The Demand For Risk And A Macroeconomic Theory of Credit Default Swaps: Part 1

A Higher Plane

In this article, I will return to the ideas proposed in my article entitled, “A Conceptual Framework For Analyzing Systemic Risk,” and once again take a macro view of the role that derivatives play in the financial system and the broader economy.  In that article, I said the following:

“Practically speaking, there is a limit to the amount of risk that can be created using derivatives. This limit exists for a very simple reason: the contracts are voluntary, and so if no one is willing to be exposed to a particular risk, it will not be created and assigned through a derivative. Like most market participants, derivatives traders are not in engaged in an altruistic endeavor. As a result, we should not expect them to engage in activities that they don’t expect to be profitable. Therefore, we can be reasonably certain that the derivatives market will create only as much risk as its participants expect to be profitable.”

The idea implicit in the above paragraph is that there is a level of demand for exposure to risk. By further formalizing this concept, I will show that if we treat exposure to risk as a good, subject to the observed law of supply and demand, then credit default swaps should not create any more exposure to risk in an economy than would be present otherwise and that credit default swaps should be expected to reduce the net amount of exposure to risk. This first article is devoted to formalizing the concept of the price for exposure to risk and the expected payout of a derivative as a function of that price.

Derivatives And Symmetrical Exposure To Risk

As stated here, my own view is that risk is a concept that has two components: (i) the occurrence of an event and (ii) a magnitude associated with that event. This allows us to ask two questions: What is the probability of the event occurring? And if it occurs, what is the expected value of its associated magnitude? We say that P is exposed to a given risk if P expects to incur a gain/loss if the risk-event occurs. We say that P has positive exposure if P expects to incur a gain if the risk-event occurs; and that P has negative exposure if P expects to incur a loss if the risk-event occurs.

Exposure to any risk assigned through a derivative contract will create positive exposure to that risk for one party and negative exposure for the other. Moreover the magnitudes of each party’s exposure will be equal in absolute value. This is a consequence of the fact that derivatives contracts cause payments to be made by one party to the other upon the occurrence of predefined events. Thus, if one party gains X, the other loses X. And so exposure under the derivative is perfectly symmetrical. Note that this is true even if a counterparty fails to pay as promised. This is because there is no initial principle “investment” in a derivative. So if one party defaults on a payment under a derivative, there is no cash “loss” to the non-defaulting party. That said, there could be substantial reliance losses. For example, you expect to receive a $100 million credit default swap payment from XYZ, and as a result, you go out and buy $1,000 alligator skin boots, only to find that XYZ is bankrupt and unable to pay as promised. So, while there would be no cash loss, you could have relied on the payments and planned around them, causing you to incur obligations you can no longer afford. Additionally, you could have reported the income in an accounting statement, and when the cash fails to appear, you would be forced to “write-down” the amount and take a paper loss. However, the derivatives market is full of very bright people who have already considered counterparty risk, and the matter is dealt with through the dynamic posting of collateral over the life of the agreement, which limits each party’s ability to simply cut and run. As a result, we will consider only cash losses and gains for the remainder of this article.

The Price Of Exposure To Risk

Although parties to a derivative contract do not “buy” anything in the traditional sense of exchanging cash for goods or services, they are expressing a desire to be exposed to certain risks. Since the exposure of each party to a derivative is equal in magnitude but opposite in sign, one party is expressing a desire for exposure to the occurrence of an event while the other is expressing a desire for exposure to the non-occurrence of that event. There will be a price for exposure. That is, in order to convince someone to pay you $1 upon the occurrence of event E, that other person will ask for some percentage of $1, which we will call the fee.  Note that as expressed, the fee is fixed. So we are considering only those derivatives for which the contingent payout amounts are fixed at the outset of the transaction. For example, a credit default swap that calls for physical delivery fits into this category. As this fee increases, the payout shrinks for the party with positive exposure to the event. For example, if the fee is $1 for every dollar of positive exposure, then even if the event occurs, the party with positive exposure’s payments will net to zero.

This method of analysis makes it difficult to think in terms of a fee for positive exposure to the event not occurring (the other side of the trade). We reconcile this by assuming that only one payment is made under every contract, upon termination. For example, assume that A is positively exposed to E occurring and that B is negatively exposed to E occurring. Upon termination, either E occurred prior to termination or it did not.

If E did occur, then B would pay to A, where F is the fee and N is the total amount of A’s exposure, which in the case of a swap would be the notional amount of the contract. If E did not occur, then A would pay . If E is the event “ABC defaults on its bonds,” then A and B have entered into a credit default swap where A is short on ABC bonds and B is long. Thus, we can think in terms of a unified price for both sides of the trade and consider how the expected payout for each side of the trade changes as that price changes.

