In the United States, the securities backed by residential mortgage loans are divided into two sectors: (1) those issued by federal agencies (one federally related institution and two government sponsored enterprises) and (2) those issued by private entities. The former securities are called agency mortgage-backed securities and the latter nonagency mortgage-backed securities.

Securities backed by loans other than traditional residential mortgage loans or commercial mortgage loans and backed by receivables are referred to as asset-backed securities. There is a long and growing list of loans and receivables that have been used as collateral for these securities. Together, mortgage-backed securities and asset-backed securities are referred to as structured financial products.

It is important to understand the classification of these sectors in terms of bond market indexes. A popular bond market index, the Lehman Aggregate Bond Index, has a sector that it refers to as the “mortgage passthrough sector.” Within the “mortgage passthrough sector,” Lehman Brothers includes only agency mortgage-backed securities that are mortgage passthrough securities. To understand why it is essential to understand this sector, consider that the “mortgage passthrough sector” represents more than one third of the Lehman Aggregate Bond Index. It is the largest sector in the bond market index. The commercial mortgage-backed securities sector represents about 2% of the bond market index. The mortgage sector of the Lehman Aggregate Bond Index includes the mortgage passthrough sector and the commercial mortgage-backed securities.

In this chapter, our focus will be on the mortgage sector. Although many countries have developed a mortgage-backed securities sector, our focus in this chapter is the U.S. mortgage sector because of its size and it important role in U.S. bond market indexes. Credit risk does not exist for agency mortgage-backed securities issued by a federally related institution and is viewed as minimal for securities issued by government sponsored enterprises. The significant risk is prepayment risk and there are ways to redistribute prepayment risk among the different bond classes created. Historically, it is important to note that the agency mortgage-backed securities market developed first. The technology developed for creating agency mortgage-backed security was then transferred to the securitization of other types of loans and receivables. In transferring the technology to create securities that expose investors to credit risk, mechanisms had to be developed to create securities that could receive investment grade credit ratings sought by the issuer. In the next chapter, we will discuss these mechanisms. We postpone a discussion of how to value and estimate the interest rate risk of both mortgage-backed and asset-backed securities until Chapter 12.

Outside the United States, market participants treat asset-backed securities more generically. Specifically, asset-backed securities include mortgage-backed securities as a subsector. While that is actually the proper way to classify these securities, it was not the convention adopted in the United States. In the next chapter, the development of the asset-backed securities (including mortgage-backed securities) outside the United States will be covered.

Residential mortgage-backed securities include: (1) mortgage passthrough securities, (2) collateralized mortgage obligations, and (3) stripped mortgage-backed securities. The latter two mortgage-backed securities are referred to as derivative mortgage-backed securities because they are created from mortgage passthrough securities.

When the lender makes the loan based on the credit of the borrower and on the collateral for the mortgage, the mortgage is said to be a conventional mortgage. The lender may require that the borrower obtain mortgage insurance to guarantee the fulfillment of the borrower’s obligations. Some borrowers can qualify for mortgage insurance which is guaranteed by one of three U.S. government agencies: the Federal Housing Administration (FHA), the Veteran’s Administration (VA), and the Rural Housing Service (RHS). There are also private mortgage insurers. The cost of mortgage insurance is paid by the borrower in the form of a higher mortgage rate.

There are many types of mortgage designs used throughout the world. A mortgage design is a specification of the interest rate, term of the mortgage, and the manner in which the borrowed funds are repaid. In the United States, the alternative mortgage designs include (1) fixed rate, level-payment fully amortized mortgages, (2) adjustable-rate mortgages, (3) balloon mortgages, (4) growing equity mortgages, (5) reverse mortgages, and (6) tiered payment mortgages. Other countries have developed mortgage designs unique to their housing finance market. Some of these mortgage designs relate the mortgage payment to the country’s rate of inflation. Below we will look at the most common mortgage design in the United States—the fixed-rate, level-payment, fully amortized mortgage. All of the principles we need to know regarding the risks associated with investing in mortgage-backed securities and the difficulties associated with their valuation can be understood by just looking at this mortgage design.

The monthly mortgage payments include principal repayment and interest. The frequency of payment is typically monthly. Each monthly mortgage payment for this mortgage design is due on the first of each month and consists of:

The difference between the monthly mortgage payment and the portion of the payment that represents interest equals the amount that is applied to reduce the outstanding mortgage balance. The monthly mortgage payment is designed so that after the last scheduled monthly mortgage payment is made, the amount of the outstanding mortgage balance is zero (i.e., the mortgage is fully repaid).

To illustrate this mortgage design, consider a 30-year (360-month), $100,000 mortgage with an 8.125% mortgage rate. The monthly mortgage payment would be $742.50. Exhibit 1 shows for selected months how each monthly mortgage payment is divided between interest and scheduled principal repayment. At the beginning of month 1, the mortgage balance is $100,000, the amount of the original loan. The mortgage payment for month 1 includes interest on the $100,000 borrowed for the month. Since the interest rate is 8.125%, the monthly interest rate is 0.0067708 (0.08125 divided by 12). Interest for month 1 is therefore $677.08 ($100,000 times 0.0067708). The $65.41 difference between the monthly mortgage payment of $742.50 and the interest of $677.08 is the portion of the monthly mortgage payment that represents the scheduled principal repayment. It is also referred to as the scheduled amortization and we shall use the terms scheduled principal repayment and scheduled amortization interchangeably throughout this chapter. This $65.41 in month 1 reduces the mortgage balance.

