Sigma Happens

Are you comfortable with probability and risk mathematics? I don't mean a passing acquaintance with the principles of throwing dice and winning at Monopoly, or figuring out the odds at a roulette table. I'm talking about a PhD in financial engineering, or at least a Master's in Mathematics with a Thesis in Probability Theory. No? Then you do not belong to the brave new world of finance and are herewith relegated to the status of dinosaur. Don't worry, you have plenty of company, Warren Buffett included.

At least that's what the new crop of frightfully (I choose my words carefully) bright kids populating the halls of finance would have us believe. I know, because sometimes they make me feel like a brontosaurus: big size, small brain.

This whole string of thought started when a reader (thanks "Kicker") asked me if I had any insights into CPDO's, or Constant Proportion Debt Obligations, a highly leveraged bet on default risk that sells Credit Default Swaps (CDS) on CDX and iTraxx indexes to generate income and capital gains to pay coupons of Libor+200 to 300 bp. It also has this rather unique feature: if the CDS premiums and capital gains don't generate enough cash flow to pay the stated coupon, this instrument is designed to automatically sell even more CDS's to make up for the difference. In gambling they call it "doubling down" after a loss. Polite society calls it "throwing good money after bad". Modern finance calls it "innovative".

The whole concept is based on the notion that if default risk rises too much above the level designed into the CPDO structure (itself calculated from historical default data), then it just has to revert back to the norm. Thus, selling even more CDS is the proper way to recoup the losses and eventually make a profit, too. In math terms, 3-sigma events are considered so rare as to be comfortably ignored - so comfortably, in fact, that rating agencies give this type of structure a AAA rating, despite leverage of up to 20 times (Oh, Brave New World!).

Let's stop it right there and use our common sense for just a minute. A AAA-rated bond that pays Libor +200? Ok then, I'll go ahead and arbitrage it against another AAA bond and just keep the spread. Being a dinosaur and all, I can think of several more such quaint and safe strategies, so when my bright banker calls recommending this CPDO I'll just throw them at him and see if he will just agree to pay me 2-3% on whatever amount I choose, without me putting up any money at all, of course. He should have no problem with that - what do the rest of you lizards think? Free lunch? Money for nothing? Chicks for free?

All right, time to get serious. This is a product that depends on two assumptions:

a) The low-default experience of the recent past will continue and,
b) If defaults rise they will quickly fall back.

But, here's the rub: the ultra low default expectation environment we are experiencing right now is ITSELF a 3-sigma event and will revert to the mean, too.

Here's a chart of the yield spread between junk bonds and Treasurys, showing exactly how far away from the mean we have moved in default expectations (i.e. the yield premium is way too small and has stayed that way for too long).

The bottom line is that the CPDO structure is a recipe for disaster.

Note: the CDX IG spread just hit 52 bp and CDX HY 430 bp. Both are new reaction highs. iTraxx is now at 35.

P.S. If you are interested in the discovery and application of probability and risk mathematics, I highly recommend Against the Gods by Peter Bernstein. It is very enjoyable and a good reference, too.