The pricing of unexpected credit losses

"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 diffusive risk--are inadequate. We argue instead that idiosyncratic default risk, or the risk of unexpected losses due to single- name defaults in necessarily 'small' credit portfolios, accounts for the major part of spreads. Because return distributions are highly skewed, diversification would require very large portfolios. Evidence from arbitrage CDOs suggests that such diversification 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 find evidence of a positive linear relationship between this risk measure and spreads on corporate bonds across rating classes