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.

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 principal 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 principal 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 principal portion. The amount allocated to principal 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 principal 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 principal back today is not the most preferred outcome. They prefer to get their principal 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 principal on each mortgage is ; and the total remaining principal on the pool is . Because each mortgage payment consists of some interest and some principal, each month, there will be a scheduled reduction in the outstanding total principal on the pool. Let denote the scheduled reduction of . That is, is the sum of all of the principal 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 principal 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 principal on that tranche by that same amount.

For example, assume that a mortgage pool contains mortgages with a total $100 million principal 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.

You’re Trespassing On My Credit Event

Insurable Interests

When you purchase fire insurance on your own home, you are said to have an insurable interest. That is, you have an interest in something and you’d like to insure it against a certain risk. In the case of fire insurance, the insurable interest is your house and the risk is fire burning your house down. Through an insurance policy, and in exchange for a fee, you can effectively transfer, to some 3rd party, financial exposure to the risk that your insurable interest (house) will burn down.

When you purchase protection on a bond through a credit default swap, you may or may not own the underlying bond. As such, you may or may not have something analogous to an insurable interest. David Merkel over at The Aleph Blog brought this issue to my attention in a comment on one of my many rants about credit default swaps. Although you should read his article in its entirety, his argument goes like this: just like you wouldn’t want someone you don’t know taking out a life insurance policy on you (because that would give them an incentive to contribute to your death), corporation ABC doesn’t want swap dealers selling protection on their bonds to those who don’t own them (since these buyers would profit from ABC’s failure). Technically, ABC wouldn’t want protection being sold to those that have a negative economic interest in ABC’s debt.

Courting Disaster

We might find it objectionable that one person takes out an insurance policy on the life of another. This is understandable. After all, we don’t want to incentivize murder. But we already incentivize creating illness. Doctors, hospitals, and pharmaceutical companies all have incentives to create illnesses that only they can cure, thus diverting money from other economic endeavors their way. More importantly, even if you don’t accept the “it’s no big deal” argument, insurance contracts have a feature that prevents the creation of incentives to destroy life and property: they are voluntary, just like derivatives.

In order for you to purchase a policy on my life, someone has to sell it to you. And like most businesses, insurance businesses are not engaged in an altruistic endeavour. So, when you come knocking on their door asking them to issue a $100 million policy on my life, they will be suspicious, and rightfully so. They will probably realize that given the fact that you are not me, $100 million is probably enough money to provide you with an incentive to have me end up under a bus. And of course, they will not issue the policy. But not because they care whether or not I end up under a bus. Rather, they will not issue the policy because it’s a terrible business decision. They know that it doesn’t cost much to kill someone, and therefore, as a general idea, issuing life insurance policies to those who have no interest in the preservation of the insured life is a bad business decision. The same applies to policies on cars, houses, etc that the policy holder doesn’t own. As is evident, the concept of an insurable interest is simply a reflection of common sense business decisions.

You Sunk My Battleship

So why do swap dealers sell protection on ABC’s bonds to people that don’t own them? Isn’t that the same as selling a policy on my life to you? Aren’t they worried that the protection buyer will go out and destroy ABC? Clearly, they are not. If you read this blog often, you know that swap dealers net their exposure. So, is that why they’re not worried? No, it is not. Even though the swap dealer’s exposure is neutral, if the dealer sold protection to one party, the dealer bought protection from another. While the network of transactions can go on for a while, it must be the case that if one party is a net buyer of protection, another is a net seller. So, somewhere along the network, someone is exposed as a net buyer and another is exposed as a net seller.

So aren’t the net sellers worried that the net buyers will go out and destroy ABC? Clearly, they are not. The only practical way to gain the ability to run a company into the ground is to gain control of it. And the only practical way to gain control of it is to purchase a large stake in it. This is an enormous barrier. A would be financial assassin would have to purchase a large enough stake to gain control and at the same time purchase more than that amount in protection through credit default swaps, and do so without raising any eyebrows. If this sounds ridiculous it’s because it is. But even if you think it’s a viable strategy, ABC should be well aware that there are those in the world who would benefit from the destruction of their company. This is not unique to protection buyers, but applies also to competitors who would love to take ABC over and liquidate their assets and take over their distribution network; or plain vanilla short sellers; or environmentalist billionaires who despise ABC’s tire burning business. In short, ABC should realize that there are those who are out to get them, whatever their motive or method, and plan accordingly.

