The Reality Of Mortgage Modification

Also published on the Atlantic Monthly’s Business Channel.

Why A Decline In Home Prices Should Not Cause Defaults

It seems that we have taken as an axiom the idea that if the price of a home drops below the face value of the mortgage, the borrower will default on the mortgage. That sounds like a good rule, since it’s got prices dropping and people defaulting at the same time, so there’s a certain intuitive appeal to it. But in reality, it makes no sense. Either the borrower can afford the mortgage based on her income alone or not.  However, it does make sense if you also assume that the borrower intended to access the equity in her home before the maturity of the mortgage. That is, the home owner bought the home with the intention of either i) selling the home for a profit before maturity or ii) refinancing the mortgage at a higher principle amount.

If neither of these are true, then why would a homeowner default simply because the home they lived in dropped in value? She wouldn’t. She might be irritated that she paid too much for a home. Additionally, she might experience a diminution in her perception of her own wealth, which may change her consumption habits. But the fact remains that at the time of purchase, she thought her home was worth X. And she agreed to a clearly defined schedule of monthly payments over the life of the mortgage assuming a price of X. The fact that the value of her home suddenly drops below X has no impact on her ability to pay, unless she planned to access equity in the home to satisfy her payment obligations.  Annoyed as she might be, she could continue to make her mortgage payments as promised.  Thus, those mortgages which default due to a drop in home prices are the result of a failed attempt to access equity in the home, otherwise known as failed speculation.

In short, if a home drops in value, it does not affect the cash flows of the occupants so long as no one plans to access equity in the home. And so, the ability of a household to pay a mortgage is unaffected in that situation. This is in contrast to being fired, having a primary earner die, or divorce. These events have a direct impact on the ability of a household to pay its mortgage.

I am unaware of any proposal to date which offers assistance to households in need under such circumstances.

The Dismal Science Of Mortgage Modification

Simply put, available evidence suggests that mortgage modifications do not work.


The charts above are from a study conducted by the Office Of the Comptroller of the Currency. The full text is available here. As the charts above demonstrate, within 8 months, just under 60% of modified mortgages redefault. That is, the borrowers default under the modified agreement. If we look only at Subprime mortgages, just over 65% of modified mortgages redefault within 8 months. This may come as a surprise to some. But in my mind, it reaffirms the theory that many borrowers bought homes relying on their ability to i) sell the home for a profit or ii) refinance their mortgage. That is, it reaffirms the theory that many borrowers were unable to afford the homes they bought using their income alone, and were actually speculating that the value of their home would increase.

Morally Hazardous And Theoretically Dubious

Why should mortgages be adjusted at all? Well, one obvious reason to modify is that the terms of the mortgages are somehow unfair. That’s a fine reason. But when did they become unfair? Were they unfair from the outset? That seems unlikely given that both the borrower and the lender voluntarily agree to the terms of a mortgage. Although people like to fuss about option arm mortgages and the like, the reality is, it’s not that hard for a borrower to understand that her payments will increase at some point in the future. Either she can afford the increased payments or not. This will be clear from the outset of the mortgage.

So, it doesn’t seem like there’s much of a case for unfairness at the outset of the agreement. Well then, did the mortgage become unfair? Maybe. If so, since the terms didn’t change, it must be because the home dropped in value and therefore the borrower is now paying above the market price for the home. That does sound unfortunate. But who should bear the loss? Should the bank? The tax payer? How about the borrower? Well, the borrower explicitly agreed to bear the loss when she agreed to repay a fixed amount of money. That is, the borrower promised “to pay back X plus interest within 30 years.” This is in contrast to “I promise to pay back X plus interest within 30 years, unless the price of my home drops below X, in which case we’ll work something out.” Both are fine agreements. But the former is what borrowers actually agree to.

Not enforcing voluntary agreements leads to uncertainty. Uncertainty leads to inefficiency. This is because those who have agreements outstanding or would like to enter into other agreements cannot rely on the terms of those agreements. And so the value of such agreements decreases and the whole purpose of contracting is defeated. In a less abstract sense, uncertainty creates an environment in which it is impossible to plan and conduct business. As a result, this type of regulatory behavior undermines the availability of credit.

