The probability of extreme default losses on portfolios of U.S. corporate debt is much greater than would be estimated under the standard assumption that default correlation arises only from exposure to observable risk factors. At the high confidence levels at which bank loan portfolio and collateralized debt obligation (CDO) default losses are typically measured for economic capital and rating purposes, conventionally based loss estimates are downward biased by a full order of magnitude on test portfolios. Our estimates are based on U.S. public nonfinancial firms between 1979 and 2004. We find strong evidence for the presence of common latent factors, even when controlling for observable factors that provide the most accurate available model of firm-by-firm default probabilities. Copyright (c) 2009 the American Finance Association.

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We introduce a novel estimator of the quadratic variation that is based on the theory of Markov chains. The estimator is motivated by some general results concerning …ltering contaminated semimartingales. Speci…cally, we show that …ltering can in principle remove the e¤ects of market microstructure noise in a general framework where little is assumed about the noise. For the practical implementation, we adopt the discrete Markov chain model that is well suited for the analysis of …nancial high-frequency prices. The Markov chain framework facilitates simple expressions and elegant analytical results. The proposed estimator is consistent with a Gaussian limit distribution and we study its properties in simulations and an empirical application. Corresponding author, email: peter.hansen@stanford.edu. Peter Hansen is also a¢ liated with CRE-ATES a center at the University of Aarhus, that is funded by the Danish National Research Foundation. The Ox language of Doornik (2001) and R were used to perform the calculations reported here. We thank seminar participants at CREATES, Oxford-Man Institute, University of Pennsylvania, and the 2008 SOFIE conference for valuable comments. We especially thank Asger Lunde for helping extract and clean the high-frequency data that are used in this paper.