Introduction
Both the Merton model and the tradeoff theory imply that CDS term structure of high leveraged firms is hump-shaped. To understand this, consider a junk bond. According to the model, the CDS term structure will be zero when maturity is close to zero (assuming that uncertainty is a diffusion); the CDS spread climbs fast as maturity in increases and then it decreases. My hunch is that the hump shape is not present in the data.
As far as I know, no one has tested the validity of the hump shape feature of the models. To test this, we need an exogenous change in the leverage; the other parameters cannot change. These conditions are very hard to get. I suggest we relax the ideal condition. With LBOs, we can check whether the CDS term structure becomes more hump-shaped. Implicitly, I make some Herculean assumptions.
I assume that other parameters do not change as a LBO firm takes over. More importantly, I assume that the volatility of unlevered assets does not change. Other models also make this assumption.
Even if the first assumption is true, it may be that the credit rating of a LBO firm goes from AAA to BBB — the firm is not junk. This can be controlled for. We can classify LBOs by the degree of leverage and would expect to find humps in the most levered firms. In fact, I am not sure if we empirically know that the credit rating of the firms gets worse after an LBO.
Mahdi had brought up the idea that a 10-year CDS is not as liquid as the 5-year CDS. I do not think that this is an issue. We are ultimately doing an event study. As long as the liquidity nature does not change with time, liquidity factor will be differenced out. As a robustness, we can also do some matching as a control group.
In this document, I do some preliminary analysis that does a sniff test. I answer the question: How many firms even have a term structure that is hump-shaped?
Exploratory Data Analysis
| UpWard Sloping | Not Upward Sloping | |
| Basic Materials | 69.4 | 30.6 |
| Consumer Goods | 54.4 | 45.6 |
| Consumer Services | 66.2 | 33.8 |
| Energy | 62.5 | 37.5 |
| Financials | 72.8 | 27.1 |
| Government | 100 | 0 |
| Healthcare | 74.8 | 25.2 |
| Industrials | 76.5 | 23.5 |
| Technology | 61.1 | 38.9 |
| Telecommunications Services | 73.9 | 26.1 |
| Utilities | 69.3 | 30.6 |
Using Mahdi’s email, I use the following filters to manage data analysis.
I filter the CDS Data to make it so that the currency is USD.
I filter the Data to only include American issuing firms,
I filter the data to only include CDS spreads with seniority “SNRFOR” and clause “XR14”
With the filters, I am left with 191214 firm day listings and 639 unique firms.
The analysis depends on the definition of a hump-shape. I define a hump shaped term structure when it is not strictly upward sloping. This definition is very stringent. For example, it may be that the 4Y CDS spread is lower than the 3 year CDS by 10 basis points and all other spreads are upward sloping. Per my definition, this curve will not be strictly upward sloping.
Then, for each firm day, I calculate whether the term structure is upward sloping. Table 1 shows the results by industry. The results were shocking for me. Contrary to my intuition, more than 25% of the observations are not always strictly upward sloping. This is more than I had expected and sounds like the end of my hunch
| UpWard Sloping | Not Upward Sloping | |
| AAA | 100 | 0 |
| AA | 89.9 | 10.1 |
| A | 76.6 | 23.4 |
| BBB | 74.8 | 25.2 |
| BB | 64.0 | 36.0 |
| B | 59.4 | 40.6 |
| CCC | 33.9 | 66.1 |
| D | ||
| Unrated | 52.9 | 47.1 |
Table 2 shows the percentage of time that the CDS term structure is upward sloping by rating. The results are in line with both the Merton model and the trade-off theory. As the rating gets worse, CDS term structure becomes less upward sloping.
To summarize, it seems that my hunch is wrong. The CDS term structure is not upward sloping for a substantial amount of time. This time is correlated with rating.
Impact of Jumps
In this section, I check to see if the results in the previous section are driven by jumps. Here, I change the definition of upward sloping slightly. I define upward sloping if 30 year CDS is above either the 10 or the 5 or the 2 year CDS spread.
How does the upward sloping characteristics change if I compare 30 and 10 year CDS spreads
| UpWard Sloping | Not Upward Sloping | |
| AAA | 100 | 0 |
| AA | 96.0 | 4.0 |
| A | 94.0 | 6.0 |
| BBB | 92.9 | 7.1 |
| BB | 88.9 | 11.1 |
| B | 82.2 | 17.8 |
| CCC | 57.7 | 42.3 |
| D | ||
| Unrated | 86.4 | 13.6 |
How does the upward sloping characteristics change if I compare 30 and 5 year CDS spreads
| UpWard Sloping | Not Upward Sloping | |
| AAA | 100 | 0 |
| AA | 98.6 | 1.4 |
| A | 97.6 | 2.4 |
| BBB | 99.7 | 0.3 |
| BB | 98.0 | 2.0 |
| B | 96.4 | 3.6 |
| CCC | 62.9 | 37.1 |
| D | ||
| Unrated | 86.4 | 13.6 |
How does the upward sloping characteristics change if I compare 30 and 2 year CDS spreads
| UpWard Sloping | Not Upward Sloping | |
| AAA | 100 | 0 |
| AA | 100 | 0 |
| A | 100 | 0 |
| BBB | 99.8 | 0.2 |
| BB | 99.2 | 0.8 |
| B | 100 | 0 |
| CCC | 85.4 | 14.6 |
| D | ||
| Unrated | 83.3 | 16.7 |
The results of Tables 3, 4 and 5 are very interesting relative to the results of Table 2. Note that if I only compare 30 year CDS to either 2, 5 or 10 year CDS spreads, then my hunch holds. Most of the time, the 30-year CDS is more than either the 2 or the 5 or the 10-year CDS.
Conclusion
There are two main implications:
We need to be careful in including the shorter term CDS spread in evaluating the term structure.
If we include the shorter term credit spreads, then jumps are important. The one year credit spreads seem to be high enough to cause distortions in the model.
I think we have a paper. We can filter out the tickers and the event study dates around the LBO announcement date. If we define upward sloping to be a difference between 30 year CDS with - 2 or 3 or 5 or 10 year CDS, then I think that we would find that most of the time, the CDS term structure is upward sloping.