Expected Payout As A Function Of Price

As mentioned above, the contingent payouts to the parties are a function of the fee. This fee is in turn a function of each party’s subjective valuation of the probability that E will actually occur. For example, if A thinks that E will occur with a probability of , then A will accept any fee less than .5 since A’s subjective expected payout under that assumption is . If B thinks that E will occur with a probability of , then B will accept any fee greater than .25 since his expected payout is . Thus, A and B have a bargaining range between .25 and .5. And because each perceives the trade to have a positive payout upon termination within that bargaining range, they will transact. Unfortunately for one of them, only one of them is correct. After many such transactions occur, market participants might choose to report the fees at which they transact. This allows C and D to reference the fee at which the A-B transaction occurred. This process repeats itself and eventually market prices will develop.

Assume that A and B think the probability of E occurring is and respectively. If A has positive exposure and B has negative, then in general the subjective expected payouts for A and B are and respectively. If we plot the expected payout as a function of F, we get the following:

The red line indicates the bargaining range.  Thus, we can describe each participant’s expected payout in terms of the fee charged for exposure. This will allow us to compare the returns on fixed fee derivatives to other financial assets, and ultimately plot a demand curve for fixed fee derivatives as a function of their price.

The Anatomy of Deflation

Slight Departure

In this article, and others to follow under the category “Slight Departure,” I will take a slight departure from the narrow topics that dominate this blog. Instead, I will focus on broader economic issues and attempt to make sense of current macro economic conditions. Enjoy!

One Way Ticket

Yields on U.S. Treasuries have fallen quite a bit over the last 12 months across maturities. This was probably caused in part by what has been dubbed a “flight to safety.” That is, investors have sold off “risky” positions in exchange for safer ones. But why? My personal opinion is that while risk aversion is certainly playing a part in the quick movement into Treasuries, this risk aversion was itself spurred by a rush to meet short term obligations. Please note that this is my own version of what happened and what is to come. Anyone claiming to have a conclusive answer to such a broad question is either incorrect or correct as a matter of coincidence.

Collective Failure

Mortgage backed securities, CDOs comprised of mortgage backed securities, and the like (collectively refereed to as “Structured Products”) were widely held and widely believed to be fairly liquid and safe. But, for reasons that will likely be debated for decades if not longer, they became illiquid as the markets in which they were traded fell apart. If you were holding one of these, you were stuck with it, unless you were willing to sell it for pennies on the dollar. But before the failure of these markets, those holding Structured Products continued to accumulate short term obligations based on the assumption that Structured Products could be sold, if necessary, to meet these short term obligations. That is, they continued to operate under the reasonable and shared assumption that at any point, Structured Products could be exchanged for an amount of cash close to the par value of the product. When this assumption failed, it caused those holding Structured Products to sell other liquid assets and if necessary draw on existing lines of credit to meet these short term obligations. In my opinion, this bout of collective selling and exhaustion of credit began the first wave of downward pressure on prices.

Capital Requirements

Many of the entities holding Structured Products were banks or other institutions subject to capital requirements and regulations. When the Structured Products they were holding became illiquid, devalued, and subsequently downgraded by the various ratings agencies, various capital regulations forced them to either raise equity capital or shift their asset allocation towards high rated assets. In order to do this, many such entities simply sold riskier assets and purchased low risk assets or held the cash. This collective selling put enormous downward pressure on asset prices across asset classes, with the notable exception of Treasuries, where prices soared and yields plummeted. Moreover, the most dramatic drops along the Treasury yield curve were front loaded, in short term Treasuries. This is consistent with a rush out of other asset classes and into short term treasuries. Thus, it is arguable that those entities holding Structured Products simply liquidated other assets en masse in order to meet short term obligations and comply with capital requirements.

The Supply Of Credit

As mentioned in the previous paragraph, many of the entities holding Structured Products were banks. And for banks, like any other business, resource allocation is a zero sum game. That is, if banks allocate more cash to one endeavor, they must allocate less to at least one other. This simple observation suggests that as banks allocated more cash to Treasuries they could have cut back on lending. The dramatic escalation in short term LIBOR rates that took place over the last year (which has since subsided) suggests that there was indeed a severe shortage of credit, particularly short term interbank lending. As the cost of credit increases, the total cost of assets purchased using credit increases, which lowers the price at which these purchasers are willing to purchase assets. So those who purchase assets using credit will become less competitive during a credit shortage when compared to those who pay for assets with cash. Thus, the demand for assets in general should be expected to shrink given a large enough contraction in the supply of credit. This exerts further downward pressure on asset prices across asset classes.

