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Moody’s Credit Values November 2007

Table of Contents: 1 2

Summary The Structured Finance Valuation Problem 3 Moody’s Discounted Cashflow Values (DCV) 3.1 Initial Coverage 3.2 Basic Scenario Analysis 3.3 Customized Scenario Analysis 4 An example 5 Conclusion 6 Appendix: Technical outline of the analytic framework 6.1 The meaning of Moody’s DCVs 6.2 A high level representation of Moody’s DCV approach 6.3 How we estimate tranche quality 6.4 Estimating the collateral pool default distribution 6.5 Estimating the discount rate 6.6 Calculating the transaction specific discounted cash flows 6.7 Calculating stressed and benign default rate scenarios 6.8 Caveats 6.9 Assumptions for corporate CDOs

1 2

Discounted Cashflow Values:

3 4 5 6 6 6

A Tool to Enhance Transparency in the Structured Finance Valuations Process

7 7 7 8 8 9 10 10 11 12

Contacts: New York

1.212.553.1653

0 Jacob Grotta Senior Director

0 Roger M. Stein Team Managing Director

Authors: Jacob Grotta Roger M. Stein Ashish Das Xiaolin Cheng

1 Summary In response to the market inquiries related to the valuations process surrounding structured finance securities Moody’s, through its Research and Analytics group and Moody’s Wall Street Analytics (“MWSA,” and collectively with Moody’s Research and Analytics, “Moody’s”) have begun work on a suite of valuation tools called Credit Values that will increase transparency and insight to the structured finance market. The first level of tools, to be provided by MWSA, incorporates a cashflow-based valuation approach that facilitates either standardized or customized analysis. This service is initially available for a large segment of cash flow structured finance transactions. Moody’s makes the results of this transactionspecific analysis available in the form of reports designed to support the structured finance market’s need for increased information transparency in the structured finance valuations process. The information and capability offered by this service is designed to facilitate the complex, time-consuming and often tedious process that market participants currently face in trying to develop this capability internally. In addition to making the process more manageable for market participants that currently have this capability, we believe that the ease of use of the Moody’s service will greatly expand the breadth of market participants that could access such information, contributing to greater liquidity and transparency in the structured finance market.

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process Moody’s initial offering in the Credit Values product line is called Moody’s Discounted Cashflow Values (“Moody’s DCV”) and provides (i) Moody’s-derived discounted cashflow valuations (“DCVs”) and measures of variability of DCVs for the corporate CDO market (the Basic Scenario Analysis or “Basic DCV”) and (ii) userdefined cash flow valuations and measures of variability for almost all types of CDOs (the Customized Scenario Analysis or “Customized DCV”). The Basic DCV daily report provides, for each tranche in a transaction, a set of four discounted cash flow values 1 along with an estimate of the variability of the DCV relative to changes in portfolio behavior. Rather than assuming a single scenario, Basic DCV generates values based on a number of different default rates, loss given default (LGD) and default timing assumptions, customized to each transaction’s underlying collateral pool. The Customized DCV is based on user-defined parameters and could be run for a larger set of deals. Customized DCVs can provide a larger number of valuation reference points for each security and more precise variability measures (as defined by a user). Importantly, the Customized DCV could also be tailored to provide additional insight into other market premia, such as those associated with liquidity, based on additional analysis methods provided by users using their own market prices in conjunction with DCVs. To our knowledge, Moody’s DCV is the first and only service to offer the following features for cash flow structures: „

A set of discounted cash valuations based on independently derived input parameters.

„

A set of discounted cash valuations based in user-defined parameters applied to waterfall engines maintained by an independent party.

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Estimates of variability of discounted cash valuations based on Moody’s-defined or user-defined variability measures.

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The ability to generate measures of market premia (including liquidity premia) based on user-defined methods and parameters.

The processes we use will be the foundation through which we will expand our services to incorporate other structured finance asset classes for both the Basic Scenario Analysis and the Customized Scenario Analysis services, including prime and sub-prime RMBS and other types of CDOs. In addition, our expectation is that future generations of Moody’s DCV will contain increasingly more sophisticated analytics, such as simulationbased and risk-neutral valuation.

Table: Moody’s DCV (Part of the Credit Values Suite of Valuation Tools) DCV Tool

# of DCV Scenarios

# of Variability Measures

# of Market Premia Measures

Parameter Inputs

# of Tranches Currently Available

Basic DCV

4

1

None

Moody’s-defined

Up to 2,000

Customized DCV

User-defined

User-defined

User-defined

User and/or Moody’s-defined

4,000+

2 The Structured Finance Valuation Problem The recent dislocation in the structured finance market has revealed certain limitations in the current valuation practices for structured finance securities. Given the complexity and relative lack of liquidity of these instruments, many market participants have begun to take the view that recent market prices may not always be indicative of true value associated with the instruments. Contributing to this market disruption has been the 1

DCVs are different from credit ratings. In contrast to a Moody’s credit rating which targets a single measure, an opinion of a tranche’s expected loss, the Moody’s DCV provides a set of valuation point estimates. A DCV, unlike expected loss, does not attempt to probability weight each point estimate to arrive at an expected loss, but rather provides a valuation for a particular scenario.

