Back in late May and early June I wrote a series of posts (“Formulas for Disaster, Parts 1, 2, 3, and 4), about some of the factors that may have contributed to the most recent Wall Street meltdown. One of the problems I mentioned there was the statistical modeling process used to estimate the risk, and the value, of collateralized debt obligations [CDOs]. There is some significant evidence that questionable assumptions in the process led to a systematic under-estimation of risk, and a corresponding over-estimation of value, by the large financial institutions that traded and held them. This is one illustration of what I perceive as a core problem: the industry’s ability to construct novel instruments considerably outpaced the ability of its managements to understand them sufficiently.
Now Prof. Andrew Appel, of the Center for Information Technology Policy at Princeton, has a blog post at “Freedom to Tinker” about a new paper that argues that there is another fundamental problem with these derivative securities. A conventional argument in favor of the creation and use of CDOs is that they can improve efficiency in the capital markets, by allowing investors’ preferences to be matched more closely even though the sellers of CDOs have information that the buyers do not. The working paper [PDF], by Sanjeev Arora, Boaz Barak, Marcus Brunnmeier, and Rong Ge, argues that the structure of CDOs makes it possible for the seller to “rig” the creation of CDO pools, so that some pools are much riskier than others (= contain a significantly higher proportion of default risk). More importantly, they show that detection of such rigging, even after the fact when losses are known, appears to be a computationally-infeasible problem; that is, if the seller rigs the pools, it is effectively impossible to prove the manipulation, even after all the evidence is in. (Technically, they are arguing that the detection is an NP-complete problem.) As Prof. Appel puts it:
Trading in derivatives brought down Lehman Brothers, AIG, and many other buyers, based on mistaken assumptions about the independence of the underlying asset prices; they underestimated the danger that many mortgages would all default at the same time. But the new paper shows that in addition to that kind of danger, risks can arise because a seller can deliberately construct a derivative with a booby trap hiding in plain sight. [Emphasis in original]
The working paper does suggest, in Section 5, an approach to designing CDOs that might mitigate the threat of pool rigging, although the authors are careful to note that they have only explored the issue in the simplified analytical context used in the paper, and that it is not clear how to apply this particular insight to the real world.
I’m sure that quite some time will pass before the last word is written about the recent Wall Street debacle; there will doubtless be more work done on the specifics of some of these issues. However, it seem to me that it is fair to draw one basic lesson from what we have learned so far: it is entirely possible for the financial services industry to develop products whose complexity exceeds its competence to manage or even understand. To suppose that an unfettered laissez-faire approach to rule-making will automagically produce good results is a leap of faith that I am personally unwilling to make.