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Logistic Regression And Financial Crises

|Includes: DFS, FNMA, JPMorgan Chase & Co. (JPM), WFC

Heavy reliance on VAR (Value at Risk) has often been quoted in various research publications as one of the enablers of Financial Crises. Goldman Sachs's CFO had famously quoted in August 2007 that they are seeing 25 Standard deviation in market volatility, when the even the 3 standard deviation was not expected. Various financial instruments were rated on 99 % VAR. The model had assumptions of what would be a rare event and that would exceed only 1% of the time.

Problem was not in VAR, but how people used VAR and how it was interpreted. There is another statistical method name logistic regression, which had a role of in the financial crises and yet is not widely discussed in Financial Press. Input and Output data into and from Logistic Regression and Cox-Proportional Hazard Regression was often abused by many people. Lack of complete understanding of the assumptions of how results are obtained led to many bad mortgages. Models have inherent limitations and this fact was often ignored. People did not completely understand the limitations of the model.

Logistic Regression helps in calculating the probability of default (PD) of a borrower. In order to calculate the PD, an institution would take existing data of its borrowers and would do a regression on the factors, which leads to default by a borrower. Various factors like credit score, income to debt ratio, Loan to collateral Value, etc are used as input. These factors are usually taken during the loan application filled by a borrower. During the early part of the decade, the regression showed that people with score above 660 are less likely to be delinquent. This reliance on output from Logistic regression led to creation of products that led to Alternate Loans (ALT-A).

ALT-A type loans provided loans to people above credit score of 660, without requiring adequate documentation on income of the borrower. Other condition like the value of the collateral (house) was also ignored. . The Regression data was obtained after regression thousands of records and since credit score was a major factor in the results, bankers developed products just on credit score. By changing the other characteristics of the loan like no need to support documentation on income, bankers had misinterpreted the data about Regression. The PD was calculated on the existing sample based on borrowers who had provided documentation. Since this documentation was provided by all borrowers, Regression did not identify this as a differentiating factor for borrowers who were current and who had defaulted. This led bankers to assume that income documentation is not a prime factor, but just the credit score.

Not requiring borrowers to submit proof of income, led borrowers to intentionally misstate the income earned by borrowers. Bankers knew that borrowers were misstating the income and chose to ignore it, as they were confident that high credit score is the main determinant of PD. Regression data is useful, but picking certain attributes of the model and ignoring other factors.

Another issue with Logistic Regression was most of the data is collected by a bank at the time of loan application and generally it pertains to individual characteristics. When the house prices increased, people who had difficulty paying the loans were able to refinance the existing loans as the value of the collateral increased. These borrowers were therefore never in default. Regression data looks at the both the current and delinquent borrowers to determine the PD. If there are many borrowers who are delinquent the Regression will identify the characteristics which makes them default, but due to refinancing the borrowers with new loan, these people never were counted as delinquent. Regression looks at current data and predicts the future. If the current data did not have high delinquencies, Regression data did not predict high delinquencies. This over reliance on the credit model (Regression models) without understanding how the credit model works, led bankers to stress that delinquencies will not increase even in 2007, even when the house prices stopped increasing.