Description
Following the 2008 financial crisis, lawmakers in the U.S. implemented minimum requiredlevels of risk retention in order to force ABS issuers to retain more skin-in-the-game. The riskretention level for U.S. ABS issuers was set at 5%. This means that ABS issuers must retain atleast 5% of any deal they structure.
The risk retention rule was implemented in a very specific way for U.S. commercial mortgagebacked securities (CMBS) issuers. Specifically, issuers can choose between differentstructures, 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 theB-piece). The figure below demonstrates the two structures (the dark portion is the risk retentionstrip): Prior to the implementation of the regulation, high quality issuers signaled their quality byretaining more risk, whereas low issuers retained less risk. In other words, the issuers thatsecuritized lemons would retain less risk. After the regulation was implemented, all issuers began retaining exactly 5% of the risk of everydeal they issued. This means that high quality issuers can no longer signal their quality using theamount of risk retention. This is known as poolingall issuers pool on the same level ofrisk retention.
Despite pooling in the amount of retention, it is still possible for high quality issuers to signal bychoosing the horizontal retention structure. In contrast, the issuers that securitize lemons choosethe vertical structure. The following questions asks you to demonstrate and discuss why highquality 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 low quality mortgages, whereas Good issuers securitize highquality mortgages. The issuer types are represented by T and are uniformly distributed withsupport 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, butit allows investors to perfectly discern whether the issuer is Good or Bad. Assume that all issuersand investors are risk neutral and that issuers are paid their expected type minus the cost ofsignaling if they choose to signal. They receive the following payoffs P to securitization thatare linear in (1) their type T (which can be Good or Bad) and (2) the cost of signaling C:
??(??) = ??[??|?? < ???],??h???? ?? < ???
??(??) = ??[??|?? ? ???] ? (??) , ??h???? ?? > ?????
Based on this information, answer the following (in all cases, show your work and justify youranswers):
- Define a no signaling equilibrium as one in which neither Good nor Bad types signal. Atwhat value(s) of C does no signaling occur?
- Define a pooling equilibrium as one in which both Good and Bad types signal. At whatvalue(s) of C does pooling occur?
- Define a separating equilibrium as one in which only Good types signal. At whatvalues(s) of C does separation occur?
Part (b): Numerical example
The values of C you solved for in which only Good types signal pin down a partially separatingequilibrium in which Good issuers purchase the signal to convey their collateral quality toinvestors, but Bad issuers do not purchase the signal. Thus, investors are able to discern whichissuers are securitizing lemons and which are securitizing high quality collateral.
As described previously, in the context of the actual risk retention requirement, good issuerssignal by choosing horizontal retention structures. However, as was conveyed by the modelabove, this signal is costly. The following exercise will demonstrate why in practice retaining viathe horizontal option always imposes a higher cost on the issuer than the vertical option, hencethe horizontal option is precisely a costly signal. (Keep in mind that issuers must retain 5% of themarket value of the deal under the horizontal option.)
Assume a deal with $100 par value of collateral. The deal consists of a senior security with a parvalue of $90 and a B-piece with a par value of $10. Suppose that the senior security prices at parbut the B-piece prices at 50% of par.
Do the following based on the assumption that issuers must retain 5% of the deal using either thehorizontal or vertical options as described above.
- Compute the par value and the market value of the deal.
- Assume the issuer takes the vertical retention option. Compute the par and market valueof the issuers risk retention. I.e., compute the values of the portion of the deal retained.
- Assume now that the issuer takes the horizontal option. Compute the par and marketvalue of the issuers risk retention. I.e., compute the values of the portion of the dealretained.
- Suppose $10 of collateral defaults with 0% recovery. Compute the total payoffs to theissuers risk retention under both the vertical and horizontal options.