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.

Systemic Counterparty Confusion: Credit Default Swaps Demystified

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.

The Not So Efficient Market (Theorem) Hypothesis

Are Capital Markets Efficient?

Let’s examine the question using elementary game theory. That is, let’s assume that given any decision, each capital market participant acts in a way that maximizes his expected utility.

But How Would We Do That?

First we explore one example of incentive structures which leads to a sell off. Then we consider how the Efficient Market Hypothesis fits into the framework of economic knowledge and the notion of economic efficiency. Finally, we conclude that even if a capital market incorporates all available price-information, it is possible that the outcome is not an efficient allocation of capital.

The Sound And The Fury

Assume that Apocalypse Ann (A) and Tag Along Teds (T1, T2, …, Tn) are all traders that hold large positions in ABC stock. Assume that A is convinced that ABC is doomed because of recent conditions in the credit markets. She may or may not be correct in her prediction, but assume she honestly believes that ABC will be placed into receivership and liquidated, with little to no money left for equity holders.  Further, assume that each of T1, T2, …, Tn is aware of A’s belief. Personally, each thinks that A is out of her mind, that ABC is well positioned to ride the current credit crisis and that current equity valuations of ABC are rational. However, they know that given A’s belief, she will certainly liquidate her position.

Assume that each of T1, T2, …, Tn is a trader for a fund that has some rather jittery investors who are awaiting quarterly results and approaching a point in their investments where they have the right to withdraw their investment.  Assume that L is the maximum decrease in total value of any ABC position that any investor in any of the funds will accept for the quarter without withdrawing their investment; and assume that no trader wants its investors to withdraw.

Assume that based on historical data and current trading volumes, if the current price of ABC stock is P1, then the price after A liquidates a 100 share lot is expected to be P2 = Δ × P1, for some  0 < Δ ≤ 1. Let the number of shares held by A be k × 100; let S be the smallest number of ABC shares held by any one of  T1, T2, …, Tn; and let P be the current price of ABC’s stock.  For any Δ < 1, we can choose k such that . That is, the expected decrease in the smallest position of ABC’s stock held by any of T1, T2, …, Tn as a result of A liquidating her position is greater than the maximum decrease in total value that any investor will accept without withdrawing their investment. Therefore, each of T1, T2, …, Tn will try to sell their positions before A does so, further deteriorating the price of ABC stock. Moreover, each has an incentive to be the first to sell.

Interesting, But That Looks Like A Very Specific Scenario

While catered to fit our current economic context, the root of the problem comes from the interactions between two sets of facts: the group of investors (the Teds) with a contingent investment horizon that could shorten dramatically upon the occurrence of a particular event (if the price of ABC tanks, the Teds’ investment horizons collapse to the present because the investors will want their money back); and the fact that the occurrence of that event is in the control of another party that benefits (or at least believes they will benefit) from its occurrence.

In the example, Ann acts as an individual. In theory and reality, Ann could be an individual or a group of individuals. Ann could be a group of short sellers. Ann could be a large bank that was forced to liquidate its assets. It doesn’t matter. So long as Ann will certainly liquidate a sufficiently large enough position, the Teds will as well.

But Doesn’t The EMH Imply That ABC’s Price Would Go Back Up?

EMH proponents would argue that in the case of such a mass liquidation, white knights will run in and bid the price up again if the underlying equity were truly “worth it.” This must be true on some level, since the number of sales must always equal the number of purchases. However, prices move. And “sell offs” cause prices to fall. This fact cuts to the nature of prices and is beyond the scope of this essay. We simply note that the fire sale dynamic creates its own little race to the bottom: each Ted has an incentive to lower their asking prices given the possibility that another Ted will go even lower.  Thus, the Teds are playing a game where expected utility decreases the longer it takes for them to close a sale. This entire fiasco is a result of the incorporation of relevant price information. That is, the fact that Ann will liquidate is relevant price information, and is therefore incorporated into the Teds’ decision to liquidate.

Straighten Out Your Mind’s Eye

We need to get our epistemology straight before we examine the consequences of what I’ve just outlined. First, the Efficient Market Hypothesis (EMH) is just that, a hypothesis. While there are 3 different flavors, the general idea is that all available information is quickly incorporated into the price of a stock in the world’s most developed stock markets. This hypothesis was then tested with empirical research. Whatever your opinion on how well the research actually tested that hypothesis, just assume for our purposes that the research conducted to date did test the hypothesis, and failed to prove it false.

Even if we assume that the EMH is supported by empirical evidence, its name is still a misnomer. While it does assume that information is observed and then quickly incorporated into the price of a stock, that process does not fit nicely into any well accepted notion of efficiency. For the EMH does not treat information as a good to be efficiently allocated. It boldly assumes that information is automatically available and incorporated to the maximum extent: to the point where no one could create an opportunity for arbitrage through the use of any information. This assumption is in and of itself puzzling and undermines the notion that information has value, which it clearly does. So, I prefer to think of pricing, which includes the incorporation of available price-information, as anterior to efficiency. That is, if assets are accurately priced, then resources will be allocated efficiently among those assets. This allows us to separate the EMH itself (the informational aspect) from its implications (efficiency). So, the EMH implies that the equity prices of companies trading in the most advanced capital markets will accurately reflect all available information, and that therefore capital will be distributed efficiently within those markets.

So How Is That Inefficient?

Good Question. As discussed earlier, the main purpose of assuming the EMH is true is to convince us that the markets distribute capital efficiently. (The observation and incorporation of information is itself interesting and important, but the goal is to allocate goods based on that information). While there are competing definitions of efficiency, the general gist is that a market is said to distribute capital efficiently if there’s no better way to distribute capital than the distribution created by the market: there might be other distributions that are just as good, but no distribution is better. “Good” and “better” are clearly imprecise terms, and we should have some definition of utility that we seek to maximize in the capital markets. However, the outcome of the Ann and Ted scenario is sub optimal under any reasonable definition of utility.

The purpose of the capital markets is to distribute capital to companies. The EMH takes as one of its corollaries that this distribution is efficient. However, as demonstrated above, the separation of control over an event and contingent investment horizons keyed to that event can lead to changes in equity prices that have nothing to do with the financial health of the underlying company. The result is that a company that becomes subject to such a situation will have a higher of cost raising capital through equity.

Q.E.D.

Assume that the state of affairs before the ABC sell off was efficient. We assume that when all other variables are fixed, there is only one efficient cost of equity capital for any company. Therefore, all variables other than the sell off being fixed, because ABC’s cost of equity capital has deviated from an efficient level, the state of affairs after the sell off must be inefficient. So, something else must have changed if the state of affairs after the sell off is to be efficient. In theory, this is entirely possible. In reality, however, given that panic sales usually go to cash or cash equivalents, it is not likely. Thus, theory agrees with common sense: even if the EMH is true, panic sales are still possible and lead to inefficient results. That is, whether or not the timely observation and incorporation of relevant price-information is a necessary condition for efficient allocation of capital, it is not a sufficient condition.