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process need for more readily available information, including for example underlying portfolio level data and easy to apply “what if” scenario analytics for the underlying structured finance deal waterfalls, on which market participants can base more informed decisions about security values. To increase the availability of relevant information on structured securities for market participants we believe that a coherent valuation methodology should address a number of fundamental challenges: (i)

Structural complexity: Cash flows to structured finance securities are subject to sometimes complex waterfall rules, triggers, and alternative third-party guarantees that determine the how cash generated from the underlying assets (mortgages, bonds, credit card receivables, etc.) is ultimately allocated to the various tranches of the structure. Since the return to investors in a specific tranche is so closely tied to this behavior, information about the nature of these rules and provisions is central to understanding how the securities might behave in a particular set of market circumstances. However, collecting, cleaning and codifying this information in sufficient volume to create a general tool that permits the analysis of these cashflows is an extremely challenging and time consuming exercise.

(ii)

Availability of general market information: Unlike the corporate debt markets in which a company’s debt is more readily valued by reference to actual bond/loan trades (and/or available bid level information), CDS levels or even equity-implied credit risk, the structured securities market is not considered transparent in terms of information flow, especially for smaller tranche sizes where this is generally very limited investor following, and generally a lot less liquidity.

(iii)

Standardization versus customization: Unlike the convention in corporate bond markets, where the structure of a typical bond is generally standardized and bonds are thus generally fungible (e.g., all senior unsecured bonds of an issuer are generally considered identical credit risk), each structured security is unique. Assessing the credit risk of a structured security requires a thorough review of the terms and conditions of each structure and relevant tranche.

(iv)

Interactions of underlying risks: An assessment of the payoffs of structured securities requires not only an analysis of the structure, but also an analysis of the collateral and macroeconomic factors that affect cashflows on both the bonds and the underlying collateral. This analysis can be challenging given the nature of the underlying assets. These assets can be relatively illiquid in many cases. In addition, information surrounding their performance is not readily available, making assessments of the impact of economic factors more difficult.

(v)

Changing Data: Structured Finance transactions evolve over the course of their tenor. The tranches and underlying assets within most structured transactions are generally changing. In order to accurately reflect this dynamic behavior, a well developed data production process and infrastructure is necessary.

3 Moody’s Discounted Cashflow Values (Moody’s DCV) Moody’s Discounted Cashflow Values are designed to address the needs outlined above. Moody’s DCVs are calculated using a combination of:

3

„

Transaction specific portfolio data (updated as it becomes available);

„

Transaction specific cashflow waterfall models (reflecting original and transaction terms as well as amendments as they are made available);

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Detailed cashflow modeling software that generates tranche specific cashflows based on the waterfall data;

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Econometric models of discount rates;

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Different LGDs and default timing vectors along with theoretical models of default distributions (to generate various scenarios); and

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Baseline assumptions on timing of default, etc. to generate a range of scenarios (using the forward LIBOR curve).

November 2007 „ White Paper „ Moody’s Credit Values - Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process Many of these specified parameters could be modified upon request to generate customized DCVs. Moody’s has built, and continues to extend, a library of structured finance deal waterfalls for various asset classes and markets. The waterfalls in this library are engineered on a transaction-by-transaction basis and are designed to be a representation of the rules that determine how cash inflows are shared among the various structured securities of each transaction. These waterfalls are combined with data on the underlying assets so that users can integrate the performance of the assets with the cash flows allotted to the deal’s tranches. Both the waterfalls and the underling portfolio information are updated when trustees make it available for individual transactions. We have also developed a series of models to better characterize both the discount rate of the bond cashflows and to better estimate stress default cases. „

The models of the discount rate are designed to assess the likely spread at which a bond would sell, given there were no extreme liquidity events. These are calculated using Moody’s database of transaction closing prices and information about various market conditions. Because structured transactions are often placed with specific investors initially, we hypothesize that the initial spread reflects relatively minimal liquidity effects. We estimate these spreads on a tranche-by-tranche basis for each transaction, based on the transaction structure and the tranche characteristics.

„

The default distribution models are based on theoretical models of bond defaults, which can be used to estimate the probability of various portfolio default rates, given information on estimated portfolio correlation and credit quality. We estimate these for each transaction based on the portfolio data.