But even if we do not accept that voluntary agreements should be enforced for reasons of efficiency, mortgages represent some of the most clear and unambiguous promises to repay an obligation imaginable. The fact that a borrower was betting that home prices would rise should not excuse them from their obligations. There are some situations where human decency and compassion could justify a readjustment of terms and socializing the resultant losses. For example, the death of a primary earner or an act of war or terrorism. But making a bad guess about future home prices is not an act that warrants anyone’s sympathy, let alone the socialization of the losses that follow.

The Elephant In The Room

This notion that Subprime borrowers were victimized as a result of some fraudulent wizardry perpetuated by Wall Street is utter nonsense. Whether securitized assets performed as promised to investors is Wall Street’s problem. Whether people pay their mortgages falls squarely on the shoulder of the borrower. Despite this, we are spending billions of public dollars, at a time when money is scarce and desperately needed, on a program that i) is demonstrably ineffective at achieving its stated goals (helping homeowners avoid foreclosure) and ii) rewards poor decision making and imprudent borrowing. Given the gravity of the moment, a greater failure is difficult to imagine. But then again, we live in uncertain times, so my imagination might prove inadequate.


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.

path_of_fundsDepending 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 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:


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.

Synthetic CDOs, Ratings, And Super Senior Tranches: Part 1

Super Senioritis

I’ve been perusing the finance blogs lately and I’ve noticed a recent obsession with Synthetic CDOs, specifically the super senior tranches of these transactions. And so I felt it was necessary for me to chime in on the debate, by applying my usual toast-dry analysis to Synthetic CDOs for the second time. This is a huge topic that requires consideration of how Synthetic CDOs function, how they’re rated, and how tranches distribute risk among investors. As a result, I’ve decided to break the article into two parts. This first part deals with the basics of rating the assets contained in CDOs. The next will examine the application of ratings to tranches of CDOs, how that translates into the world of synthetic CDOs, and ultimately, culminate in a discussion of what are known as “super senior tranches.”

Required Reading

You are likely to struggle greatly with this article unless you have some familiarity with Synthetic CDOs. And because I am an unabashed self-promoter, I highly recommend you read my introductory article on Synthetic CDOs and my article on Tranches. If you’re going to read only one, then read the one on tranches.

Tranches And Structured Products

Payment waterfalls allow the risks of an investment to be allocated among different groups of investors, or tranches. For example, in the case of Mortgage Backed Securities, a fixed amount of prepayment risk can be allocated to one tranche by tailoring the rules in the payment waterfall to pass all prepayments of principal to that tranche. But there are risks beyond prepayment risk. One obvious example is default risk. In the MBS world, this is the risk that because of defaults in the underlying mortgages the cash flows from the mortgages backing the notes will be inadequate to make payments on those notes. Obviously, default risk will be a primary concern of any investor. The risk that you will not get paid is arguably paramount to all others. So, payment waterfalls have been developed to address this risk and tailor the distribution of default risk in a way that allows each investor to assume a desired default risk level. But before we can understand how investors distinguish between these different levels of default risk, we must understand how rating systems describe these different levels.

Rating Systems And Rating Agencies

You have undoubtedly heard terms such as “AAA rated” and “AA rated” thrown somewhere near names like S&P and Moody’s. It’s not necessary to become familiar with the peculiarities of each rating agency’s system to appreciate the general idea: the ranking of default risk. That is, the market wants a short-hand system that both describes the probability of default for a particular financial product and can be compared across a disparate class of financial products. So, rating agencies developed models and systems of ratings (using confusingly similar labels like “AAA,” “Baa,” etc.) that purport to do just that.

