# 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.

[IMAGES REMOVED BY UST; SEE REPORT LINK BELOW]

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.

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

# 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.

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. # 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.

#### 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.”

# Synthetic CDOs Demystified

#### Synthetic Debt

Before we can understand how a synthetic CDO works, we must understand how credit default swaps create synthetic exposure to credit risk. Let’s begin with an example. Assume that D sold protection on $100 worth of ABC bonds through a CDS. Assume that on the day that the CDS becomes effective, D takes$100 of his own capital and invests it in risk-free bonds, e.g., U.S. Treasuries (in reality Treasuries are not risk-free, but if they go, we all go). Assume that the annual interest rate paid on these Treasuries is R. Further, assume that the annualized swap fee is F. It follows that so long as a default does not occur, D’s annual income from the Treasuries and the CDS will be I = $100 x (R + F) until the CDS expires. If there is a default, D will have to payout$100 but will have received some multiple of I over the life of the agreement prior to default.

So, D sets aside $100 and receives the risk free rate plus a spread in exchange. If ABC defaults, D loses$100. If ABC doesn’t default, D keeps $100 plus the income from the Treasuries and the swap fee. Thus, the cash flows from the CDS/Treasuries package look remarkably similar to the cash flows from$100 worth of ABC bonds. As a result, we say that D is synthetically exposed to ABC credit risk.

But what if D doesn’t want this exposure? Well, we know that he could go out to the CDS market and buy protection, thereby hedging his position. But let’s say he’s tired of that old trick and wants to try something new. Well, he could issue synthetic ABC bonds. How? D receives $100 from investors in exchange for promising to: pay them interest annually in the amount of $100 \cdot (R + F - \Delta)$; pay them$100 in principle at the time at which the underlying CDS expires; with both promises conditioned upon the premise that ABC does not trigger an event of default, as that term is defined in the underlying CDS. In short, D has passed the cash flows from the Treasury/CDS package onto investors, in exchange for pocketing a fee ($\Delta$). As noted above, the cash flows from this package are very similar to the cash flows received from ABC bonds. As a result, we call the notes issued by D synthetic bonds.

#### Synthetic CDOs

In reality, if D is a swap dealer, D probably sold protection on more than just ABC bonds. Let’s say that D sold protection on k different entities, $E_1, ... , E_k$, where the notional amount of protection sold on each is $n_1, ..., n_k$ and the total notional amount is $N = \sum_{i=1}^k n_i$. Rather than maintain exposure to all of these swaps, D could pass the exposure onto investors by issuing notes keyed to the performance of the swaps. The transaction that facilitates this is called a synthetic collateralized debt obligation or synthetic CDO for short. There are many transactions that could be categorized fairly as a synthetic CDO, and these transactions can be quite complex. However, we will explore only a very basic example for illustrative purposes.

So, after selling protection to the swap market as described above, D asks investors for a total of $N$ dollars. D sets up an SPV, funds it with the money from the investors, and buys $n_i$ dollars worth of protection on $E_i$ for each $i \leq k$ from the SPV. That is, D hedges all of his positions with the SPV. The SPV takes the money from the investors and invests it. For simplicity’s sake, assume that the SPV invests in the same Treasuries mentioned above. The SPV then issues notes that promise to:  pay investors their share of $N - L$ dollars after all underlying swaps have expired, where L is the total notional amount of protection sold by the SPV on entities that triggered an event of default; and pay investors their share of annual interest, in amount equal to $(R + F - \Delta) \cdot (N - L)$, where $F$ is the sum of all swap fees received by D.

So, if every entity on which the SPV sold protection defaults, the investors get no principle back, but may have earned some interest depending on when the defaults occurred. If none of the entities default, then the investors get all of their principle back plus interest. So each investor has synthetic exposure to a basket of synthetic bonds. That is, if any single synthetic bond defaults, they still receive money. Thus, the process allows investors to achieve exposure to a broad base of credit risk, something that would be very difficult and expensive to do in the bond market.

# A Conceptual Framework For Analyzing Systemic Risk

#### The Cart Before The Horse

There has been a lot of chatter about the systemic risks posed by derivatives, particularly credit default swaps. Rather than offer any formal method of evaluating an enormously complicated question, pundits wield exclamation points and false inferences to distract from the glaring holes in their logic. Below I will not offer any definite answers to any questions about the systemic risks posed by derivatives. Rather, I will describe what I think is a reasonable and useful framework for analyzing systemic risks posed by derivatives. Unfortunately for some, this will involve the use of mathematics. And while the math used is fairly elementary, the concepts are not. This is especially true of the last section. That said, even if you do not fully understand the entirety of this article, one thing should be clear: questions about systemic risk are complex and anyone who gives declarative answers to such questions is almost certain to have no idea what they are talking about.

