Why are spreads on corporate bonds so wide relative to expected losses from default? The spread on Baa-rated bonds, for example, has been about four times the expected loss. We suggest that the most commonly cited explanations taxes, liquidity and systematic di¤usive risk are inadequate. We argue instead that idiosyncratic default risk, or the risk of unexpected losses due to singlename defaults in necessarily small credit portfolios, accounts for the major part of spreads. Because return distributions are highly skewed, diversi cation would require very large portfolios. Evidence from arbitrage CDOs suggests that such diversi cation is not readily achievable in practice, and idiosyncratic risk is therefore unavoidable. Taking a cue from CDO subordination structures, we propose value-at-risk at the Aaa-rated con dence level as a summary measure of risk in feasible credit portfolios. We nd evidence of a positive linear relationship between this risk measure and spreads on corporate bonds across rating classes. JEL Classi cation Numbers: C13, C32, G12, G13, G14 Keywords: credit spread puzzle, jump-at-default risk, Sharpe ratio, collateralised debt obligation We thank Franklin Allen, Claudio Borio, Pierre Collin-Dufresne, Joost Driessen, Darrell Du¢ e, Craig Fur ne, Jacob Gyntelberg, Jean Helwege, John Hull, Rich Rosen, Philipp Schonbucher, Til Schuermann, Ken Singleton and participants at the Moodys-LBS Second Credit Risk conference for helpful comments; Christopher Flanagan and Rishad Ahluwalia of JPMorgan Chase, Nitin Prabhu and John Convery of Deutsche Bank, and Jerome Anglade of Morgan Stanley for helpful discussions on CDOs; JPMorgan Chase and Moodys for providing us with data; and Dimitri Karampatos for research assistance. The views expressed are those of the authors and do not necessarily reect those of the BIS.