Monday, March 12, 2007

How does a CDO work?

A CDO (collateralized debt obligation) is nothing more than a redistribution of credit risk, much in the same way a CMO is a redistribution of prepayment risk. This post will quickly go through the basic math of a CDO. For illustration purposes, I'm going to use a real ABS CDO featuring mostly RMBS as the base for the percentages of each tranche. I'm going to make some simplifications to the structure just to keep the example easy to understand. Regardless, this should be a pretty good basic lesson on how a CDO works and where the risks are. I'm going to use an ABS deal as my example, but any credit-risky security could be used. Also, I'm going to use fixed interest rates just for simplicity, but almost all CDOs are floating rate. Just that LIBOR is 5.30% and stays static over time.

We start with a $100 portfolio of ABS bonds which yield 7%. This is called the collateral portfolio. The collateral portfolio has a average rating of BBB. In order to fund the purchase of this portfolio, 5 different securities are sold. The amount, credit rating and interest rate of the first four are as follows.

$75 Class A, rated AAA, yields 5.51%
$10 Class B, rated AA, yields 5.80%
$5 Class C, rated A, yields 7.20%
$5 Class D, rated BBB, yields 9.00%

These are called the debt tranches. Some of you may notice that those yields for Class C and D are far in excess of what typical bonds with similar ratings yield.

The fifth security sold is the equity tranche. That is another $5. We'll get to the equity in a minute.

Why are the tranches rated differently? Because interest and principal are paid sequentially, starting with Class A and ending with the equity tranche. Only once Class A has been paid what its due does Class B get paid, and so on.

So our portfolio of bonds pays $7 per year in interest. The CDO then owes interest on the debt it sold:

Class A: $4.13
Class B: $0.58
Class C: $0.36
Class D: $0.45

That makes a total of $5.52. So there is $1.48 left over. In a deal like this, the manager probably charges around 0.20%, and there is another 0.05% for admin fees. So net of fees there is $1.23. That passes through to the equity. Notice the return on the equity is a quite attractive 24.6%. Now many times a portion of the excess spread is held aside to cover losses, but I'll ignore that for now.

So that's how it works if you have zero defaults, but of course, that's not going to happen. Let's say that 2% of the collateral portfolio defaults, and the recovery is 50%. So now there is $99 in the collateral portfolio with a 7% yield. Instead of having $7 in interest, we only have $6.93. So far, everything is fine, because we had $1.23 which we were paying the equity. Now we only have $1.16, but that's still over 20% IRR for the equity tranche.

Now let's say that the deal suffers 2% defaults per year for 10-years at which time principal on the debt tranches becomes due. So that's a total of 10% losses (2% x 50% recovery x 10 years). You've been able to cover interest costs all along, because even after $10 in principal losses, you are still have $6.30 interest earned vs. $5.52 interest costs plus $0.25 in fees. You're still $0.53 in the black.

But what about paying off the principal on the debt tranches? You only have $90 in principal left in your portfolio to pay off $95 in debt. If that were the end of the story, Class A would get paid its $75, then Class B its $10, then Class C its $5, and Class D would default, and get no principal at all.

Now you might say, net-of-recovery losses of 1% doesn't seem too extreme. How the hell would the Class D tranche get an investment grade rating? There are a couple of things that complicate the math, and make the Class D tranche a little safer. First, there are usually two coverage tests which CDO's calculate: interest coverage (IC) and overcollateralization (OC). The IC test has the total interest earned in the numerator, and the total interest cost of a given tranche and all tranches senior as the denominator plus fees. So in our case, the IC on Class B at the onset of the deal would be $7/($0.58+$4.13+$0.25)=141%. Some trigger is set for how high that number needs to be for each tranche and if the actual number is lower than the trigger, some remedy is required. For example, it might be that money that would have gone to the equity is used to pay down some of the debt tranches. Since the size of the collateral portfolio is the same but the size of the debt is lower, the IC calculation improves.

The OC test is similar, except the numerator is the principal value of the portfolio and the denominator is the outstanding amount of a given tranche and all bonds senior. So for Class B at the outset, the OC test would be $100/($75+$10)=118%. Here again, some trigger level is established when the deal is sold, and if the OC falls below that trigger, some remedy is required.

The triggers are usually higher for more senior tranches. So the top tranches aren't just protected by the extra cash flow of the deal, but also by the fact that if anything starts to go wrong, cash flow will be diverted from other tranches. The trigger levels also tend to be higher in deals with riskier collateral. A deal with all BB-rated bank loans will have higher IC and OC tests compared with an investment grade resi ABS deal.