The mortgage balance at the end of month 1 (beginning of month 2) is then $99,934.59 ($100,000 minus $65.41). The interest for the second monthly mortgage payment is $676.64, the monthly interest rate (0.0067708) times the mortgage balance at the beginning of month 2 ($99,934.59). The difference between the $742.50 monthly mortgage payment and the $676.64 interest is $65.86, representing the amount of the mortgage balance paid off with that monthly mortgage payment. Notice that the mortgage payment in month 360—the final payment—is sufficient to pay off the remaining mortgage balance.

As Exhibit 1 clearly shows, the portion of the monthly mortgage payment applied to interest declines each month and the portion applied to principal repayment increases. The reason for this is that as the mortgage balance is reduced with each monthly mortgage payment, the interest on the mortgage balance declines. Since the monthly mortgage payment is a fixed dollar amount, an increasingly larger portion of the monthly payment is applied to reduce the mortgage balance outstanding in each subsequent month.

Payments are made to security holders each month. However, neither the amount nor the timing of the cash flow from the pool of mortgages is identical to that of the cash flow passed through to investors. The monthly cash flow for a passthrough is less than the monthly cash flow of the underlying pool of mortgages by an amount equal to servicing and other fees. The other fees are those charged by the issuer or guarantor of the passthrough for guaranteeing the issue (discussed later). The coupon rate on a passthrough is called the passthrough rate. The passthrough rate is less than the mortgage rate on the underlying pool of mortgages by an amount equal to the servicing and guaranteeing fees.

The timing of the cash flow is also different. The monthly mortgage payment is due from each mortgagor on the first day of each month, but there is a delay in passing through the corresponding monthly cash flow to the security holders. The length of the delay varies by the type of passthrough security.

Not all of the mortgages that are included in a pool of mortgages that are securitized have the same mortgage rate and the same maturity. Consequently, when describing a passthrough security, a weighted average coupon rate and a weighted average maturity are determined. A weighted average coupon rate, or WAC, is found by weighting the mortgage rate of each mortgage loan in the pool by the percentage of the mortgage outstanding relative to the outstanding amount of all the mortgages in the pool. A weighted average maturity, or WAM, is found by weighting the remaining number of months to maturity for each mortgage loan in the pool by the amount of the outstanding mortgage balance.

For example, suppose a mortgage pool has just five loans and the outstanding mortgage balance, mortgage rate, and months remaining to maturity of each loan are as follows:

While Freddie Mac and Fannie Mae are commonly referred to as “agencies” of the U.S. government, both are corporate instrumentalities of the U.S. government. That is, they are government sponsored enterprises; therefore, their guarantee does not carry the full faith and credit of the U.S. government. In contrast, Ginnie Mae is a federally related institution; it is part of the Department of Housing and Urban Development. As such, its guarantee carries the full faith and credit of the U.S. government. The passthrough securities issued by Fannie Mae and Freddie Mac are called conventional passthrough securities. However, in this book we shall refer to those passthrough securities issued by all three entities (Ginnie Mae, Fannie Mae, and Freddie Mac) as agency passthrough securities. It should be noted, however, that market participants do reserve the term “agency passthrough securities” for those issued only by Ginnie Mae.¹¹⁹

In order for a loan to be included in a pool of loans backing an agency security, it must meet specified underwriting standards. These standards set forth the maximum size of the loan, the loan documentation required, the maximum loan-to-value ratio, and whether or not insurance is required. If a loan satisfies the underwriting standards for inclusion as collateral for an agency mortgage-backed security, it is called a conforming mortgage. If a loan fails to satisfy the underwriting standards, it is called a nonconforming mortgage.

Nonconforming mortgages used as collateral for mortgage passthrough securities are privately issued. These securities are called nonagency mortgage passthrough securities and are issued by thrifts, commercial banks, and private conduits. Private conduits may purchase nonconforming mortgages, pool them, and then sell passthrough securities whose collateral is the underlying pool of nonconforming mortgages. Nonagency passthrough securities are rated by the nationally recognized statistical rating organizations. These securities are supported by credit enhancements so that they can obtain an investment grade rating. We shall describe these securities in the next chapter.

Passthrough prices are quoted in the same manner as U.S. Treasury coupon securities. A quote of 94-05 means 94 and 5 32nds of par value, or 94.15625% of par value. The price that the buyer pays the seller is the agreed upon sale price plus accrued interest. Given the par value, the dollar price (excluding accrued interest) is affected by the amount of the pool mortgage balance outstanding. The pool factor indicates the percentage of the initial mortgage balance still outstanding. So, a pool factor of 90 means that 90% of the original mortgage pool balance is outstanding. The pool factor is reported by the agency each month.

The dollar price paid for just the principal is found as follows given the agreed upon price, par value, and the month’s pool factor provided by the agency:

For example, if the parties agree to a price of 92 for $1 million par value for a passthrough with a pool factor of 0.85, then the dollar price paid by the buyer in addition to accrued interest is:

The buyer does not know what he will get unless he specifies a pool number. There are many seasoned issues of the same agency with the same coupon rate outstanding at a given point in time. For example, in early 2000 there were more than 30,000 pools of 30-year Ginnie Mae MBSs outstanding with a coupon rate of 9%. One passthrough may be backed by a pool of mortgage loans in which all the properties are located in California, while another may be backed by a pool of mortgage loans in which all the properties are in Minnesota. Yet another may be backed by a pool of mortgage loans in which the properties are from several regions of the country. So which pool are dealers referring to when they talk about Ginnie Mae 9s? They are not referring to any specific pool but instead to a generic security, despite the fact that the prepayment characteristics of passthroughs with underlying pools from different parts of the country are different. Thus, the projected prepayment rates for passthroughs reported by dealer firms (discussed later) are for generic passthroughs. A particular pool purchased may have a materially different prepayment rate from the generic. Moreover, when an investor purchases a passthrough without specifying a pool number, the seller has the option to deliver the worst-paying pools as long as the pools delivered satisfy good delivery requirements.

