Valuing CDOs of ABSs

Charles Smithson and Neil Pearson discuss the valuation of collateralised debt obligations (CDOs), with a close look at CDOs of subprime residential mortage-backed securities

In this article, we value tranches of CDOs of asset-backed securities (ABSs), with particular focus on CDOs of subprime residential mortgage-backed securities (RMBSs).

CDOs of ABSs are more difficult to value than CDOs referenced to corporate credits. This is because:

- The assets in the CDO collateral pool are themselves tranches of ABS deals, which in turn are supported by collateral pools containing the ultimate underlying assets, for example, subprime mortgages. A CDO of ABSs is therefore two levels above the underlying mortgages, and the impact of mortgage defaults on the CDO depends on both the structure of the CDO and the structure of perhaps hundreds of ABS deals.

- In contrast to the all-or-nothing defaults for corporate bonds or loans (or credit default swaps on bonds or loans), the ABS tranches in CDOs of ABS collateral pools can incur fractional defaults. For example, if more than the expected number of borrowers default on their mortgages, the tranche of the RMBS will suffer interest shortfalls and possibly principal writedowns. If the rate of default increases, the tranche suffers further interest shortfalls and principal writedowns (see box on page 40).

We believe the fair value of a tranche of a CDO (for net-asset-value or financial statement purposes) could be obtained using either brute-force scenario analysis or a market-implied model. However, we believe a brute-force scenario analysis approach is the only way to obtain the 'scrap value' of a tranche of a CDO (that is, the value of the asset in a worst-case situation). The market-implied model approach treats the market prices of the ABS tranches in the collateral pool as 'correct'. This assumption is useful when calculating a mark-to-market value, but it makes the approach less useful for trading, where an important question is whether market prices are consistent or inconsistent with a notion of fundamental value.

The remainder of this column will deal with these two approaches.

Brute-force scenario analysis

The concept is deceptively simple, encompassing only four steps:

1. Calculate the monthly cashflows for each of the ABS tranches in the collateral pool underlying the CDO.

2. Aggregate the cashflows from the individual ABS tranches to obtain the monthly cashflows for the collateral pool underlying the CDO.

3. Calculate the cashflows to the tranche being evaluated (based on the cashflows to the collateral pool and the value of the collateral pool).

4. Discount the cashflows to the tranche being evaluated to obtain the value of the CDO.

The difficulty arises in the implementation of these four steps:

- The analyst must have software containing mathematical descriptions of the manner in which the value of the collateral pool will be distributed to the holders of the tranches over time (generally referred to as waterfalls), including the changes that would occur if interest coverage or collateral pool value triggers are hit. This software must include not only the waterfall for the CDO itself, but also the waterfalls for all the ABSs represented in the collateral pool.

- The analyst must have software capable of generating and tracking: the cashflows generated by the collateral pools underlying the ABSs referenced by the CDO (for example, the cashflows generated by a specific pool of subprime mortgages); the cashflows from the pools underlying the ABSs to the specific ABS tranches in the collateral pool underlying the CDO (for example, the cashflows to the A-rated tranche of a specific subprime RMBS); and the cashflows from the collateral pool underlying the CDO to the tranche of the CDO being evaluated.

- The analyst must specify a scenario that includes projections regarding the rate of prepayments, the rate of defaults and the term structure of interest rates. It is the specification of the scenario that presents the most difficulties.

- Obtaining the scrap value. The challenge facing the analyst is the definition of the worst-case scenario in terms of the prepayment and default rates for the collateral underlying the ABSs and the interest rate term structure. Market prices are ordinarily viewed as being equal to expected discounted cashflows, and therefore can be used to make inferences about the expected outcomes, but not worst-case outcomes. While the multiple Markit ABX.HE indexes provide some information about the probabilities of extreme outcomes, this information is less than complete and difficult to tease out of the market prices.1

1 For example, in March, the price of the ABX.HE 06-02 AAA index was 82.57. This tells us the probability of scenarios in which the AAA tranches of the underlying RMBS deals suffer losses is high enough that the (risk-neutral) expected value of the discounted payments on the protection leg of the index is about $18 per $100 of notional. This is useful, but still incomplete, information about the probability of high-loss scenarios. Further, it may not be relevant to deals based on different collateral pools

CDSs on ABSs with PAUG settlement

A credit default swap (CDS) on an asset-backed security (ABS) normally references a specific tranche of a securitisation. The cashflows from the ABS tranche are often very different from those of corporate bonds or loans. For instance:

- Failure to pay interest generally does not trigger default of an ABS.

- Prior to the subprime crisis, it was rare for an ABS tranche to default before its legal maturity. However, even in the absence of default, the investor in the ABS tranche may suffer an interest shortfall or a principal write-down.

- It is possible a tranche that has been written down may subsequently be written back up.

For the cashflows from the CDS to mirror the cashflows of the reference ABS tranches, pay-as-you-go (PAUG) settlement was introduced in December 2005. Instead of the one contingent payment triggered by a single credit event (as in CDSs on corporate credits), the PAUG format involves two-way payments between the protection seller and protection buyer throughout the life of the CDS contract. For example, if the reference ABS tranche suffers an interest shortfall, the protection seller will compensate the protection buyer for that amount. If the shortfall is reversed in a subsequent period, the protection buyer will repay the amount received from the protection seller for the shortfall.

2 It may be easier to see the logic by viewing the implementation as a four-step process: 1) use software to generate cashflows for the RMBS tranches for each of the N scenarios; 2) assign initial probabilities to each of the N scenarios; 3) compute the model value of each of the RMBS tranches; 4) compare model value with actual value for each of the RMBS tranches. If the model values are not sufficiently close to the actual value, adjust the probabilities assigned to each of the 11 scenarios and repeat steps 3 and 4; if the model values are sufficiently close to the actual value, the process is complete

Selecting discount rates

If analysts wish to extract market-implied probabilities for default scenarios for subprime RMBS, they need the discount rates - or market risk premiums - for the various RMBS tranches that underlie the CDO.

For example, in January 2008, the market prices of the RMBS tranches in the collateral pool for a CDO of subprime RMBSs ranged from a high of approximately 65 to a low of approximately 10.

- The discount rate for the RMBS tranche with a price of 65 would have been approximately 10% - a risk premium of approximately 5%. That RMBS tranche was trading like a bond that had been downgraded to junk status. Such a bond would have a significant risk premium, but it would still be less than that of a typical common stock: a risk premium of 5% is about 60% of the risk premium of a typical common stock.1

- The discount rate for the RMBS tranche with a price of 10 would have been approximately 25% - a risk premium of approximately 20%. While this RMBS tranche is likely to be among the riskiest of bonds, it should have a risk premium no greater than the risk premiums on the riskiest common stocks. The risk premium of 20% is about the size of the risk premium appropriate for the riskiest of publicly traded common stocks.2

- The discount rates for the RMBS tranches with prices between 11 and 65 could have been interpolated between 10% and 25%.

1 The historical market risk premium is about 8% a year, with estimates differing somewhat depending on the time period used to calculate the risk premium. This historical market risk premium is a capitalisation-weighted average of the risk premiums of the common stocks that comprise the market, and is thus also the risk premium of a typical common stock

2 Using a historical market risk premium of 8%, the risk premium of 20% corresponds to a market beta coefficient of 2.5 (20% = 2.5 x 8%)

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