Kamakura Corporation released a study today demonstrating that conventional analysis of CDO tranches values was consistently more optimistic in valuation than a simulation which correctly incorporates business-cycle driven defaults in valuation.
The paper, with Kamakura managing sirector of Research Professor Robert Jarrow as lead author, shows that the commonly used "copula" approach leads to incorrect valuations due to a number of critical simplifying assumptions. The study, titled "CDO Valuation: Fact and Fiction," points out three critical simplifications that cause errors when using the copula approach: a single period modeling horizon, constant default probabilities, and highly simplified assumptions about the nature of correlation in default events. The analysis relies on simulations of up to 10 million scenarios using the multiple models approach embedded in the Kamakura web-based CDO valuation tool KRIS-CDO. Kamakura founder Dr. Donald R. van Deventer and managing sirectors Li Li and Mark Mesler joined Professor Jarrow in co-authoring the study.
"Two years ago the Wall Street Journal in a page 1 story pointed out the dangers in relying on the copula approach for CDO valuation, but investors were slow to realize the magnitude of their model risk," said Warren Sherman, Kamakura president and coo. "The credit events of the last six months make it more obvious that macro-economic factors like home prices and interest rates are critical drivers of correlated defaults in a world where default probabilities rise and fall. This study shows that the copula approach dramatically overstates the value of CDO tranches compared to a reduced form model approach where the business cycle is correctly modeled. The authors performed credit portfolio simulations using more than 25 different approaches and conclude that very large model risk is fundamental to the nature of the CDO structure. They conclude that 6 to 11 million scenarios are necessary to have a high degree of confidence that CDO valuation is within the typical bid-offered spread seen in more conventional markets."
Kamakura noted that all simulations were done using the same reference collateral, a five year horizon modeled as 60 monthly periods, and using the same starting default probabilities in each case. The initial inspiration for the study was a presentation done by Michel Araten at the ICBI Risk Minds Convention in Geneva in December 2006. Earlier versions of the study were reviewed at the International Association of Credit Portfolio Managers meeting in Zurich in June 2007 and at the University of Chicago Credit Conference in October 2007.
