### Legal Tender

The governments of the world..............they're going to keep doing this year after year, as long as they possibly can, and God only knows where it's leading us.

by Tyler Durden

Jan 23, 2009 3:30 PM

It is always entertaining to listen to Mark "Hogan's Bottom" Haines speculate about implied defaults, recoveries and what not... So we decided to dispel some ambiguity and speculation by presenting a brief overview of what the implied bankruptcy rate is, at least mathematically.

We have chosen as a reference security the HY10 index, one of the most liquid indices indicative of the High Yield space, which consists of 100 different HY companies (for constituents click here). We will write about some more advanced topics such as the fair value spread between the index and the implied spread based on its constituents in another day. If instead of High yield defaults, one is interested in implied defaults for Investment Grade names, then the appropriate index would be the IG11, or the most recent roll, of Markit's index representation of 125 investment grade companies. For most of all synthetic traded indices you can click here.

The implied default spread for a "security" such as the HY10 index can be calculated easily using the CDSW function in Bloomberg. As the implied default cumulative default probability is simply a mathematical function based of the price of the security, or alternatively the spread, and its projected recovery rate, we can easily see what JPM calculates the cumulative default rate for a security or an index would be thru any given point in time. Below we present a CDSW screen based on a 40% assumed recovery (more on this in a second). The output cell is highlighted, and highlights that based purely on math, there is a 67% cumulative chance of default by March 2014. As this is an index, the argument would probably go that 67 of the 100 companies that make up the index would go belly up over the next 5 years.

A peculiar twist arises if one changes the recovery assumption for the cume default formula: the default assumption is 40% for a security such as the HY10 index (one particular class of outliers are municipal CDS, where the recovery rate is set to 80% - the next several months will present ample chances to test this assumption). So if instead of using 40% we drop the recovery rate to 20%, as all this does is fudges with the price equivalent spread, we get a different cumulative default probability as shown below:

As one can see, the default prob drops substantially by 13% at the 5 year border. Of course if one were to crank the recovery rate all they way down, the default prob drops to a manageable 45%.

So this is all the secrecy behind the math. There are many resources on the web that dig much deeper into this and I encourage additional reading. Like I mentioned earlier, if instead of the HY universe one is interested in the IG world, then the appropriate index would be IG11. There are other indices such as XO and Main which focus on crossover credit names, or euro denominated, so you can tailor the exposure to your liking and see what the implied default is.

Again keep in mind this is merely math, and the default rate is cumulative. There is no fundamental analysis involved at all in default probability projections. So for all those who say the price implies Great Depression type default level and how this is extremely insane, keep in mind this is what the market is saying. And unless you are AQR Capital, the market is usually always right... unless it's wrong of course.

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- Jan 23, 2009 3:30 PM