By combining all of these pieces - deal waterfalls and underlying deal assets, sophisticated cashflow projection tools, and models of discount rates and portfolio performance, we are able to calculate the cashflows for a particular tranche, discount these at a reasonable spread, and to do this for a variety of reasonable default scenarios. The appendix in Section 6 provides a more detailed discussion of the DCV methodology. A predefined measure of variability associated with the DCVs will be provided to help market participants assess potential sensitivity of the discounted value of a security to different collateral performance assumptions. Moody’s goal is to provide the market with a suite of tools and data that can be integrated into clients’ valuation processes. This includes the ability to adapt our tools to different sets of assumptions (standard assumptions or those customized by the user). This turns out to be a feature of our tools that has recently gained attention among market participants as it provides the ability to use the tools to perform “what-if” analysis on the underlying assets in order to quantify the impact of these assumptions on the cash flows of the structured finance tranches. Users could also define their own measures of dispersion. In addition, users with access to market prices can provide these prices and a calculation algorithm to calculate market premia. Both of these user-defined algorithms can be automatically calculated as part of the user’s customized daily reporting package. While some investors have the ability to perform such “what-if” analysis themselves, others have asked us to provide a service in which this analysis is performed by Moody’s in order to derive specific estimates of cash flows to their investments under specific conditions. Moody’s believes that making such capabilities available on a wider basis, specifically an independently calculated cash flow-based valuation, will serve to enhance market liquidity and transparency.

3.1 Initial Coverage In order to provide more information to the market related to evaluations for complex structured instruments, Moody’s will initially offer Moody’s-derived DCVs for up to 500 corporate cash flow CDOs, primarily CLOs, comprising up to 2,000 tranches. We calculate DCVs for four standard scenarios. Investors can use this information as part of their price discovery process and to enhance the quality of information that currently exists in the market. Market participants may also retrieve the actual cash flows, and associated timing of such cash flows. Please see Appendix A for an example report. We produce and deliver this report on a daily basis initially in Excel sheets through MWSA’s website.

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process Beyond the Moody’s-derived DCVs, Moody’s will offer customized DCVs for over 1,000 CDOs, including Corporate CDOs (CLO), ABS CDOs, some European CLOs and TRUPsCDOs.

3.2 Basic Scenario Analysis (“Basic DCV”) In addition to the moderate-case scenario, Moody’s basic scenario analysis includes a “benign” and two “stress” case DCVs. These cases demonstrate the behavior of the DCV in fairly mild and fairly severe portfolio loss settings. In these cases, assumptions underlying the scenarios are the same as in the moderate case, but the default rate has been adjusted, based on an estimate of the underlying portfolio default distribution, so that the default rates represent more extreme positive and negative levels than the average. In the most severe case, the recovery rate is also adjusted to reflect lower recovery rates and default timing is accelerated. The lower recovery rates and accelerated default timing approximate assumptions used in Moody’s ratings methodology 2 . Importantly, these cases do not represent best and worst case DCVs. Since many other assumptions can affect the cashflows of a structured security (e.g., default timing, term structure of interest rates, etc.), the benign and severe default cases could actually be better than many cases with lower default rates but other, more detrimental, assumptions. The Customized Scenario Analysis, discussed below, offers market participants a more comprehensive tool to assess a wider range of possible cash flow outcomes. We feel that the moderate case and these additional cases offered by the Basic DCV tool provide valuable insight into the variability of the DCV. Market participants have suggested a number of applications for this information, such as: (i) Assessing the reasonableness of market quotes. A range of “what-if” DCV scenarios may inform market participants’ views on the reasonableness of quoted prices. (ii) Assessing the uncertainty of values: Some tranches may show relatively consistent values over a range of default and LGD assumptions where others may be far more sensitive to changes in the default (and loss) behavior as represented in the more extreme scenarios. This difference in valuation can inform the views of investors with respect to the potential volatility in their investments. The Basic DCV will also provide a variability measure that offers one estimate of the sensitivity of the DCVs to change in collateral performance. (iii) Assessing first-order market premia: Market participants may find the DCV useful in broadly quantifying the liquidity and risk premia reflected in quoted prices. The difference between various scenarios and quoted prices can be seen as one measure of these premia in secondary markets 3 . The Customized DCV, discussed below, will optionally provide users with an implied market premium given the necessary inputs. (iv) Identifying potential mispricings: Some market participants have commented that having access to DCVs will allow them to identify securities that may be mispriced relative to their intrinsic value. While such mispricings are often difficult to uncover due to the complexity of the structured instruments, the DCVs should provide some insight into this problem.

