Credit Default Swaps And Mortgage Backed Securities

Like Your Grandsire In Alibaster

In this article, I will apply my usual dispassionate analysis to the role that credit default swaps play in the world of Mortgage Backed Securities (MBSs). We will take a brief look at the interactions between the issuance of mortgages, MBSs, and how the concept of loss plays out in the context of derivatives and mortgages. Then we will explore how the expectations of the parties to a lender/borrower relationship differ from that of a protection seller/buyer relationship and how credit default swaps, by allowing markets to express a negative view of mortgage default risk, facilitate price correction and mitigate net losses. This is done by applying the concepts in my previous article, The Demand For Risk And A Macroeconomic Theory of Credit Default Swaps: Part 2, to the context of credit default swaps on MBSs. This article can be considered a more concrete application of the concepts in that article, which will hopefully clear up some of the confusion in that article’s comment section.

The Path Of Funds In the MBS Market

Mortgage backed securities allow investors to gain exposure to the housing market by taking on credit risk linked to a pool of mortgages. Although the underlying mortgages are originated by banks, the existence of investor demand for MBSs allows the originators to effectively pass the mortgages off to the investors and pocket a fee. Thus, the greater the demand for MBSs, the greater the total value of mortgages that originators will issue and ultimately pass off to investors. So, the originators might front the money for the mortgages in many cases, but the effective path of funds is from the investors, to the originators, and onto the borrower. As a result, investors in MBSs are the effective lenders in this arrangement, since they bear the credit risk of the mortgages.

This market structure also has an effect on the interest rates charged on the underlying mortgages. As investor demand for MBSs increases, the amount of cash available for mortgages will increase, pushing the interest rates charged on the underlying mortgages down as originators compete for borrowers.

Loss In The Context Of Derivatives And Mortgages

I often note that derivatives cannot create net losses in an economy. That is, they simply transfer money between two parties. If one party loses X, the other gains X, so the net loss between the two parties is zero. For more on this, go here. This is not the case with a mortgage. The lender gives money to the borrower, who then spends this money on a home. Assume that a lender and borrower entered into a mortgage and that before maturity the value of the home falls, prompting the borrower to default on its mortgage. Further assume that the lender forecloses on the property, selling it at a loss. Since the buyer receives none of the foreclosure proceeds, the buyer can be viewed as either neutral or incurring a loss, since at least some of the borrower’s mortgage payments went towards equity ownership and not just occupancy. It follows that there is a loss to the lender and either no change in or a loss to the borrower and therefore a net loss. This demonstrates what we have all recently learned: poorly underwritten mortgages can create net losses.

Net Losses And Efficiency

You can argue that even in the case that both parties to an agreement incur losses, the net loss to the economy is zero, since the cash transferred under the agreement was not destroyed but merely moved through the economy to market participants that are not a party to the agreement. That is, if you expand the number of parties to a sufficient degree, all transactions will net to zero. While this must be the case, it misses an essential point: I am using net losses to bilateral agreements as a proxy for inefficient allocation of capital. That is, both parties expected to benefit from the agreement, yet both lost money, which implies that neither benefited from the agreement. For example, in the case of a mortgage, the borrower expects to pay off the mortgage but benefit from the use and eventual ownership or sale of the home. The lender expects to profit from the interest paid on the mortgage. When both of these expectations fail, I take this as implying that the initial agreement was an inefficient allocation of capital. This might not always be the case and depends on how you define efficiency. But as a general rule, it is my opinion that net losses to a bilateral agreement are a reasonable proxy for inefficient allocation of capital.

Expectations Of Lender/Borrower vs. Protection Seller/Buyer

As mentioned above, under a mortgage, the lender expects to benefit from the interest paid on the mortgage while the borrower expects to benefit from the use and eventual ownership or sale of the home. Implicit in the expectations of both parties is that the mortgage will be repaid. Economically, the lender is long on the mortgage. That is, the lender gains if the mortgage is fully repaid. Although application of the concepts of long and short to the borrower’s position is awkward at best, the borrower is certainly not short on the mortgage. That is, in general, the borrower does not gain if he fails to repay the mortgage. He might however mitigate his losses by defaulting and declaring bankruptcy. That said, the takeaway is that both the lender and the borrower expect the mortgage to be repaid. So, if we consider only lenders and borrowers, there are no participants with a true short position in the market. Thus, price, which in this case is an interest rate, will be determined by participants with similar positive expectations and incentives. Anyone with a negative view of the market has no role to play and therefore no effect on price.

