Contractible Signals and Security Design

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 his project is exposed to. Should the security payoff correlate with his own private information if this is contractible? We prove that in general it should and 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).