2

Moody’s rating methodology incorporates various default timing patterns, one of which assumes that half the defaults occur in year 1 and the rest are evenly spaced in the following five years (or shorter, for shorter maturity pools). The vector used for this DCV calculation approximates that assumption. Furthermore, the LGD used in this DCV case approximates that used by Moody’s to rate Aaa notes whereas in the other DCV cases the LGD is closer to the implied Baa/Ba levels used in the rating methodology. One interpretation of this higher LGD is that it serves as a first order approximation to the correlation between LGD and default probability, with lower recoveries coinciding with higher default rates, as could be the case in a severe scenario. 3 Note that this would be only a rough approximation as disentangling these premia requires a rich valuation framework in which DCVs are only one component.

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process 3.3 Customized Scenario Analysis (“Customized DCV”) For market participants that demand even more comprehensive information, we can calculate custom DCVs for those who have designed their own assumptions. These power-users can customize their DCVs by defining any or all of the following model parameters: 1.

default rates;

2.

recovery rates;

3.

prepayment rates;

4.

default correlations;

5.

default timing;

6.

discount rates; and

7.

interest rates.

Customized DCV users could also use the tool to create their own measures of (i) variability (in addition to Moody’s predetermined measure) and, (ii) to the extent they provide market prices and a reference DCV (and a calculation algorithm), market premia. Importantly, the Customized DCV is available for most types of CDOs, including corporate CDOs, some European CLOs, ABS CDOs and TRUPS CDOs.

4 An example See the attached Exhibit I for a sample report.

5 Conclusion In response to the recent market turmoil in the Structured Finance market and resulting market inquiries, Moody’s has embarked on the creation of Credit Values, a suite of valuation tools for the structured finance market. The first level of tools in the suite, Moody’s DCV, incorporates a cashflow-based valuation approach that facilitates either standardized (“Basic DCV”) or customized (“Customized DCV”) analysis. The results of analysis using this methodology have been designed to support the structured finance market’s need for increased information transparency in the structured finance valuations process. Moody’s initial offering in this product line provides Moody’s-derived discounted cashflow valuations for the corporate CDO market and customized cash flow values for most types of cash flow CDOs. This tool, called Moody’s Credit Values DCV (Moody’s DCV) gives a set of discounted cash flow valuations for each tranche in a structured transaction along with a measure of DCV variability. Moody’s DCV generates values based on a number of different default rates, LGD and default timing scenarios, customized to each transaction’s underlying collateral pool. In providing an independently-derived set of DCVs and offering to apply the underlying analytic engines to run DCVs based on user-defined customized parameters, the Moody’s DCV service fills an important market need of improved market transparency. We expect to expand this methodology to cover additional asset classes, including prime and subprime RMBS, and that future generations of Moody’s DCV will contain increasingly more sophisticated analytics, such as simulation-based and risk-neutral valuation measures.

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process

6

Appendix: Technical outline of the analytic framework for Moody’s-Derived DCVs (Basic Scenario Analysis)

6.1 The meaning of Moody’s DCVs; Basic Scenario Analysis Moody’s DCVs are estimates of the present value of the cashflows of structured transactions based on a set of assumptions on defaults, prepayments, etc. The discount rate used to calculate the present value of the cashflows is estimated based on transaction and market characteristics at the time of the analysis. Currently DCVs account only for a small number of scenarios rather than the full distribution of possible outcomes. While valuation is a complicated problem, this first version of DCVs seeks to provide a basic valuation scheme and will likely continue to evolve over time. Importantly, DCVs are not market values. Further, we would consider DCVs to be “fair” values only to the extent the assumptions under which they are calculated represent users’ true estimates the effective expected outcomes. While, DCVs do not accommodate liquidity premia or other market technicals they do provide insight into the value of a structured transaction’s tranches under reasonable assumptions about default rates, interest rates and so on. Further, they permit a detailed analysis of the impact on the discounted value of the tranche of changes in these assumptions.

6.2 A high level representation of Moody’s DCV approach The table below outlines the five step process we use for calculating DCVs.