This is not the case with credit default swaps (CDSs) referencing MBSs. In such a CDS, the protection seller is long on the MBS and therefore long on the underlying mortgages, and the protection buyer is short. That is, if the MBS pays out, the protection seller gains on the swap; and if the MBS defaults, the protection buyer gains on the swap. Thus, through the CDS, the two parties express opposing expectations of the performance of the MBS. Thus, the CDS market provides an opportunity to express a negative view of mortgage default risk.

The Effect Of Synthetic Instruments On “Real” Instruments

As mentioned above, the CDS market provides a method of shorting MBSs. But how does that effect the price of MBSs and ultimately interest rates? As described here, the cash flows of any bond, including MBSs, can be synthesized using Treasuries and CDSs. Using this technique, a fully funded synthetic bond consists of the long end of a CDS and a Treasury. The spread that the synthetic instrument pays over the risk free rate is determined by the price of protection that the CDS pays the investor (who in this case is the protection seller). One consequence of this is that there are opportunities for arbitrage between the market for real bonds and CDSs if the two markets don’t reach an equilibrium, removing any opportunity for arbitrage. Because this opportunity for arbitrage is rather obvious, we assume that it cannot persist. That is, as the price of protection on MBSs increases, the spread over the risk free rate paid by MBSs should widen, and visa versa. Thus, as the demand for protection on MBSs increases, we would expect the interest rates paid by MBSs to increase, thereby increasing the interest rates on mortgages. Thus, those with a negative view of MBS default risk can raise the cost of funds on mortgages by buying protection through CDSs on MBSs, thereby inadvertently “correcting” what they view as underpriced default risk.

In addition to the no-obvious-arbitrage argument outlined above, we can consider how the existence of synthetic MBSs affects the supply of comparable investments, and thereby interest rates. As mentioned above, any MBS can be synthesized using CDSs and Treasuries (when the synthetic MBS is unfunded or partially funded, it consists of CDSs and other investments, not Treasuries). Thus, investors will have a choice between investing in real MBSs or synthetic MBSs. And as explained above, the price of each should come to an equilibrium that excludes any opportunity for obvious arbitrage between the two investments. Thus, we would expect at least some investors to be indifferent between the two.

Depending on whether the synthetics are fully funded or not, the principle investment will go to the Treasuries market or back into the capital markets respectively. Note that synthetic MBSs can exist only when there is a protection buyer for the CDS that comprises part of the synthetic. That is, only when interest rates on MBSs drop low enough, along with the price of protection on MBSs, will protection buyers enter CDS contracts. So when protection buyers think that interest rates on MBSs are too low to reflect the actual probability of default, their desire to profit from this will facilitate the issuance of synthetic MBSs, thereby diverting cash from the mortgage market and into either Treasuries or other areas of the capital markets. Thus, the existence of CDSs operates as a safety valve on the issuance of MBSs. When interest rates sink too low, synthetics will be issued, diverting cash away from the mortgage market.

The Demand For Risk And A Macroeconomic Theory of Credit Default Swaps: Part 2

Redux And Reduction

In the previous article, we defined a highly abstract framework that considered the subjective expected payout of both sides of a fixed fee derivative.  In this article, we will apply that model to the context of credit default swaps and will show that the presence of credit default swaps and synthetic bonds should be expected to reduce the demand for “real” bonds (as opposed to synthetic bonds) and thereby reduce the net exposure of an economy to credit risk.

The Demand For Credit Default Swaps

In the previous article, we plotted the expected payout of each party to a credit default swap as a function of the fee and each party’s subjective valuation of the probability that a default will occur. The simple observation gleaned from that chart was that if we fix the subjective probabilities of default, protection sellers expect to earn more as the price of protection increases and protection buyers expect to earn more as the price of protection decreases.  Thus, as the the price of protection increases, we would expect protection seller side “demand” to increase and expect protection buyer side “demand” to decrease.  But how can demand be expressed in the context of a credit derivative? The general idea is to assume that holding all other variables constant, the size of the desired notional amount of the CDS will vary with price. So in the case of protection sellers, the greater the price of protection, the greater the notional amount desired by any protection seller.