Joe The Plumber

A decline in asset prices across asset classes decreases the balance sheet wealth of not only institutions, but individuals as well. This could lead to a decrease in consumer spending as the perceived wealth of individuals decreases, which would exert downward pressure on non-financial asset prices. This is consistent with the recent decline in the CPI.

And in addition to the individual’s role in the so called “real economy,” the individual also plays a role in the financial system. If individuals do not believe that the assets they have in the financial system (bank deposits, mutual funds, etc.) will maintain their value, they will have an incentive to sell these assets in exchange for cash. This not only exerts downward pressure on asset prices, but it exerts upward pressure on the cost of capital, particularly for banks, since this type of behavior erodes the deposit base.

Rinse, Lather, Repeat

A decline in asset prices across asset classes could cause the capital structure of a bank and therefore its ability and willingness to lend to deteriorate. As mentioned above, it could also cause its cost of capital to increase. As a result, the entire process outlined above could begin anew as a result of it having occurred once, compounding the downward pressure on asset prices.

Tis Good To Be King

So what should we do to stop this financial recursion? I have a few ideas. Again, these are my ideas, and you should keep that in mind. These problems are maddeningly complex and gigantic in scale and so you may not agree with my ideas for any number of reasons. That said, something must be done. And despite deep reservations, I think that U.S. government spending during this crisis is the thing to do.

Right now, the U.S. Government is able to borrow at almost 0% interest at a time that the U.S. dollar is at its strongest in years against certain currencies. This is a truly odd combination, but could be explained if we accept that people are leaving capital markets all over the world and running for the hills, i.e., U.S. Treasuries and therefore U.S. dollar denominated assets. This market dynamic will change in the long run, hopefully. So, my plan to exploit this aberration would be as follows:

Flood the market with short term and medium term U.S. Treasuries and thereby borrow to the hilt. Spend this money on fixing the U.S. financial system (creating more repo facilities, buying toxic assets, etc.) and U.S. infrastructure projects (to create jobs and demand for non-financial assets). The net effect of this is to allow the private entities in the U.S. economy to borrow at near 0% interest, giving the U.S. a tremendous near term advantage over the rest of the world.

At some point, this borrowing will push the interest rates on Treasuries up and will push the dollar down. When interest rates on treasuries reach non-bargain basement levels of borrowing, the U.S. should stop borrowing. But what about the green back? As a bonus, because the U.S. dollar will eventually fall from its current heights, the U.S. debt issued until that point will depreciate in value.

Thus, the U.S. could borrow for almost no interest, pump that money into its own economy, and then get a free principle reduction at the end. As for the rest of the world, yes, my solution rests your fate on the shoulders of the U.S. economy. I’m sorry, but I just don’t have enough time to think of a way out of your mess as well.

That’s Certainly Not Why Credit Default Swaps

Upon Closer Inspection

On Monday November 17, 2008, I posted a link to an article by Arnold Kling entitled, “Why Credit Default Swaps,” which forms the impetus for the hackneyed title of this article. At the time, I dubbed it a “good article,” but expressed my reservations about its conclusions. For whatever reason, I read the article for a second time earlier today. Upon closer inspection, with all due respect to Mr. Kling, my reservations have grown into outright rejection of both his facts and his conclusions.

You Forgot To Add The Basel

Kling begins his analysis with the conclusory statement that credit default swaps have no “natural seller.” That sounds brilliant. But what does it mean? Well, my personal opinion is that it means absolutely nothing. Kling seems to think that it means that credit default swaps exist only to evade regulation. You can read more conclusory remarks about the absence of natural sellers in his other article here. Let’s accept for the moment that he is correct. That is, suspend disbelief, and accept that the CDS market exists for the sole purpose of evading regulation. A natural question to ask is, which regulations are these CDS folks trying to evade? Well, Kling boldly states that banks and other unspecified entities “could hold AAA-rated or AA-rated bonds but … are precluded from holding B-rated bonds.” Unfortunately for Mr. Kling, this statement is completely false. But don’t believe me, believe the Bank For International Settlements. After all, they did write the regulations. The full regulatory text, Basel II, is available here. The Basel II risk weighting regulations are here, and I recommend you turn to page 19 of the risk weighting regulations, where they explain exactly how a few classes of B rated bonds are treated under the system.