Objective

Implementation

1

Determine tranche credit quality to use in estimation of spread

Use Moody’s binomial approach to estimate tranche PD

2

Determine idealized pool default distribution for calculating stress cases

Use portfolio WARF and Diversity Score to estimate pool PD and correlation and use this to imply a default distribution

3

Determine discount rate for tranche cash flows

Use estimate of at issuance spread based on • tranche PD from (1) and • mkt conditions

4

Generate cashflows based on baseline default assumptions and discount to calculate PV

Use mean pool PD from (2) to generate collateral cashflows and deal-specific waterfall using MWSA cashflow engines

5

Generate stress and benign cases by substituting default rates (and recovery rates for the most stressed case) for baseline assumptions

Keeping both spread and timing of defaults constant, calculate desired quantile of pool default distribution and repeat Step (4), substituting value of quantile for mean default rate (adjust recovery rates and default timing for the most stressed case)

While the outline illustrates some elements that are consistent with Moody’s CDO rating methodology, there are differences. Common features include application of the BET to estimate credit risk of CDO tranches, the use of the Moody’s WARF and correlation estimates, where available (note that these are used differently in the DCV approach than in the rating methodologies). Also, default timing and LGDs are similar in some cases. However, both the modeling framework and the assumptions that drive the methodologies are quite different from a quantitative perspective, making direct comparisons difficult 4 . Futhermore, the ratings process also includes assessments of legal and qualitative factors that are not incorporated in the DCV calculation.

4

Note that the difference is by design since a DCV service is based on a limited number of scenarios whereas a rating is based on an expected loss calculated by probability weighting losses under a wide variety of theoretical scenarios.

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process 6.3 How we estimate tranche quality We use a variant of Moody’s Binomial Expansion Technique to calculate the approximate probability of default associated with each tranche under all possible (idealized) default scenarios and weight them according to their probability. This approach is similar to the one used to rate cashflow CDOs. However, since not all CDOs are rated, and since probabilities of default are continuous, rather than discrete, reapplying the methodology in each run allows us to better differentiate between tranche quality. We show this schematically in the figure. Note however, that Moody’s Investors Service, in rating actual transactions, conducts a much more detailed analysis of both quantitative and legal components of structured finance instruments and uses a different analytic framework for assigning ratings than the DCV approach, as mentioned in the previous section. As such, it is not surprising when DCVs and agency ratings diverge. Though DCVs, in either the Basic or Customized form, are currently not formally part of Moody’s CDO ratings process, they may be considered for future use by Moody’s CDO rating analysts as part of their surveillance tools.

Probability of 1, 2, …defaults as binomial tree

...

Tranche A

Tranche B Tranche C Equity

6.4 Estimating the collateral pool default distribution In order to generate stress and benign default scenarios we require an estimate of the distribution of defaults on the underlying collateral. This distribution, characterized by the mean probability of default and correlation among the assets in the collateral pool, tells us how likely it is that a large number of defaults will occur at the same time. This is obviously important for calculating the value of both the debt and equity for structured transactions. Pools characterized by high correlation are likely to experience very few defaults during benign economic periods and large numbers of defaults during periods of stress. In contrast, pools with lower correlation levels are more likely to exhibit more even default rates across economic periods. Correlation does not affect the average default rate of the portfolio, but it does affect the probability that the defaults happening all at once is high or low. Since the mean default rate does not change, this means that the correlation causes the probability of zero or many defaults to shift. As a result, correlation tends to be beneficial to equity holders (who typically suffer the first losses) because the higher the correlation, the more likely it is that there will either be few defaults or very high levels of default. Since any defaults affect equity value dramatically, the equity holders prefer to trade a high probability of low losses for a lower probability of severe losses because in many cases regardless of whether there are two or twenty defaults, the equity may be wiped out. In contrast, the holders of senior notes prefer low correlation. This makes sense. The senior notes only experience losses when a very large number of defaults occur over the life of the transaction. In lower correlation pools, there tends to be less “all or nothing” behavior. The default rate of the pool tends to be more even and extreme numbers of defaults (such as those required to affect the senior notes) are much rarer. The figure below demonstrates this relationship graphically. The figure shows the default distribution of two different theoretical pools. Both pools have identical mean default rates. However, one pool (low correlation pool) has a fairly low correlation among the assets in the pool. The other (high correlation pool) has relatively

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process high correlation among the assets in the pool. It is clear that though the average (expected) default rate for both pools is identical, the manner in which the defaults occur can be quite different. The low correlation pool experiences most of its defaults around the 10% range, near the expected default rate of the pool most of the time. However, the highly correlated pool is far less likely to experience 10% defaults. Rather it tends to experience much lower defaults or, on occasion, very high defaults.

