resolving adverse selection in ABS

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. commercial mortgage
backed securities (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 “pooling”—all 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 low quality mortgages, 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:

𝑷(𝑇) = 𝐸[𝑇|𝑇 < 𝑇′],𝑤h𝑒𝑛 𝑇 < 𝑇′

𝑷(𝑇) = 𝐸[𝑇|𝑇 ≥ 𝑇′] − (𝐶) , 𝑤h𝑒𝑛 𝑇 > 𝑇′

Based on this information, answer the following (in all cases, show your work and justify your

Define a no signaling equilibrium as one in which neither Good nor Bad types signal. At
what value(s) of C does no signaling occur?

Define a pooling equilibrium as one in which both Good and Bad types signal. At what
value(s) of C does pooling occur?

Define a separating equilibrium as one in which only Good types signal. At what
values(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 separating
equilibrium” in which Good issuers purchase the signal to convey their collateral quality to
investors, but Bad issuers do not purchase the signal. Thus, investors are able to discern which
issuers are securitizing lemons and which are securitizing high quality collateral.

As described previously, in the context of the actual risk retention requirement, good issuers
signal by choosing horizontal retention structures. However, as was conveyed by the model
above, this signal is costly. The following exercise will demonstrate why in practice retaining via
the horizontal option always imposes a higher cost on the issuer than the vertical option, hence
the horizontal option is precisely a costly signal. (Keep in mind that issuers must retain 5% of the
market 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 par
value of $90 and a B-piece with a par value of $10. Suppose that the senior security prices at par
but 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 the
horizontal 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 value
of the issuer’s 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 market
value of the issuer’s risk retention. I.e., compute the values of the portion of the deal

Suppose $10 of collateral defaults with 0% recovery. Compute the total payoffs to the
issuer’s risk retention under both the vertical and horizontal options.

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