Measuring Default Risk Premia from Default Swap Rates and EDFs

This paper estimates the degree of variation over time in the price for bearing exposure to U.S. corporate default risk during 2000-2004, based on the relationship between default probabilities, as estimated by Moody’s KMV EDFs, and default swap (CDS) market rates. The default-swap data, obtained through CIBC from 39 banks and specialty dealers, allow us to establish a strong link between actual and risk-neutral default probabilities in the three sectors that we analyze: broadcasting and entertainment, healthcare, and oil and gas. We find dramatic variation over time in risk premia, from peaks in the third quarter of 2002, dropping by roughly 50% to late 2003. Default Risk Premia 1 This paper estimates the degree of variation over time in the price for bearing default risk, above and beyond expected default loss, for U.S. corporate debt. We exploit the close but time-varying relationship between default probabilities, as estimated by the Moody’s KMV EDF measure, and default swap (CDS) market rates. Our default-swap data, obtained by CIBC from 39 banks and specialty dealers, allow us to establish a strong link between actual and risk-neutral default probabilities for the 93 firms in the three sectors that we analyzed: broadcasting and entertainment, healthcare, and oil and gas. Based on over 180,000 CDS rate quotes, 5-year EDFs explain over 74% of the variation in 5-year CDS rates across issuers and time, controlling for non-linearity and for sectoral and time fixed effects. For a given default probability, we find substantial variation over time in credit spreads. For example, after peaking in the third quarter of 2002, credit risk premia declined steadily and dramatically through late 2003, when, for a given default probability, credit spreads were on average roughly 50% lower than at their peak. For example, fixing a default probability, CDS rates were 41% lower in December 2003 than in August 2002 in the oil-and gas-sector, 69% lower in the broadcasting-and-entertainment sector, and 49% lower in the healthcare sector. A potential explanation for these declines in default risk premia is that by mid2002 the corporate debt market had experienced a reduction in risk-bearing capacity, relative to the amount of risk to be borne, driving risk premia to relatively high levels at that time. This may have been due in part to large default losses in prior months and increases in market volatility, perhaps exacerbated by frictions in the entry of new risk capital. Under this hypothesis, fresh capital flowed into this market over the subsequent months in order to take advantage of the high risk premiums offered, eventually (but not immediately) driving these risk premia down. This is similar to the explanation offered by Froot and O’Connell (1999) for dramatic increases in catastrophic risk insurance premia after major losses of capital, with subsequent slow Default Risk Premia 2 declines in premia over time as new capital is attracted into the sector. Consistent with this interpretation, we find that credit risk premia are strongly dependent on general stock-market volatility, as measured by the VIX, after controlling for the influence of firm-specific volatility on default probabilities. This may simply reflect the fact that credit spreads match the supply and demand for risk bearing: when the amount of available capital for bearing default risk is small relative to the level of risk, the price for bearing a given amount of default risk is higher. We are not aware, however, of evidence that the market price of risk in equity markets varies to such a large degree over similarly short periods of time, including this particular period. We will discuss whether the measured reductions in default risk premia could also be influenced by errors in estimating default probabilities, by “reaching for yield” by money managers, or by changes in expected recoveries in the event of default, among other potential explanations. Our study is based on an extensive database of credit default swap (CDS) rates from CIBC, and on Moody’s KMV estimated default frequency (EDF) data. First panel-regression models, and then arbitrage-free term-structure time-series models, are used to estimate how default risk premia vary over time. Previous work such as Driessen (2005) has established evidence that risk-neutral default probabilities are significantly higher than actual default probabilities. This ratio may be viewed as the proportional premium for bearing default risk. For example, if this ratio is 2.0 (for a particular firm, date, and maturity), then market-based insurance of default would be priced at roughly twice the expected discounted default loss. In terms of the average over time of default risk premia, our evidence is generally consistent with previous work. Our main focus is the degree to which these premia vary over time. We explore various alternative interpretations of our finding that the risk premia do indeed vary dramatically. A weakness of our study is the lack of data bearing on risk-neutral mean loss given Default Risk Premia 3 default (LGD). The highest annual cross-sectional 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 risk-neutral mean loss given default, our measured relationship between CDS and EDF implies that short-term risk-neutral default probabilities are roughly double their actual-probability counterparts, on average, although this premium is higher for high-quality firms than for low-quality firms, and higher for firms in the broadcasting-and-entertainment sector than for oil-and-gas or healthcare firms. In particular, this ratio was dramatically higher in mid-2002 than in late 2003. If the risk-neutral mean LGD were constant over time, at any particular level, then our results on relative changes over time in default risk premia would be largely unaffected by the assumed level of risk-neutral mean LGD. The results of Altman, Brady, Resti, and Sironi (2003), however, indicate that average realized LGDs tend to be positively correlated with aggregate default rates. As a robustness check, we provide some indication of the potential impact of such correlation on estimated CDS rates. As an illustrative example, Figure 1, which shows estimated actual and riskneutral 1-year default probabilities for Disney, is consistent with the typical pattern in our sample of high default risk premia in the third quarter of 2002, particularly in the broadcasting-and-entertainment sector. More generally, Figure 2 shows the median, within the broadcasting-and-entertainment sector, of the estimated ratios of risk-neutral to actual default probabilities at each of three maturities: instantaneously short, one year, and five years. The remainder of the paper is structured as follows. Section I places our work in the context of prior empirical research on default risk premia. Section II describes our data, including a discussion of the terms of default swap contracts and an overview of the construction of the Moody’s KMV EDF measure of default probability. Section III presents panel-regression evidence of a strong relationship between CDS rates Default Risk Premia 4 Jun01 Dec01 Jun02 Dec02 Jun03 Dec03 Jun04 Dec04 0 1 2 3 4 5 6 risk−neutral actual Date D ef a u lt p ro b a b il it y (p er ce n t) Figure 1: Estimated actual and risk-neutral 1-year default probabilities for Disney. and EDFs across several sectors, with higher risk premia for high-quality firms, and dramatically declining risk premia from mid-2002 to late 2003. Section IV introduces a time-series model of actual default intensities, and our methodology for maximumlikelihood parameter estimation. Section IV also contains parameter estimates for each firm, based on 12 years of monthly observations of 1-year EDFs for each firm. Section V provides a reduced-form pricing model for default swaps, based on timeseries models of actual and risk-neutral default intensities. Section B introduces our parameterization of the time-series model for risk-neutral default intensities, using both EDFs and CDS rates. Section C provides estimates of the parameters for each of the three sectors. Section VI provides a discussion of the implications of the results. Default Risk Premia 5 Jul02 Oct02 Jan03 Apr03 Aug03 Nov03 Feb04 Jun04 Sep04 Dec04 0 1 2 3 4 5 6 7 8 9 instantaneous 1 year 5 year Date R a ti o o f ri sk -n eu tr a l to a ct u a l d ef a u lt p ro b a b il it y Figure 2: Within-sector medians of the ratios of risk-neutral to actual default probabilities, for the broadcasting-and-entertainment sector, at various maturities.