Paper Points to Problems with CDO Models

A draft of a paper, “Innovations in Credit Risk Transfer: Implications for Financial Stability,” by Stanford’s Darrell Duffie, investigates ” the design, prevalence, and effectiveness of credit risk transfer,” with an eye to implications for the financial system.

The paper is worth reading for those seriously interested in the CDO/CLO markets, and sets forth a “summary of opinions” some of which were speculative. One was particularly interesting:

While the gross level of credit derivative and CLO activity by banks is large, the available data do not yet provide a clear picture of whether the banking system as a whole is using these forms of CRT to shed a major fraction of the total expected default losses of loans originated by banks. The recent dramatic growth of CRT markets is driven mainly by various other business activities by banks and non-bank financial entities.

Duffie appears to have been diligent in mining available information, including regulatory data. The fact that he could not determine how much credit derivative activity of banks is on their own behalf, as opposed to clients, points to a large gap in knowledge. One would think regulators would have required banks to report on their use of derivatives to transfer risk as a part of their research and oversight.

Another finding is that “toxic waste” is aptly named:

Incidentally, the latest available data regarding returns on the equity pieces of CDOs is rather discouraging. Of all 59 CLO deals that had terminated in time for Moodys’ January 2007 report on CDO equity returns, the mean across deals of the internal rate of return on the equity pieces of CLOs was estimated by Moodys to be 2.35% with a standard deviation of 21.14%. For collateralized bond obligations, the mean IRR of the equity tranches across 36 terminated deals was −14.2% with a standard deviation of 43.5%.

Duffie also finds flaws in model construction, namely the assumptions on default correlation. In lay terms, this means how diversified the portfolio is from a default risk perspective. He says in pretty unvarnished terns that there is no empirical foundation for current practice:

Currently, the weakest link in the risk measurement and pricing of CDOs is the modeling of default correlation. There is relatively little emphasis in practice on data or analysis bearing on default correlation. When valuing CDOs, somewhat arbitrary “copula” default correlation models are typically calibrated to the observed prices of CDS-index tranches, a class of derivatives that behave much like CDOs, as explained in the Appendix. Some of the industry-standard calibrated correlation models are internally inconsistent, as we shall see by example, in that the correlation model that matches the price of one tranche of a CDO structure is typically much different than that of another tranche of the same structure. Although these differences are sometimes eliminated in practice with proprietary copula models that have a richer set of parameters, the additional parametric details are usually not based on information that bears realistically on default correlation. A model with enough flexibility can be made to match market prices, without necessarily capturing reality in any significant way. Risk managing the mark-to-market valuation of CDOs, moreover, is not treated directly by the current copula approach to valuation, which has no place in its modeling framework for uncertain changes in credit spreads.

The dependence of the market on CDO valuation methodology is particularly weak in the case of bespoke CDOs, those based on a customized portfolio of names. Bespoke CDO correlation assumptions tend to be based on extremely slender analysis, largely extrapolation of CDS-index-tranche-implied correlation parameters, with little evidence or analysis of the degree to which common risk factors are present in the actual bespoke portfolio.

Institutional investors tend to rely on the ratings of structured credit products, including CDOs, when making investment decisions. Methodologies for rating CDOs, however, are still at a relatively crude stage of development. Correlation parameters used in ratings models tend to be based on rudimentary assumptions, for example treating all pairs of names within a given industrial sector as though they have the same default correlation, and treating all pairs of names not within the same industrial sector as though they have the same default correlation. As opposed to valuation models often used for dealing, investment and hedging decisions, ratings decisions place at least some emphasis on data bearing directly on correlation.

The Appendix delves further into the default correlation issue. Duffie posits it may explain why hedges of CDOs have not worked correctly:

The predominant industry approach to pricing and hedging CDOs and tranched index products is known as the “copula.” A key parameter for the Gaussian copula model, the version of the copula model most commonly used for quotation purposes, is known as the “base correlation.”…..The copula correlation parameter is in theory a property of the underlying pool of debt, not a property of the tranches. ….

Because hedging depends on accurate pricing, the lack of reliable industry models for CDO pricing is especially problematic for dealers in tranche products, or levered hedge funds, who tend to hedge their mark-to-market exposures to certain tranche products with positions in other products…..The current lack of reliable default correlation models also leaves significant doubt about the quality of pricing of “bespoke” tranches, those based on a pool of collateralizing debt that is tailored to the specifications of investors.….

A notorious example of the ineffectiveness of delta hedging of tranches occurred with the rating downgrade of General Motors (GM) debt in May, 2005. Theoretically, the loss that occurred to a seller of protection on the equity CDX tranche should have been largely offset by buying protection with a mezzanine tranche position, sized to offset the delta exposure of one tranche with the delta exposure of the other. For example, the deltas shown in Table 4 would have implied buying mezzanine protection for 71.4/18.4 = 3.9 times the total CDX debt principal underlying the equity tranche position. Some market participants who took this Delta-based approach to hedging equity tranche positions with mezzanine tranche positions suffered significant losses when the mezzanine tranche price did not respond to the GM downgrade as suggested by the delta estimates that were used at the time of the downgrade. Indeed, the mezzanine tranche prices responded much less vigorously than predicted by the copula-based Delta models available at the time, and in fact responded in the opposite direction to that suggested by standard models. Rather then reducing their losses, hedgers following this approach slightly increased their losses! In mid-2007, a hedge fund managed by Bear Sterns suffered significant losses on CDOs backed in part by
sub-prime mortgages.

Even when theoretically correct, delta hedging need not be especially effective in the face of large sudden price changes. In the case of the GM downgrade, standard copula-based delta models were inadequate to the task. Reporters also questioned whether efficient market pricing was a reliable approach during the GM downgrade, given the limited amount of capital available to take advantage of tranche price distortions caused by a rush by some market participants to exit their losing positions. The situation was further exacerbated by the fact that the rating downgrade moved GM debt from investment grade to speculative grade. Investors specializing in investment grade debt (by design or by contractual limitation) would have needed to sell an exceptionally large amount of GM debt relative to the entire size of the speculative grade bond market. The associated price impact, or at least anticipation by traders of the potential price impact, could have further pushed market prices away from their efficient-market levels.

The more I learn about CDOs, the more I am convinced that this form of financial alchemy will come to be recognized as junk science. While the basic structure and objectives of CDOs and other tranched products, namely, assigning priority in payments of principal and cash flow in order to create new securities with particular characteristics (in this case, triple A credit ratings) to satisfy market demand, is valid, many of the analytical and pricing approaches are either flawed or based on insufficient data.

And the notion that Bear Stearns hedge fund problem of hedges failing to work, and that possibly being a result of shortcomings in default correlation, is disturbing, for it suggests it isn’t the last time we will see this sort of mishap. Portfolio insurance, a technique of automated selling that was supposed to improve the safety of institutional equity holdings, instead acted as an accelerant in the 1987 crash. Will failed CDO delta hedges play the same role in this credit contraction?