# 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.

# Tranches And Risk

#### What Is A Tranche?

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

#### Payment Waterfalls

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

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

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

#### Mortgage Backed Securities And Prepayment Risk

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

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

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

#### Prepayment Risk And Payment Waterfalls

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

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

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