Bond and CDS Spreads

For the sake of completeness, it should be further mentioned that another strand of the literature deals with extracting default risk information from credit-related securities instead of equities. A discussion of bond and CDS pricing is obviously beyond the scope of this thesis, but using default risk information in the prices of such securities deserves a few comments, especially since regulators have actively advocated the use of this kind of information in risk management (EBA 2014, p.

23).

18Futher details on the estimation of (13) are provided in the second research paper.

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Compared with the CDS market, the corporate bond market has a much longer history. Chan-Lau (2006) provides a brief introduction on default risk implied by bond prices. The expected payoff B of a zero-bond with a face value of one unit maturing in one period is given as

B = (1−P D) +P D×RR

1 +r , (14)

where RRis the recovery rate in case of default and r is the risk-free rate. Under the assumption that bonds are priced by risk-neutral agents, the implied PD can be easily solved from (14). Along the lines of Fons (1987), this framework can be extended in a straightforward way to coupon bonds with any maturity.

How informative are bond spreads about defaults? The evidence is extremely sparse. The findings of Giesecke et al. (2010) suggest bond spreads are not infor-mative about defaults. A large proportion of bond spreads is driven by factors that are unrelated to credit quality, such as interest rate, tax and liquidity risk (Driessen 2004, Huang & Huang 2012). From an empirical perspective, an important fac-tor hampering the use of bond spreads in PD models is the vast heterogeneity of issue-specific clauses in the bond market. Bharath & Shumway (2008) state their database is seriously reduced after the elimination of bonds with special features.

After all, they are left with 58 defaults. Hence, their finding that bond spreads contain useful information in predicting defaults comes with a caveat. Further-more, it is noteworthy that Giesecke et al. (2010) who search for defaults in the U.S. bond market from 1866-2008 in a cumbersome manual cross-database anal-ysis are able to identify only 143 defaults. In practice, it seems impossible to use bond spreads as a basis for PD forecasts for these reasons.

Compared with the corporate bond market, the CDS market is smaller but more standardized and thus easier to handle in empirical work. There is a clear theo-retical link between bond yields and CDS spreads that is best illustrated by an arbitrage argument. On the one hand, consider a fixed-rate corporate bond with maturityN and a yield-to-maturity y. Furthermore, assume that theN year CDS spread for the same reference entity is defined as s. As above, r is the N year risk-free rate. Ignoring restrictions on short selling, counterparty risk, tax and liquidity premia, no arbitrage implies that the pay-off from a portfolio of the cor-porate bond and a long position in the CDS, should be equal to a long position in the risk-free bond. This intuition is formalized in (15):

(y−s)−r= 0. (15)

If the left-hand side of the parity (15) is larger (smaller) than zero, it will be profitable to assume a long (short) position in the corporate bond and the CDS while assuming a short (long) position in the risk-free bond. Even though the hypothetical CDS used in this no-arbitrage argument also ignore some real world contractual features of CDS, such as the so-called “cheapest-to-deliver” option, Hull et al. (2012) find the relationship postulated in (15) holds well empirically.¹⁹ The CDS spreads is an insurance premium and it implies a PD. Following Chan-Lau (2006), I assume the perspective of a protection seller in the CDS market.

Given the same hypothetical zero-bond assumed in (14), her expected loss L is just the mirror image of the bondholder’s expected pay-off:

L=P D×(1−RR), (16)

where the PD and the recovery rate are deemed to be independent. Under the assumptions underlying the relationship (15), the CDS spreads for the zero-bond is given as the discounted expected loss (16):

s= P D×(1−RR)

1 +r . (17)

Thus, the PD can be recovered from (17) if the recovery rate, the risk-free rate and the spread are given. The CDS pricing theory pioneered by Hull & White (2000) paves the way to obtain a more sophisticated framework with multiple coupon periods that enables us to solve for the PD if we observe the CDS spread. In essence, the spread s, which is the market price of default risk, will equalize the expected discounted pay-offs from protection sellers and buyers. It is quite difficult to implement this model for empirical purposes. Berndt & Obreja (2010) show the approximation (18)

P D= 4×log(1 + s

4×RR) (18)

suffices, if the arbitrage argument made explicit in (15) holds and CDS coupons are paid on a quarterly basis, as it is now standard in the market.²⁰ Like PDs

19This options leaves some freedom with regard to the specific issues that are to be delivered by the protection buyer in the event of default.