As is evident, the fulcrum of Kling’s argument, namely the existence of some regulation that credit default swaps were engineered to evade, is a nullity. At this point, his argument falls apart. But we continue onward and analyze the broken pieces to expose more troubling aspects of his argument, namely his economic analysis of how the purported regulatory evasion worked.

Conclusione Confusione

Assume for the moment that banks are precluded from holding B rated paper, despite the fact that reality disagrees. Kling claims that what banks want is the higher returns that a well diversified portfolio of B rated paper offers. And because B rated paper is forbidden fruit in his world, banks use credit default swaps to indirectly obtain B rated paper levels of returns. But how? This is done, he claims, by purchasing protection on B rated bonds, which the regulations allow under his analysis. The protection sellers, he claims, engage in all of the diversification, and although he doesn’t mention it, I presume that the rate of protection these sellers charge is somehow discounted by virtue of this diversification process. Now, as we all know, protection buyers are just that, buyers. That is, protection costs money. In the case of a CDS, the protection buyer pays an amount similar to the risk premium paid on the underlying bond. Thus, the protection buyer gives up some of its returns in exchange for safety. Therefore, buying protection on a bond decreases the returns on a bond. And fully protecting a bond should bring the returns close to the risk free rate, else there would be opportunities for rather obvious arbitrage (though there should be some room for counterparty and liquidity risk). Kling acknowledges this, by saying that the protection seller gets to keep most of the additional returns.

While it is possible that there is some wiggle room to profit from protecting a B rated bond to the point that it’s treated as an A rated bond, there shouldn’t be much, since it’s a rather obvious scheme and arbitrageurs will eventually pick up on it and cause prices to stabilize to arbitrage-free levels. Despite this, Kling places the weight of the entire credit default swap empire on the tiny spread between the price of protection and risk premiums on bonds, which as we discussed, should not be a long term phenomenon.

Finally, as mentioned above, in Kling’s regulatory world, banks are allowed to purchase A rated paper. So why would such an elaborate ruse be necessary when banks could simply invest in an A rated tranche of a CDO comprised of a diversified portfolio of B rated bonds? It would not be. So even in Kling’s hypothetical world, his argument completely fails to explain the existence of credit default swaps.

So, Why Credit Default Swaps?

I will write an article on this topic, soon. It is my personal opinion that the CDS market has transformed credit risk into a product that can be traded like a commodity future. But the short answer is liquidity. That is, corporate bond markets are not very liquid markets. And the market for loans is even less liquid. The CDS market by contrast is a very liquid market with highly standardized agreements that allow credit risk to be sliced up and allocated in ways that are prohibitively expensive if not impossible with ordinary debt instruments.

Synthetic CDOs, Ratings, And Super Senior Tranches: Part 3

Prescience and Precedent

In the previous articles (part 1 and part 2), we discussed both the modeling and rating of  CDOs and their tranches. In this article, we will discuss the rating of synthetic CDOs and those fabled “super senior” tranches. As mentioned in the previous articles, I highly recommend that you read my article on Synthetic CDOs and my article on tranches.

Funded And Unfunded Synthetic CDOs

As explained here, the asset underlying a synthetic CDO is a portfolio of the long positions of credit default swaps. That is, investors in synthetic CDOs have basically sold protection on various entities to the CDS market through the synthetic CDO structure. Although most CDS agreements will require collateral to be posted based on who is in the money (and may also require an upfront payment), as a matter of market practice, the protection seller does not fund the long position. That is, if A sold $1 million worth of protection to B, A would not post the $1 million to B or a custodian. (Note that this is a market convention and could change organically or by fiat at any moment given the current market context). Thus, B is exposed to the risk that A will not payout upon a default.

Because the long position of a CDS is usually unfunded, Synthetic CDOs can be funded, unfunded, or partially funded. If the investors post the full notional amount of protection sold by the SPV, then the transaction is called a fully funded synthetic CDO. For example, if the SPV sold $100 million worth of protection to the swap market, the investors could put up $100 million in cash at the outset of the synthetic CDO transaction. In this case, the investors would receive some basis rate, usually LIBOR, plus a spread. Because the market practice does not require a CDS to be funded, the investors could hang on to their cash and simply promise to payout in the event that a default occurs in one of the CDSs entered into by the SPV. This is called an unfunded synthetic CDO. In this case, the investors would receive only the spread over the basis rate. If the investors put up some amount less than the full notional amount of protection sold by the SPV, then the transaction is called a partially funded synthetic CDO. Note that the investors’ exposure to default risk does not change whether the transaction is funded or unfunded. Rather, the SPV’s counterparties are exposed to counterparty risk in the case of an unfunded transaction. That is, the investors could fail to payout upon a default and therefore the SPV would not have the money to payout on the protection it sold to the swap market. Again, this is not a risk borne by the investors, but by the SPV’s counterparties.