Hands Off My Ether

The fact that others are willing to sell protection on ABC to those who don’t own ABC bonds suggests that any insurable interest that ABC has is economically meaningless. For if it weren’t the case, as in the life policy examples, no one would sell protection. But they do. So, it follows that protection sellers don’t buy the arguments about the opportunities for murderous arbitrage. So what is ABC left with? An ethereal and economically meaningless right to stop other people from referencing them in private contracts. This is akin to saying “you can’t talk about me.” That is, they are left with the right to stop others from trespassing on their credit event. And that’s just strange.

Mark To No Market Accounting

The Meaning Of It All

In this article I explore an oft discussed topic: mark to market accounting. I will not come down on either side of the debate. Rather, I will try to make sense of the implications and assumptions of mark to market accounting. But before we can explore the world of mark to market accounting, we must understand the economic significance of the data reported under accounting regimes in general. And in order to do that, we must have a practical concept of economic loss/gain. From here on, we simply write the term loss to signify both loss and gain, except where context indicates otherwise (philosophers, please relax, the meaning is clear).

What Is Economic Loss?

In my mind, the answer depends on who you ask and when. That is, every economic endeavor involves multiple parties with different rights and obligations that vary over time, and so any meaningful concept of loss should consider both who incurs “loss” and when. As usual, we will proceed by way of example.

Assume that Tony (T) has had a life long passion for the manufacturing of shoes. He decides to raise money from investors to open up a factory that will manufacture a new line of shoes, “Tony’s Shoes.” The investors contribute a total of $100 to T’s endeavor through debt. Assume that T bought manufacturing equipment from M for $70 and that T’s debt to the investors is secured by the factory equipment. After 6 months, it becomes clear that the market is not ready for T’s postmodern shoe design, and so T’s factory generates no income whatsoever. As a result, T commits suicide. T leaves only $15 and title to the manufacturing equipment in his estate, having set his entire inventory on fire in a rage prior to his suicide. The investors successfully obtain title to the machinery and claim the remaining $15. Because the machinery has been used for 6 months, they are only able to recover $30 for it in an auction.

So who lost what and when? Well, as an initial matter, in order for there to be loss, there must be change. It follows that we should ask how the state of affairs has changed over some time frame. Let’s mark the beginning of our time frame at just before T’s purchase of the manufacturing equipment and the end at immediately after the investors liquidate the manufacturing equipment. So, our concept of loss will compare the state of affairs at those two points in time for each participant. In our example, T began alive with $100 cash and $100 in debt, and ended up dead with his estate owing $55 to the investors.  The investors started out with notes with a par value of $100 and ended up with $45 in cash. M started out with manufacturing equipment and ended up with $70 in cash.

The first problem we face is comparing dissimilar assets. That is, T started out with cash and debt, the investors started out with notes and ended up with cash, and the manufacturer started out with equipment and ended up with cash. While the choice of a common basis is arbitrary, we choose cash. So, assume that at the beginning of our time period T valued his debt at negative $100, the investors valued the notes at par ($100) and that M valued the equipment at $60. One reasonable interpretation of the facts is that over the relevant time period T lost nothing, the investors lost $55, and M gained $10. It is reasonable to say that T lost nothing because he began with a net cash value of zero and although his estate still owed the investors $55, there was nothing left to pay them with. We could be pedants and say that T ended with a negative $55 cash value, but what would that mean? Nothing. The investors’ claim is worthless since T is dead and his estate is empty. If T had survived or if his estate expected to receive assets or income at some future time, then T or T’s estate could be indebted in an economically meaningful way. But since this is not the case in our fact pattern, the investors have a worthless claim against T’s estate.

A Truly Human Story

In my mind, the goal of any accounting system is to tell a story about economically significant events that occurred over a given time period. And so, in designing a system of accounting, we must choose which aspects of each market participant’s state of affairs that we want to report, simply because there could be events we don’t find particularly relevant to our story. For example, T died. We may or may not want to report that. Whether or not we choose to report it, T’s death did have economic significance. Because T died and left an estate with inadequate resources to cover his liabilities, the debts owed by T’s estate were worthless. As is evident, it would be impractical to report the death of every market participant. But as T’s case demonstrates, there are some events we wouldn’t normally consider economically significant which turn out to have a meaningful impact on the rights and obligations of market participants.

Truth In Numbers

We must also have a method of valuation. In our example above, we simply relied upon the subjective valuations of the market participants. Given that market participants will likely have an incentive to misrepresent the value of certain assets, we probably don’t want to rely too heavily on purely subjective valuations. For example, we calculated M’s gain based on M’s valuation of the equipment. What if M’s valuation was pure wishful thinking? What if his cost of inputs and labor suggested a price closer to $150? It would follow in that case that M actually lost money by selling the equipment for $70. What we need is a method of valuation that limits each participant’s ability to misrepresent, whether through wishful thinking or malice, the value of assets. There are several ways to go about doing so. We could establish guidelines, rules, or allocate valuation to trusted entities. Another approach is to simply quote the price of an asset from a market in which the asset is usually bought and sold.