20Berndt & Obreja (2010) find a common factor in European CDS spreads is highly correlated with catastrophe risk, i.e. the risk of an economic event which will lead to a simultaneous

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extracted from bond spreads, (18) yields a risk neutral probability. To illustrate the implications of using such risk neutral measures for default forecasts, consider the following case study of four European industrial firms. On the left axis, figure 3 depicts the physical Merton-PD, which has been computed using (13) at the beginning of every month between 2008-2015. Furthermore, the right axis in figure 3 shows the risk neutral probabilities implied by the 1-year senior unsecured CDS spread given by (18).

These figures shows time series plots of PDs implied by the Merton (1974) model and CDS. The Merton model has been computed at the beginning of every month from 03/2008 to 05/2105 using one year of historically observable daily equity returns and balance sheet data. The latter has been lagged by six months to account for the publication bias. A PD has been extraced from CDS spreads using the approximation (18). All data has been downloaded from Datastream.

Figure 3: Case Study - Physical vs. Risk Neutral Probabilities

CDS implied PDs are at many times a multiple of physical PDs. Hence, mar-ket participants in the CDS marmar-ket are not risk neutral but risk averse. In fact, CDS implied PDs can exceed one in extreme situations, for instance when there

default of several blue chip companies.

are rumours about bankruptcy, which was the case at the end of 2009 for Heidel-bergCement. Moreover, such situations seem to cause large disturbance in CDS spreads even after the physical PDs have returned to uncritical levels. These re-sults underline that CDS should not be used for default forecasts (Jarrow 2012).

Strictly speaking, (18) does not yield a probability but a pricing measure. The same applies to bond spreads. A conclusive study of the forecasting power of CDS implied PDs does not exist. Another practical reason for this is that the CDS market is very small and defaults are very rare.²¹ The fourth research paper pre-sented in section 4 analyzes the entire cross-section of French, German, Italian and Spanish CDS. The number of firms with existing contracts is only 108. Moreover, the efficiency of the CDS market remains a debated issue. Recent research sug-gests the CDS market is characterized by imperfect competition, market frictions (G¨und¨uz et al. 2012) and illiquidity (Junge & Trolle 2013). Up until now, CDS appear to be useless for default forecasts, as well.

So far, the section has been a wrap-up of the main ideas behind distress risk models.

The goal was to discuss the reliability of several approaches to measure distress risk. On the one hand, there is a variety of reduced form accounting models and, on the other hand, there is the Merton (1974) model. A final conclusion as to how well these approaches measure default risk is the main concern of the second research paper and deferred to the summary of the empirical results in section 4.

Moreover, it has been explained that approaches based on bond and CDS spreads are no viable alternative for the problem at hand. In theory and practice, there is a much stronger and well-known consensus about methods to cope with market risk than with credit risk. Dealing with market risk is now a standard subject in undergraduate and postgraduate finance courses, credit risk is typically barely touched in university courses. Bohn (2011), who provides one of the few textbooks on credit risk, suggests the lack of data as a main explanation for this phenomenon.

Estimating and testing models requires data that are generally unavailable to the public and require a lot of manual work. Rating agencies have a clear advantage in this regard because they have been building large proprietary databases for a long time. Storing the data in a safe and secret place keeps them in business, but it basically prevents external reviews of the performance of ratings as risk measures.

What credit ratings really achieve as forecasters remains largely unclear in the literature. This opens up the debate about the use of structural and reduced form accounting models in empirical research. There is only one way to make sure these models provide precise estimates of distress risk, namely a quantitative evaluation of their forecasting performance. The results for such an analysis are summarized

21A history of credit events dealt with in the CDS market is available on the website http:

//www.creditfixings.com. There were 10 worldwide corporate credit events in 2008 and 6 in 2016.

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in section 4.