Credit Default Swaps And Mortgage Backed Securities

February 2, 2009March 11, 2019 / erdosfan / 11 Comments

Like Your Grandsire In Alibaster

In this article, I will apply my usual dispassionate analysis to the role that credit default swaps play in the world of Mortgage Backed Securities (MBSs). We will take a brief look at the interactions between the issuance of mortgages, MBSs, and how the concept of loss plays out in the context of derivatives and mortgages. Then we will explore how the expectations of the parties to a lender/borrower relationship differ from that of a protection seller/buyer relationship and how credit default swaps, by allowing markets to express a negative view of mortgage default risk, facilitate price correction and mitigate net losses. This is done by applying the concepts in my previous article, The Demand For Risk And A Macroeconomic Theory of Credit Default Swaps: Part 2, to the context of credit default swaps on MBSs. This article can be considered a more concrete application of the concepts in that article, which will hopefully clear up some of the confusion in that article’s comment section.

The Path Of Funds In the MBS Market

Mortgage backed securities allow investors to gain exposure to the housing market by taking on credit risk linked to a pool of mortgages. Although the underlying mortgages are originated by banks, the existence of investor demand for MBSs allows the originators to effectively pass the mortgages off to the investors and pocket a fee. Thus, the greater the demand for MBSs, the greater the total value of mortgages that originators will issue and ultimately pass off to investors. So, the originators might front the money for the mortgages in many cases, but the effective path of funds is from the investors, to the originators, and onto the borrower. As a result, investors in MBSs are the effective lenders in this arrangement, since they bear the credit risk of the mortgages.

This market structure also has an effect on the interest rates charged on the underlying mortgages. As investor demand for MBSs increases, the amount of cash available for mortgages will increase, pushing the interest rates charged on the underlying mortgages down as originators compete for borrowers.

Loss In The Context Of Derivatives And Mortgages

I often note that derivatives cannot create net losses in an economy. That is, they simply transfer money between two parties. If one party loses X, the other gains X, so the net loss between the two parties is zero. For more on this, go here. This is not the case with a mortgage. The lender gives money to the borrower, who then spends this money on a home. Assume that a lender and borrower entered into a mortgage and that before maturity the value of the home falls, prompting the borrower to default on its mortgage. Further assume that the lender forecloses on the property, selling it at a loss. Since the buyer receives none of the foreclosure proceeds, the buyer can be viewed as either neutral or incurring a loss, since at least some of the borrower’s mortgage payments went towards equity ownership and not just occupancy. It follows that there is a loss to the lender and either no change in or a loss to the borrower and therefore a net loss. This demonstrates what we have all recently learned: poorly underwritten mortgages can create net losses.

Net Losses And Efficiency

You can argue that even in the case that both parties to an agreement incur losses, the net loss to the economy is zero, since the cash transferred under the agreement was not destroyed but merely moved through the economy to market participants that are not a party to the agreement. That is, if you expand the number of parties to a sufficient degree, all transactions will net to zero. While this must be the case, it misses an essential point: I am using net losses to bilateral agreements as a proxy for inefficient allocation of capital. That is, both parties expected to benefit from the agreement, yet both lost money, which implies that neither benefited from the agreement. For example, in the case of a mortgage, the borrower expects to pay off the mortgage but benefit from the use and eventual ownership or sale of the home. The lender expects to profit from the interest paid on the mortgage. When both of these expectations fail, I take this as implying that the initial agreement was an inefficient allocation of capital. This might not always be the case and depends on how you define efficiency. But as a general rule, it is my opinion that net losses to a bilateral agreement are a reasonable proxy for inefficient allocation of capital.

Expectations Of Lender/Borrower vs. Protection Seller/Buyer

As mentioned above, under a mortgage, the lender expects to benefit from the interest paid on the mortgage while the borrower expects to benefit from the use and eventual ownership or sale of the home. Implicit in the expectations of both parties is that the mortgage will be repaid. Economically, the lender is long on the mortgage. That is, the lender gains if the mortgage is fully repaid. Although application of the concepts of long and short to the borrower’s position is awkward at best, the borrower is certainly not short on the mortgage. That is, in general, the borrower does not gain if he fails to repay the mortgage. He might however mitigate his losses by defaulting and declaring bankruptcy. That said, the takeaway is that both the lender and the borrower expect the mortgage to be repaid. So, if we consider only lenders and borrowers, there are no participants with a true short position in the market. Thus, price, which in this case is an interest rate, will be determined by participants with similar positive expectations and incentives. Anyone with a negative view of the market has no role to play and therefore no effect on price.

