The determinants of CDS spreads: evidence from the model space

A credit default swap (CDS) is a financial agreement that provides insurance against default risk of a reference entity. The seller of the CDS will compensate the buyer in the event of a loan default or some other predefined credit event. In exchange, the buyer of the CDS makes a series of payments (the CDS spread or premium, usually measured in basis points) to the seller.

For a thorough review of the literature on CDS spreads, the reader is referred to Bujack and Santamaria (2016) or Augustin et al. (2014).

The long-run multiplier (also called long-run propensity) is the cumulative effect that a change in the variable \(X_{t}\) has on \(Y_{t}\), \(Y_{t+1}\), ..., \(Y_{t+h}\), with \(h\rightarrow \infty \). The exact mathematical definition is provided in Sect. 3.2.

For an excellent paper on model risk and the consequences of model risk for the risk exposure of option writers the reader is referred to Green and Figlewski (1999). For more literature on model risk, see, e.g., Derman (1996), Hull and Suo (2002), Daníelsson (2008), Buocher et al. (2014).

With the CDS Big Bang on April 8, 2009 a move towards more standardized CDS contracts took place. Since then, contracts with no restructuring (XR) have become the convention for North America.

We observe high CDS spreads and spread changes especially for firms of the high yield index (CDX NA HY). The market kurtosis of the investment grade index (CDX NA IG) is considerably lower (skewness = -2.0479; kurtosis = 35.4789) than that of the overall market index as CDS in this index are characterized by a lower volatility. In Sect. 4.3, we provide a robustness check of our analysis that only considers investment grade index CDS contracts and confirms the results of our main analysis.

Estimating a principal component using only these 35 firms gives us a first principal component that is able to explain about \(35\%\) of the entire variation over the full sample period. The second principal component only explains approx. \(3\%\) of the remaining variance.

To control for firm value, we multiply the number of shares outstanding with the current share price.

To this day, many authors have applied BMA to economic topics, especially to empirical growth. The seminal papers on model averaging and growth are Fernandez et al. (2001) and Sala-I-Martin et al. (2004). Aside from empirical growth, model averaging techniques are also applied in forecasting financial variables such as stock returns (e.g. Avramov 2002; Cremers 2002) or exchange rates (e.g. Wright 2008). In the macro forecasting, Garratt et al. (2003) employ BMA to predict inflation and output growth in the UK and Wright (2009) forecasts U.S. inflation by BMA. Surprisingly, BMA is not yet established in the Finance literature.

For example, Baele et al. (2015) examine the systemic risk in U.S. banking and show that BMA reduces the root mean square error and therefore leads to a better out-of-sample performance.

Note that model averaging using smoothed AIC weights instead of BIC in the literature is often referred to as smoothed AIC estimator (S-AIC), see, e.g., Hansen (2007). We, however, use the term BMA more generally, to cover also the AIC weight variation. For a good overview of several weighting schemes suggested in the literature see, e.g., Moral-Benito (2015).

While this assumption is often made in the literature, some authors like Sala-I-Martin et al. (2004) actually define a prior for the model probabilities and suggest that there is usually a prior belief of researchers that the true model is rather parsimoniously specified. Since we restrict our model space to a maximum of four regressors, we do not face the problem of very large models.

The use of S-AIC weights is sometimes referred to in the literature as S-AIC estimator (Hansen 2007) or information-theoretic model averaging (Kapetanios et al. 2008).

A related strand of the model uncertainty literature suggests analyzing a Model Confident Set (MCS) (Hansen et al. 2011) which is also intended to overcome the problem of selecting one best model. The advantage of the MCS is that conditional on the limits to the information of the data, MCS seeks to find a group of models that are equally likely to be superior. A hypothesis test for equal predictive ability (EPA) is performed on the set of initial models M using an equivalence confidence level \(1-\alpha \). If the null hypothesis is rejected, an elimination rule is employed to remove an inferior model. The process is then repeated until the null hypothesis is not rejected and the remaining set of models is the MCS. Recently, authors like Samuels and Sekkel (2011) have applied MCS to create a set of best predictors by trimming the worst models. Applying three different trimming techniques (fixed trimming, MCS trimming, Occam’s window), Samuels and Sekkel (2011) show that trimmed forecast combinations outperform BMA on an untrimmed model space due to the parameter estimation error in small sample sizes.

BMA should be preferred over the elastic net approach when there is an interest in analyzing (and filtering) the composition of the OLS model space. In addition, elastic net coefficient estimates are biased (while showing a smaller prediction error variance than OLS) which is induced by the penalty term used in the optimization setup.