FINE 7650 Assignment 4: resolving adverse selection in ABS

10 points total

Submit via Canvas

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 “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 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.

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

retained.

• 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.