This is not the case with credit default swaps (CDSs) referencing MBSs. In such a CDS, the protection seller is long on the MBS and therefore long on the underlying mortgages, and the protection buyer is short. That is, if the MBS pays out, the protection seller gains on the swap; and if the MBS defaults, the protection buyer gains on the swap. Thus, through the CDS, the two parties express opposing expectations of the performance of the MBS. Thus, the CDS market provides an opportunity to express a negative view of mortgage default risk.

The Effect Of Synthetic Instruments On “Real” Instruments

As mentioned above, the CDS market provides a method of shorting MBSs. But how does that effect the price of MBSs and ultimately interest rates? As described here, the cash flows of any bond, including MBSs, can be synthesized using Treasuries and CDSs. Using this technique, a fully funded synthetic bond consists of the long end of a CDS and a Treasury. The spread that the synthetic instrument pays over the risk free rate is determined by the price of protection that the CDS pays the investor (who in this case is the protection seller). One consequence of this is that there are opportunities for arbitrage between the market for real bonds and CDSs if the two markets don’t reach an equilibrium, removing any opportunity for arbitrage. Because this opportunity for arbitrage is rather obvious, we assume that it cannot persist. That is, as the price of protection on MBSs increases, the spread over the risk free rate paid by MBSs should widen, and visa versa. Thus, as the demand for protection on MBSs increases, we would expect the interest rates paid by MBSs to increase, thereby increasing the interest rates on mortgages. Thus, those with a negative view of MBS default risk can raise the cost of funds on mortgages by buying protection through CDSs on MBSs, thereby inadvertently “correcting” what they view as underpriced default risk.

In addition to the no-obvious-arbitrage argument outlined above, we can consider how the existence of synthetic MBSs affects the supply of comparable investments, and thereby interest rates. As mentioned above, any MBS can be synthesized using CDSs and Treasuries (when the synthetic MBS is unfunded or partially funded, it consists of CDSs and other investments, not Treasuries). Thus, investors will have a choice between investing in real MBSs or synthetic MBSs. And as explained above, the price of each should come to an equilibrium that excludes any opportunity for obvious arbitrage between the two investments. Thus, we would expect at least some investors to be indifferent between the two.

path_of_funds 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.

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

December 18, 2008March 12, 2023 / erdosfan / 15 Comments

A Higher Plane

In this article, I will return to the ideas proposed in my article entitled, “A Conceptual Framework For Analyzing Systemic Risk,” and once again take a macro view of the role that derivatives play in the financial system and the broader economy. In that article, I said the following:

“Practically speaking, there is a limit to the amount of risk that can be created using derivatives. This limit exists for a very simple reason: the contracts are voluntary, and so if no one is willing to be exposed to a particular risk, it will not be created and assigned through a derivative. Like most market participants, derivatives traders are not in engaged in an altruistic endeavor. As a result, we should not expect them to engage in activities that they don’t expect to be profitable. Therefore, we can be reasonably certain that the derivatives market will create only as much risk as its participants expect to be profitable.”

The idea implicit in the above paragraph is that there is a level of demand for exposure to risk. By further formalizing this concept, I will show that if we treat exposure to risk as a good, subject to the observed law of supply and demand, then credit default swaps should not create any more exposure to risk in an economy than would be present otherwise and that credit default swaps should be expected to reduce the net amount of exposure to risk. This first article is devoted to formalizing the concept of the price for exposure to risk and the expected payout of a derivative as a function of that price.

Derivatives And Symmetrical Exposure To Risk

As stated here, my own view is that risk is a concept that has two components: (i) the occurrence of an event and (ii) a magnitude associated with that event. This allows us to ask two questions: What is the probability of the event occurring? And if it occurs, what is the expected value of its associated magnitude? We say that P is exposed to a given risk if P expects to incur a gain/loss if the risk-event occurs. We say that P has positive exposure if P expects to incur a gain if the risk-event occurs; and that P has negative exposure if P expects to incur a loss if the risk-event occurs.

