Saturday, July 21, 2007

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.

12 comments:

  1. Thanks! That was more than I expected.

    CPDOs remind me of another "double down" product, the CPPI products of the 1980's. It was the popularity of CPPI products that lead to Black Monday.

    When automated convex trading strategies dominate, volatility is always increased. That may explain the 3 sigma event we're currently seeing in the credit markets (thanks for pointing that out).

    The interesting bit is trying to figure out how convex strategies break. I doubt anybody would have predicted that CPPI products would have resulted in a 20% drop in the DJIA in a single day.

    CDPOs are programmed to roll every six months to the new series in the index and the indexes are highly diversified. This keeps the default risk low. You'd need several "Enron" type events in a six month period to have significant default risk even with the leverage they employ.

    To break a CDPO, you'd need a violent sell off in the CDS market. This would increase the roll costs enough to break the CDPO structure. Without a violent sell off, you'd need a grinding bear market for credit that lasted several years.

    Either of these events would put a stake in the heart of equity markets. I doubt we'd be able to avoid a recession. Thoughts?

    A decent article on the structure of CPDOs can be found here

    ReplyDelete
  2. Re: "In math terms, 3-sigma events are considered so rare as to be comfortably ignored..."
    And that is the basis for the book Black Swan. Life is not a bell curve, but more random and thus not rare! (If I interpret the book properly.)

    ReplyDelete
  3. Great article and Mover Mike has added some thoughts at his site.

    ReplyDelete
  4. It won't take a series of big defaults to break a CPDO - all that is needed is for credit spreads overall to rise and keep rising for 2-3 roll periods. As the CPDO suffers capital losses, its structure forces it to increase exposure at the same time by increasing their leverage even more. It will very quickly run out of equity and have to shut down - there is no gambler that has infinite cash.

    Don't forget, a CPDO is highly leveraged to begin with. At 15x all it takes is a 7% move to wipe you out completely.

    Regards

    ReplyDelete
  5. This also reminds me of the "doubling down" type strategies on spread trades that lead to the LTCM collapse (as described in "When Genius Failed" by Roger Lowenstein).
    Was it Jim Grant who said that all human knowledge is cumulative, except in finance, where it is merely cyclical?

    ReplyDelete
  6. "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."

    What evidence is there that default probabilities are mean-reverting?

    ReplyDelete
  7. Re: cyclicality and reversion to mean of default rates. Please see:

    By Moodys:
    1. Corporate Bond Defaults and default rates 1938-1995 (1/1996).

    2. Measuring Corporate Default Rates (11/2006)

    By Prof. Altman (NYU):

    About Corporate Default Rates (2007)

    Regards

    ReplyDelete
  8. Thanks for the links. I skimmed these papers, but I only saw one statement relevant to the issue of mean-reversion of default probabilities. The statement I saw is in Altman's paper where he says:

    "Much has been written and discussed, of late (e.g., see Altman, 2006), about the unusually low default rate period and whether conditions will revert back to the average rate or whether the extreme, massive liquidity picture will remain with us for a long time to come. We do observe another benign period from 1993 to 1998, so while it is possible that the current period will persist, we are of the opinion that there will be a reversion to the mean and, indeed, this is perhaps overdue."

    The first paper is a general survey and I couldn't see any mention of mean-reversion.

    The second paper from Moody's concerns the issue of how to adjust default probability estimates for rating withdraws.

    Did I overlook something?

    ReplyDelete
  9. Please see today's post. The references were mostly to provide the historical default data, standard deviations, etc.

    You should also look more carefully at the data on cumulative default rates and ultimate default rates based on original credit ratings.

    ReplyDelete
  10. From an event held at S&P in Jan 07...

    "Neil Budnick, President of bond issurer MBIA, believes that there will be an “elongated adjustment and spotty”. He is “generally optomistic on the market”. And most importantly he said that there is “lots of money out there to correct problems”. He was referring to the private equity and hedge funds willingness to take either significant equity or debt positions in companies prior to default, recapitalizing companies with shaky capital structures."

    http://shopyield.com/blog/2007/01/26/looking-out-into-the-credit-cycle/

    Budnick was ushered out of MBIA several days after this event...the important point is the vast liquidity available to recap shaky structures mitigating default...and liquidity be drying up...so we be looking at a new default landscape...

    ReplyDelete
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