Probability

High correlation (red) vs. Low correlation (black) (mean default rate=10%,low cor=2.5%, high cor=20%)

0.0

0.1

0.2

0.3

0.4

0.5

Portfolio default rate

To see how this affects different classes of debt, consider a CDO with only three tranches: a 10% equity tranche, a 20% mezzanine tranche and a 70% senior tranche. (Assume for simplicity that there is no recovery on defaulted bonds.) The senior debt holder prefers the low correlation portfolio since it is quite unlikely that defaults will exceed even 20%, let alone the 30% that would be required for the senior note holder to experience a loss. On the other hand, the equity tranche holder prefers the high correlation portfolio since any defaults at or above 10% wipe the equity tranche out and in the high correlation portfolio there is a much greater probability that defaults will be below 10% than in the low correlation portfolio. It is difficult to estimate the correlation structure of an asset portfolio in general without very detailed information about the assets. This suggests analytic approximations based on portfolio characteristics. In order to characterize the default distribution we use an idealized default distribution parameterized by estimates of the correlation and average default rate. We use econometric models to convert the values of the diversity score and the WARF (or other credit quality measure) into the mean and correlation required to estimate the default distribution. Importantly, when it is available we use the lower of the current default rate of the pool and the WARF trigger in the bond indenture for the transaction. While this is an abstraction, it is not unreasonable as a first approximation to asset pool behavior.

6.5

Estimating the discount rate

We calculate the discount rate based on the PD for the tranche 5 , current market conditions, asset characteristics, etc. using spread at issuance as a benchmark. We have developed an econometric model that provides reasonable estimates of the spread at issuance of individual structured finance instruments. We sourced these spreads from Moody’s extensive database of structured instruments and pricing. 5

Note for clarity that here we use the tranche PD not the pool PD which is used for estimating the shape of the default distribution in the previous step, since the tranche PD speaks to the credit quality of the investment, which directly affects the value of the tranche, whereas the pool PD speaks to the credit quality of the pool, which only indirectly affects the value of the tranche, subject to waterfall structure, etc.

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process We chose the spread at closing since our goal is to assess the likely spread at which a bond would trade, given there were no extreme liquidity events. Because structured transactions are often placed with specific investors initially, we hypothesize that the initial spread reflects relatively minimal liquidity effects.

The model contains factors that capture: „

estimated credit risk of the tranche (see section 6.3)

„

credit environment

„

interest rate environment

We use this model to estimate spreads on a tranche-by-tranche basis for each transaction and update these estimates as new data becomes available.

6.6 Calculating the transaction specific discounted cash flows

Scenarios

Tranche Cashflows PV=99.95

Tranche A PV=99.35

...

Collateral Collateral

Tranche B Tranche C Equity

We use our DCV assumptions (see section 6.9) and the mean default rate for the collateral pool to generate collateral cashflows and run these through deal-specific waterfalls using the MWSA waterfall engines. Once these cashflows are generated, we discount the cashflows using the tranche-specific rate (see section 6.5) to arrive at the DCV for the standard scenario and assumption set. This process is shown schematically in the figure below.

6.7 Calculating high and low default rate scenarios (and the high default/high LGD scenario) It is useful to understand how sensitive DCVs are to changes in default behavior. One way to do this is to change the default rate on the portfolio and examine the impact of doing so on various tranches. But which default rates should be used? We could use the same stress default rates (e.g., a depression stress-test default rate) across all transactions, but, as we discussed in Section 6.4, the shape of the default distribution will be different for pools with different average default rates and correlation structures. This suggests using the default distribution itself to determine stress or benign cases. We can use the idealized collateral pool default distribution to calculate pool default rates under various scenarios by choosing default rates that represent quantiles of the distribution that have high and low probabilities. For example, an investor might be interested in comparing all of the CDO tranches she has in her portfolio using the same level of default stress. In this case, she might decide that a favorable economic environment would be represented by default rates that were lower than 95% of all possible default rates for the portfolio underlying each CDO. Similarly, the stress case might represent for each transaction the default

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process rate that represents worst 95% of possible default rates. Using the default distribution for each transaction, we can achieve this by calculating the 5% and 95% quantiles of the default distribution and then using these values to generate cashflows and thus DCVs. This is shown graphically in the figure below.

Default Distribution (p=10%,cor=20%) q05

Probability

q95

0.0

0.1

0.2

0.3

0.4

0.5

Portfolio default rate

The need to use the portfolio specific loss distribution rather than a standard assumption becomes obvious when we consider how our two example portfolios might be evaluated in this context. (For convenience, we assume a number of conditions in calculating what follows.) Even though both portfolios have the same mean default rate, in the case of the low correlation portfolio, the 95% worst case result in a default rate of approximately 15%, while 95% worst case for the high correlation portfolio would result in a default rate of approximately 27%, almost double that of the low correlation portfolio. Importantly, the 95% worst default scenario is NOT the 95% worst DCV scenario. Since many other assumptions can affect the cashflows of a structured instrument (e.g., default timing, term structure of interest rates, etc.), the 95% worst default case could actually be better than many cases with lower default rates but more detrimental assumptions. It is important to also keep in mind that the theoretical default distribution that we assume for ease of calculation probably differs from the true underlying default distribution of the portfolio. Future generations of DCVs will incorporate full simulation which will permit the calculation of the full distribution of DCVs and thus worst-case analysis for DCVs. All of this said, the use of the identical quantiles of each transaction’s default distribution provides an interesting and consistent metric by which different transaction’s sensitivity to benign and adverse economic events can be compared. Moody’s DCVs include a fourth value that combines the high default case assumptions with a more severe LGD. This “high default and high LGD” scenario provides a more severe stress scenario portfolio loss given that the LGDs increase as defaults also increase. This relationship of high LGDs and high default rates is consistent with observed historical data.

