Politicized Economy

Synthetic CDOs Demystified

/ erdosfan / 12 Comments

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 100 \cdot (R + F - \Delta); 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 (\Delta). 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, E_1, ... , E_k, where the notional amount of protection sold on each is n_1, ..., n_k and the total notional amount is N = \sum_{i=1}^k n_i. 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 N dollars. D sets up an SPV, funds it with the money from the investors, and buys n_i dollars worth of protection on E_i for each i \leq k 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 N - L 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 (R + F - \Delta) \cdot (N - L), where F 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.

synthetic-cdo

A Conceptual Framework For Analyzing Systemic Risk

/ erdosfan / 20 Comments

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 M=1 - \frac{P_d}{P} where P_d is the price of an ABC series I bond after the risk-event (default) occurs and P 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, M = .7 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 P_i 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 P_i is a counterparty, which we will call N_i, and (ii) M. 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 P_i. So, if P_i is a net seller of protection, N_i will be negative and therefore its exposure, N_i \cdot M, 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 k market participants, \sum_{i=1}^kN_i = 0. The total notional amount of the entire market is given by N_T = \frac{1}{2} \sum_{i=1}^k|N_i|. 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.

cds-market-diagram

In the example above, D is a dealer and his net notional amount is zero, and therefore his exposure to the risk-event is 0 \cdot M = 0 . 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 p?” 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 M_e = p^* \cdot M where p^* is our assumed implied probability of default and M 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 P_i entered into CDS contracts at m_i different prices. For example, he entered into four contracts at 20 bp and eight contracts at 50bp, and no others. In this case, m_i = 2. For each P_i, assign an arbitrary ordering, (c_{i,1}, ... , c_{i,m_i}), to the sets of contracts that were entered into at different prices by P_i. In the example where m_i = 2, we could let c_{i,1} be the set of eight contracts entered into at 50bp and let c_{i,2} 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 n_{i,j} as the net notional amount of the contracts in c_{i,j} and p_{i,j} as the implied probability of default of the contracts in c_{i,j} for each 1 \leq j \leq m_i. We define the expected exposure of P_i as:

EX_i = M_e \cdot \sum_{j = 1}^{m_i}\left(\frac{p^* - p_{i,j}}{1 - p_{i,j}} \cdot n_{i,j}\right) .

Note that when p^* = 1,

EX_i = M \cdot \sum_{j = 1}^{m_i}\left(\frac{1 - p_{i,j}}{1 - p_{i,j}} \cdot n_{i,j}\right) = M \cdot N_i .

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

/ erdosfan / 31 Comments

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.

cds-swap-dealer

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.

Securitization Demystified

/ erdosfan / 10 Comments

What Is Securitization?

Securitization is a process that allows the cash flows of an asset to be isolated from the cash flows of that asset’s original owner. There are countless variations on this theme, and since our purpose here at derivative dribble is to foster clarity and simplicity, we will discuss only the main theme, and will avoid the Glen Gould variations.

Cui Bono?

We will explain how securitization works by first exploring the most basic motivation for isolating assets: access to cheaper financing. Assume B is a local bank that focuses primarily on taking deposits and earning money through very low risk investments of those deposits. Further, assume that B is a stable and solvent bank, but that it lacks the credit quality of some of the larger national banks and as such it has a higher cost of financing. This higher cost of financing means that it can’t lend at the same low rates as national banks. B’s local community is one in which home values are high and stable, and as a result the rate of default on mortgages is extremely low. As such, B would like to be able to compete in the local mortgage market, but is struggling to do so because its rates are higher than the national banks. What B would really like to do is borrow money for the limited purpose of issuing mortgages in its local community. That is, B wants to separate its credit quality from the credit quality of the mortgages it issues in its community. Securitization is the process that facilitates this isolation.

The Nuts And Bolts

The overall process is quite simple and reasonable, despite its portrayal in the popular press. We know that so long as B owns the mortgages, B’s creditors will still consider B’s credit as an institution when lending to it, even if that lending is for the limited purpose of issuing local mortgages. The solution to that problem is simple: B sells the mortgages off shortly after issuing them. But to whom? Well, common sense tells us that investors are not going to be too excited about buying mortgages piecemeal. So, B will wait until it has issued a pool of mortgages large enough to attract the attention of investors. Then, it will set up a special purpose vehicle (SPV) where that SPV’s special purpose is to buy the mortgages from B, using money from the investors, and issue notes to those same investors.

So, the SPV owns the mortgages since B is completely bought out by the cash from the investors. And the notes issued to the investors are basically bonds issued by the SPV with the mortgages as collateral. As a result, B is out of the picture from an investor’s perspective. In reality, B might still service the mortgages (i.e., sending bills to borrowers, maintaining address information on borrowers, etc.) but because the mortgages have been sold to the SPV, the notes issued by the trust have no credit risk exposure to B. So if B goes bust, the assets in the SPV are safe and will continue to pay.

So What Does That Accomplish?

B wanted to enter the local mortgage market but was struggling to do so because it couldn’t lend at the same rates as national banks. This was due to B’s inferior credit standing relative to large national banks. But the securitization process above allows B to isolate the credit quality of the mortgages it issues from its own credit quality as an institution. Thus, the rate paid on the notes issued by the SPV will be determined by examining the credit quality of the mortgages themselves, with no reference to B. Since the rate on the notes is determined only by the quality of the mortgages, the rate on any individual mortgage will be determined by the quality of that mortgage. As such, B will be able to issue mortgages to its local community at the market rate and profit from this by servicing the mortgages for a fee.

