Quantitative Equilibrium Impacts of Short-Sale and Leverage Constraints

In this research project, we quantify the joint impact of short-sale and leverage constraints on asset pricing quantities including asset prices, market volatility, and speculative premium. For a stock, the speculative premium exists when a stock valuati ons of some agents in the economy are different from each other's and different from the market price. In practice, those two types of constraints are pervasively active and are frequently implemented simultaneously in financial markets. However, due to t echnical challenges, in the existing literature only either type of constraints can be considered. Specifically, in this project, we study an dynamic discrete-time economy where economic agents are heterogeneous both in risk aversion and beliefs, more pes simistic agents face short-sale constraints and less risk averse agents face borrowing constraints. In such an economic setting, constraints are endogenously binding. Moreover, in my model agents have Epstein-Zin recursive preferences. This feature of the model allows us to match broad empirical asset pricing moments, and quantitatively calculate the magnitudes of the impacts of multiple constraints on the asset pricing quantities of interest. Main challenge of this research is the simultaneous presences of multiple constraints and recursive preferences. Multiple constraints, leverage and short-sale, alone already make the model hard to solve because of market incompleteness, which requires to solve for consumptions and investments simultaneously at any point of time. In continuous time settings, multiple constraints can cause multiple equilibria. In addition, for the two types of constraints to bind endogenously, it is required to model heterogeneity both in beliefs and risk aversion. The benchmark mode l alone is also hard to handle. Recursive preferences makes the model path-dependent. One needs additional state variables to capture this, adding an extra layer of complication to the computation of the model.