Following the 2008 financial crisis, lawmakers in the U.S. implemented minimum required levels of risk retention in order to force ABS issuers to retain more skin-in-the-game. The risk retention level for U.S. ABS issuers was set at 5%. This means that ABS issuers must retain at least 5% of any deal they structure. The risk retention rule was implemented in a very specific way for U.S. CMBS issuers. Specifically, issuers can choose between different structures, or methods of retaining risk. Under the horizontal structure, issuers retain the B-piece of the deal, and the B-piece must account for at least 5% of the market value of the deal. Under the vertical structure, issuers retain 5% of every security in the deal stack (including the B-piece). The figure below demonstrates the two structures (the dark portion is the risk retention strip):

Prior to the implementation of the regulation, high quality issuers signaled their quality by retaining more risk, whereas low issuers retained less risk. In other words, the issuers that securitized lemons would retain less risk. After the regulation was implemented, all issuers began retaining exactly 5% of the risk of every deal they issued. This means that high quality issuers can no longer signal their quality using the amount of risk retention. This is known as poolingall issuers pool on the same level of risk retention. Despite pooling in the amount of retention, it is still possible for high quality issuers to signal by choosing the horizontal retention structure. In contrast, the issuers that securitize lemons choose the vertical structure. The following questions asks you to demonstrate and discuss why high quality issuers signal with horizontal retention structure.

Part (a): Model Consider the following model in which there are two types of CMBS issuers: Good and Bad. Bad issuers always securitize lemons, whereas Good issuers securitize high quality mortgages. The issuer types are represented by T and are uniformly distributed with support on [0,1]. Issuers with T closer to 0 are worse than issuers with T closer to 1. Issuer types are not directly observable but can be signaled to investors. The signal is costly, but it allows investors to perfectly discern whether the issuer is Good or Bad. Assume that all issuers and investors are risk neutral and that issuers are paid their expected type minus the cost of signaling if they choose to signal. They receive the following payoffs P to securitization that are linear in (1) their type T (which can be Good or Bad) and (2) the cost of signaling C:

Based on this information, do the following: Solve for T in terms of C. (T is known as the critical value of T.) At what value(s) of C do both the Good and Bad issuers signal? Show your work and justify your answer. At what value(s) of C do neither the Good nor the Bad issuers signal? Show your work and justify your answer. At what values(s) of C do only Good types signal? Show your work and justify your answer.

P(T) = E[T\T T' P(T) = E[T\T T