Limited Commitment, Business Cycle, and Portfolio Selection

We study a continuous-time model of consumption and portfolio selection with the stochastic investment opportunity and the credit constraints endogenously determined in the business cycle modeled by the regime switch. By using the martingale approach and transformation into optimal stopping problems, we derive the time-varying endogenous credit limit and optimal consumption and investment strategies in closed-form. We show that the credit limit is cyclical: it is lower (higher) when the Sharpe ratio of the risky asset is high (low). We find that a change in the credit limit and the counter-cyclical Sharpe ratio generate a heterogeneous investment pattern that differs for the rich and the poor: The rich tend to increase the proportion of risky investment in downturns whereas the poor decrease it, a finding which is also verified by the Survey of Consumer Finance data