There are three points to keep in mind in the discussion in this section. First, we will look at how the actual or historical prepayment rate of a mortgage pool is calculated. Second, we will see later how in projecting the cash flow of a mortgage pool, an investor uses the same prepayment measures to project prepayments given a prepayment rate. The third point is that we are just describing the mechanics of calculating prepayment measures. The difficult task of projecting the prepayment rate is not discussed here. In fact, this task is beyond the scope of this chapter. However, the factors that investors use in prepayment models (i.e., statistical models used to project prepayments) will be described in Section III F.

For a mortgage-backed security, we know that the principal repayments (scheduled payments and prepayments) are made over the life of the security. While a mortgage-backed has a “legal maturity,” which is the date when the last scheduled principal payment is due, the legal maturity does not tell us much about the characteristic of the security as its pertains to interest rate risk. For example, it is incorrect to think of a 30-year corporate bond and a mortgage-backed security with a 30-year legal maturity with the same coupon rate as being equivalent in terms of interest rate risk. Of course, duration can be computed for both the corporate bond and the mortgage-backed security. (We will see how this is done for a mortgage-backed security in Chapter 12.) Instead of duration, another measure widely used by market participants is the weighted average life or simply average life. This is the convention-based average time to receipt of principal payments (scheduled principal payments and projected prepayments).

Mathematically, the average life is expressed as follows: where T is the number of months.

The average life of a passthrough depends on the prepayment assumption. To see this, the average life is shown below for different prepayment speeds for the pass-through we used to illustrate the cash flow for 100 PSA and 165 PSA in Exhibits 3 and 4:

The current mortgage rate affects prepayments. The spread between the prevailing mortgage rate in the market and the rate paid by the homeowner affects the incentive to refinance. Moreover, the path of mortgage rates since the loan was originated affects prepayments through a phenomenon referred to as refinancing burnout. Both the spread and path of mortgage rates affect prepayments that are the product of refinancing.

By far, the single most important factor affecting prepayments because of refinancing is the current level of mortgage rates relative to the borrower’s contract rate. The greater the difference between the two, the greater the incentive to refinance the mortgage loan. For refinancing to make economic sense, the interest savings must be greater than the costs associated with refinancing the mortgage. These costs include legal expenses, origination fees, title insurance, and the value of the time associated with obtaining another mortgage loan. Some of these costs will vary proportionately with the amount to be financed. Other costs such as the application fee and legal expenses are typically fixed.

Historically it had been observed that mortgage rates had to decline by between 250 and 350 basis points below the contract rate in order to make it worthwhile for borrowers to refinance. However, the creativity of mortgage originators in designing mortgage loans such that the refinancing costs are folded into the amount borrowed has changed the view that mortgage rates must drop dramatically below the contract rate to make refinancing economic. Moreover, mortgage originators now do an effective job of advertising to make homeowners cognizant of the economic benefits of refinancing.

The historical pattern of prepayments and economic theory suggests that it is not only the level of mortgage rates that affects prepayment behavior but also the path that mortgage rates take to get to the current level. To illustrate why, suppose the underlying contract rate for a pool of mortgage loans is 11% and that three years after origination, the prevailing mortgage rate declines to 8%. Let’s consider two possible paths of the mortgage rate in getting to the 8% level. In the first path, the mortgage rate declines to 8% at the end of the first year, then rises to 13% at the end of the second year, and then falls to 8% at the end of the third year. In the second path, the mortgage rate rises to 12% at the end of the first year, continues its rise to 13% at the end of the second year, and then falls to 8% at the end of the third year.

If the mortgage rate follows the first path, those who can benefit from refinancing will more than likely take advantage of this opportunity when the mortgage rate drops to 8% in the first year. When the mortgage rate drops again to 8% at the end of the third year, the likelihood is that prepayments because of refinancing will not surge; those who want to benefit by taking advantage of the refinancing opportunity will have done so already when the mortgage rate declined for the first time. This is the prepayment behavior referred to as the refinancing burnout (or simply, burnout) phenomenon. In contrast, the expected prepayment behavior when the mortgage rate follows the second path is quite different. Prepayment rates are expected to be low in the first two years. When the mortgage rate declines to 8% in the third year, refinancing activity and therefore prepayments are expected to surge. Consequently, the burnout phenomenon is related to the path of mortgage rates.

There is another way in which the prevailing mortgage rate affects prepayments: through its effect on the affordability of housing and housing turnover. The level of mortgage rates affects housing turnover to the extent that a lower rate increases the affordability of homes. However, even without lower interest rates, there is a normal amount of housing turnover. This is attribute to economic growth. The link is as follows: a growing economy results in a rise in personal income and in opportunities for worker migration; this increases family mobility and as a result increases housing turnover. The opposite holds for a weak economy.

