Security Design with Correlated Hidden Cash Flows:The Optimality of Performance Pricing

Abstract

This paper studies optimal security design in a dynamic setting with an agency problem that arises when an agent in charge of a project can divert cash flows for his own consumption at the expense of an outside investor. Cash flows are unobservable and unverifiable by the outside investor, who relies on the agent’s reports, and has the right to liquidate the project. Unlike previous analyses, we allow cash flows to be correlated over time. We solve for the optimal contract and show that it can be implemented using a credit line with an interest rate that increases with the balance on the credit line. This finding is consistent with the fact that the majority of commercial loans are lines of credit with performance pricing. Thus, our model provides theoretical evidence that performance pricing is used to mitigate the agency cost. In addition, we develop a new recursive method to deal with a correlated privately observed variable in dynamic agency settings. It allows us to reduce the dimensionality of the problem and obtain a closed-form solution for the optimal contract.