Now you can see how freakin' complicated the cash flow can get. It becomes extremely hard to determine what default level would sink a given tranche. For example, a tranche may be able to survive 5% annual defaults for all 10-years, but might not be able to survive 10% defaults in year 2. A relatively high level of defaults spread out over time is more easily cured through the excess interest the deal collects. But a spike in defaults would usually result in more senior tranches being paid down, and there might not be enough left over to pay principal on more junior classes.

Another complication is the recovery rate. It is often true that the weaker credits in the deal also recovery at a lower rate. For example, you might have a deal that is 50% prime RMBS and 50% B/C Home Equity. That might have an average recovery rate of 50%, because the prime RMBS recovers at 75% and the B/C Home Equity recovers at 25%. But since the B/C stuff is more likely to default, who cares what the "average" recovery is? The only thing that matters is the recovery on the bonds that actually default.

The interest spread is probably uneven as well. For example, if the whole deal yields 7%, it might be that the 50% prime RMBS is at 6.5% and the B/C is at 7.5%. So if a B/C piece defaults, there is a larger decline in overall interest earned than what the straight average yield would imply.

So CDOs can get pretty complicated, and its impossible to say just how many defaults it will take to sink a given tranche. The concern should be with buyers of BBB and A-rated tranches of sub-prime residential deals. If there is a large default spike in 2007-2008, and recovery rates come in much lower than expected, these tranches will likely perform poorly. If you are an equity investor... well... good luck.

38 comments:

RW said...

Thanks for that explanation Tom; I think I'm beginning to at least gain some conceptual understanding of this type of security even if I may never be able to accurately predict what they are going to do. Part of my concern of course was that, somewhat akin to portfolio insurance in the 80's, even those who created them might not be able to accurately predict CDO (or CDS) behavior if/when the system became subjected to great(er) stress.

At least I have a better sense of why a Class 'A' or 'B' tranche could receive a higher credit rating than its contents might otherwise warrant and that is something I didn't have before (even though I still think the lower tranche and equity holders are going to get the shaft if things unfold as I believe they might).

Tom G. said...

The way these deals work, equity holders usually get clobbered if things go badly. Basically they get a great return if everything occurs normally, and get wiped out if things go badly. That's the game.

The advantage of CDO equity for certain buyers is that its huge leverage with no recourse. Think about it. The equity in the deal I used as an example was 5%. In essense, 20/1 leverage. But you can only lose what you put in. No margin calls, no pledged assets, none of that.

There are hedge funds that invest in nothing but CDO equity and debt tranches of busted deals. I know we're going to start hearing about hedge funds closing that were invested in a slew of ABS CDO's. The investors might have thought that they were in a diversified investment, but as I said in an earlier post, you are only as diversified as your riskiest pieces.

Anonymous said...

Great explanations , thanks so much

Chris said...

Question for you...

If you are a CDO manager trying to manage/maximize your recovery rates let's say you have the following scenario.

You have a bond that is distressed. You can reasonably assume that at some point the bond is going to stop cashflowing and become worthless. It's basically a credit IO.

If you could sell the bond for some value (say 15 cents on the dollar) does your recovery value for that asset get determined by % of Par (15%) or is it based on your current mark on the bond?

In this scenario are you better off getting some value for the bond or waiting it out and clipping the coupon until it stops cashflowing?

Thx,
Chris

TDDG said...

Chris:

Now we are getting into the nitty gritty.

If a manager had no motivation other than maximizing the value of the CDO portfolio, then s/he would compare the PV of the expected cash flow and compare that with the market price. It may be that the market thinks the bond will do better than the manager, or vice versa.

In real life, the manager's situation is more complicated. Selling the bond may cause an OC test failure, maybe because the pricing service doesn't properly value the bond. Or because the documents are poorly written and somehow the manager can still count the bonds at par for OC test purposes.

Also, CDO managers usually get some kind of performance fee. It may be that the manager isn't going to make his/her performance fee hurdle on this deal unless some good things break his/her way. Maybe s/he decides to hold onto the bond hoping against hope that the bond recovers.

I'd say generally, that over the years, the covenants and what not have been tightened to try to avoid these kind of perverse incentives. But people always find loop holes and/or they get law firms to write the documents in an unorthodox way. Only when things are going badly do investors realize this, unfortunately.

Anonymous said...

