# 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.

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.

# The Not So Efficient Market (Theorem) Hypothesis

#### Are Capital Markets Efficient?

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

#### But How Would We Do That?

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

#### The Sound And The Fury

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

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

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

#### Interesting, But That Looks Like A Very Specific Scenario

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

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

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

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

#### Straighten Out Your Mind’s Eye

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

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

#### So How Is That Inefficient?

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

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

#### Q.E.D.

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