Mark to Market Accounting

The basic premise of mark to market accounting is that the reported value of a given asset should be based upon the price at which that asset could be presently sold in a market that trades such assets. For example, assume that ABC stock is traded on the highly reputable XYZ exchange. The reported value of 1 share of ABC stock on September 10, 2008 under a mark to market regime should be based on the prices quoted for ABC stock over some period of time near September 10, 2008. You might want to construct an average, or exclude a particular day’s quotes, but the general idea is that the market provides the basis of the price. So if 1 share of ABC’s stock had an average closing bid price of $25 from September 1, 2008 to September 10, 2008, a company holding ABC stock could be required to use this average price as the basis for calculating the value of its holding of ABC stock for a report issued under some mark to market regime.

Market Prices And Expected Value

Returning to our example above, we determined that the investors had lost money once T’s estate was liquidated since they had no other methods of recovering the money that they had lent and was owed to them. But what if we wanted to consider their losses at some point before T was obligated to make a payment on his debts? Had the investors lost anything at that point? Any such loss would be anticipatory since the loss would occur before the repayment of debt was obligated. So, while the loss hasn’t been realized yet, we can still anticipate it. For example, if T had killed himself before any payment was due, losses would be anticipatory, but anticipated with certainty. As is evident, the amount of an anticipated loss, or expected loss, is a function of the probability that an expected cash flow will fail to materialize.

Market price quotes are used to estimate the expected value of an asset, which is the value of all the asset’s cash flows discounted to reflect the time value of money and the probability that any of the asset’s cash flows will fail to materialize. Many economists subscribe to the belief that the market price for an asset is the expected value of an asset. That is, they believe that the collective decision making of all market participants leads to the creation of a price which accurately reflects all relevant price inputs. But even if we accept this logical catapult, it is still possible for a market to produce inefficient prices. For example, market participants could have mistaken the correlation of default between certain investments, creating a short term shortage of cash, leading to massive and collective sell offs across asset classes. That should sound familiar. Such a scenario would arguably create opportunities for arbitrage for those fortunate enough to have cash on hand.

Even if you don’t buy the theoretical arguments for inefficient markets, or the glaring recent examples, you must still wonder when it was that markets became efficient. Were they always efficient? And even if they were, can they become inefficient?

The Takeaway

Whether or not you think that markets price assets efficiently, market price quotes are without question a good measure of how much cash you can exchange an asset for at any given point in time. So, whether or not markets price assets efficiently does not determine whether mark to market accounting is “good” or “bad.” Rather, we have to ask what it is that we are using mark to market accounting for. Then, we can determine whether a given application of mark to market accounting is “good” or “bad.”

Truly Derivative Dribble

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Friday June 26, 2009

My breakfast of choice

Friday May 29, 2009

My latest for the Atlantic: Could Government Intervention Help Markets Function Better?

Saturday May 16, 2009

My latest for the Atlantic: How NPR Mangled Geithner’s Plan For OTC Derivatives

Thursday May 7, 2009

My latest for the Atlantic: Boring Banking Will Not Save You

Friday May 1, 2009

My latest for the Atlantic: The Sorry State Of The Dismal Science

Thursday April 30, 2009

YOU MUST WATCH THIS: John Authers interviews Richard Thaler, behavorial economist and author of Nudge.

Friday April 17, 2009

My Latest for the Atlantic: Credit Default Swaps and Control Rights

Tuesday April 14, 2009

My latest for the Atlantic: The Art of the Banking Controversy

Friday April 10, 2009

My latest for the Atlantic: The Regulatory Pendulum and Electoral Guillotine

Wednesday April 8, 2009

My latest for the Atlantic

Friday April 3, 2009

Very nice chart from the FT on debt and demographics

Monday March 30, 2009

Recommended: FT interview with Obama

Friday March 27, 2009

Derivative Dribble on Twitter

My latest for the Atlantic Business

Wednesday March 25, 2009

High speed photos of exploding objects

Bank Executive’s home vandalized

MUST READ: Resignation letter of form AIGFP employee

HIGHLY RECOMMENDED: John Authers takes a look at the EMH and the future of wealth management

Friday March 20, 2009

HIGHLY RECOMMENDED: Washington Post takes us inside AIG-FP (“If they give back the money, then they will walk. And they will walk into the arms of AIG’s counterparties.”)