#### Risk Magnification And Syndication

As discussed here, derivatives operate by creating and allocating risks that did not exist before the two parties entered into the transaction. That is an unavoidable fact. Moreover, there is no physical limit to the notional amount of any given contract or the number of derivative contracts that parties can enter into. It is entirely up to them. That said, derivatives can be used to negate risks that parties were already exposed to in exchange for assuming other risks, thereby acting as a risk-switching/risk-transferring device. So, a corollary of these observations is that derivatives could be used to create unlimited amounts of risk but through that risk creation they could be used to negate an unlimited amount of risk that parties are already exposed to and thereby effectively “transfer” an unlimited amount of risk to those willing to be exposed to it.

Practically speaking, there is a limit to the amount of risk that can be created using derivatives. This limit exists for a very simple reason: the contracts are voluntary, and so if no one is willing to be exposed to a particular risk, it will not be created and assigned through a derivative. Like most market participants, derivatives traders are not in engaged in an altruistic endeavor. As a result, we should not expect them to engage in activities that they don’t expect to be profitable. Therefore, we can be reasonably certain that the derivatives market will create only as much risk as its participants expect to be profitable. Whether their expectations are correct is an entirely different matter, and any criticism on that front is not unique to derivatives traders. Rather, the problem of flawed expectations permeates all of human decision making.

Even if we ignore the practical limits to the creation of risk, derivatives allow for unlimited syndication of risk. That is, there is no smallest unit of risk that can be transferred. Consequently, any fixed amount of risk can be syndicated out to an arbitrarily large number of parties, thereby minimizing the probability that any individual market participant will fail as a result of that risk.

Finally, we should ask ourselves, what does the term systemic risk even mean? The only thing it can mean in the context of derivatives is that the obligations created by two parties will have an effect on at least one other third party. So, even assuming that derivatives create such a “problem,” how is this “problem” any different than that created by a landlord who plans to pay a contractor with the rent he receives from his tenants? It is not.

#### A Closer Look At Risk

As stated here, my own view is that risk is a concept that has two components: (i) the occurrence of an event and (ii) a magnitude associated with that event. This allows us to ask two questions: What is the probability of the event occurring? And if it occurs, what is the expected value of its associated magnitude? We say that P is exposed to a given risk if P expects to incur a gain/loss if the risk-event occurs. As is evident, under this rubric, that whole conversation above was grossly imprecise. But that’s ok. Its import is clear enough. From here on, however, we will tolerate no such imprecision.

#### Identifying And Defining Risks

Using the definition above, let’s try to define one of the risks that all parties who sold protection on ABC’s series I bonds through a CDS that calls for physical delivery are exposed to. This will allow us to begin to understand the systemic risk that such credit default swaps create. There is no hard rule about how to go about doing this. If we do a poor job of identifying and defining the relevant risks, we will have a poor understanding of those relevant risks. However, common sense tells us that any protection seller’s risk exposure is going to have something to do with triggering a payout under a CDS. So, let’s define the risk-event as any default on ABC series I bonds. For simplicities sake, let’s limit our definition of default to ABC’s failure to pay interest or principle. So, our risk-event is: ABC fails to pay interest or principle on any of its bonds. But what is our risk-magnitude? Since we are trying to define a risk that protection sellers are exposed to, our associated magnitude should be the basis upon which all payments by protection sellers are made. So, we will define the risk-magnitude as $M=1 - \frac{P_d}{P}$ where $P_d$ is the price of an ABC series I bond after the risk-event (default) occurs and $P$ is the par value of an ABC series I bond. For example, if ABC’s series I bonds are trading at 30 cents on the dollar after default, $M = .7$ and a protection seller would have to payout 70 cents for every dollar of notional amount. The amount that bonds trade at after a default is called the recovery value.

#### One Man’s Garbage Is Another Man’s Glory

When one party to a derivative makes a payment, the other receives it. That seems simple enough. But it follows that if we consider only those payments made under the derivative contract itself, the net position of the two parties is unchanged over the life of the agreement. That is, derivatives create zero-sum games and simply shift and reallocate money that already existed between the two parties. So in continuing with our example above, it follows that we’ve also defined a risk that buyers of protection on ABC series I bonds are exposed to. However, protection buyers have positive exposure to that risk. That is, if ABC defaults, protection buyers receive money.

#### Exposure To Risk And Settlement Flow Analysis

If our concept of exposure is to have any real economic significance, it must take into account the concept of netting. So, we define the exposure of $P_i$ to the risk-event defined above as the product of (i) the net notional amount of all credit default swaps naming ABC series I bonds as a reference obligation to which $P_i$ is a counterparty, which we will call $N_i$, and (ii) $M$. The net notional amount is simply the difference between the total notional amount of protection bought and the total notional amount of protection sold by $P_i$. So, if $P_i$ is a net seller of protection, $N_i$ will be negative and therefore its exposure, $N_i \cdot M$, will be either negative or zero.

Because the payments between the two counterparties of each derivative net to zero, it follows that the sum of all net notional amounts is always zero. That is, if there are $k$ market participants, $\sum_{i=1}^kN_i = 0$. The total notional amount of the entire market is given by $N_T = \frac{1}{2} \sum_{i=1}^k|N_i|$. This is the figure that is most often reported by the media. As is evident, it is impossible to determine the economic significance of this number without first knowing the structure of the market. That is, we must know how much is owed and to whom. However, after we have this information, we can choose different recovery values and then calculate each party’s exposure. This would enable us to determine how much cash each participant would have to set aside for a default at various recovery values (simply calculate each party’s exposure at the various recovery values).