Two characteristics of the underlying residential mortgage loans that affect prepayments are the amount of seasoning and the geographical location of the underlying properties. Seasoning refers to the aging of the mortgage loans. Empirical evidence suggests that prepayment rates are low after the loan is originated and increase after the loan is somewhat seasoned. Then prepayment rates tend to level off, in which case the loans are referred to as fully seasoned. This is the underlying theory for the PSA prepayment benchmark discussed earlier in this chapter. In some regions of the country the prepayment behavior tends to be faster than the average national prepayment rate, while other regions exhibit slower prepayment rates. This is caused by differences in local economies that affect housing turnover.

To understand the significance of prepayment risk, suppose an investor buys a 9% coupon passthrough security at a time when mortgage rates are 10%. Let’s consider what will happen to prepayments if mortgage rates decline to, say, 6%. There will be two adverse consequences. First, a basic property of fixed income securities is that the price of an option-free bond will rise. But in the case of a passthrough security, the rise in price will not be as large as that of an option-free bond because a fall in interest rates will give the borrower an incentive to prepay the loan and refinance the debt at a lower rate. This results in the same adverse consequence faced by holders of callable bonds. As in the case of those instruments, the upside price potential of a passthrough security is compressed because of prepayments. (This is the negative convexity characteristic explained in Chapter 7.) The second adverse consequence is that the cash flow must be reinvested at a lower rate. Basically, the faster prepayments resulting from a decline in interest rates causes the passthrough to shorten in terms of the timing of its cash flows. Another way of saying this is that “shortening” results in a decline in the average life. Consequently, the two adverse consequences from a decline in interest rates for a passthrough security are referred to as contraction risk.

Now let’s look at what happens if mortgage rates rise to 15%. The price of the passthrough, like the price of any bond, will decline. But again it will decline more because the higher rates will tend to slow down the rate of prepayment, in effect increasing the amount invested at the coupon rate, which is lower than the market rate. Prepayments will slow down, because homeowners will not refinance or partially prepay their mortgages when mortgage rates are higher than the contract rate of 10%. Of course this is just the time when investors want prepayments to speed up so that they can reinvest the prepayments at the higher market interest rate. Basically, the slower prepayments associated with a rise in interest rates that causes these adverse consequences are due to the passthrough lengthening in terms of the timing of its cash flows. Another way of saying this is that “lengthening” results in an increase in the average life. Consequently, the adverse consequence from a rise in interest rates for a passthrough security is referred to as extension risk.

Therefore, prepayment risk encompasses contraction risk and extension risk. Prepayment risk makes passthrough securities unattractive for certain financial institutions to hold from an asset/liability management perspective. Some institutional investors are concerned with extension risk and others with contraction risk when they purchase a passthrough security. This applies even for assets supporting specific types of insurance contracts. Is it possible to alter the cash flow of a passthrough so as to reduce the contraction risk or extension risk for institutional investors? This can be done, as we shall see, when we describe collateralized mortgage obligations.

When the cash flows of mortgage-related products are redistributed to different bond classes, the resulting securities are called collateralized mortgage obligations (CMO). The mortgage-related products from which the cash flows are obtained are referred to as the collateral. Since the typical mortgage-related product used in a CMO is a pool of passthrough securities, sometimes market participants will use the terms “collateral” and “passthrough securities” interchangeably. The creation of a CMO cannot eliminate prepayment risk; it can only distribute the various forms of this risk among different classes of bondholders. The CMO’s major financial innovation is that the securities created more closely satisfy the asset/liability needs of institutional investors, thereby broadening the appeal of mortgage-backed products.

There is a wide range of CMO structures.¹²⁵ We review the major ones below.

To illustrate a sequential-pay CMO, we discuss FJF-01, a hypothetical deal made up to illustrate the basic features of the structure. The collateral for this hypothetical CMO is a hypothetical passthrough with a total par value of $400 million and the following characteristics: (1) the passthrough coupon rate is 7.5%, (2) the weighted average coupon (WAC) is 8.125%, and (3) the weighted average maturity (WAM) is 357 months. This is the same passthrough that we used in Section III to describe the cash flow of a passthrough based on some PSA assumption.

From this $400 million of collateral, four bond classes or tranches are created. Their characteristics are summarized in Exhibit 5. The total par value of the four tranches is equal to the par value of the collateral (i.e., the passthrough security).¹²⁶ In this simple structure, the coupon rate is the same for each tranche and also the same as the coupon rate on the collateral. There is no reason why this must be so, and, in fact, typically the coupon rate varies by tranche.

Now remember that a CMO is created by redistributing the cash flow—interest and principal—to the different tranches based on a set of payment rules. The payment rules at the bottom of Exhibit 5 describe how the cash flow from the passthrough (i.e., collateral) is to be distributed to the four tranches. There are separate rules for the distribution of the coupon interest and the payment of principal (the principal being the total of the scheduled principal payment and any prepayments).

While the payment rules for the disbursement of the principal payments are known, the precise amount of the principal in each month is not. This will depend on the cash flow, and therefore principal payments, of the collateral, which depends on the actual prepayment rate of the collateral. An assumed PSA speed allows the cash flow to be projected. Exhibit 6 shows the cash flow (interest, scheduled principal repayment, and prepayments) assuming 165 PSA. Assuming that the collateral does prepay at 165 PSA, the cash flow available to all four tranches of FJF-01 will be precisely the cash flow shown in Exhibit 6.

