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Donald R. Van Deventer, Ph.D.

Don founded Kamakura Corporation in April 1990 and currently serves as its chairman and chief executive officer where he focuses on enterprise wide risk management and modern credit risk technology. His primary financial consulting and research interests involve the practical application of leading edge financial theory to solve critical financial risk management problems. Don was elected to the 50 member RISK Magazine Hall of Fame in 2002 for his work at Kamakura.

# CDO Valuation: What to Expect While You’re Expecting (Updated April 22, 2009)

04/14/2009 05:41 AM

The classic book for expectant parents, What to Expect When You’re Expecting (by Heidi Murkoff and Sharon Mazel), ranks 65th of the 2 million books on amazon.com for a very good reason: it helps people who are about to do something unlike anything they’ve ever done before to get ready for what’s ahead with more accurate expectations and better preparation than they would have otherwise had.  The same kind of primer is necessary for the owners of CDO tranches, many of them happily thinking “It’s just like a bond.”  Unfortunately, CDO tranches are nothing like bonds.  With a very high probability, they are “heaven or hell” securities which, with very high probability, leave the owner either with all of his principal returned or none of it returned.  This blog entry tells why.

Our April 13, 2009 blog entry focused on the FASB Staff Position regarding the valuation of complex securities.  The FASB document reads very much like instructions for valuing a bond, when, in fact, collateralized debt obligations have very little in common with traditional bond structures.  Traditional bonds, even when they default, return some consideration to the owner of the bond in almost 100% of the cases for senior debt issues. There is almost no probability of getting nothing.  Moreover, getting 100% of principal returned is typical. With CDO tranches, there is a completely different distribution of outcomes.  There is a relatively high probability of 100% return of principal, there is a relatively high probability of 0% return of principal, and there is almost zero probability of any partial return of principal.  This may be obvious to some readers, but to the vast majority of CDO tranche holders that we speak to this is a surprising result.  Let’s go through the reasons for it.

Consider a CDO with $1 billion of collateral underlying it. To make the exposition simple, let’s assume that it’s been divided in 100 tranches of$10 million each, so each tranche represents 1% of notional principal.   What if the ultimate losses on the CDO are exactly $183 million? The first 18 tranches, which total$180 million of underlying principal, get nothing.  The 19th tranche gets $7 million of the$10 million in principal returns, and the remaining 81 tranches get 100% of principal returned.  Only 1 of 100 tranches gets a partial return of principal, the equivalent of the recovery on a bond that has defaulted.  99% of the tranches get all or nothing.

Now let’s turn the clock back to time zero, when the CDO was originated.  Assume you are a close relative of God, and He tells you “Losses on the collateral are equally likely to fall anywhere in the range from 0 to $200 million, and there is no probability that losses will be more than$200 million.”  Therefore we know that 80 of the tranches will have 100 percent of principal returned, and 1 of the 20 most subordinated tranches will have a partial loss.  The other 19 tranches will either lose everything or nothing, just like the example above.  Because we are a close relative of God, we know that the 20 tranches that take first losses each have a 1/20 probability of a partial loss. As in the example above, 99% of the tranches are in an all or nothing state.

This has very important implications for what an investor in a CDO tranche should expect to see as time passes after origination.  Initially, pricing will have been set so that a funded CDO (as opposed to a cashless synthetic CDO) tranche is priced near par.  As time passes valuations will begin to deviate from par, with the most subordinated tranches going to zero quickly.  The tranches with a moderate risk of principal loss will see values deteriorate to 80%, 70%, 60% or 50% of par.  These are the tranches with the highest likelihood of a partial return of principal, but we know from our example above that only 1 out of 100 tranches will actually experience this outcome.  As time passes, this cluster of tranches with values “in the middle” of the range between par value and zero will split into two groups–the lucky ones, who just escape taking losses.  As maturity approaches, it will be more and more obvious that they are going to take no losses and valuations will converge to par value.  For the unlucky ones, the fact that they are going to take losses will also become more and more obvious, and since only one of our 100 tranches will take partial losses, we know that the values of the rest of this unlucky bunch will go to zero.

Because of this phenomenon, the concept of “other than temporary impairment” is almost an oxymoron.  With a bond trading between 30% of par and 70% of par, one would normally say that the bond holder’s fate is determined and he’s highly likely to take a loss.  With a narrow banded CDO tranche like the 100 “1 percent” tranches we are talking about here, the CDO tranches that are trading between 30% of par and 70% of par halfway through the life of the CDO have a much different outlook than a bond trading at the same price levels.  The bond will never be valued at zero (if it’s senior debt, except in truly extraordinary circumstances), but many of the CDO tranches will go to zero.  Many of the CDO tranches trading between 30 and 70 will emerge from this pack to be “lucky ones” that go back to par–the “other than temporary impairment” has in fact turned out to be temporary indeed–something very unlikely for the bond trading at those levels.  Finally, only one of the tranches trading in the 30 to 70 range is likely to be the one that suffers a partial loss.

Basically, with these narrow tranche bands, the tranche payoff of principal is a zero/one event, like a digital default swap that is a function of the total loss on the pool of collateral.  The speed with which valuations can go from 100% to 0% or 100% to 30% to 100% is astonishing to many investors in CDO tranches, but this is the nature of the beast.  Since this is not a beast most investors would like to have on-going exposure to, the very structure itself has a gloomy future now that investors have a better understanding of the risks of credit loss-related tranching.

What about a more traditional tranche structure where the loss bands are 0 to 3% of losses, 3 to 7% of losses, 7 to 10% of losses, 10 to 15%, 15 to 30%, and 30% and over?  While the widths of the bands are wider and not uniform, the same basic principles apply.  Only 1 of the tranches will take partial losses and end with a value between 0 and 100 at maturity.  The others are heaven or hell/all or nothing outcomes.  As one does a monte carlo simulation of potential future values, ultimately all of the tranches will have the biggest probability weights on the all or nothing outcomes.  As the tranche gets more senior, there will be more probability weights on the 100% return of principal outcome and less probability weights on the total loss scenarios (which can occur at multiple points in time).  As time passes, there will be less and less probability weight “in the middle” as it becomes more clear which tranche will get a partial return of principal.

Back to the What to Expect if You’re Expecting analogy.  if you are a newly minted parent, you have nearly a 100% probability of being happy with the outcome.  For CDO tranche holders, however, many of them will be left with the CDO equivalent of dirty diapers and nothing else.

Donald R. van Deventer
Kamakura Corporation
Honolulu, April 15, 2009