My latest for The Atlantic

HIGHLY RECOMMENDED: This Blog

Tuesday March 17, 2009

Fortune does a good job getting the facts straight about CDS

Friday March 13, 2009

Recommended: The Economist takes a look at credit markets

Berkshire downgraded by Fitch

Thursday March 12, 2009

Gates back on top as crisis wipes out other billionaires

Monday March 9, 2009

Hilarious

Friday March 6, 2009

Alpha Ville on the ocean of looming corporate defaults

Thursday March 5. 2009

Citi drops below $1

My latest for the Atlantic

Wednesday March 4, 2009

FDIC might go insolvent

Tuesday March 3, 2009

Derivatives market remains profitable business for J.P. Morgan

Very interesting data on the multiplier effect from the CBO

Tuesday February 24, 2009

My latest article for the Atlantic

Monday February 23, 2009

HIGHLY RECOMMENDED: Howard Davies, head of LSE and former FSA Chairman, on bank regulation

FT on the prospect of a depression in Spain

Rick Santelli rouses traders over Obama’s housing plan

Sunday February 22, 2009

Citi in talks with U.S. Government over common equity stake

Thursday February 19, 2009

Must read: Buiter rips apart Obama’s housing plan

Saturday February 14, 2009

Collective decision making in animals and humans

Thursday February 12, 2009

New York edges closer to expanding rent control

Wednesday February 11, 2009

Rep. Kanjorski tells us how close to the edge we were

Treasury’s 6 and a half page plan to save the world

Tuesday February 10, 2009

Great article by the FT’s John Authers on the prospects of an equity bounce-back

Friday February 5, 2009

U.S. cuts almost 600,000 jobs

Wednesday February 4, 2009

My latest article for the Atlantic Business Channel

Tuesday February 3, 2009

E.U. pushes CDS exchange

Monday February 2, 2009

For my fellow music lovers: Classic Arts Showcase on YouTube

Consumers turn to thrift

Unemployment hits China

S&P says 200 defaults expected

Thursday January 30, 2009

Crash like this expected only once over next 34,000 years

Contraction bad, but better than expected

Wednesday January 28, 2009

John Authors on the perception of a bargain

Capacity drops in France and Italy

World growth worst in 60 years

Tuesday January 27, 2009

Japanese CDS spreads widen

The original Carlo Ponzi

Madoff Jr. gets busted in $400 million Ponzi scheme

Great article from Atlantic’s new business section

Monday January 26, 2009

Iceland’s government tumbles under pressure

Unemployment rate looms over banking sector

Redemptions slam hedge funds

Wednesday January 23, 2009

Obama thinks stimulus package could be ready mid February

Muni derivatives under investigation

Cocoa prices on the move

Very interesting John Authers video on the prospect of a slow down in China

Pope goes digital

U.K. officially in a recession

Wednesday January 22, 2009

Google beats the heard

N.Y. Times provides some perspective on the severity of the crisis

U.S. accuses China of currency manipulation

Tuesday January 21, 2009

Bank market capitalization, then and now

John Authers article and video on the second wave of banking turmoil

Black Rock’s profits plummet

Monday January 20, 2009

Obama sworn in

Reality might be a hologram

Banking crisis part II?

Thursday January 15, 2009

Volatility back on the rise

California to go insolvent in weeks

Big numbers for foreclosures in 2008

The wealthy slammed by the down turn

Testosterone and income

Roubini predicts more gloom

Bank stocks plummet

Mortgage rates hit record low

Wednesday January 14, 2009

Credit markets show signs of life despite rest of world

Martin Wolf takes on Obama’s stimulus package

CDS market predicts bleak future for sovereigns

Greece downgraded

Retail takes a nose dive

Banks need bigger TARP

Tuesday January 13, 2009

Citi gets closer to break up

Still no Russian gas flowing into E.U.