Let’s consider a concrete example. In the diagram below, an edge coming from a participant represents protection sold by that participant and consequently an incoming edge represents protection bought by that participant. The amounts written beside these edges represent the notional amount of protection bought/sold. The amounts written beside the nodes represent the net notional amounts.

In the example above, D is a dealer and his net notional amount is zero, and therefore his exposure to the risk-event is $0 \cdot M = 0$ . As is evident, we can vary the recovery value to determine what each market participant’s exposure would be in that case. We could then consider other risk-events that occur in conjunction with any given risk-event. For example, we could consider the conjunctive risk-event “ABC defaults and B fails to pay under any CDS” (in which case D’s exposure would not be zero) or any other variation that addresses meaningful concerns. For now, we will focus on our single event risk for explanatory purposes. But even if we restrict ourselves to single event risks, there’s more to a CDS than just default. Collateral will move through the above system dynamically throughout the lives of the contracts. In order to understand how we can analyze the systemic risks posed by the dynamic shifting of collateral, we must first examine what it is that causes collateral to be posted under a CDS.

#### We’re In The Money

CDS contracts come in and out of the money to a party based on the price of protection. If a party is out of money, the typical market practice is to require that party to post collateral. For example, if I bought protection at a price of 50bp, and suddenly the price jumps to 100bp, I’m in the money and my counterparty is out of the money. Thus, my counterparty will be required to post collateral. We can view the price of protection as providing an implied probability of default. Exactly how this is done is not important. But it should be clear that there is a connection between the cost of protecting debt and the probability of default on that debt (the higher the probability the higher the cost). Thus, as the implied probability of default changes over the life of the agreement, collateral will change hands.

#### Collateral Flow Analysis

In the previous sections, we assumed that the risk-event was certain to occur and then calculated the exposures based on an assumed recovery value. So, in effect, we were asking “what happens when parties settle their contracts at a given recovery value?” But what if we want to consider what happens before any default actually occurs? That is, what if we want to consider “what happens if the probability of default is $p$?” Because collateral will be posted as the price of protection changes over the life of the agreement and the price of protection provides an implied probability of default, it follows that the answer to this question should have something to do with the flow of collateral.

Continuing with the ABC bond example above, we can examine how collateral will move through the system by asking two questions: (i) what is the implied probability of the risk-event (ABC’s default) occurring and (ii) what is the expected value of the risk-magnitude (the basis upon which collateral payments are made). As discussed above, the implied probability of default will change over the life of the agreement, which will in turn affect the flow of collateral in the system. Since our goal in this section is to test the system’s behavior at different implied probabilities of default, the expected value of our risk-magnitude should be a function of an assumed implied probability of default. So, we define the expected value of our risk-magnitude as $M_e = p^* \cdot M$ where $p^*$ is our assumed implied probability of default and $M$ is defined as it is above. It follows that this analysis will break CDS contracts into categories according to the price at which they were entered into. That is, you can’t ask how much something changed without first knowing what it was to begin with.

Assume that $P_i$ entered into CDS contracts at $m_i$ different prices. For example, he entered into four contracts at 20 bp and eight contracts at 50bp, and no others. In this case, $m_i = 2$. For each $P_i$, assign an arbitrary ordering, $(c_{i,1}, ... , c_{i,m_i})$, to the sets of contracts that were entered into at different prices by $P_i$. In the example where $m_i = 2$, we could let $c_{i,1}$ be the set of eight contracts entered into at 50bp and let $c_{i,2}$ be the set of four contracts entered into at 20 bp. Each of these sets will have a net notional amount and an implied probability of default (since each is categorized by price). Define $n_{i,j}$ as the net notional amount of the contracts in $c_{i,j}$ and $p_{i,j}$ as the implied probability of default of the contracts in $c_{i,j}$ for each $1 \leq j \leq m_i$. We define the expected exposure of $P_i$ as:

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

Note that when $p^* = 1$,

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

That is, this is a generalized version of the settlement analysis above, and when we assume that default is certain, collateral flow analysis reduces to settlement flow analysis.

#### So What Does That Awful Formula Tell Us?

A participant’s expected exposure is a reasonable estimate for the amount of collateral that will be posted or received by that participant at an assumed implied probability of default. The exact amount of collateral that will be posted or received under any contract will be determined by the terms of that contract. As a result, our model is approximate and not exact. However, the direction that collateral moves in our model is exact. That is, if a party’s expected exposure is negative, it will not receive collateral, and if it is positive, it will not post collateral. It also shows that even if a party is completely hedged in the event of a default, it is possible that it is not completely hedged to posting collateral. That is, even if it bought and sold the same notional amount of protection, it could have done so at different prices.

# Securitization Demystified

#### What Is Securitization?

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

#### Cui Bono?

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

#### The Nuts And Bolts

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

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

#### So What Does That Accomplish?

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