The popular press is filled with stories quoting the probabilities of default for big public companies based on the credit default swap market quotations. This analysis, however, assumes that the credit default swap represents nothing but default risk. Nothing could be farther from the truth--the spread is where the supply and demand for credit are equalized, and default probabilities are just one element in supply and demand.
What is the relationship between default probabilities and credit default swap quotes? This is one of the issues that the Kamakura Risk Information Services public firm default probability service addresses in order to help clients correctly measure "plus alpha" or even "negative alpha" performance opportunities in the credit markets. In addition to default probabilities, the KRIS default probability service also contains the estimated credit default swap (“CDS”) quotations for each of the 22,000 companies in KRIS, i.e. “Implied Spreads.” These implied spreads rely on the joint assumptions that (a) CDS contracts were actually traded for that particular company and that (b) CDS quotes are consistent with the average relationship between spreads and company attributes that prevailed over the period in which the implied spreads were fitted to a very large CDS data set. A complete description of the calculation of implied spreads is contained in Appendix D to the KRIS Version 4.1 Technical Guide. Appendix D was authored by Professor Robert A. Jarrow, Li Li, Mark Mesler and Dr. Donald R. van Deventer in 2006 and available to KRIS subscribers only. A companion paper was published in RISK Magazine in September 2007.
KRIS Implied Spreads
The KRIS implied spread calculation was design to address a simple and frequently asked question like this: “The CDS market has ABC company with a 50 basis point 5 year spread, and Kamakura’s version 4.1 KDP-jc Jarrow Chava default probabilities are 10 basis points; why are the numbers different?”
In 2003 and 2004, the early days of the credit default swap market, many traders believed that the credit default swap quotes were linked to default probabilities in a very simple way:
CDS=(1- recovery rate)(Default Probability)
Although believers that this relationship was true were very passionate, a look at the data made it obvious that it is definitely untrue. A fixed income trader for a major pension fund explained the reason very simply. “If all I got providing credit insurance in the CDS market was expected loss, why would I want to do that?” Put another way, the credit default swap represents the intersection of supply and demand for credit for that particular corporate name. Supply and demand for credit are impacted by many attributes of the underlying reference name, and the five year default probability is just one of many potential variables that can best explain the level of CDS spreads for all issuers at all points in time in the data base used to fit the implied spread function.
The next section explains how implied spreads were estimated from a very large data base of CDS bids, offereds and traded prices provided by the broker GFI. Going back to the question above, what does it tell us if the implied spread for ABC company is 42 basis points at this point in time, when the default probability for ABC is 10 basis points and the “mid market’ CDS quote is 50 basis points? The implied spread calculation tells us this: If CDS market participants were behaving “on average” as they did during the historical period from which the data were taken, ABC Company would have a CDS spread of 42 basis points when its default probability is 10 basis points. The difference between the actual spread of 50 basis points and the “average” implied spread of 42 basis is either (a) an arbitrage opportunity or (b) a rational increment to the historical “average” because of some special factor that is not yet reflected in the KRIS models. For example, ABC may have just announced that it has lost $500 million in the 2009 Bernie Madoff hedge fund fraud. As KRIS is updated once a day, the previous day’s inputs would not have reflected this bad news, and it is indeed rational for the current CDS to be at a different level than the level consistent with historical average market behavior. What the implied spread does tell us, however, is that 32 basis points of the difference between CDS spreads and default probabilities (42 basis point implied spread – 10 basis point default probability) is “normal,” and the remaining 8 basis points (50 basis point market CDS spread – 42 basis point implied spread) is unexplained by the KRIS models. We turn now to the estimation of implied spreads on KRIS.
KRIS Implied Spread Calculations
The KRIS default probability service includes four default models each of which has 7 different maturities (note only 1 year maturities are available for the Merton model because of the single period nature of that model) of default probabilities available. The KRIS service currently covers 22,000 public companies in 30 countries, and for most companies, default probabilities are available back to January 1990. The CDS quotes that are used for the implied CDS spreads modeling were supplied by the broker GFI. The GFI CDS database includes daily data from January 2, 2004 to November 3, 2005 with about 500,000 total credit default swap bid, offered, and traded price observations. Statistical relationships for bid prices, offered prices and traded prices were all estimated separately.
Many analysts fit linear equations between credit spreads and the relevant explanatory variables. Kamakura has instead chosen the logistic function to model spreads because it always produces credit spreads that are greater than or equal to zero, unlike a linear spread function. Three separate logistic functions were fitted to CDS bid prices, offered prices, and traded prices. All maturities are fitted in one function, since the data available was too scarce for some maturities to produce a reasonable spread curve otherwise.
Bid, offered and traded implied CDS prices were calculated using a hybrid model that includes a wide variety of variables that sophisticated market participants believe are relevant to the supply and demand for credit. The hybrid model incorporates the KRIS 3.0 reduced form default term structure and its inputs, KRIS 3.0 Merton structural model default probability, CDS maturities, ratings, and all of the individual macro-economic factors and other inputs to the Jarrow-Chava version 3.0 reduced form models. Contrary to the trader’s view summarized above, 45 other variables in addition to the five year default probability are statistically significant in predicting the credit default swap levels. The most statistically significant variables are the full term structure of the Jarrow Chava version 3.0 default models, the KRIS Merton default probability, dummy variables for ratings levels, the nature of the credit event definition, whether or not the borrower was Japanese (because of the unique main bank system behind Japanese public firms), and various financial ratios and stock-price related returns and volatilities. The three implied spread functions for bid prices, offered prices, and traded prices explain 80-83% of the variation in CDS quotes over the 500,000 observations in the data base. The implied spread functions are updated with each new version of KRIS.
These implied spreads allow market participants to clearly see how much of the current default swap quote is the default probability, how much is the normal premium to the default probability, and how much of the CDS spread is unexplained--representing either an arbitrage opportunity or something special that isn't captured by historical patterns of movements between default probabilities and credit spreads.
Donald R. van Deventer
Honolulu, March 18, 2009