Pension funds hammered, seek Federal money

Release of TARP funds faces stiff opposition

U.S. imports plummet

Bernanke says fiscal measures not enough

Monday January 12, 2009

John Authers takes a look at sovereign default and the Euro

Proprietary trading winding down

Banks suspected in facilitating purchase of weapons for Iran

Barney Frank proposes drastic changes to TARP and Hope For Homeowners Act (a summary of the bill and the actual text can be found here)

A look at China

Sovereign downgrades looming

Friday January 9, 2009

Cash flowing back to emerging markets

No exit

Obama puts pressure on Congress over stimulus package

Congress points fingers at Treasury over TARP

Thursday January 8, 2009

Citi supports bankruptcy law reform

Very interesting article on government bonds

Dismal retail figures

Wednesday January 7, 2009

Gas supply to Europe cut

BofA finally sells stake in Chinese Bank

Rough month for employment

A closer look at Larry Summers

German bond auction fails: bad sign for sovereigns

Tuesday January 6, 2009

Pending home sales drop to record lows

Oil picks up steam

Monday January 5, 2009

Dim lights ahead

A bit of unexpected historical perspective on the credit crisis

Wednesday December 31, 2008

John Authers constructs a timeline of the disasters of 2008

Steepest drop ever for commodities

Muni market dries up as states face looming budget gaps

A brief history of numbers

Paulson says U.S. lacked tools to handle crisis

Tuesday December 30, 2008

Good series of video interviews of Roubini

All about numbers

U.S. home prices plummet 18%

Automakers consider change to supply model to prevent supply-side failures

The economics of climate change

Monday December 29, 2008

Retail bankruptcies and store closings on the rise

Corporate profits likely to continue losing streak

Conventional media outlets seek partnership with internet big wigs

John Authers sees gloomy future for equities

High hopes and big numbers

Tuesday December 23, 2008

U. Chicago points fingers at the bailout

Interactive applet rating financial big wigs

Monday December 22, 2008

Pound sinks to record low against basket of currencies

Toyota predicts first loss ever

Oil continues to slide despite OPEC cuts

Friday December 19, 2008

Mortgage interest rates drop

China blocks sale of assets

Sarkozy forces lending

Early Christmas for automakers

Thursday December 18, 2008

Gather ye rosebuds while ye may

Mining sector calls for unprecedented cut backs

Obama taps new SEC chief

Wednesday December 17, 2008

Tis dangerous on the high seas!

Deflation hits E.U.

Thrifty Texan to buy up banks

Public perception dims

More monoline madness

Tuesday December 16, 2008

Up to your ears

Free money!

Monday December 15, 2008

The long arm of Madoff

Derivative Dribble spots economic news faster than the MSM

Friday December 12, 2008

Bifurcation of the debt markets

Goldman predicts slow recovery for oil

California gets downgraded

The story of 2008

The ever entertaining Jim Rogers

India gets roped into the slow down

Senate puts the brakes on the Big 3

Thursday December 11, 2008

When fiat fails

It was a very bad year

This time the floor is falling

Wednesday December 10, 2008

The beginning of a market for toxic instruments?

Deflationary pressure in China?

Costly advice

John Authers looks back

Tuesday December 9, 2008

The title speaks for itself

Russia walks the sovereign plank: debt downgraded

OTC commodities central clearing house ready for launch

Corporate default rates set to rise

Monday December 8, 2008

BREAKING NEWS: Federal legislation proposed to regulate OTC Market

The invisible hand and the sovereign strangle

Video game nerds prove recession proof

Friday December 5, 2008

Economics at ground level

More truly awful news, this time it’s California

Distraction from all the bad news

Thursday December 4, 2008

Black Friday yields red November for retail

China Investment Corp won’t invest in U.S. financial institutions

$25 Oil

Wednesday December 3, 2008

CDS Index hits record level

Some rather awful news

Great explanation of Money Markets

Real yield on Treasuries dip into negative territory

Tuesday December 2, 2008

Bigger than the bail out

The ever increasing interest in CDS

Paulson v. Paulson

Monday December 1, 2008

BRIC nations to offer consumption through downturn

U.S. officially in recession

The Swiss financial throne under siege

Wednesday November 26, 2008

Banker’s Compensation

The space near zero

Shift from OTC to exchanges gains more momentum

Ship while you can

Tuesday November 25, 2008

The science of petty crime

New lending facility for instruments backed by consumer debt

Monday Novemer 24, 2008

Treasury pony’s up huge money

Buffett discloses info on Berkshire’s portfolio of financial weapons of mass destruction

More historical data on declines

Daily Liquidation

Citi gets early Christmas present and Paulson works another weekend

Friday November 21, 2008

Goldman predicts bleak outlook for U.S. Economy

One way ticket to safety

Thursday November 20, 2008

Slightly cooler heads in Iceland after IMF/Nordic bailout

The CDS Market becomes the new economic indicator

I’ve seen more and more of this type of analysis. The CDS market is becoming more and more relevant as an economic indicator. Keep up the good work Alpha Ville!

Inventories Swell Kudos to Naked Capitalism!