Exposure to any risk assigned through a derivative contract will create positive exposure to that risk for one party and negative exposure for the other. Moreover the magnitudes of each party’s exposure will be equal in absolute value. This is a consequence of the fact that derivatives contracts cause payments to be made by one party to the other upon the occurrence of predefined events. Thus, if one party gains X, the other loses X. And so exposure under the derivative is perfectly symmetrical. Note that this is true even if a counterparty fails to pay as promised. This is because there is no initial principle “investment” in a derivative. So if one party defaults on a payment under a derivative, there is no cash “loss” to the non-defaulting party. That said, there could be substantial reliance losses. For example, you expect to receive a $100 million credit default swap payment from XYZ, and as a result, you go out and buy $1,000 alligator skin boots, only to find that XYZ is bankrupt and unable to pay as promised. So, while there would be no cash loss, you could have relied on the payments and planned around them, causing you to incur obligations you can no longer afford. Additionally, you could have reported the income in an accounting statement, and when the cash fails to appear, you would be forced to “write-down” the amount and take a paper loss. However, the derivatives market is full of very bright people who have already considered counterparty risk, and the matter is dealt with through the dynamic posting of collateral over the life of the agreement, which limits each party’s ability to simply cut and run. As a result, we will consider only cash losses and gains for the remainder of this article.

The Price Of Exposure To Risk

Although parties to a derivative contract do not “buy” anything in the traditional sense of exchanging cash for goods or services, they are expressing a desire to be exposed to certain risks. Since the exposure of each party to a derivative is equal in magnitude but opposite in sign, one party is expressing a desire for exposure to the occurrence of an event while the other is expressing a desire for exposure to the non-occurrence of that event. There will be a price for exposure. That is, in order to convince someone to pay you $1 upon the occurrence of event E, that other person will ask for some percentage of $1, which we will call the fee. Note that as expressed, the fee is fixed. So we are considering only those derivatives for which the contingent payout amounts are fixed at the outset of the transaction. For example, a credit default swap that calls for physical delivery fits into this category. As this fee increases, the payout shrinks for the party with positive exposure to the event. For example, if the fee is $1 for every dollar of positive exposure, then even if the event occurs, the party with positive exposure’s payments will net to zero.

This method of analysis makes it difficult to think in terms of a fee for positive exposure to the event not occurring (the other side of the trade). We reconcile this by assuming that only one payment is made under every contract, upon termination. For example, assume that A is positively exposed to E occurring and that B is negatively exposed to E occurring. Upon termination, either E occurred prior to termination or it did not.

sym-exposure2

If E did occur, then B would pay $N \cdot(1 - F)$ to A, where F is the fee and N is the total amount of A’s exposure, which in the case of a swap would be the notional amount of the contract. If E did not occur, then A would pay $N\cdot F$ . If E is the event “ABC defaults on its bonds,” then A and B have entered into a credit default swap where A is short on ABC bonds and B is long. Thus, we can think in terms of a unified price for both sides of the trade and consider how the expected payout for each side of the trade changes as that price changes.

Expected Payout As A Function Of Price

As mentioned above, the contingent payouts to the parties are a function of the fee. This fee is in turn a function of each party’s subjective valuation of the probability that E will actually occur. For example, if A thinks that E will occur with a probability of $\frac{1}{2}$ , then A will accept any fee less than .5 since A’s subjective expected payout under that assumption is $N (\frac{1}{2}(1 - F) - \frac{1}{2}F ) = N (\frac{1}{2} - F)$ . If B thinks that E will occur with a probability of $\frac {1}{4}$ , then B will accept any fee greater than .25 since his expected payout is $N (\frac{3}{4} F - \frac{1}{4}(1 - F)) = N (F - \frac{1}{4} )$ . Thus, A and B have a bargaining range between .25 and .5. And because each perceives the trade to have a positive payout upon termination within that bargaining range, they will transact. Unfortunately for one of them, only one of them is correct. After many such transactions occur, market participants might choose to report the fees at which they transact. This allows C and D to reference the fee at which the A-B transaction occurred. This process repeats itself and eventually market prices will develop.

Assume that A and B think the probability of E occurring is $p_A$ and $p_B$ respectively. If A has positive exposure and B has negative, then in general the subjective expected payouts for A and B are $N (p_A - F)$ and $N ( F - p_B)$ respectively. If we plot the expected payout as a function of F, we get the following:

payout-v-fee4

The red line indicates the bargaining range. Thus, we can describe each participant’s expected payout in terms of the fee charged for exposure. This will allow us to compare the returns on fixed fee derivatives to other financial assets, and ultimately plot a demand curve for fixed fee derivatives as a function of their price.

Tranches And Risk

December 1, 2008March 11, 2019 / erdosfan / 3 Comments

What Is A Tranche?

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

Payment Waterfalls

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

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

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

Mortgage Backed Securities And Prepayment Risk

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

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

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

Prepayment Risk And Payment Waterfalls

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

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

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