In order to further formalize this concept, we should consider each reference entity as defining a unique demand curve for each market participant. We should also distinguish between demand for buying protection and demand for selling protection. For convenience’s sake, we will refer to the demand for selling protection as the supply of credit protection and demand for buying credit protection as the demand for credit protection. For example, consider protection seller X’s supply curve and protection buyer Y’s demand curve for CDSs naming ABC as a reference entity. The following chart expresses the total notional amount of all CDSs desired by X and Y as a function of the price of protection.

As the price of protection approaches zero, Y’s desired notional amount should approach infinity, since at zero, Y is getting free protection and should desire an unbounded “quantity” of credit protection. The same is true for X as the price of protection approaches infinity.

Synthetic Bonds As Competing Goods With “Real” Bonds

Imagine a world without credit derivatives and therefore without synthetic bonds. In that world, there will be a demand curve for real ABC bonds as a function of the spread the bonds pay over the risk free rate, holding all over variables constant. Now imagine that credit default swaps were introduced to this world. We know that the cash flows of any bond can be synthesized using Treasuries and credit default swaps. For example, assume we have synthesized the cash flows of ABC’s bonds using the method described here. We would expect at least some investors to be indifferent between real ABC bonds and synthetic ABC bonds, since they both produce the same cash flows. Thus, the two are competing products in the sense that investors in real ABC bonds should be potential investors in synthetic ABC bonds. So because some investors will be indifferent between synthetic ABC bonds and real ABC bonds, synthetic ABC bonds will siphon some of the cash that would have otherwise gone to real ABC bonds. Thus, in a world with credit derivatives, we would expect there to be less demand for real bonds than would be present without credit derivatives. In the following chart we express the macroeconomic demand for real ABC bonds in terms of the spread over the risk free rate and the total par value desired by the market.

Thus, the demand for credit derivatives diminishes the demand for real bonds. Although we cannot know exactly what the effect on the demand curve for real bonds will be, we can safely assume that it will be diminished at all levels of return, since at each level, at least some investors will be indifferent to real bonds and synthetic bonds, since each offers the same return.

Real Cash Losses Versus Wealth Transfers Through Derivatives

Economics already has a term to describe payouts under credit default swaps: wealth transfers. Although ordinarily used to describe the cash flows of tax regimes, the term applies equally to the payments under a credit default swap. As described in the previous article, there are no net cash losses under a credit default swap. There is a payment of money from one party to another, the net effect of which is a wealth transfer. That is, credit default swaps, like all derivatives, simply rearrange the current allocation of cash in the financial system, and nothing is lost in process (ignoring transaction costs, which are not relevant to this discussion).

When a real bond defaults, a net cash loss occurs. The borrower has taken the money lent to it by investors, lost it, and the investors are not fully paid back. Therefore, both the borrower and the investors incur a cash loss, creating a net cash loss to the economy. So, in the case of a synthetic ABC bond, upon the default of one of ABC’s bonds,  a wealth transfer occurs from the protection seller to the protection buyer and the net effect is null. In the case of a real ABC bond, upon the default of that bond, the investors will lose some of their principle and ABC has already lost some of the money it was lent, the net effect of which is a loss to the economy.

So every dollar siphoned away from real bonds by synthetic bonds is a dollar that will not be lost in the economy upon the occurrence of a credit event. If there were no credit derivatives, then that dollar would have been invested in real bonds and thereby lost upon the occurrence of a credit event. Therefore, the net losses to the economy upon the occurrence of a credit event is less with credit derivatives than without. In the following diagram, the two circles of each transaction represent the parties to that transaction. In the case of real bonds, one of the parties is ABC and the other is an investor. In the case of synthetic bonds, one is the protection seller and the other is the protection buyer of the credit default swap underlying the synthetic bond.

This diagram simply demonstrates what was described above. Namely, that with credit derivatives, some investors will choose synthetic bonds rather than real bonds, thereby reducing the amount of cash exposed to credit risk. Thus, rather than increase the impact of credit risk, credit default swaps actually decrease the impact of credit risk by placating the demand for exposure to credit risk with synthetic instruments that are incapable of producing net losses. However, there may be consequences arising from credit default swaps that cause actual cash losses to an economy, such as a firm failing because of its obligations under credit default swaps. But the failure is not caused by the instrument itself. The nature of the instrument is to reduce the impact of credit risk. The firm’s failure is caused by that firm’s own poor risk management.