Analyzing The Risks Of Synthetic CDOs

As mentioned above, whether a synthetic CDO is funded, unfunded or partially funded does not affect the default risks that investors are exposed to. That said, investors in synthetic CDOs are exposed to counterparty risk. That is, if a counterparty fails to make a swap fee payment to the SPV, the investors will lose money. Thus, a synthetic CDO exposes investors to an added layer of risk that is not present in an ordinary CDO transaction. So, in addition to being exposed to the risk that a default will occur in any of the underlying CDSs, synthetic CDO investors are exposed to the risk that one of the SPV’s counterparties will fail to pay. Additionally, there could be correlation between these two risks. For example, the counterparty to one CDS could be a reference entity in another CDS. Although such obvious examples of correlation may not exist in a given synthetic CDO, counterparty risk and default risk could interact in much more subtle and complex ways. Full examination of this topic is beyond the scope of this article.

In a synthetic CDO, the investors are the protection sellers and the SPV’s counterparties are the protection buyers. As such, the payments owed by the SPV’s counterparties could be much smaller than the total notional amount of protection sold by the SPV. Additionally, any perceived counterparty risk could be mitigated through the use of collateral. That is, those counterparties that have or are downgraded to low credit ratings could be required to post collateral. As a result, we might choose to ignore counterparty risk altogether as a practical matter and focus only on default risk. This would allow us to more easily compare synthetic and ordinary CDOs and would allow us to use essentially the same model to rate both. Full examination of this topic is also beyond the scope of this article. For more on this topic and and others, go here.

Synthetic CDO Ratings And Super Senior Tranches

After we have decided upon a model and run some simulations, we will produce a chart that provides the probability that losses will exceed X. We will now compare two synthetic CDOs with identical underlying assets but different tranches. Assume that the tranches are broken down by color in the charts below. Additionally, assume that in our rating system (Joe’s Rating System), a tranche is AAA rated if the probability of full repayment of principle and interest is at least 99%.

Note that our first synthetic CDO has only 3 tranches, whereas the second has 4, since in in the second chart, we have subdivided the 99th percentile. The probability that losses will reach into the green tranche is lower than the probability that losses will reach into the yellow tranches of either chart. Because the yellow tranches are AAA rated in both charts, certain market participants refer to the green tranche as super senior. That is, the green tranche is senior to a AAA rated tranche. This is a bit of a misnomer. Credit ratings and seniority levels are distinct concepts and the term “super senior” conflates the two. A bond can be senior to all others yet have a low credit rating. For example, the most senior obligations of ABC corporation, which has been in financial turmoil since incorporation, could be junk-rated. And a bond can be subordinate to all others but still have a high credit rating. So, we must treat each concept independently. That said, there is a connection between the two concepts. At some point, subordination will erode credit quality. That is, if we took the same set of cash flows and kept subdividing and subordinating rights in that set of cash flows, eventually the lower tranches will have a credit rating that is inferior to the higher tranches. It seems that the two concepts have been commingled in the mental real estate of certain market participants as a result of this connection.

Blessed Are The Forgetful

So is there a difference between AAA notes subordinated to some “super senior” tranche and plain old senior AAA rated notes? Yes, there is, but that shouldn’t surprise you if you distinguish between credit ratings and seniority. You should notice that the former note is subordinated while the latter isn’t. And bells should go off in your mind once you notice this. The rating “AAA” describes the probability of full payment of interest and principle. Under Joe’s Ratings, it tells you that the probability that losses will reach the AAA tranche is less than 1%. The AAA rating makes no other statements about the notes. If losses reach the point X = L*, investors in the subordinated AAA notes (the second chart, yellow tranche) will receive nothing while investors in the senior AAA notes (the first chart, yellow tranche) will not be fully paid, but will receive a share of the remaining cash flows. This difference in behavior is due to a difference in seniority, not credit rating. If we treat these concepts as distinct, we should anticipate such differences in behavior and plan accordingly.

Synthetic CDOs, Ratings, And Super Senior Tranches: Part 2

Bait And Switch

My apologies, but this is going to be a three part article.  I have come to the conclusion that each topic warrants separate treatment. In this article, I will discuss the rating of CDO tranches. In the next, I will discuss the rating of Synthetic CDOs and those illusive “Super Senior” tranches.

