A New Look at Second Liens

We use data from credit reports and deed records to better understand the extent to which second liens contributed to the housing crisis by allowing buyers to purchase homes with small down-payments. At the top of the housing market, second liens were quite prevalent: As many as 45 percent of home purchases in coastal markets and bubble locations involved a piggyback second lien. Owner-occupants were more likely to use piggyback second liens than were investors. Second liens in the form of home equity lines of credit (HELOCs) were originated to relatively high-quality borrowers, and originations were declining near the peak of the housing boom. By contrast, characteristics of closed-end second liens (CES) were worse on all these dimensions. Default rates of second liens are generally similar to that of the first lien on the same home, although HELOCs perform better than CES. About 20 to 30 percent of borrowers will continue to pay their second lien for more than a year while remaining seriously delinquent on their first mortgage. By comparison, about 40 percent of credit card borrowers and 70 percent of auto loan borrowers will continue making payments a year after defaulting on their first mortgage. Finally, we show that delinquency rates on second liens, especially HELOCs, have not declined as quickly as those on most other types of credit, raising a potential concern for lenders with large portfolios of second liens on their balance sheets

Application of Stochastic Optimal Control to Financial Market Debt Crises

This interdisciplinary paper explains how mathematical techniques of stochastic optimal control can be applied to the recent subprime mortgage crisis. Why did the financial markets fail to anticipate the recent debt crisis, despite the large literature in mathematical finance concerning optimal portfolio allocation and stopping rules? The uncertainty concerns the capital gain, the return on capital and the interest rate. An optimal debt ratio is derived where the drift is probabilistic but subject to economic constraints. The crises occurred because the market neglected to consider pertinent economic constraints in the dynamic stochastic optimization. The first constraint is that the firm should not be viewed in isolation. The optimizer should be the entire industry. The second economic constraint concerns the modeling of the drift of the price of the asset. The vulnerability of the borrowing firm to shocks from the capital gain, the return to capital or the interest rate, does not depend upon the actual debt/net worth per se. Instead it increases in proportion to the difference between the Actual and Optimal debt ratio, called the excess debt. A general measure of excess debt is derived and I show that it is an early warning signal of the recent crisis