Estimating Default Risk Premia from Default Swap Rates and EDFs
This paper estimates recent default risk premia for U.S. corporate debt, based on a close relationship between default probabilities, as estimated by the Moodyâ€™s KMV EDF measure, and market default swap (CDS) rates. The default-swap data, obtained by CIBC from a large number of dealers and bank counterparties, allows us to establish a strong link between actual and risk-neutral default probabilities for 69 firms in the three sectors that we analyzed: broadcasting and entertainment, healthcare, and oil and gas. Based on over 49,000 CDS rate quotes beginning September 2000, we find that five-year EDFs explain over 70% of the variation in daily five-year CDS rates, across all firms and days. Better explanatory power can be obtained by controlling for sectors and calendar periods. Our preliminary results suggest that, during our sample period, credit spreads widened by approximately 16 basis points for each additional 10 basis points of EDF, with adjustments that we shall describe for non-linearities and for variation across sectors and calendar quarters. If a given firmâ€™s risk-neutral default intensity lambda* and risk-neutral expected fraction L* of notional lost at default are assumed to be relatively stable over time, the firmâ€™s CDS rate and the par-coupon credit spread would be approximately equal to the risk-neutral mean loss rate, lambda*L*. The actual sample-mean of loss given default during our sample period was reported by Altman, Brady, Resti, and Sironi (2003) to be approximately 75%. Using 75% as a rough estimate for L*, our measured relationship between CDS and EDF implies that risk-neutral default intensities are roughly double actual default intensities (proxied by EDFs). This ratio of risk-neutral to actual default intensities is a default-timing risk premium whose measurement is a primary objective of our analysis. This simple factor-of-two estimate of the default risk premium does not consider: (i) the effect of random fluctuations in actual and risk-neutral default intensities, (ii) the potential impact of illiquidity on CDS rates, (iii) the distinction between actual and risk-neutral mean fractional losses given default, (iv) correlation between fluctuations over time in risk-neutral mean losses given default and risk-neutral default intensities, (v) the effect of cheapest-to-deliver settlement options on default swap rates, and (vi) sample noise. We shall address the impact of each of these in the paper. Driessen (2002) recently estimated the relationship between actual and risk-neutral default probabilities, using U.S. corporate bond price data (rather than CDS data), and using average long-horizon default frequencies by credit rating (rather than contemporaneous firm-by-firm EDFs). Driessen reported an average risk premium across his data of 1.89, after accounting for tax and liquidity effects, that is roughly in line with the estimates that we provide here. While the conceptual foundations of Driessenâ€™s study are similar to ours, there are substantial differences in our respective data sources and methodology. First, the time periods covered are different. Second, the corporate bonds underlying Driessenâ€™s study are less homogeneous with respect to their sectors, and have significant heterogeneity with respect to maturity, coupon, and time period. Each of our CDS rate observations, on the other hand, is effectively a new 5-year par-coupon credit spread on the underlying firm that is not as corrupted, we believe, by tax and liquidity effects, as are corporate bond spreads. Most importantly, we do not rely on historical average default rates by credit rating as a proxy for current conditional default intensities. Because the corporate bonds in Driessenâ€™s study involve taxable coupon income, extracting credit spreads required an estimation by him of the portion of the bond yield spread that is associated with taxes. As for the estimated actual default probabilities, Driessenâ€™s reliance on average frequency of default for bonds of the same rating rules out conditioning on current market conditions, which Kavvathas (2001) and others have shown to be significant. Reliance on default frequency by rating also rules out consideration of distinctions in default risk among bonds of the same rating. Moodyâ€™s KMV EDF measures of default probability provide significantly more power to discriminate among the default probabilities of firms (Kealhofer (2003), Kurbat and Kurbalev (2002)). Finally, although there is no solid empirical evidence yet regarding liquidity effects on bond-yield spreads versus liquidity effects on CDS rates, our enquiries of market participants have led us to the view that default swaps, because they are â€œun-funded exposures,â€ in the language of dealers, have rates that are less sensitive to liquidity effects than are bond yield spreads. As opposed to Driessen, however, we have not estimated the portion of CDS rates due to illiquidity. The potential applications of our study are numerous, and include: (i) the relationship between risk and expected return for the credit component of corporate debt, and (ii) analysis of the extent to which the default-risk premia of different firms have common factors. These applications can, in turn, be further applied to a range of pricing and portfolio investment decisions involving corporate credit risk
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