Portfolio Loss Versus Tranche Loss

In the previous article, we discussed how rating agencies model the expected losses on the portfolio of bonds underlying a CDO. The end result was a chart that plotted losses against a scale of probabilities. This chart purports to answer the question, “how likely is it that the portfolio will lose more than X?” So if our CDO has a single tranche, that is if the payment waterfall simply passes the cash flows onto investors, then this chart would presumably contain all the information we need about the default risks associated with the CDO. But payment waterfalls can be used to distribute default risk differently among different tranches. So, if our CDO has multiple tranches, then we need to know the payment priorities of each tranche before we can make any statements about the expected losses of any tranche. After we know the payment priorities, we will return to our chart and rate the tranches.

Subordination And Default Risk

Payment waterfalls can be used to distribute default risk among different tranches by imposing payment priorities on cash flows. But in the absence of payment priorities, cash flows are shared equally among investors. For example, if each of 10 investors had equal claims on an investment that generated $500, each investor would receive $50. Assuming each made the same initial investment, each would have equal gains/losses. However, by subordinating the rights of certain investors to others, we can insulate the senior investors. For example, continuing with our 10 investors, assume there are 2 tranches, A and B, where the A notes are paid only the first $500 generated by the investment and the B notes are paid the remainder. Assume that 5 investors hold A notes and that 5 investors hold B notes. If the investment generates only $500, the A investors will receive $100 each while the B investors will receive nothing. If however the investment generates $1,500 the A investors will receive $100 each and the B investors will receive $200 each. This is just one example. In reality, the payment waterfall can assign cash flows under any set of rules that the investors will agree to.

If the investment in the previous example is a portfolio of bonds with an expected total return of $1,000, then the payment waterfall insulates the A investors against the first $500 of loss. That is, even if the portfolio loses $500, the A investors will be fully paid. So, the net effect of the payment waterfall is to shift a fixed amount of default risk to the B investors.

Rating CDO Tranches

As a general rule, rating agencies define their various gradations of quality according to the probability of full payment of principal and interest as promised under the bonds. Assume that Joe’s Rating Agency defines their rating system as follows:

AAA rated bonds have at least a 99% probability of full payment of principal and interest;

AA rated bonds have at least a 95% probability of full payment of principal and interest;

A rated bonds have at least a 90% probability of full payment of principal and interest; and

Any bonds with less than a 90% probability of principal and interest are “Sub Investment Grade (SIG).”

Assume that the bonds underlying our CDO collectively promise to pay a total of $100 million in principal and interest over the life of the bonds. For simplicity’s sake, assume that the CDO investors will receive only one payment at maturity. Further, assume that we have conducted several hundred thousand simulations for our CDO and constructed the chart below:

It follows from the data in the chart that the probability that losses on the CDO will be less than or equal to: $35 million is 90%; $40 million is 95%; $65 million is 99%. We define the tranches as follows: tranche A is paid the lesser of (i) $35 million and (ii) the total return on the CDO pool (the green tranche);  tranche B is paid the lesser of (i) $25 million and (ii) the total return on the CDO pool less any amounts paid to tranche A (the yellow tranche); tranche C is paid the lesser of (i) $5 million and (ii) the total return on the CDO pool less any amounts paid to tranches A and B (the blue tranche); and tranche D is paid the lesser of (i) $35 million and (ii) the total return on the CDO pool less any amounts paid to tranches A, B, and C (the red tranche).

After some thought, you should realize that, according to Joe’s Ratings, tranche A is AAA; tranche B is AA; tranche C is A; and tranche D is SIG.

Synthetic CDOs, Ratings, And Super Senior Tranches: Part 1

Super Senioritis

I’ve been perusing the finance blogs lately and I’ve noticed a recent obsession with Synthetic CDOs, specifically the super senior tranches of these transactions. And so I felt it was necessary for me to chime in on the debate, by applying my usual toast-dry analysis to Synthetic CDOs for the second time. This is a huge topic that requires consideration of how Synthetic CDOs function, how they’re rated, and how tranches distribute risk among investors. As a result, I’ve decided to break the article into two parts. This first part deals with the basics of rating the assets contained in CDOs. The next will examine the application of ratings to tranches of CDOs, how that translates into the world of synthetic CDOs, and ultimately, culminate in a discussion of what are known as “super senior tranches.”

Required Reading

You are likely to struggle greatly with this article unless you have some familiarity with Synthetic CDOs. And because I am an unabashed self-promoter, I highly recommend you read my introductory article on Synthetic CDOs and my article on Tranches. If you’re going to read only one, then read the one on tranches.

