Materiality of RMBS Breaches: A Statistical Approach

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1 Materiality of RMBS Breaches: A Statistical Approach ORIGINAL forensic analysis + visualization Background Residential Mortgage Backed Securities ( RMBS ) litigations hinge to a great extent on the existence of breaches in representations and warranties made in Pooling and Servicing Agreements ( PSAs ). Under these provisions, if there is a breach that materially and adversely affects the interests of the Certificateholders in that Mortgage Loan, the seller is obligated to cure the breach or replace or repurchase the Mortgage Loan. Materiality is thus a significant factor in forcing cures based on breaches. Two distinct standards have emerged for materiality in RMBS litigations: materiality of breaches in inducing purchase of Certificates and materiality of breaches as they effect loss causation. 2 Other RMBS Products and Notes: The Pool Sifter mortgage analysis tool RMBS Technical Note: Understanding Loan Pool Data The purchase standard argues that if the breaches had been disclosed, the buyer would not have purchased the Certificates, and therefore are material; the loss causation standard argues that even if there were breaches, if they didn t cause the loss, they aren t material. The loss causation standard presents a higher standard to plaintiffs because they must prove that the identified breaches caused the loss as opposed to the crash in the real estate market and the economy. While there were certainly breaches, there was certainly a crash and subsequent recession, and disentangling those two factors from one another isn t easy. However, there exists a science to do just that disentangling: statistics. To the best of my knowledge, statistics have not been used to address materiality in any prominent RMBS cases. Indeed, in the Bank of New York Mellon ( BNYM ) matter where BNYM, as Trustee, acted as petitioner for 50 RMBS trusts, expert Barry E. Adler, Material and Adverse, 2, (20), %20Affect.pdf. 2 In Lehman Brothers Holdings, Inc. v. Laureate Realty Services, Inc., 2007 WL (S.D. Ind. Sept. 28, 2007) the purchase standard seemed to be accepted, in Wells Fargo Bank N.A. v. LaSalle Bank Nat l Ass n, :07- cv MRM (Apr., 22, 2009) the loss causation standard was adopted (and the purchase standard explicitly rejected). Copyright ORIGINAL forensic analysis + visualization, 202, All Rights Reserved.

2 Brian Lin did not even address materiality of breaches in his damage estimation report. Instead, Lin s report focused on three haircuts he gave to potential damage amounts: Severity Rate, (45 to 60 percent) the percentage of lost principal after the loan is foreclosed or sold; Breach Rate, (a flat 6 percent) estimated by a third party completing a forensic examination of 250,000 loans from similar contemporaneous deals; and Success Rate, (a flat 40 percent), representing the percentage of loans submitted that are assumed to be repurchased. 4 Assuming that Lin s three factor formula is adopted for settlement purposes, the haircut coefficients are of supreme importance. Materiality figures into the Success Rate coefficient. As Lin wrote in his report, There is a possibility that BofA (Bank of America) may offer resistance relating to some of these loans, resulting in a buyback rejection. 5 Indeed, if the alleged breaches can be shown to be non- material, the Success Rate coefficient will be lower, and vice versa. 2 To put this in context, a 0 percent increase or decrease in Lin s Success Rate coefficient would have changed his Low Range settlement value of $8.8 billion by +/- $2.2 billion, or 25 percent. Techniques The goal of all statistical methods is to pull meaning out of data. The methods described below are methods of pulling meaning out of loan pool data. I believe they can directly address the loss causation standard of materiality by statistically assessing the differences in traits between performing and non- performing loans. Contingency Tables One method that could be helpful for evaluating RMBS pools is to create contingency tables and then analyze them for their significance. In RMBS loan pools, the loans can be categorized under two binary (yes or no) variables: are the loans performing and were there breaches in the underwriting? Table. Contingency Table 6 Brian Lin, Opinion Concerning Contemplated Settlement Amount for 50 Trusts, 8, (20), t%20amount%20for%2050%20trusts.pdf. 4 Id. at 8. 5 See Supra note at 2. 6 All data are from a hypothetical loan pool of 62 loans. Copyright ORIGINAL forensic analysis + visualization, 202, All Rights Reserved.