Following the money supply

Wednesday November 19, 2008

More monoline downgrades

CDS markets predict bleak future

CDS clearing house seems likely

Tuesday November 18, 2008

Detroit gets coals for Christmas

Fun with economic data

Japan wins economic beauty contest

Historical perspective on volatility

CIA Factbook v2

Monday November 17, 2008

Highly recommended: Interviews with Jim Rogers

The dangers of subjective valuation

Good article, even though I disagree

New York City real estate falls from grace

Greetings from Earth!

Citibank throws garage sale

Japan in technical recession

Friday November 14, 2008

FDIC to insure home mortgages

Eurozone in technical recession

Pensioners driven to theft

Thursday November 13, 2008

More complex than a synthetic CDO

Derivative Dribble considers asking Fed for money

Germany in technical recession

Greenwich points to Wall Street

Would be CDS regulator vindicated (?)

Paulson pulls the TARP from under the market

Pounded

In The Shadows Of Geometry

Synthetic CDOs Demystified

Synthetic Debt

Before we can understand how a synthetic CDO works, we must understand how credit default swaps create synthetic exposure to credit risk. Let’s begin with an example. Assume that D sold protection on $100 worth of ABC bonds through a CDS. Assume that on the day that the CDS becomes effective, D takes $100 of his own capital and invests it in risk-free bonds, e.g., U.S. Treasuries (in reality Treasuries are not risk-free, but if they go, we all go). Assume that the annual interest rate paid on these Treasuries is R. Further, assume that the annualized swap fee is F. It follows that so long as a default does not occur, D’s annual income from the Treasuries and the CDS will be I = $100 x (R + F) until the CDS expires. If there is a default, D will have to payout $100 but will have received some multiple of I over the life of the agreement prior to default.

So, D sets aside $100 and receives the risk free rate plus a spread in exchange. If ABC defaults, D loses $100. If ABC doesn’t default, D keeps $100 plus the income from the Treasuries and the swap fee. Thus, the cash flows from the CDS/Treasuries package look remarkably similar to the cash flows from $100 worth of ABC bonds. As a result, we say that D is synthetically exposed to ABC credit risk.

But what if D doesn’t want this exposure? Well, we know that he could go out to the CDS market and buy protection, thereby hedging his position. But let’s say he’s tired of that old trick and wants to try something new. Well, he could issue synthetic ABC bonds. How? D receives $100 from investors in exchange for promising to: pay them interest annually in the amount of ; pay them $100 in principle at the time at which the underlying CDS expires; with both promises conditioned upon the premise that ABC does not trigger an event of default, as that term is defined in the underlying CDS. In short, D has passed the cash flows from the Treasury/CDS package onto investors, in exchange for pocketing a fee (). As noted above, the cash flows from this package are very similar to the cash flows received from ABC bonds. As a result, we call the notes issued by D synthetic bonds.

Synthetic CDOs

In reality, if D is a swap dealer, D probably sold protection on more than just ABC bonds. Let’s say that D sold protection on k different entities, , where the notional amount of protection sold on each is and the total notional amount is . Rather than maintain exposure to all of these swaps, D could pass the exposure onto investors by issuing notes keyed to the performance of the swaps. The transaction that facilitates this is called a synthetic collateralized debt obligation or synthetic CDO for short. There are many transactions that could be categorized fairly as a synthetic CDO, and these transactions can be quite complex. However, we will explore only a very basic example for illustrative purposes.

So, after selling protection to the swap market as described above, D asks investors for a total of dollars. D sets up an SPV, funds it with the money from the investors, and buys dollars worth of protection on for each from the SPV. That is, D hedges all of his positions with the SPV. The SPV takes the money from the investors and invests it. For simplicity’s sake, assume that the SPV invests in the same Treasuries mentioned above. The SPV then issues notes that promise to:  pay investors their share of dollars after all underlying swaps have expired, where L is the total notional amount of protection sold by the SPV on entities that triggered an event of default; and pay investors their share of annual interest, in amount equal to , where is the sum of all swap fees received by D.

So, if every entity on which the SPV sold protection defaults, the investors get no principle back, but may have earned some interest depending on when the defaults occurred. If none of the entities default, then the investors get all of their principle back plus interest. So each investor has synthetic exposure to a basket of synthetic bonds. That is, if any single synthetic bond defaults, they still receive money. Thus, the process allows investors to achieve exposure to a broad base of credit risk, something that would be very difficult and expensive to do in the bond market.