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.

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.

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.

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.

The Mythology Of Credit Default Swaps

Systemic Speculation

Pundits from all corners have been chiming in on the debate over derivatives. And much like the discourse that has dominated the rest of human history, reason, temperance, and facts play no role in the debate. Rather, the spectacular, outrage, and irrational blame have been the big winners lately. As a consequence, credit default swaps have been singled out as particularly dangerous to the financial system. Why credit default swaps have been targeted as opposed to other derivatives is not entirely clear to me, although I do have some theories. In this article I debunk many of the common myths about credit default swaps that are circulating in the popular press. For an explanation of how credit default swaps work, see this article.

The CDS Market Is Not The Largest Thing Known To Humanity

The media likes to focus on the size of the market, reporting shocking figures like $45 trillion and $62 trillion. These figures refer to the notional amount of the contracts, and because of netting, these figures do not provide a meaningful picture of the amount of money that will actually change hands. That is, without knowing the structure of the credit default swap market, we cannot determine the economic significance of these figures. As such, these figures should not be compared to real economic indicators such as GDP.

But even if you’re too lazy to think about how netting actually operates, why would you focus on credit default swaps? Even assuming that the media’s shocking double digit trillion dollar amounts have real economic significance, the credit default swap market is not even close in scale to the interest rate swap market, which is an even more shocking $393 trillion market. But alas, we are in the midst of a “credit crisis” and not an “interest rate crisis.” As such, headlines containing the terms “interest rate swap” will not fare as well as those containing “credit default swap” in search engines or newsstands. Perhaps one day interest rate swaps will have their moment in the sun, but for now they are an even larger and equally unregulated market that’s just as boring and uneventful as the credit default swap market.

Credit Default Swaps Do Not Facilitate “Gambling”

One of the most widely stated criticisms of credit default swaps is that they are a form of gambling. Of course, this allegation is made without any attempt to define the term “gambling.” So let’s begin by defining the term “gambling.” In my mind, the purest form of gambling involves the wager of money on the outcome of events that cannot be controlled or predicted by the person making the wager. For example, I could go to a casino and place a $50 bet that if a casino employee spins a roulette wheel and spins a ball onto the wheel, the ball will stop on the number 3. In doing so, I have posted collateral that will be lost if an event (the ball stopping on the number 3) fails to occur, but will receive a multiple of my collateral if that event does indeed occur. I have no ability to affect the outcome of the event and more importantly for our purposes, I have absolutely no way of predicting what the outcome will be. In short, my “investment” is a blind guess as to the outcome of a random event.

Now let’s compare that with someone (B) buying protection on ABC’s bonds through a credit default swap. Assume that B is as villainous as he could be: that is, assume that he doesn’t own the underlying bond. This evildoer is in effect betting upon the failure of ABC. What a nasty thing to do. And why would he do such a thing? Well, B might reasonably believe that ABC is going to fail in the near future based on market conditions and information disclosed by ABC. But why should someone profit from ABC’s failure? Because if B’s belief in ABC’s impending failure is shared by others, their collective selfish desire to profit will push the price of protection on ABC’s bonds up, which will signal to the market-at-large that the CDS market believes that there will be an event of default on ABC issued debt. That is, a market full of people who specialize in recognizing financial disasters will inadvertently share their expertise with the world.

So, in the case of the roulette wheel, we have money committed to the occurrence of an event that cannot be controlled or predicted by the person making the commitment. Moreover, this “investment” is made for no bona fide economic purpose with an expected negative return on investment. In the case of B buying protection through a CDS on a bond he did not own, we have money committed to the occurrence of an event that cannot be controlled by B but can be reasonably predicted by B, and through collective action we have the serendipitous effect of sharing information. To call the latter gambling is to call all of investing gambling. For there is no difference between the latter and buying stock, buying bonds, investing in the college education of your children, etc.