3 No Breach Breach(es) Performing 06 Non- Performing 2 In the 2 x 2 contingency table above, most of the data falls along the diagonal (gray cells), which is indicative of positive association. That is, loans with no breaches are generally performing and loans with breaches are generally not performing. The degree of association between the variables can be measured using a number of different tests, the most common of which is Pearson s Phi. With binary data (like that above), Pearson s Phi can be thought of as a correlation between the variables. The number will be between and -, with and - indicating a perfect positive or negative relationship and 0 indicating no relationship. Running Pearson s Phi on the contingency table above yields a phi of 0.644, indicating there is a relationship between breaches and non- performance, or more to the point, that the breaches were material to loss causation. If the phi had been close to zero, it would indicate there is little or no materiality of breaches to loss causation. Conditional Probabilities Another way of working with contingency tables is to evaluate conditional probabilities. Conditional probabilities give you the probability of one event happening given that another event has already happened. When examining RMBS loan pools these techniques can address the probabilities of performance or non- performance given the existence (or non- existence) of breaches. If the probability of loan performance is high given no breaches and the probability of loan non- performance is high given breaches, then the existence of breaches is material in causing losses, and vice versa. Table 2, below, gives the conditional probabilities for the loan pool sample in Table. Table 2. Conditional Probabilities 7 P(P NB) Probability of Performing Given No Breach P(P B) Probability of Performing Given Breach(es) 89.8% 25.00% P(NP NB) Probability of Non- Performance Given No Breach P(NP B) Probability of Non- Performance Given Breach(es) 0.7% 75.00% In this data sample, the event of breaches clearly increases the probability of non- performance, and vice versa. If the off- diagonal, P(NP NB) and P(P B), 7 See Supra note 6. Copyright ORIGINAL forensic analysis + visualization, 202, All Rights Reserved.

4 probabilities had been higher, they would argue for non- materiality of breaches in loss causation. This is because in the P(NP NB) case there would have been non- performance even when there were no breaches, and in the P(P B) case there would have been performance given breaches. Conditional probabilities could also be run on the number of breaches per loan. Table, below, gives the conditional probabilities for loan performance or non- performance given different numbers of breaches. Table. Conditional Probabilities by Number of Breaches 8 Number of Breaches Performing 89.8% 70.00% 40.00% 0.00% 0.00% 0.00% 0.00% Non- Performing 0.7% 0.00% 60.00% 00.00% 00.00% 00.00% 00.00% The sample data show that the probability of non- performance goes up with the number of breaches, indicative of the materiality of breaches in loss causation. If the probabilities of non- performance had not gone up with the number of breaches, the data would show the non- materiality of breaches. 4 Analysis of Variance A powerful technique for analyzing different events in a sample space is analysis of variance ( ANOVA ). ANOVA compares differences in averages of subsets of a sample space and is frequently used in medicine and industry. In the analysis of the materiality of breaches, ANOVA can be used to create subsets of performing and non- performing loans, and then compare the average number of breaches in each subset. If the average number of breaches is different, then the breaches are material in loss causation, if the average number of breaches is the same, then there is no materiality to the breaches. Chart, below shows the average number of breaches for the performing and non- performing subsets. Chart. ANOVA 9 8 See Supra note 6. 9 Id. Copyright ORIGINAL forensic analysis + visualization, 202, All Rights Reserved.

5 ANOVA Number of Breaches Loan Status (0 = Performing, = Non- Performing) As can be clearly seen, the average number of breaches in the performing loans is 0.28 compared to a non- performing loan average of These numbers are indicative of the materiality of breaches in loss causation. Conversely, if the averages were close to the same, the breaches would not be material to loss causation. Furthermore, with ANOVA, the statistical significance of the differences in averages can be measured with an F- Test. The data used to calculate the chart above had an F- test of , which is significant at the level. Survival Analysis Borrowing a technique from medicine, the loan pool can be analyzed using the Kaplan- Meier survival distribution function to examine how the loans perform over time. To analyze the materiality of breaches, the loan pool is first divided into breach and no- breach subsets and the survival analysis is run on each subset. 5 The survival analysis yields the probability of any loan in the subset performing after a given time from Certificate issuance. In this instance, the time frame was 24 months from Certificate issuance. Chart 2, below, shows the incremental change in the survival distribution function for the breach and no- breach subsets. Chart 2. Survival Distribution Function 0 0 Id. Copyright ORIGINAL forensic analysis + visualization, 202, All Rights Reserved.

6 Survival Function by Breach/No Breach Subsets 00% 90% 80% 70% 60% 50% 40% 0% 20% 0% 0% Months to Non- Performance Blue Line = Breaches, Green Line = No Breaches 6 The difference in steepness of line slopes immediately shows that the breaches subset experienced many more non- performances than the no- breaches subset during the first 24 months from Certificate issuance. The survival functions further support this visual evaluation, with the breaches subset having a 52. percent probability of any loan performing for 24 months and the the no- breaches subset having a 94.9 percent probability of any loan performing for 24 months. Conclusion The statistical methods presented above result in empirical measures of the materiality of breaches in loss causation. Both plaintiffs and defendants would benefit from knowing these measures. Copyright ORIGINAL forensic analysis + visualization, 202, All Rights Reserved.

7 About ORIGINAL forensic analysis + visualization ORIGINAL is a securities litigation and support firm with broad and deep experience in RMBS and other securitized products. We also have extensive data analysis and visualization experience. Our securities expertise and data analysis skills come together to help pull the meaning out of data and use it to tell a story. Contact Jack Duval Principal + senior analyst jack@ofav.pro Visit us at Copyright ORIGINAL forensic analysis + visualization, 202, All Rights Reserved.