How CDO Ratings Work

Part 1: Past Performance And Correlation

The models that rating agencies use to produce their ratings are backward looking. That is, the first step in the process is to accumulate data about how financial products have behaved in the past. Rating agencies, and investors, will look to the past and produce charts like this:


They will note that in the past, of all bonds that Moody’s deemed Aaa, less than 1% of such bonds defaulted within 10 years of issuance. People then assume, quite reasonably, that this data provides probabilities of default across time for the various ratings. That is, they assume that if we wish to know the probability that a B rated bond will default in year three, we simply look to the above chart and discover that it is .1977 or 19.77%. Examination of this assumption is beyond the scope of this article. But for a great article on that topic (containing the above table and more!) go here.

A CDO is in essence a portfolio of bonds. So in order to model the cash flows of the portfolio, rating agencies turn to charts like the one above and examine the past performance of bonds similar to those in the portfolio. They also look at the correlation of default between the bonds in the CDO portfolio. Correlation, in this context, is a very precise term. And it’s impossible to do justice to the concept in a few sentences. That said, in layman’s terms, when considering the correlation of default between two bonds, rating agencies are looking for a connection between the bonds defaulting. That is, if bond 1 defaults, how does that change our expectation of the probability that bond 2 will default? Exactly how this is done is also well beyond the scope of this article. For those of you who are interested, you can read all about this and more here.

Part 2: Scenario Analysis

So after we have all of our data, we can begin to construct a chart of how likely a given level of loss is. This is done through scenario analysis. That is, the models are run hundreds of thousands of times (and possibly more) using different inputs. In each of these simulations, some bonds might “default.” That is, the model predicts that given a particular set of inputs, certain bonds will default. After each of these simulations, an amount of loss will be calculated, which is based on the estimated recovery values for the bonds in the pool that “defaulted” during that particular simulation. We can then ask, out of all of the simulations, how many times did the loss go above X? So if we ran our simulation 500,000 times, and if the loss was greater than $1 million in only 5,000 of these simulations, then we could say that the probability of the loss being greater than $1 million is .01, or 1%.


Tranches And Risk

What Is A Tranche?

Tranche is a French word that means slice. Every investment will convey certain rights in the cash flows produced by the investment to the investors. A tranche is a slice of those rights. Quite literally, each tranche represents a unique piece of the investment pie. So the term tranche connotes a fairly accurate indication of how the term is used in finance. And after all, it’s easier to tell investors that they’re buying tranches as opposed to “pits” or “buckets.”

Payment Waterfalls

A payment waterfall determines who gets paid what and when. That is, each dollar produced by an investment will be “pushed through” a payment waterfall and allocated according to the rules in the payment waterfall. For example, assume that there are 3 investors, A, B and C. They collectively invest in venture X. The payment waterfall for X is defined as follows: on the first of each month, A will be paid the lesser of (i) $100 and (ii) all of the cash flows produced by X in the previous month; B will be paid the lesser of (i) $100 and (ii) all of the cash flows produced by X in the previous month less any amounts paid to A; and C will be paid the lesser of (i) $100 and (ii) all of the cash flows produced by X in the previous month less any amounts paid to A and B.

Assume that in month 1, X produced $300 in cash. On the first day of month 2, the $300 will be pushed through the waterfall. So A will get $100; B will get $100; and C will get $100. Note that in the case of C, the two choices will produce equal amounts, so the term “lessor of” isn’t technically accurate. But assume that when the choice is between equal amounts, we simply pay that amount. Now assume that X produced $150 in month 1. On the first day of month 2, the $150 will be pushed through the waterfall. So A will get $100; B will get $50; and C will get $0. Because A is “first” to get paid, so long as X produces $100 per month, A is fully paid. B is fully paid so long as X produces $200 per month and C at $300 per month. So in this case, A’s tranche is said to be the least risky of the 3 tranches, with B and C being more risky in that order. Note that I am not using my technical definition of risk.

So why would C agree to be last in the pecking order? Well, one simple explanation is that C paid the least for his tranche. In another example we could have given C the right to any amounts left over each month after all other tranches are paid. This type of right is called a residual right. It is basically an equity stake. So in that case C would bear the risk that X’s cash flows will fall short in exchange for the right to acquire any excess cash flows produced by X. As is evident, the terms of the waterfall can be anything that the parties agree to. As such, we can cater the payment priorities to meet the specific desires of investors and distribute risks accordingly.