Tom: I have read many articles and Primers on CDOs and none were able to encapsulate the subject as precisely as you succeeded in doing. Thanks for the great blog.

Anonymous said...

you may want to contribute to the wikipedia article on CDOs, it needs a lot of work (as do the other articles on finance).

Anonymous said...

I found this blog accidently via seeking alpha. A really GREAT explanation of cdo's, understandable by even a "lay" investor like me.

Jan

TDDG said...

Thanks to all for the kind words. There is sure a lot of misinformation out there on CDOs so if I can be a beacon of truth in the dark, that's great.

Anonymous said...

I'm still a bit confused about what occurs at maturity of these CDOs. If the collateral in the CDOs are, for example, MBS which are backed by 30 yr. mortgages, and the CDO is a 5yr, where is the principal getting repaid from and how much will the value of whatever is being sold fluctuate at the time the principal is needed?

I'm likely missing a key here, but I guess I'm confused as to to the mismatching maturity of the CDO versus the collateral, especially if the collateral is amortizing, like a mortgage.

TDDG said...

Any CDO with RMBS collateral (or anything else that's prepayable, like CMBS or student loans, etc.) will normally have a very long stated maturity. They will market the thing with some average life. Its common that the CDO will have some "reinvestment" period, where principal repaid is reinvested. After that period is over, any principal will be used to repay tranche holders.

Anonymous said...

Thanks for that...

as a follow up then; are there typical limitations as to how the repaid principle is reinvested?
Does the reivestment period coincide with the tail end of the CDO maturity, or for the entire life? and does the performance of the collateral affect the reinvestment period, or the aggressiveness of the securties invested in?

thanks again...

TDDG said...

Not surprisingly, it depends on the deal. I'd say its pretty common to see something like a 3-5 year reinvestment period. Lately I've seen more and more ABS-backed deals with no reinvestment period, which I think is meant to strengthen the credit.

Reinvestment might depend on whether you are meeting all your covenants too. Like I've seen where the reinvestment only occurs if the IC/OC tests are passing.

You usually also have covenants on elements like average credit quality, weighted average life etc. So if the deal is going poorly, you might have to reinvest in higher-quality collateral.

Nicolas said...

Hello Tom, thanks for your blog, I really enjoy reading it!

One question however on your cdo example: how do you compute the yield on each tranche?

thanks, Nicolas

TDDG said...

I'm going to make a bet that Nicolas is in banking. Am I right?

The stated yield is usually 3 month LIBOR plus a spread. Sometimes its 1 month LIBOR. Either way, the coupon would be set at whatever 3 month LIBOR is at the coupon date plus the spread. So the AAA tranche might be LIBOR + 23. Today 3 month LIBOR is 5.36%. So the coupon for that 3 month period would be 5.59%.

If the bond is trading above or below par, then you'd amortize the premium/discount over the expected life of the issue and add/subtract that from the coupon rate.

On the equity tranche, there isn't a yield per se. Really only a total return.

Nicolas said...

Hi Tom, you should have put money on your bet...
thanks for the explaination. I guess the spread is function of the market price for similar securities? thanks
(how did u know for banking..?)

TDDG said...

Because people in banking usually talk in terms of yield and people in investment management usually talk in terms of total return. Bankers don't live in the constant mark-to-market measure you versus an index world. On the other hand, investment managers are OK with losing money so long as the index lost more. Bankers can't get away with that. Its just two different worlds.

Actually, CDO spreads are almost universally wider than similarly rated corporate bonds. I'd say there are various reasons for this. Lower liquidity is an obvious one. But I also think the "worst case" is worse for a CDO than an individual bond. If a CDO tranche defaults, the odds are its worthless. Particularly junior tranches. This is because all the cash flow in the deal will be diverted to pay the senior tranches down, likely leaving nothing for the junior tranches. I'm planning on writing a post about this idea sometime soon.

Nicolas said...

Tom, I still have one more naive question: after the first default on the collateral portfolio, why the yield of the collateral remain unchanged?
Thanks, Nicolas

TDDG said...

Nicolas:

For simplicity, I assumed the yield on the performing bonds remained the same, and reduced the par value of bonds in total. So I went from $100 par times 7% yield to $99 (or 2% defaults with 50% recovery) times 7% yield. The interest collected goes from $7 to $6.93.

Some argue that the yield would probably fall, because the bond most likely to default is going to be your highest yielding bond. That's probably true. But that was getting too complicated for my post.

