| Kazuhiko Ohashi, Hitotsubashi University Tano Santos, University of Chicago |
| Contractible Signals and Security Design |
| Session: C-12-10 Wednesday 16 August 2000 by Ohashi, Kazuhiko |
| An entrepreneur has ongoing project whose random payoff will be realized at some future, terminal date. At an interim date the entrepreneur will learn about the profitability of the project. This information is known only to him. At some earlier initial date the entrepreneur decides to design and issue a security to hedge the risks that his project is exposed to. Should the security payoff correlate with his own private information if this is contractible? We address this quesiton in a usual model of noisy rational expectation equilibrium with CARA utilities and normally distributed shocks. We prove that under the traditional assumption on the nature of the private information signals, which is commonly made when noise traders are excluded, the payoff of the optimally designed security should be in general correlated with the issuer's private information signals. We further prove that equity can never replicate the allocation of the optimal linear security. These results stand in contrast with recent results by Rahi (1996) and DeMarzo and Duffie (1999) where it is shown under different assumptions that the payoff of the optimal security should not be correlated with the issuer's private signals as long as they are contractible. |