Loan Write-Downs Cited as Optimal Loan Modification Scheme

As a result of the current housing crisis, many homeowners have defaulted on their mortgage, and lenders must decide whether to complete a loan modification or start foreclosure proceedings.

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Modifications result in a lowering of the present value of the loan, while foreclosing incurs deadweight costs that reduce the recovery value of the home, said Professor Sanjiv R. Das of the ""Leavey School of Business at Santa Clara University"":http://www.scu.edu/business/ in his recent paper _The Principal Principle: Optimal Modification of Distressed Home Loans_. According to his research, foreclosure filings numbered 321,480 or approximately one out of every 400 homes in May 2009-up 18 percent from the year before, and it is estimated that loan modifications versus premature foreclosures will save $180 billion or 1 percent of GDP per year.

Loan modifications seem to be the clear choice, but that's easier said than done. Das' paper develops a framework for reducing foreclosure losses by loan modification and how best to implement this solution. He says an optimal loan modification must be cognizant of the borrower's ability to pay and willingness to pay, and different prescription apply depending on the level of interest rates and home price volatility.

""Finding an optimal loan modification scheme requires an analysis of the game between the borrower and lender, where the lender chooses the modification scheme to maximize loan value by minimizing the value of the option to default held by the borrower, and the borrower chooses an optimal default strategy given loan parameters chosen by the lender,"" Das wrote in his paper.

To analyze the optimal loan modification, Das used mathematical equations weighing risk, negative equity, borrower's debt capacity, and servicer costs. His model showed that both rate reductions and maturity extensions are suboptimal, and found that writing down principal on the loan is better than either of these practices.

Das explained that current loan modification schemes that are being used focus on adjusting the loan terms to make the loan affordable on a monthly basis, but these modifications pay less attention to the borrower's default incentives in the game between the lender and borrower. As a result, he argues that loan modifications via rate reductions and maturity extensions are suboptimal, leading to dissipation in loan value to the lender and resulting in a high probability of re-default by homeowners even after modification of their loans.

Although not a favored recipe and often prohibited by covenants, Das says loan write-downs (the Principal Principle) are mostly optimal.

He said the first step to completing an optimal loan modification lies in correctly determining the level of monthly service payment on the loan that are affordable to the distressed borrower, calibrating the loan to the borrower's ability to pay. The next step involves the borrower's willingness to pay.

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There are many loan configurations that lead to the same monthly payment level, so Das shows how to select the one that is most favorable in maximizing the value of the loan to the lender. The analysis involves a value decomposition of the loan into a risk-free component, a default put option, and a component for expected deadweight foreclosure costs. The optimal loan configuration maximizes lender net value aggregated across all three components, Das said.

As part of his study, Das evaluated a recent innovation in mortgage restructuring which offers the borrower a reduced monthly payment in return for the lender taking a share of the upside of the home value. The shared-appreciation mortgage (SAM) or home equity fractional interest (HEFI) loan is conditional on the home value increasing above the loan value.

Through his comparative analysis, Das found that SAMs enhance the borrower's ability to pay but may also increase willingness to re-default. He also found that SAMs delay immediate foreclosure, postpone imposition of the resultant deadweight costs, and discourage from adverse selection against lenders. Due to these positive results, Das believes the SAM is an important innovation that deserves more detailed analysis in future work.

Das' theoretical analysis showed that principal write-down modifications maximize the willingness to pay, thereby maximizing the loan's economic value to the lender. However, current practices aren't following this method. He noted that he number of loan modifications increased almost three fold from 68,801 in the first quarter of 2008 to 185,159 in the first quarter of 2009. More than half of these modifications entailed reduced monthly payments, and two-thirds of the modifications were combination modifications, entailing changes to loan rates, maturity, and/or adjustments to principal, Das said.

""These modifications are opposite of what the theory describes,"" he said. ""As a consequence, the re-default rate evidenced is extremely high. Of the loans modified in Q1 2008, 68 percent were foreclosed or delinquent a year later.""

In manipulating the borrower's willingness to pay, Das found that managing negative equity is vital. According to his source (Foote, Gerardi, Goette, and Willen) a 10 percent fall in house prices raises the probability of delinquency by more than 50 percent. In an analysis of a database from McDash Analytics of 30 million loans, it was found that while only 12 percent of loans had negative equity, these loans accounted for 47 percent of all foreclosures.

In short, Das found that banks would suffer fewer defaults among modified loans if they would shorten the duration of the loans they modify, rather than lengthening as they tend to do, and if they would forgive part of the loan, which many are unwilling to do. He said loan modifications have shied away from writing down principal simply because the accounting impact would be much more negative than with other types of iso-service loan modifications, but given the contagion effects that foreclosures have on other homes, it is even more important that the tide of foreclosures be stemmed by optimal write-downs.

Das said the prescription to write-down loan balances in a modification is bitter medicine for lenders, but it is better than the palliatives being attempted in current practice. ""This long-term solution to the housing crisis must be complemented by short-term tactical loan modification based on optimal principles,"" he said.