Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications


Review of Economic Studies

April 2007, vol. 74, n°2, pp.345-390

Departments: Finance

An entrepreneur with limited liability needs to finance an infinite horizon investment project. An agency problem arises because she can divert operating cash flows before reporting them to the financiers. We first study the optimal contract in discrete time. This contract can be implemented by cash reserves,debt, and equity. The latter is split between the financiers and the entrepreneur and pays dividends when retained earnings reach a threshold. To provide appropriate incentives to the entrepreneur, the firm is downsized when it runs short of cash. We then study the continuous-time limit of the model. We provethe convergence of the discrete-time value functions and optimal contracts. Our analysis yields rich implications for the dynamics of security prices. Stock prices follow a diffusion reflected at the dividend barrier and absorbed at 0. Their volatility, as well as the leverage ratio of the firm, increase after badperformance. Stock prices and book-to-market ratios are in a non-monotonic relationship. A more severe agency problem entails lower price-earning ratios and firm liquidity and higher default risk