A Conceptual Framework For Analyzing Systemic Risk

The Cart Before The Horse

There has been a lot of chatter about the systemic risks posed by derivatives, particularly credit default swaps. Rather than offer any formal method of evaluating an enormously complicated question, pundits wield exclamation points and false inferences to distract from the glaring holes in their logic. Below I will not offer any definite answers to any questions about the systemic risks posed by derivatives. Rather, I will describe what I think is a reasonable and useful framework for analyzing systemic risks posed by derivatives. Unfortunately for some, this will involve the use of mathematics. And while the math used is fairly elementary, the concepts are not. This is especially true of the last section. That said, even if you do not fully understand the entirety of this article, one thing should be clear: questions about systemic risk are complex and anyone who gives declarative answers to such questions is almost certain to have no idea what they are talking about.

Risk Magnification And Syndication

As discussed here, derivatives operate by creating and allocating risks that did not exist before the two parties entered into the transaction. That is an unavoidable fact. Moreover, there is no physical limit to the notional amount of any given contract or the number of derivative contracts that parties can enter into. It is entirely up to them. That said, derivatives can be used to negate risks that parties were already exposed to in exchange for assuming other risks, thereby acting as a risk-switching/risk-transferring device. So, a corollary of these observations is that derivatives could be used to create unlimited amounts of risk but through that risk creation they could be used to negate an unlimited amount of risk that parties are already exposed to and thereby effectively “transfer” an unlimited amount of risk to those willing to be exposed to it.

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. Whether their expectations are correct is an entirely different matter, and any criticism on that front is not unique to derivatives traders. Rather, the problem of flawed expectations permeates all of human decision making.

Even if we ignore the practical limits to the creation of risk, derivatives allow for unlimited syndication of risk. That is, there is no smallest unit of risk that can be transferred. Consequently, any fixed amount of risk can be syndicated out to an arbitrarily large number of parties, thereby minimizing the probability that any individual market participant will fail as a result of that risk.

Finally, we should ask ourselves, what does the term systemic risk even mean? The only thing it can mean in the context of derivatives is that the obligations created by two parties will have an effect on at least one other third party. So, even assuming that derivatives create such a “problem,” how is this “problem” any different than that created by a landlord who plans to pay a contractor with the rent he receives from his tenants? It is not.

A Closer Look At 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. As is evident, under this rubric, that whole conversation above was grossly imprecise. But that’s ok. Its import is clear enough. From here on, however, we will tolerate no such imprecision.

Identifying And Defining Risks

Using the definition above, let’s try to define one of the risks that all parties who sold protection on ABC’s series I bonds through a CDS that calls for physical delivery are exposed to. This will allow us to begin to understand the systemic risk that such credit default swaps create. There is no hard rule about how to go about doing this. If we do a poor job of identifying and defining the relevant risks, we will have a poor understanding of those relevant risks. However, common sense tells us that any protection seller’s risk exposure is going to have something to do with triggering a payout under a CDS. So, let’s define the risk-event as any default on ABC series I bonds. For simplicities sake, let’s limit our definition of default to ABC’s failure to pay interest or principle. So, our risk-event is: ABC fails to pay interest or principle on any of its bonds. But what is our risk-magnitude? Since we are trying to define a risk that protection sellers are exposed to, our associated magnitude should be the basis upon which all payments by protection sellers are made. So, we will define the risk-magnitude as where is the price of an ABC series I bond after the risk-event (default) occurs and is the par value of an ABC series I bond. For example, if ABC’s series I bonds are trading at 30 cents on the dollar after default, and a protection seller would have to payout 70 cents for every dollar of notional amount. The amount that bonds trade at after a default is called the recovery value.

One Man’s Garbage Is Another Man’s Glory

When one party to a derivative makes a payment, the other receives it. That seems simple enough. But it follows that if we consider only those payments made under the derivative contract itself, the net position of the two parties is unchanged over the life of the agreement. That is, derivatives create zero-sum games and simply shift and reallocate money that already existed between the two parties. So in continuing with our example above, it follows that we’ve also defined a risk that buyers of protection on ABC series I bonds are exposed to. However, protection buyers have positive exposure to that risk. That is, if ABC defaults, protection buyers receive money.

Exposure To Risk And Settlement Flow Analysis

If our concept of exposure is to have any real economic significance, it must take into account the concept of netting. So, we define the exposure of to the risk-event defined above as the product of (i) the net notional amount of all credit default swaps naming ABC series I bonds as a reference obligation to which is a counterparty, which we will call , and (ii) . The net notional amount is simply the difference between the total notional amount of protection bought and the total notional amount of protection sold by . So, if is a net seller of protection, will be negative and therefore its exposure, , will be either negative or zero.

