Limited Commitment, Business Cycle, and Portfolio Selection

We study a continuous-time model of consumption and portfolio selection with limited commitment in a stochastic environment. The credit constraints of a household are determined endogenously in the credit market where creditors know that the household is not committed to payment of debt. By using a duality approach, we transform the problem into a dual minimization problem and subsequently 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: the rich tend to increase the proportion of risky investment in downturns whereas the poor decrease it, a finding supported by the Survey of Consumer Finance data