6.8 Caveats It is important to note that we make a number of assumptions in calculating DCVs. We also use stylized models of portfolio behavior and default timing to facilitate transparent interpretation of DCVs. DCVs should only be considered only “fair” values under these assumptions and models.

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Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process These assumptions and models, while reasonable, are not the only sets of assumptions or models one might consider. We do not feel that our assumptions and models cover all possible behaviors of structured transactions or that they are appropriate for all specific securities. Rather, we feel that they provide reasonable paths under which we can evaluate the discounted value of structured transaction cashflows and high levels of transparency into the derivation of the DCV. Users who wish to use different models and assumptions to reflect specific views of the world or to examine specific transaction behavior are encouraged to do so, and we provide the ability for Moody’s DCV users to conduct this analysis (customized DCVs).

6.9 Assumptions for corporate CDOs Collateral: Mean default rate: function of WARF Default timing: Non-“high default/high LGD” cases: straight line to WAL High default/high LGD case: 50% in year 1 and straight-line afterward Correlation: function of Diversity Score LGD: Non-“high default/high LGD” cases: High default/high LGD case:

40%

55%

Prepayment rate: ~WR rate @ comparable PD Prepayment timing: straight line to WAL Interest rate: current forward curve Fair value spread: ~Spread @ origination Benign/stressed quantiles of default distribution: 10% and 90%

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Moody’s Credit Values

Report Date 11/13/2007

Low Defaults CDO Name Name

Coupon (%)