To demonstrate how the payment rules for FJF-01 work, Exhibit 6 shows the cash flow for selected months assuming the collateral prepays at 165 PSA. For each tranche, the exhibit shows: (1) the balance at the end of the month, (2) the principal paid down (scheduled principal repayment plus prepayments), and (3) interest. In month 1, the cash flow for the collateral consists of a principal payment of $709,923 and an interest payment of $2.5 million (0.075 times $400 million divided by 12). The interest payment is distributed to the four tranches based on the amount of the par value outstanding. So, for example, tranche A receives $1,215,625 (0.075 times $194,500,000 divided by 12) of the $2.5 million. The principal, however, is all distributed to tranche A. Therefore, the cash flow for tranche A in month 1 is $1,925,548. The principal balance at the end of month 1 for tranche A is $193,790,076 (the original principal balance of $194,500,000 less the principal payment of $709,923). No principal payment is distributed to the three other tranches because there is still a principal balance outstanding for tranche A. This will be true for months 2 through 80. The cash flow for tranche A for each month is found by adding the amounts shown in the “Principal” and “Interest” columns. So, for tranche A, the cash flow in month 8 is $1,483,954 plus $1,169,958, or $2,653,912. The cash flow from months 82 on is zero based on 165 PSA.

After month 81, the principal balance will be zero for tranche A. For the collateral, the cash flow in month 81 is $3,318,521, consisting of a principal payment of $2,032,197 and interest of $1,286,325. At the beginning of month 81 (end of month 80), the principal balance for tranche A is $311,926. Therefore, $311,926 of the $2,032,196 of the principal payment from the collateral will be disbursed to tranche A. After this payment is made, no additional principal payments are made to this tranche as the principal balance is zero. The remaining principal payment from the collateral, $1,720,271, is distributed to tranche B. Based on an assumed prepayment speed of 165 PSA, tranche B then begins receiving principal payments in month 81. The cash flow for tranche B for each month is found by adding the amounts shown in the “Principal” and “Interest” columns. For months 1 though 80, the cash flow is just the interest. There is no cash flow after month 100 for tranche B.

Exhibit 6 shows that tranche B is fully paid off by month 100, when tranche C begins to receive principal payments. Tranche C is not fully paid off until month 178, at which time tranche D begins receiving the remaining principal payments. The maturity (i.e., the time until the principal is fully paid off) for these four tranches assuming 165 PSA would be 81 months for tranche A, 100 months for tranche B, 178 months for tranche C, and 357 months for tranche D. The cash flow for each month for tranches C and D is found by adding the principal and the interest for the month.

The principal pay down window or principal window for a tranche is the time period between the beginning and the ending of the principal payments to that tranche. So, for example, for tranche A, the principal pay down window would be month 1 to month 81 assuming 165 PSA. For tranche B it is from month 81 to month 100.¹²⁷ In confirmation of trades involving CMOs, the principal pay down window is specified in terms of the initial month that principal is expected to be received to the final month that principal is expected to be received.

Let’s look at what has been accomplished by creating the CMO. Earlier we saw that the average life of the passthrough is 8.76 years assuming a prepayment speed of 165 PSA. Exhibit 7 reports the average life of the collateral and the four tranches assuming different prepayment speeds. Notice that the four tranches have average lives that are both shorter and longer than the collateral, thereby attracting investors who have a preference for an average life different from that of the collateral.

There is still a major problem: there is considerable variability of the average life for the tranches. We’ll see how this can be handled later on. However, there is some protection provided for each tranche against prepayment risk. This is because prioritizing the distribution of principal (i.e., establishing the payment rules for principal) effectively protects the shorter-term tranche A in this structure against extension risk. This protection must come from somewhere, so it comes from the three other tranches. Similarly, tranches C and D provide protection against extension risk for tranches A and B. At the same time, tranches C and D benefit because they are provided protection against contraction risk, the protection coming from tranches A and B.

To see this, consider FJF-02, a hypothetical CMO structure with the same collateral as our previous example and with four tranches, each with a coupon rate of 7.5%. The last tranche, Z, is an accrual tranche. The structure for FJF-02 is shown in Exhibit 8.

Exhibit 9 shows cash flows for selected months for tranches A and B. Let’s look at month 1 and compare it to month 1 in Exhibit 6. Both cash flows are based on 165 PSA. The principal payment from the collateral is $709,923. In FJF-01, this is the principal paydown for tranche A. In FJF-02, the interest for tranche Z, $456,250, is not paid to that tranche but instead is used to pay down the principal of tranche A. So, the principal payment to tranche A in Exhibit 9 is $1,166,173, the collateral’s principal payment of $709,923 plus the interest of $456,250 that was diverted from tranche Z.

The expected final maturity for tranches A, B, and C has shortened as a result of the inclusion of tranche Z. The final payout for tranche A is 64 months rather than 81 months; for tranche B it is 77 months rather than 100 months; and, for tranche C it is 113 months rather than 178 months.

The average lives for tranches A, B, and C are shorter in FJF-02 compared to our previous non-accrual, sequential-pay tranche example, FJF-01, because of the inclusion of the accrual tranche. For example, at 165 PSA, the average lives are as follows:

Thus, shorter-term tranches and a longer-term tranche are created by including an accrual tranche in FJF-02 compared to FJF-01. The accrual tranche has appeal to investors who are concerned with reinvestment risk. Since there are no coupon payments to reinvest, reinvestment risk is eliminated until all the other tranches are paid off.

