Endogenous Credit, Business Cycle, and Portfolio Selection

We study a continuous-time model of consumption and portfolio selection of an agent with a limited ability to commit to a debt contract in which the credit limit is endogenously determined. We consider the case where the agent borrows against future income and/or collateral assets. We also study the determination of the credit limit in a general equilibrium model. We derive the credit limit in closed form. The credit limit is smaller than the natural limit because of limited commitment and an increasing function of both income and the collateral price. We extend the baseline model to the case with a regime switch and show that the credit limit is cyclical; it is lower (higher) when the Sharpe ratio is high (low). The model predicts that the rich tend to increase the proportion of risky investments in downturns, whereas the poor decrease them.