Coupon Formula

Moody's Rating

Outstanding Balance

Stated Maturity Date

WAL

DCV

Moderate Defaults WAL

DCV

High Defaults WAL

DCV

High Defaults/High LGD WAL

DCV

CDO I

A

5.25

LIBOR 3MO + 0.2700

Aaa

225,000,000

1/15/2020

6.27

98.93

6.23

98.94

6.16

98.95

5.07

99.12

CDO I

B

5.43

LIBOR 3MO + 0.4500

Aa2

10,000,000

1/15/2020

9.31

99.85

9.26

99.85

9.17

99.85

7.36

99.88

CDO I

C

5.78

LIBOR 3MO + 0.8000

A2

22,000,000

1/15/2020

10.11

100.79

10.06

100.79

10.00

100.79

8.20

100.68

CDO I

D

6.83

LIBOR 3MO + 1.8500

Baa2

10,000,000

1/15/2020

10.91

95.26

10.87

95.28

10.85

95.28

9.29

95.75

CDO I

E

9.78

LIBOR 3MO + 4.8000

Ba2

11,000,000

1/15/2020

11.48

73.81

11.48

72.38

11.47

70.71

9.59

55.26

CDO I

Equity

0.00

FIXED

N/R

12,500,000

1/15/2020

2.42

49.79

3.03

36.54

1.77

30.68

1.62

24.12

CDO II

A

5.43

LIBOR 3MO + 0.2500

Aaa

225,000,000

7/15/2020

7.08

98.92

7.04

98.92

6.17

99.04

5.25

99.17

CDO II

B

5.60

LIBOR 3MO + 0.4200

Aa2

12,500,000

7/15/2020

10.57

99.63

10.48

99.63

9.22

99.67

7.71

99.72

CDO II

C

5.86

LIBOR 3MO + 0.6800

A2

20,000,000

7/15/2020

11.11

98.75

11.02

98.76

9.97

98.85

8.53

98.98

CDO II

D

6.68

LIBOR 3MO + 1.5000

Baa2

9,000,000

7/15/2020

11.62

84.72

11.53

84.8

10.63

85.51

9.51

86.5

CDO II

E

8.83

LIBOR 3MO + 3.6500

Ba2

10,000,000

7/15/2020

9.83

70.08

10.79

65.82

10.96

57.33

12.88

33.8

CDO II

Equity

0.00

FIXED

N/R

25,000,000

7/15/2020

4.50

67.38

3.62

49.84

2.40

42.23

1.21

34.26

CDO III

A1

5.38

LIBOR 3MO + 0.2600

Aaa

225,000,000

1/10/2021

6.67

98.78

6.22

98.85

5.29

99.00

4.12

99.2

CDO III

A2

5.55

LIBOR 3MO + 0.3200

Aa2

19,000,000

1/10/2021

9.66

98.81

9.14

98.86

7.66

99.00

6.34

99.14

CDO III

B

5.84

LIBOR 3MO + 0.5600

A2

20,000,000

1/10/2021

10.37

98.86

9.96

98.89

8.63

99.00

6.68

99.18

CDO III

C

6.56

LIBOR 3MO + 1.5000

Baa2

9,000,000

1/10/2021

10.84

85.24

10.68

85.36

9.77

86.15

6.94

89.06

CDO III

D

8.71

LIBOR 3MO + 4.5000

Ba2

11,000,000

1/10/2021

11.06

72.53

11.05

72.54

10.90

72.61

7.38

65.07

CDO III

Equity

0.00

FIXED

N/R

30,000,000

1/10/2021

5.34

65.18

5.11

34.84

4.10

23.24

3.25

16.72

CDO IV

A

7.67

FIXED

Baa1

4,500,000

8/15/2013

1.25

103.33

1.25

103.33

1.25

103.33

1.25

103.33

CDO IV

B

7.59

LIBOR 6MO + 2.2000

C

15,000,000

8/15/2013

2.32

22.88

2.27

22.2

2.21

21.61

2.21

20.91

CDO IV

C

9.12

FIXED

C

25,000,000

8/15/2013

2.28

26.35

2.23

25.86

2.18

25.43

2.18

24.61

CDO V

A1

5.47

LIBOR 3MO + 0.2700

Aaa

315,000,000

3/25/2017

4.82

98.95

4.77

98.96

4.74

98.96

4.81

98.95

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Moody’s Credit Values

Report Date 11/13/2007

Low Defaults CDO Name Name CDO V

A2

CDO V

Coupon (%)

Coupon Formula

Moody's Rating

50,000,000

Stated Maturity Date 3/25/2017

WAL

4.37

DCV

99.05

Moderate Defaults WAL

4.32

DCV

99.06

High Defaults WAL

DCV

99.07

WAL

4.33

DCV

LIBOR 3MO + 0.2450

B1

5.56

LIBOR 3MO + 0.3600

Aa1

13,000,000

3/25/2017

6.63

99.1

6.59

99.11

6.56

99.11

6.71

99.09

CDO V

B2

5.65

LIBOR 3MO + 0.4500

Aa2

22,500,000

3/25/2017

7.25

97.4

7.23

97.4

7.25

97.39

7.50

97.32

CDO V

C

6.00

LIBOR 3MO + 0.8000

A2

22,500,000

3/25/2017

7.70

96.6

7.70

96.6

7.73

96.59

8.10

96.46

CDO V

D

7.15

LIBOR 3MO + 1.9500

Baa2

30,000,000

3/25/2017

8.51

89.87

8.50

89.88

8.57

89.82

8.95

85.51

CDO V

Equity

0.00

FIXED

N/R

27,000,000

3/25/2017

7.12

74.66

4.35

45.59

3.29

26.58

0.98

5.65

CDO VI

A-1A

5.82

LIBOR 3MO + 0.2350

Aaa

140,000,000

9/20/2017

4.93

98.98

4.88

98.99

4.85

99.00

4.90

98.99

CDO VI

A-1B

5.96

LIBOR 3MO + 0.3700

Aaa

40,000,000

9/20/2017

6.92

99.4

6.89

99.41

6.89

99.41

7.04

99.39

CDO VI

A-2

5.84

LIBOR 3MO + 0.2500

Aaa

30,000,000

9/20/2017

5.32

98.98

5.27

98.99

5.24

99.00

5.32

98.98

CDO VI

B

6.09

LIBOR 3MO + 0.5000

Aa2

8,000,000

9/20/2017

7.59

99.98

7.57

99.98

7.58

99.98

7.88

99.98

CDO VI

C

6.34

LIBOR 3MO + 0.7500

A2

19,500,000

9/20/2017

8.21

100.31

8.17

100.31

8.18

100.31

8.50

100.32

CDO VI

D

7.36

LIBOR 3MO + 2.0000

Baa2

17,500,000

9/20/2017

8.96

104.56

8.92

104.55

8.94

104.56

9.33

104.7

CDO VI

PREF

0.00

FIXED

N/R

22,500,000

9/20/2017

4.33

38.31

3.74

20.86

3.18

13.52

1.21

5.49

November 2007 „ White Paper „ Moody’s Credit Values - Discounted Cashflow Values: A Tool to Enhance Transparency in the Structured Finance Valuations Process

4.28

High Defaults/High LGD

5.45

14

Aaa

Outstanding Balance

99.06

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