Tranches And Structured Products

Payment waterfalls allow the risks of an investment to be allocated among different groups of investors, or tranches. For example, in the case of Mortgage Backed Securities, a fixed amount of prepayment risk can be allocated to one tranche by tailoring the rules in the payment waterfall to pass all prepayments of principal to that tranche. But there are risks beyond prepayment risk. One obvious example is default risk. In the MBS world, this is the risk that because of defaults in the underlying mortgages the cash flows from the mortgages backing the notes will be inadequate to make payments on those notes. Obviously, default risk will be a primary concern of any investor. The risk that you will not get paid is arguably paramount to all others. So, payment waterfalls have been developed to address this risk and tailor the distribution of default risk in a way that allows each investor to assume a desired default risk level. But before we can understand how investors distinguish between these different levels of default risk, we must understand how rating systems describe these different levels.

Rating Systems And Rating Agencies

You have undoubtedly heard terms such as “AAA rated” and “AA rated” thrown somewhere near names like S&P and Moody’s. It’s not necessary to become familiar with the peculiarities of each rating agency’s system to appreciate the general idea: the ranking of default risk. That is, the market wants a short-hand system that both describes the probability of default for a particular financial product and can be compared across a disparate class of financial products. So, rating agencies developed models and systems of ratings (using confusingly similar labels like “AAA,” “Baa,” etc.) that purport to do just that.

How CDO Ratings Work

Part 1: Past Performance And Correlation

The models that rating agencies use to produce their ratings are backward looking. That is, the first step in the process is to accumulate data about how financial products have behaved in the past. Rating agencies, and investors, will look to the past and produce charts like this:

They will note that in the past, of all bonds that Moody’s deemed Aaa, less than 1% of such bonds defaulted within 10 years of issuance. People then assume, quite reasonably, that this data provides probabilities of default across time for the various ratings. That is, they assume that if we wish to know the probability that a B rated bond will default in year three, we simply look to the above chart and discover that it is .1977 or 19.77%. Examination of this assumption is beyond the scope of this article. But for a great article on that topic (containing the above table and more!) go here.

A CDO is in essence a portfolio of bonds. So in order to model the cash flows of the portfolio, rating agencies turn to charts like the one above and examine the past performance of bonds similar to those in the portfolio. They also look at the correlation of default between the bonds in the CDO portfolio. Correlation, in this context, is a very precise term. And it’s impossible to do justice to the concept in a few sentences. That said, in layman’s terms, when considering the correlation of default between two bonds, rating agencies are looking for a connection between the bonds defaulting. That is, if bond 1 defaults, how does that change our expectation of the probability that bond 2 will default? Exactly how this is done is also well beyond the scope of this article. For those of you who are interested, you can read all about this and more here.

Part 2: Scenario Analysis

So after we have all of our data, we can begin to construct a chart of how likely a given level of loss is. This is done through scenario analysis. That is, the models are run hundreds of thousands of times (and possibly more) using different inputs. In each of these simulations, some bonds might “default.” That is, the model predicts that given a particular set of inputs, certain bonds will default. After each of these simulations, an amount of loss will be calculated, which is based on the estimated recovery values for the bonds in the pool that “defaulted” during that particular simulation. We can then ask, out of all of the simulations, how many times did the loss go above X? So if we ran our simulation 500,000 times, and if the loss was greater than $1 million in only 5,000 of these simulations, then we could say that the probability of the loss being greater than $1 million is .01, or 1%.

Tranches And Risk

What Is A Tranche?

Tranche is a French word that means slice. Every investment will convey certain rights in the cash flows produced by the investment to the investors. A tranche is a slice of those rights. Quite literally, each tranche represents a unique piece of the investment pie. So the term tranche connotes a fairly accurate indication of how the term is used in finance. And after all, it’s easier to tell investors that they’re buying tranches as opposed to “pits” or “buckets.”

Payment Waterfalls

A payment waterfall determines who gets paid what and when. That is, each dollar produced by an investment will be “pushed through” a payment waterfall and allocated according to the rules in the payment waterfall. For example, assume that there are 3 investors, A, B and C. They collectively invest in venture X. The payment waterfall for X is defined as follows: on the first of each month, A will be paid the lesser of (i) $100 and (ii) all of the cash flows produced by X in the previous month; B will be paid the lesser of (i) $100 and (ii) all of the cash flows produced by X in the previous month less any amounts paid to A; and C will be paid the lesser of (i) $100 and (ii) all of the cash flows produced by X in the previous month less any amounts paid to A and B.