In this case, we create a floater and an inverse floater from tranche C. A floater could have been created from any of the other tranches. The par value for this tranche is $96.5 million, and we create two tranches that have a combined par value of $96.5 million. We refer to this CMO structure with a floater and an inverse floater as FJF-03. It has five tranches, designated A, B, FL, IFL, and Z, where FL is the floating-rate tranche and IFL is the inverse floating-rate tranche. Exhibit 10 describes FJF-03. Any reference rate can be used to create a floater and the corresponding inverse floater. The reference rate for setting the coupon rate for FL and IFL in FJF-03 is 1-month LIBOR.

The amount of the par value of the floating-rate tranche will be some portion of the $96.5 million. There are an infinite number of ways to slice up the $96.5 million between the floater and inverse floater, and final partitioning will be driven by the demands of investors. In the FJF-03 structure, we made the floater from $72,375,000 or 75% of the $96.5 million. The coupon formula for the floater is 1-month LIBOR plus 50 basis points. So, for example, if LIBOR is 3.75% at the reset date, the coupon rate on the floater is 3.75% + 0.5%, or 4.25%. There is a cap on the coupon rate for the floater (discussed later).

Unlike a floating-rate note in the corporate bond market whose principal is unchanged over the life of the instrument, the floater’s principal balance declines over time as principal payments are made. The principal payments to the floater are determined by the principal payments from the tranche from which the floater is created. In our CMO structure, this is tranche C.

Since the floater’s par value is $72,375,000 of the $96.5 million, the balance is par value for the inverse floater. Assuming that 1-month LIBOR is the reference rate, the coupon formula for the inverse floater takes the following form: where K and L are constants whose interpretation will be explained shortly.

In FJF-03, K is set at 28.50% and L at 3. Thus, if 1-month LIBOR is 3.75%, the coupon rate for the month is:

K is the cap or maximum coupon rate for the inverse floater. In FJF-03, the cap for the inverse floater is 28.50%. The determination of the inverse floater’s cap rate is based on (1) the amount of interest that would have been paid to the tranche from which the floater and the inverse floater were created, tranche C in our hypothetical deal, and (2) the coupon rate for the floater if 1-month LIBOR is zero.

We will explain the determination of K by example. Let’s see how the 28.5% for the inverse floater is determined. The total interest to be paid to tranche C if it was not split into the floater and the inverse floater is the principal of $96,500,000 times 7.5%, or $7,237,500. The maximum interest for the inverse floater occurs if 1-month LIBOR is zero. In that case, the coupon rate for the floater is

The L or multiple in the coupon formula to determine the coupon rate for the inverse floater is called the leverage. The higher the leverage, the more the inverse floater’s coupon rate changes for a given change in 1-month LIBOR. For example, a coupon leverage of 3 means that a 1-basis point change in 1-month LIBOR will change the coupon rate on the inverse floater by 3 basis points.

As in the case of the floater, the principal paydown of an inverse floater will be a proportionate amount of the principal paydown of tranche C.

Because 1-month LIBOR is always positive, the coupon rate paid to the floater cannot be negative. If there are no restrictions placed on the coupon rate for the inverse floater, however, it is possible for its coupon rate to be negative. To prevent this, a floor, or minimum, is placed on the coupon rate. In most structures, the floor is set at zero. Once a floor is set for the inverse floater, a cap or ceiling is imposed on the floater.

In FJF-03, a floor of zero is set for the inverse floater. The floor results in a cap or maximum coupon rate for the floater of 10%. This is determined as follows. If the floor for the inverse floater is zero, this means that the inverse floater receives no interest. All of the interest that would have been paid to tranche C, $7,237,500, would then be paid to the floater. Since the floater’s principal is $72,375,000, the cap rate on the floater is $7,237,500/$72,375,000, or 10%.

In general, the cap rate for the floater assuming a floor of zero for inverse floater is determined as follows:

The cap for the floater and the inverse floater, the floor for the inverse floater, the leverage, and the floater’s spread are not determined independently. Any cap or floor imposed on the coupon rate for the floater and the inverse floater must be selected so that the weighted average coupon rate does not exceed the collateral tranche’s coupon rate.

Let’s look at how a structured IO is created using an illustration. Thus far, we used a simple CMO structure in which all the tranches have the same coupon rate (7.5%) and that coupon rate is the same as the collateral. A structured IO is created from a CMO structure where the coupon rate for at least one tranche is different from the collateral’s coupon rate. This is seen in FJF-04 shown in Exhibit 11. In this structure, notice that the coupon interest rate for each tranche is less than the coupon interest rate for the collateral. That means that there is excess interest from the collateral that is not being paid to all the tranches. At one time, all of that excess interest not paid to the tranches was paid to a bond class called a “residual.” Eventually (due to changes in the tax law that do not concern us here), structurers of CMO began allocating the excess interest to the tranche that receives only interest. This is tranche IO in FJF-04.

Notice that for this structure the par amount for the IO tranche is shown as $52,566,667 and the coupon rate is 7.5%. Since this is an IO tranche there is no par amount. The amount shown is the amount upon which the interest payments will be determined, not the amount that will be paid to the holder of this tranche. Therefore, it is called a notional amount. The resulting IO is called a notional IO.

Let’s look at how the notional amount is determined. Consider tranche A. The par value is $194.5 million and the coupon rate is 6%. Since the collateral’s coupon rate is 7.5%, the excess interest is 150 basis points (1.5%). Therefore, an IO with a 1.5% coupon rate and a notional amount of $194.5 million can be created from tranche A. But this is equivalent to an IO with a notional amount of $38.9 million and a coupon rate of 7.5%. Mathematically, this notional amount is found as follows: where

For example, for tranche A:

Similarly, from tranche B with a par value of $36 million, the excess interest is 100 basis points (1%) and therefore an IO with a coupon rate of 1% and a notional amount of $36 million can be created. But this is equivalent to creating an IO with a notional amount of $4.8 million and a coupon rate of 7.5%. This procedure is shown in Exhibit 12 for all four tranches.