The Credit Default Swap Market Is Not An Insurance Market

Credit default swaps operate like insurance at a bilateral level. That is, if you only focus on the two parties to a credit default swap, the agreement operates like insurance for both parties. But to do so is to fail to appreciate that a credit default swap is exactly that: a swap, and not insurance. Swap dealers are large players in the swap markets that buy from one party and sell to another, and pocket the difference between the prices at which they buy and sell. In the case of a CDS dealer, dealer (D) sells protection to A and then buys protection from B, and pockets the difference in the spreads between the two transactions. If either A or B has dodgy credit, D will require collateral. Thus, D’s net exposure to the bond is neutral. While this is a simplified explanation, and in reality D’s neutrality will probably be accomplished through a much more complicated set of trades, the end goal of any swap dealer is to get close to neutral and pocket the spread.

That said, insurance companies such as MBIA and AIG did participate in the CDS market, but they did not follow the business model of a swap dealer. Instead, they applied the traditional insurance business model to the credit default swap market, with notoriously less than stellar results. The traditional insurance business model goes like this: issue policies, estimate liabilities on those policies using historical data, pool enough capital to cover those estimated liabilities, and hopefully profit from the returns on the capital pool and the fees charged under the policies.  Thus, a traditional insurer is long on the assets it insures while a swap dealer is risk-neutral to the assets on which it is selling protection, so long as its counterparties pay. So, a swap dealer is more concerned about counterparty risk: the risk that one of its counterparties will fail to payout. As mentioned above, if either counterparty appears as if it is unable to pay, it will be required to post collateral. Additionally, as the quality of the assets on which protection is written deteriorates, more collateral will be required. Thus, even in the case of counterparty failure, collateral will mitigate losses.

This collateral feature is missing on both ends of the traditional insurance model. Better put, there is no “other end” for a traditional insurer. That is, the insurance business model does not hedge risk, it absorbs it. So if a traditional insurer sold protection on bonds that had risks it didn’t understand, e.g., mortgage backed securities, and it consequently underestimated the amount of capital it needed to store to meet liabilities, it would be in some serious trouble. A swap dealer in the same situation, even if its counterparties failed to appreciate these same risks, would be compensated gradually over the life of the agreement through collateral.

Derivatives/Synthetic Instruments Demystified

What Is A Derivative?

A derivative is a contract that derives its value by reference to “something else.” That something else can be pretty much anything that can be objectively observed and measured. For example, two parties, A and B, could get together and agree to take positions on the Dow Jones Industrial Average (DJIA). That’s an index that can be objectively observed and measured. A could agree to pay B the total percentage-wise return on that index from October 31, 2007 to October 31, 2008 multiplied by a notional amount, where that amount is to be paid on October 31, 2008. In exchange, B could agree to make quarterly payments of some percentage of the notional amount (the swap fee) over that same time frame. Let’s say the notional amount is $100 (a position that even Joe The Plumber can take on); the swap fee is 10% per annum; and the total return on the DJIA over that period is 15%. It doesn’t take Paul Erdős to realize that this leaves B in the money and A out of the money (A pays $15 and receives $10, so he loses $5).

But what if the DJIA didn’t gain 15%? What if it tanked 40% instead? In that case, we have to look to our agreement. Our agreement allocated the DJIA’s returns to B and fixed payments to A. It didn’t mention DJIA loss. The parties can agree to distribute gain and loss in the underlying reference (the DJIA) any way they like: that’s the beauty of enforceable contracts. Let’s say that under their agreement, B agreed to pay the negative returns in the DJIA multiplied by the notional amount.  If the market tanked 40%, then B would have made the fixed payments of 10% over the life of the agreement, plus another 40% at the end. That leaves him down $50. Bad year for B.

Follow The Money

So what is the net effect of that agreement? B always pays 10% to A, whether the DJIA goes up, down, or stays flat over the relevant time frame. If the DJIA goes up, A has to pay B the percentage-wise returns. If the DJIA goes down, B has to pay A the percentage-wise losses. So, A profits if the DJIA goes down, stays flat, or goes up less than 10% and B profits if the DJIA goes up more than 10%. So, A is short on the DJIA going up 10% and B is long on the DJIA going up 10%. This is accomplished without either of them taking actual ownership of any stocks in the DJIA. We say that A is synthetically shorting the DJIA and B is synthetically long on the DJIA. This type of agreement is called a total return swap (TRS). This TRS exposes A to the risk that the DJIA will appreciate by more than 10% over the life of the agreement and B to the risk that the DJIA will not appreciate by more than 10%.