Assume that in month 1, X produced $300 in cash. On the first day of month 2, the $300 will be pushed through the waterfall. So A will get $100; B will get $100; and C will get $100. Note that in the case of C, the two choices will produce equal amounts, so the term “lessor of” isn’t technically accurate. But assume that when the choice is between equal amounts, we simply pay that amount. Now assume that X produced $150 in month 1. On the first day of month 2, the $150 will be pushed through the waterfall. So A will get $100; B will get $50; and C will get $0. Because A is “first” to get paid, so long as X produces $100 per month, A is fully paid. B is fully paid so long as X produces $200 per month and C at $300 per month. So in this case, A’s tranche is said to be the least risky of the 3 tranches, with B and C being more risky in that order. Note that I am not using my technical definition of risk.

So why would C agree to be last in the pecking order? Well, one simple explanation is that C paid the least for his tranche. In another example we could have given C the right to any amounts left over each month after all other tranches are paid. This type of right is called a residual right. It is basically an equity stake. So in that case C would bear the risk that X’s cash flows will fall short in exchange for the right to acquire any excess cash flows produced by X. As is evident, the terms of the waterfall can be anything that the parties agree to. As such, we can cater the payment priorities to meet the specific desires of investors and distribute risks accordingly.

Mortgage Backed Securities And Prepayment Risk

Securitization is a fairly simple process to grasp in the abstract. In reality, turning thousands of mortgages into interest bearing notes is not a simple process. However, we can at least begin to understand the process by considering how a payment waterfall can be used to streamline the payments to investors. Viewed as a bond, a mortgage is a bond where the borrower, in this case the mortgagor, has a right to call the bond at any point in time. That is, at any point in time, a mortgagor can simply repay the full amount owed and terminate the lending agreement. Additionally, even if the mortgagor doesn’t pay the full amount owed, it is free to pay more than the amount obligated under the mortgage and allocate any additional amounts to the outstanding principle on the mortgage. For example, if A has a mortgage where A is obligated to make monthly payments of $100, A could pay $150 in a particular month, and request that the lender allocate the additional $50 to reduce the outstanding principle on the mortgage.

The typical practice for a mortgage is to require the mortgagor to make fixed payments over the life of the mortgage. So each payment will consist of an interest portion and a principle portion. The amount allocated to principle is predetermined and said to amortize over the life of the mortgage. And as mentioned above, any amount over the fixed amount can be allocated to principle at the option of the mortgagor. The risk that any given loan will pay an amount above the required fixed payment is called prepayment risk.

While getting your money back is usually a good thing, investors prefer to defer repayment to some future date in exchange for receiving more money than they invested. So getting all of their principle back today is not the most preferred outcome. They prefer to get their principle at maturity plus interest over the life of the agreement. For example, if all of the mortgages in a pool of mortgages that have been securitized prepay the full amount before the anticipated maturity date of the notes, then the investors will presumably be repaid, but will not receive the remaining interest payments over the anticipated life of the notes. If this prepayment en masse occurs on the second day of the life of the notes, it would defeat the purpose of the investment.

Prepayment Risk And Payment Waterfalls

We can use payment waterfalls to distribute prepayment risk into different tranches. In reality, this can become a mind numbingly complex endeavor. We propose one simple example to demonstrate how tranches can be used to redistribute complex risks.

Assume that our mortgage pool consists of mortgages; the remaining principle on each mortgage is ; and the total remaining principle on the pool is . Because each mortgage payment consists of some interest and some principle, each month, there will be a scheduled reduction in the outstanding total principle on the pool. Let denote the scheduled reduction of . That is, is the sum of all of the principle portions of the fixed payments to be made in the pool. If there are any prepayments in the underlying mortgages, the actual reduction in will exceed the scheduled reduction. Let denote the actual reduction in . The question now becomes, what do we do with ? That is, how do we distribute the amount by which the actual reduction in total principle exceeds the scheduled reduction? The simple answer, and the one considered here, is to push the entire prepayment amount onto one tranche, and reduce the outstanding principle on that tranche by that same amount.

For example, assume that a mortgage pool contains mortgages with a total $100 million principle outstanding and that $100 million worth of notes were issued against that pool. Further, assume that there are two tranches of notes: the A series and B series, with $50 million face value of each outstanding. For simplicity’s sake, assume the notes pay interest monthly. On any interest payment date, we could pay the B series the entire prepayment amount and reduce the face value on the B series notes by . For example, if on the first interest payment date, $10 million, then we would pay the $10 million to the B series note holders and reduce the face value on the B series to $40 million. Thus, any prepayment amount less than or equal to $50 million will be completely absorbed by the B series note holders. So the net effect is to cushion the A series against a certain amount of prepayment risk. The B series note holders will likely demand something in return for bearing this risk.