In 1987, several structures came to market that shared the following characteristic: if the prepayment speed is within a specified band over the collateral’s life, the cash flow pattern is known. The greater predictability of the cash flow for these classes of bonds, now referred to as planned amortization class (PAC) bonds, occurs because there is a principal repayment schedule that must be satisfied. PAC bondholders have priority over all other classes in the CMO structure in receiving principal payments from the collateral. The greater certainty of the cash flow for the PAC bonds comes at the expense of the non-PAC tranches, called the support tranches or companion tranches. It is these tranches that absorb the prepayment risk. Because PAC tranches have protection against both extension risk and contraction risk, they are said to provide two-sided prepayment protection.

To illustrate how to create a PAC bond, we will use as collateral the $400 million passthrough with a coupon rate of 7.5%, an 8.125% WAC, and a WAM of 357 months. The creation requires the specification of two PSA prepayment rates—a lower PSA prepayment assumption and an upper PSA prepayment assumption. In our illustration the lower PSA prepayment assumption will be 90 PSA and the upper PSA prepayment assumption will be 300 PSA. A natural question is: How does one select the lower and upper PSA prepayment assumptions? These are dictated by market conditions. For our purpose here, how they are determined is not important. The lower and upper PSA prepayment assumptions are referred to as the initial PAC collar or the initial PAC band. In our illustration the initial PAC collar is 90 - 300 PSA.

The second column of Exhibit 13 shows the principal payment (scheduled principal repayment plus prepayments) for selected months assuming a prepayment speed of 90 PSA, and the next column shows the principal payments for selected months assuming that the passthrough prepays at 300 PSA.

The last column of Exhibit 13 gives the minimum principal payment if the collateral prepays at 90 PSA or 300 PSA for months 1 to 349. (After month 349, the outstanding principal balance will be paid off if the prepayment speed is between 90 PSA and 300 PSA.) For example, in the first month, the principal payment would be $508,169 if the collateral prepays at 90 PSA and $1,075,931 if the collateral prepays at 300 PSA. Thus, the minimum principal payment is $508,169, as reported in the last column of Exhibit 13. In month 103, the minimum principal payment is also the amount if the prepayment speed is 90 PSA, $1,446,761, compared to $1,458,618 for 300 PSA. In month 104, however, a prepayment speed of 300 PSA would produce a principal payment of $1,433,539, which is less than the principal payment of $1,440,825 assuming 90 PSA. So, $1,433,539 is reported in the last column of Exhibit 13. From month 104 on, the minimum principal payment is the one that would result assuming a prepayment speed of 300 PSA.

In fact, if the collateral prepays at any one speed between 90 PSA and 300 PSA over its life, the minimum principal payment would be the amount reported in the last column of Exhibit 13. For example, if we had included principal payment figures assuming a prepayment speed of 200 PSA, the minimum principal payment would not change: from month 1 through month 103, the minimum principal payment is that generated from 90 PSA, but from month 104 on, the minimum principal payment is that generated from 300 PSA.

This characteristic of the collateral allows for the creation of a PAC tranche, assuming that the collateral prepays over its life at a speed between 90 PSA to 300 PSA. A schedule of principal repayments that the PAC bondholders are entitled to receive before any other tranche in the CMO structure is specified. The monthly schedule of principal repayments is as specified in the last column of Exhibit 13, which shows the minimum principal payment. That is, this minimum principal payment in each month is the principal repayment schedule (i.e., planned amortization schedule) for investors in the PAC tranche. While there is no assurance that the collateral will prepay at a constant speed between these two speeds over its life, a PAC tranche can be structured to assume that it will.

Exhibit 14 shows a CMO structure, FJF-05, created from the $400 million, 7.5% coupon passthrough with a WAC of 8.125% and a WAM of 357 months. There are just two tranches in this structure: a 7.5% coupon PAC tranche created assuming 90 to 300 PSA with a par value of $243.8 million, and a support tranche with a par value of $156.2 million.

Exhibit 15 reports the average life for the PAC tranche and the support tranche in FJF-05 assuming various actual prepayment speeds. Notice that between 90 PSA and 300 PSA, the average life for the PAC bond is stable at 7.26 years. However, at slower or faster PSA speeds, the schedule is broken, and the average life changes, extending when the prepayment speed is less than 90 PSA and contracting when it is greater than 300 PSA. Even so, there is much greater variability for the average life of the support tranche.

The support tranche typically is divided into different tranches. All the tranches we have discussed earlier are available, including sequential-pay support tranches, floater and inverse floater support tranches, and accrual support tranches.

The support tranche can even be partitioned to create support tranches with a schedule of principal payments. That is, support tranches that are PAC tranches can be created. In a structure with a PAC tranche and a support tranche with a PAC schedule of principal payments, the former is called a PAC I tranche or Level I PAC tranche and the latter a PAC II tranche or Level II PAC tranche or scheduled tranche (denoted SCH in a prospectus). While PAC II tranches have greater prepayment protection than the support tranches without a schedule of principal repayments, the prepayment protection is less than that provided PAC I tranches.