What Is Risk?

There are a number of competing definitions depending on the context. My own personal view is that risk 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. For example, in the TRS between A and B, A is exposed to the risk that the DJIA will appreciate by more than 10% over the life of agreement. That risk has two components: the event (the DJIA appreciating by more than 10%) and a magnitude associated with that event (the amount by which it exceeds 10%). In this case, the occurrence of the event and its associated magnitude are equivalent (any non-zero positive value for the magnitude implies that the event occurred) and so our two questions reduce to one question: what is the expected value of the DJIA at the end of the agreement? That obviously depends on who you ask. So, can we then infer that A expects the DJIA to gain less than 10% over the life of the agreement? No, we cannot. If A actually owns $100 worth of the DJIA, A is fully hedged and the agreement is equivalent to bona fide financing. That is, A has no exposure to the DJIA (short on the DJIA through the TRS and long through actually owning it) and makes money only through the swap fee. B’s position is the same whether A owns the underlying index or not: B is long on the DJIA, as if he actually owned it. That is, B has synthesized exposure to the DJIA. So, if A is fully hedged the TRS is equivalent to a financing agreement where A “loans” B $100 to buy $100 worth of the DJIA, and then A holds the assets for the life of agreement (like a collateralized loan). As such, B will never agree to pay a swap fee on a TRS that is higher than his cost of financing (since he can just go get a loan and buy the reference asset).

How Derivatives Create, Allocate, And “Transfer” Risk

It is commonly said that derivatives transfer risk. This is not technically true, but often appears to be the case.  Derivatives operate by creating risks that were not present before the parties entered into the derivative contract. For example, assume that A and B enter into an interest rate swap, where A agrees to pay B a fixed annual rate of 8% and B agrees to pay A a floating annual rate, say LIBOR, where each is multiplied by a notional amount of $100. Each party agrees to make quarterly payments. Assume that on the first payment date, LIBOR = 4%.  It follows that A owes B $2 and B owes A $1. So, after netting, A pays B $1.

Through the interest rate swap, A is exposed to the risk that LIBOR will fall below 8%. Similarly, B is exposed to the risk that LIBOR will increase above 8%. The derivative contract created these risks and assigned them to A and B respectively. So why do people say that derivatives transfer risk? Assume that A is a corporation and that before A entered into the swap, A issued $100 worth of bonds that pay investors LIBOR annually. By issuing these bonds, A became exposed to the risk that LIBOR would increase by any amount. Assume that the payment dates on the bonds are the same as those under the swap. A’s annual cash outflow under the swap is (.08 – LIBOR) x 100. It’s annual payments on the bonds are LIBOR x 100. So it’s total annual cash outflow under both the bonds and the swap is:

(.08 – LIBOR) x 100 +  LIBOR x 100 = .08 x 100 – LIBOR x 100  + LIBOR x 100 = 8%.

So, A has taken its floating rate LIBOR bonds and effectively transformed them into fixed rate bonds. We say that A has achieved this fixed rate synthetically.

At first glance, it appears as though A has transferred its LIBOR exposure to B through the swap.  This is not technically true. Before A entered into the swap, A was exposed to the risk that LIBOR would increase by any amount. After the swap, A is exposed to the risk that LIBOR will fall under 8%. So, even though A makes fixed payments, it is still exposed to risk: the risk that it will pay above its market rate of financing (LIBOR). For simplicity’s sake, assume that B was not exposed to any type of risk before the swap. After the swap, B is exposed to the risk that LIBOR will rise above 8%. This is not the same risk that A was exposed to before the swap (any increase in LIBOR) but it is a similar one (any increase in LIBOR above 8%).

So What Types Of Risk Can Be Allocated Using Derivatives?

Essentially any risk that has an objectively observable event and an objectively measureable associated magnitude can be assigned a financial component and allocated using a derivative contract. There are derivative markets for risks tied to weather, energy products, interest rates, currency, etc. Wherever there is a business or regulatory motivation, financial products will appear to meet the demand. What is important is to realize that all of these products can be analyzed in the same way: identify the risks, and then figure out how they are allocated. This is usally done by simply analyzing the cash flows of the derivative under different sets of assumptions (e.g., the DJIA goes up 15%).