Anonymous said...

Hi,

Could i just clarify whether the equity tranche gets a fixed rate coupon or it gets whatever that is left after all the distribution?

TDDG said...

Equity gets whatever is left. Its easiest to think of the CDO like an operating company. The equity holders own the operating company and have borrowed to buy all the supplies they need to operate. At the end of the day, once all their expenses and debt service is paid, what do they get? Whatever is left.

Anonymous said...

Great stuff!

But WHY do CDOs happen? An interesting answer here:

http://www.newcombat.net/article_whats_a_cdo.html

Anonymous said...

Great job!
Can you describe par erosion in CDOs? What can a manager do in this case and when does par erosion trigger an early payout?

Any help would be great.

Accrued Interest said...

By par erosion, do you mean where the CDO manager buys an assets above or below par?

Anonymous said...

What is the obligation banks have to their off-balance sheet entities- I thought they can cut them off and let them fail.(except for the few instances like MER which had committed to buy-back terms with a hedge fund (WSJ, Nov 2nd).

Or is there such a strong implicit guarantee to their SIVs?

Accrued Interest said...

Many banks put guarantees on their SIV debt. So they may be forced to take it on balance sheet.

Anonymous said...

TDDG,

A silly question for you:
a.if the CDO manager is being forced to sale the assets or collaterals is the new buyer just owned the underlying pool of borrower or they got a tranche?(think of senior trance here)
B.I know it is on the wrong section here but in your do not underestimate piece, what is the hyphotetical break even price of that senior tranche with say 15% default rate and 30% recovery rate
C. How many quarters is normally the through from writedowns to recovery via extra ordinary income in accounting for bank operating in housing loan?

Cant help myself for asking you a lot of question Thanks

Anonymous said...

Thanks for the explanation. How would you know by reading through a CDO offer document that a senior subordinated notes tranche was in fact an equity tranche especially when the details suggest it is to bear interest at a stipulated fixed rate from a stipulated date? Are there any clues in the document that would suggest it was an equity tranche other than it having no rating?

Prince of Thrift said...

Thanks, after reading that definition, I am more confused then ever.

Anonymous said...

I post this comment because I think the author has mada a fundamental error in his thinking: He thinks that redistribution of risk through the entire economy (or banking system) is a good thing.

In fact this is not correct: The complicated stuff that is traded only pumps up the risk of an entire system default.

Motivation: Even the financial people have problems with understanding when and how CDO's break down.

And now that we are likely on a path that will wipe out over 10 trillion US$ in US family home equity, who knows what will happen?

Xanadou said...

One of the best explanations I have read so far on CDOs...great job!

One last question: what is the standard approach (if there is one) for valuing those securities, apart from relying on a secondary market driven by demand and supply? Do you think a Monte-Carlo simulation of correlated default paths would make it ?

Accrued Interest said...

Monte Carlo is the way to analyze cash flows of a CDO. Of course, it was bad inputs into MC simulations that lead to so many poorly rated CDO deals!

kunal said...

Hey thanks a lot Tom!..awesome explanation

Anupam said...

Good Explanation !!

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crabsofsteel said...

AI,

Sorry, I seem to have stumbled on your blog a bit later than most. Actually, what you have described here is a description of how a residential MBS with OC and IC triggers works, except that in MBS the equity is called the non-rated tranche. CDOs work the same way, with principal paying off bonds sequentially and losses applied in reverse, but there are many factors which make CDOs more complicated. First off, they are generally private placements, so documents and data on them are hard to come by. In addition, CDOs were most often resecuritizations of existing debt instruments (e.g. B-rated RMBS debt), so AAAs are leveraged against losses to the 2nd power. Also, there were static vs. managed deals. The latter were not REMICs, as the collateral was not fixed at issuance and could be swapped out, usually for a five-year period. Moral hazard, anyone? Deals were being sold based on cashflows getting posted on Bloomberg but no one such as Intex tied out with them or the prospectus, eventually leading to chaos in and disappearance of the 2ndary market. Once the parade really got going, CDOs were being done based on synthetic collateral; in other words, selling a credit default swap on an asset or a pool of assets. Once you could do deals without owning the collateral or tying out with Intex, it became the free-for-all we know about now. Citi and Merrill, thanks for nothing!

john said...

Thanks for that explanation Tom; I think I'm beginning to at least gain some conceptual understanding of this type of security even if I may never be able to accurately predict what they are going to do.

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Anonymous said...

Fuck these people