distressed market

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

/ erdosfan / 15 Comments

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.

sym-exposure2

If E did occur, then B would pay N \cdot(1 - F) 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 N\cdot F. 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 \frac{1}{2}, then A will accept any fee less than .5 since A’s subjective expected payout under that assumption is N (\frac{1}{2}(1 - F) - \frac{1}{2}F ) = N (\frac{1}{2} - F). If B thinks that E will occur with a probability of \frac {1}{4}, then B will accept any fee greater than .25 since his expected payout is N (\frac{3}{4} F - \frac{1}{4}(1 - F)) = N (F - \frac{1}{4} ). 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 p_A and p_B respectively. If A has positive exposure and B has negative, then in general the subjective expected payouts for A and B are N (p_A - F) and N ( F - p_B) respectively. If we plot the expected payout as a function of F, we get the following:

payout-v-fee4

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.

Mark To No Market Accounting

/ erdosfan / 4 Comments

The Meaning Of It All

In this article I explore an oft discussed topic: mark to market accounting. I will not come down on either side of the debate. Rather, I will try to make sense of the implications and assumptions of mark to market accounting. But before we can explore the world of mark to market accounting, we must understand the economic significance of the data reported under accounting regimes in general. And in order to do that, we must have a practical concept of economic loss/gain.

What Is Economic Loss?

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

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

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

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

A Truly Human Story

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

Truth In Numbers

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

Mark to Market Accounting

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

Market Prices And Expected Value

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

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

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

The Takeaway

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