Derivatives/Synthetic Instruments Demystified

/ erdosfan / 12 Comments

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%).

Systemic Counterparty Confusion: Credit Default Swaps Demystified

/ erdosfan / 33 Comments

It Is A Tale Told By An Idiot

The press loves a spectacle. There’s a good reason for this: panic increases paranoia, which increases the desire for information, which increases their advertising revenues. Thus, the press has an incentive to exaggerate the importance of the events they report. As such, we shouldn’t be surprised to find the press amping up fears about the next threat to the “real economy.”

When written about in the popular press, terms such as “derivative” and “mortgage backed security” are almost always preceded by adjectives such as “arcane” and “complex.” They’re neither arcane nor complex. They’re common and straightforward. And the press shouldn’t assume that their readers are too dull to at least grasp how these instruments are structured and used. This is especially true of credit default swaps.

Much Ado About Nothing

So what is the big deal about these credit default swaps? Surely, there must be something terrifying and new about them that justifies all this media attention? Actually, there really isn’t. That said, all derivatives allow risk to be magnified (which I plan to discuss in a separate article). But risk magnification isn’t particular to credit default swaps. In fact, considering the sheer volume of spectacular defaults over the last year, the CDS market has done a damn good job of coping.  Despite wild speculation of impending calamity by the press, the end results have been a yawn . So how is it that Reuters went from initially reporting a sensational $365 billion in losses to reporting (12 days later) only $5.2 billion in actual payments? There’s a very simple explanation: netting, and the fact that they just don’t understand it. The CDS market is a swap market, and as such, the big players in that market aren’t interested in taking positions where their capital is at risk. They are interested in making money by creating a market for swaps and pocketing the difference between the prices at which they buy and sell. They are classic middlemen and essentially run an auction house.

Deus Ex Machina

The agreements that document credit default swaps are complex, and in fairness to the press, these are not things we learn about in grammar school – for a more detailed treatment of these agreements, look here. Despite this, the basic mechanics of a credit default swap are easy to grasp. Let’s begin by introducing everyone: protection buyer (B) is one party and swap dealer (D) is the other. These two are called swap counterparties or just counterparties for short. Let’s first explain what they agree to under a credit default swap, and then afterward, we’ll examine why they would agree to it.

What Did You Just Agree To?

Under a typical CDS, the protection buyer, B, agrees to make regular payments (let’s say monthly) to the protection seller, D. The amount of the monthly payments, called the swap fee, will be a percentage of the notional amount of their agreement. The term notional amount is simply a label for an amount agreed upon by the parties, the significance of which will become clear as we move on. So what does B get in return for his generosity? That depends on the type of CDS, but for now we will assume that we are dealing with what is called physical delivery. Under physical delivery, if the reference entity defaults, D agrees to (i) accept delivery of certain bonds issued by the reference entity named in the CDS and (ii) pay the notional amount in cash to B. After a default, the agreement terminates and no one makes anymore payments. If default never occurs, the agreement terminates on some scheduled date. The reference entity could be any entity that has debt obligations.

Now let’s fill in some concrete facts to make things less abstract. Let’s assume the reference entity is ABC. And let’s assume that the notional amount is $100 million and that the swap fee is at a rate of 6% per annum, or $500,000 per month. Finally, assume that B and D executed their agreement on January 1, 2008 and that B made its first payment on that day.  When February 1, 2008 rolls along, B will make another $500,000 payment. This will go on and on for the life of the agreement, unless ABC triggers a default under the CDS. Again, the agreements are complex and there are a myriad of ways to trigger a default. We consider the most basic scenario in which a default occurs: ABC fails to make a payment on one of its bonds. If that happens, we switch into D’s obligations under the CDS. As mentioned above, D has to accept delivery of certain bonds issued by ABC (exactly which bonds are acceptable will be determined by the agreement) and in exchange D must pay B $100 million.

Why Would You Do Such A Thing?

To answer that, we must first observe that there are two possibilities for B’s state of affairs before ABC’s default: he either (i) owned ABC issued bonds or (ii) he did not. I know, very Zen. Let’s assume that B owned $100 million worth of ABC’s bonds. If ABC defaults, B gives D his bonds and receives his $100 million in principal (the notional amount). If ABC doesn’t default, B pays $500,000 per month over the life of the agreement and collects his $100 million in principal from the bonds when the bonds mature. So in either case, B gets his principal. As a result, he has fully hedged his principal. So, for anyone who owns the underlying bond, a CDS will allow them to protect the principal on that bond in exchange for sacrificing some of the yield on that bond.

Now let’s assume that B didn’t own the bond. If ABC defaults, B has to go out and buy $100 million par value of ABC bonds. Because ABC just defaulted, that’s going to cost a lot less than $100 million. Let’s say it costs B $50 million to buy ABC issued bonds with a par value of $100 million. B is going to deliver these bonds to D and receive $100 million. That leaves B with a profit of $50 million. Outstanding. But what if ABC doesn’t default? In that case, B has to pay out $500,000 per month for the life of the agreement and receives nothing. So, a CDS allows someone who doesn’t own the underlying bond to short the bond. This is called synthetically shorting the bond. Why? Because it sounds awesome.

So why would D enter into a CDS? Again, most of the big protection sellers buy and sell protection and pocket the difference. But, this doesn’t have to be the case. D could sell protection without entering into an offsetting transaction. In that case, he has synthetically gone long on the bond. That is, he has almost the same cash flows as someone who owns the bond.