Adjustable rate mortgages are somewhat complex securities because they contain contingent elements that become relevant when interest rates hit certain levels. The first contingency is the risk of default, that especially in the subprime case, increases with interest rates. The second contingency is the risk of prepayment that likewise increases.
Subprime securities are rarely traded and difficult to value. Wall Street then divides these pooled loans into tranches, or segments. The most senior Moody’s AAA tranches have cash flow and collateral priorities. In an absence of a market, these packages are then valued by financial model.
We were curious about what that financial model might be. The industry standard is a computer program called the LoanPerformance RiskModel.
The model, according the company, “built by scientists, statisticians, financial software engineers”, “significantly increases the precision of our clients’ pricing and loss reserving practices…by tracking the delinquency and prepayment performance of 50 million active individual mortgage payments per month.”
The main features of this model are as follows:
1) Monte Carlo simulation, that takes by computer thousands of samples of interest rate levels: either assumed in a statistical distribution or from the historical record. An assumed statistical distribution is just that, assumed and fairly arbitrary. A sampling of interest rates from the historical record is not arbitrary; but due to the statistical nature of interest rates, does not converge on any most typical value. A rarely mentioned assumption of the Central Limit Theorem, that ensures Gaussian convergence of successive samplings from a non Gaussian data series, is that the component parent series must have finite variances. Many, if not most, economic data series do not have this property; interest rates will therefore not converge to a most typical value, enabling valuation. *
For floating rate mortgages written under ordinary conditions, the theoretical point above might be a quibble. However a derived value for subprime mortgage tranches, where defaults and prepayments are major valuation factors, is very suspect.
2) The second feature is behavioral. The model derives default and prepayment rates, from the historical record of like mortgages, given certain levels of interest rates. Since there was a marked deterioration of underwriting standards in 2006 and 2007, the resulting events are likely to be more notable than typical.
The recent failure of two Bear Stearns structured credit funds on 7/07 (containing the AAA and AA rated derivatives of the riskier tranches) shows a certain lack of common sense. Although the mortgage valuation model has theoretical problems, the company then went on to lever both funds, which contained a total of $29.7 billion in assets (both long and short) against $1.56 billion in investors’ equity, resulting in a very high average leverage ratio of 19:1.
In every business cycle, the object of speculation changes. In this cycle, the objects of speculation are sliced and diced loan assets and residential real estate, speculation caused by the credit bubble built up over the last five years.
* We question such global models. This does not say that all quantitative models are useless. We think that quantitative models are very useful to answer what-if questions. The resulting answer is at least directionally valid, if the “if” can be reasonably specified, in any problem. Then you will be aware of your major assumptions.