Because the payments between the two counterparties of each derivative net to zero, it follows that the sum of all net notional amounts is always zero. That is, if there are market participants, . The total notional amount of the entire market is given by . This is the figure that is most often reported by the media. As is evident, it is impossible to determine the economic significance of this number without first knowing the structure of the market. That is, we must know how much is owed and to whom. However, after we have this information, we can choose different recovery values and then calculate each party’s exposure. This would enable us to determine how much cash each participant would have to set aside for a default at various recovery values (simply calculate each party’s exposure at the various recovery values).

Let’s consider a concrete example. In the diagram below, an edge coming from a participant represents protection sold by that participant and consequently an incoming edge represents protection bought by that participant. The amounts written beside these edges represent the notional amount of protection bought/sold. The amounts written beside the nodes represent the net notional amounts.

In the example above, D is a dealer and his net notional amount is zero, and therefore his exposure to the risk-event is . As is evident, we can vary the recovery value to determine what each market participant’s exposure would be in that case. We could then consider other risk-events that occur in conjunction with any given risk-event. For example, we could consider the conjunctive risk-event “ABC defaults and B fails to pay under any CDS” (in which case D’s exposure would not be zero) or any other variation that addresses meaningful concerns. For now, we will focus on our single event risk for explanatory purposes. But even if we restrict ourselves to single event risks, there’s more to a CDS than just default. Collateral will move through the above system dynamically throughout the lives of the contracts. In order to understand how we can analyze the systemic risks posed by the dynamic shifting of collateral, we must first examine what it is that causes collateral to be posted under a CDS.

We’re In The Money

CDS contracts come in and out of the money to a party based on the price of protection. If a party is out of money, the typical market practice is to require that party to post collateral. For example, if I bought protection at a price of 50bp, and suddenly the price jumps to 100bp, I’m in the money and my counterparty is out of the money. Thus, my counterparty will be required to post collateral. We can view the price of protection as providing an implied probability of default. Exactly how this is done is not important. But it should be clear that there is a connection between the cost of protecting debt and the probability of default on that debt (the higher the probability the higher the cost). Thus, as the implied probability of default changes over the life of the agreement, collateral will change hands.

Collateral Flow Analysis

In the previous sections, we assumed that the risk-event was certain to occur and then calculated the exposures based on an assumed recovery value. So, in effect, we were asking “what happens when parties settle their contracts at a given recovery value?” But what if we want to consider what happens before any default actually occurs? That is, what if we want to consider “what happens if the probability of default is ?” Because collateral will be posted as the price of protection changes over the life of the agreement and the price of protection provides an implied probability of default, it follows that the answer to this question should have something to do with the flow of collateral.

Continuing with the ABC bond example above, we can examine how collateral will move through the system by asking two questions: (i) what is the implied probability of the risk-event (ABC’s default) occurring and (ii) what is the expected value of the risk-magnitude (the basis upon which collateral payments are made). As discussed above, the implied probability of default will change over the life of the agreement, which will in turn affect the flow of collateral in the system. Since our goal in this section is to test the system’s behavior at different implied probabilities of default, the expected value of our risk-magnitude should be a function of an assumed implied probability of default. So, we define the expected value of our risk-magnitude as where is our assumed implied probability of default and is defined as it is above. It follows that this analysis will break CDS contracts into categories according to the price at which they were entered into. That is, you can’t ask how much something changed without first knowing what it was to begin with.

Assume that entered into CDS contracts at different prices. For example, he entered into four contracts at 20 bp and eight contracts at 50bp, and no others. In this case, . For each , assign an arbitrary ordering, , to the sets of contracts that were entered into at different prices by . In the example where , we could let be the set of eight contracts entered into at 50bp and let be the set of four contracts entered into at 20 bp. Each of these sets will have a net notional amount and an implied probability of default (since each is categorized by price). Define as the net notional amount of the contracts in and as the implied probability of default of the contracts in for each . We define the expected exposure of as:

.

Note that when ,

.

That is, this is a generalized version of the settlement analysis above, and when we assume that default is certain, collateral flow analysis reduces to settlement flow analysis.

So What Does That Awful Formula Tell Us?

A participant’s expected exposure is a reasonable estimate for the amount of collateral that will be posted or received by that participant at an assumed implied probability of default. The exact amount of collateral that will be posted or received under any contract will be determined by the terms of that contract. As a result, our model is approximate and not exact. However, the direction that collateral moves in our model is exact. That is, if a party’s expected exposure is negative, it will not receive collateral, and if it is positive, it will not post collateral. It also shows that even if a party is completely hedged in the event of a default, it is possible that it is not completely hedged to posting collateral. That is, even if it bought and sold the same notional amount of protection, it could have done so at different prices.