Mortgage Backed Securities And Prepayment Risk

Securitization is a fairly simple process to grasp in the abstract. In reality, turning thousands of mortgages into interest bearing notes is not a simple process. However, we can at least begin to understand the process by considering how a payment waterfall can be used to streamline the payments to investors. Viewed as a bond, a mortgage is a bond where the borrower, in this case the mortgagor, has a right to call the bond at any point in time. That is, at any point in time, a mortgagor can simply repay the full amount owed and terminate the lending agreement. Additionally, even if the mortgagor doesn’t pay the full amount owed, it is free to pay more than the amount obligated under the mortgage and allocate any additional amounts to the outstanding principal on the mortgage. For example, if A has a mortgage where A is obligated to make monthly payments of $100, A could pay $150 in a particular month, and request that the lender allocate the additional $50 to reduce the outstanding principal on the mortgage.

The typical practice for a mortgage is to require the mortgagor to make fixed payments over the life of the mortgage. So each payment will consist of an interest portion and a principal portion. The amount allocated to principal is predetermined and said to amortize over the life of the mortgage. And as mentioned above, any amount over the fixed amount can be allocated to principal at the option of the mortgagor. The risk that any given loan will pay an amount above the required fixed payment is called prepayment risk.

While getting your money back is usually a good thing, investors prefer to defer repayment to some future date in exchange for receiving more money than they invested. So getting all of their principal back today is not the most preferred outcome. They prefer to get their principal at maturity plus interest over the life of the agreement. For example, if all of the mortgages in a pool of mortgages that have been securitized prepay the full amount before the anticipated maturity date of the notes, then the investors will presumably be repaid, but will not receive the remaining interest payments over the anticipated life of the notes. If this prepayment en masse occurs on the second day of the life of the notes, it would defeat the purpose of the investment.

Prepayment Risk And Payment Waterfalls

We can use payment waterfalls to distribute prepayment risk into different tranches. In reality, this can become a mind numbingly complex endeavor. We propose one simple example to demonstrate how tranches can be used to redistribute complex risks.

Assume that our mortgage pool consists of N mortgages; the remaining principal on each mortgage is p_i; and the total remaining principal on the pool is P = p_1 + \cdots + p_N. Because each mortgage payment consists of some interest and some principal, each month, there will be a scheduled reduction in the outstanding total principal on the pool. Let S denote the scheduled reduction of P. That is, S is the sum of all of the principal portions of the fixed payments to be made in the pool. If there are any prepayments in the underlying mortgages, the actual reduction in P will exceed the scheduled reduction. Let A denote the actual reduction in P. The question now becomes, what do we do with A - S? That is, how do we distribute the amount by which the actual reduction in total principal exceeds the scheduled reduction? The simple answer, and the one considered here, is to push the entire prepayment amount onto one tranche, and reduce the outstanding principal on that tranche by that same amount.

For example, assume that a mortgage pool contains mortgages with a total $100 million principal outstanding and that $100 million worth of notes were issued against that pool. Further, assume that there are two tranches of notes: the A series and B series, with $50 million face value of each outstanding. For simplicity’s sake, assume the notes pay interest monthly. On any interest payment date, we could pay the B series the entire prepayment amount A - S and reduce the face value on the B series notes by A - S. For example, if on the first interest payment date, A - S = $10 million, then we would pay the $10 million to the B series note holders and reduce the face value on the B series to $40 million. Thus, any prepayment amount less than or equal to $50 million will be completely absorbed by the B series note holders. So the net effect is to cushion the A series against a certain amount of prepayment risk. The B series note holders will likely demand something in return for bearing this risk.

You’re Trespassing On My Credit Event

Insurable Interests

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

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

Courting Disaster

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

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

You Sunk My Battleship

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

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

Hands Off My Ether

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

Mark To No Market Accounting

The Meaning Of It All

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

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.”