks, heterogeneous investors, and portfolio constraints

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.