The support tranche without a principal repayment schedule can be used to create any type of tranche. In fact, a portion of the non-PAC II support tranche can be given a schedule of principal repayments. This tranche would be called a PAC III tranche or a Level III PAC tranche. While it provides protection against prepayments for the PAC I and PAC II tranches and is therefore subject to considerable prepayment risk, such a tranche has greater protection than the support tranche without a schedule of principal repayments.

The CMO structure we will discuss is the Freddie Mac (FHLMC) Series 1706 issued in early 1994. The collateral for this structure is Freddie Mac 7% coupon passthroughs. A summary of the deal is provided in Exhibit 19.

There are 17 tranches in this structure: 10 PAC tranches, three scheduled tranches, a floating-rate support tranche, and an inverse floating-rate support tranche.¹²⁹ There are also two “TAC” support tranches. We will explain a TAC tranche below. Let’s look at all tranches.

First, we know what a PAC tranche is. There are 10 of them: tranches A, B, C, D, E, G, H, J, K, and IA. The initial collar used to create the PAC tranches was 95 PSA to 300 PSA. The PAC tranches except for tranche IA are simply PACs that pay off in sequence. Tranche IA is structured such that the underlying collateral’s interest not allocated to the other PAC tranches is paid to the IO tranche. This is a notional IO tranche and we described earlier in this section how it is created. In this deal the tranches from which the interest is stripped are the PAC tranches. So, tranche IA is referred to as a PAC IO. (As of the time of this writing, tranches A and B had already paid off all of their principal.)

The prepayment protection for the PAC bonds is provided by the support tranches. The support tranches in this deal are tranches LA, LB, M, O, OA, PF, and PS. Notice that the support tranches have been carved up in different ways. First, there are scheduled (SCH) tranches. These are what we have called the PAC II tranches earlier in this section. The scheduled tranches are LA, LB, and M. The initial PAC collar used to create the scheduled tranches was 190 PSA to 250 PSA.

There are two support tranches that are designed such that they are created with a schedule that provides protection against contraction risk but not against extension. We did not discuss these tranches in this chapter. They are called target amortization class (TAC) tranches. The support tranches O and OA are TAC tranches. The schedule of principal payments is created by using just a single PSA. In this structure the single PSA is 225 PSA.

Finally, the support tranche without a schedule (that must provide support for the scheduled bonds and the PACs) was carved into two tranches—a floater (tranche PF) and an inverse floater (tranche PS). In this structure the creation of the floater and inverse floater was from a support tranche.

Now that we know what all these tranches are, the next step is to analyze them in terms of their relative value and their price volatility characteristics when rates change. We will do this in Chapter 12.

We have already seen interest-only type mortgage-backed securities: the structured IO. This is a product that is created within a CMO structure. A structured IO is created from the excess interest (i.e., the difference between the interest paid on the collateral and the interest paid to the bond classes). There is no corresponding PO class within the CMO structure. In contrast, in a stripped mortgage-backed security, the IO class is created by simply specifying that all interest payments be made to that class.

Since there is no interest that will be paid to the investor in a principal-only mortgage strip, the investor’s return is determined solely by the speed at which he or she receives the $225 million. In the extreme case, if all homeowners in the underlying mortgage pool decide to prepay their mortgage loans immediately, PO investors will realize the $225 million immediately. At the other extreme, if all homeowners decide to remain in their homes for 30 years and make no prepayments, the $225 million will be spread out over 30 years, which would result in a lower return for PO investors.

Let’s look at how the price of the PO would be expected to change as mortgage rates in the market change. When mortgage rates decline below the contract rate, prepayments are expected to speed up, accelerating payments to the PO investor. Thus, the cash flow of a PO improves (in the sense that principal repayments are received earlier). The cash flow will be discounted at a lower interest rate because the mortgage rate in the market has declined. The result is that the PO price will increase when mortgage rates decline. When mortgage rates rise above the contract rate, prepayments are expected to slow down. The cash flow deteriorates (in the sense that it takes longer to recover principal repayments). Couple this with a higher discount rate, and the price of a PO will fall when mortgage rates rise.

Exhibit 20 shows the general relationship between the price of a principal-only mortgage strip when interest rates change and compares it to the relationship for the underlying passthrough from which it is created.

Let’s look at the expected price response of an IO to changes in mortgage rates. If mortgage rates decline below the contract rate, prepayments are expected to accelerate. This would result in a deterioration of the expected cash flow for an IO. While the cash flow will be discounted at a lower rate, the net effect typically is a decline in the price of an IO. If mortgage rates rise above the contract rate, the expected cash flow improves, but the cash flow is discounted at a higher interest rate. The net effect may be either a rise or fall for the IO.

Thus, we see an interesting characteristic of an IO: its price tends to move in the same direction as the change in mortgage rates (1) when mortgage rates fall below the contract rate and (2) for some range of mortgage rates above the contract rate. Both POs and IOs exhibit substantial price volatility when mortgage rates change. The greater price volatility of the IO and PO compared to the passthrough from which they were created is due to the fact that the combined price volatility of the IO and PO must be equal to the price volatility of the passthrough.

Exhibit 20 shows the general relationship between the price of an interest-only mortgage strip when interest rates change and compares it to the relationship for the corresponding principal-only mortgage strip and underlying passthrough from which it is created.

An average life for a PO can be calculated based on some prepayment assumption. However, an IO receives no principal payments, so technically an average life cannot be computed. Instead, for an IO a cash flow average life is computed, using the projected interest payments in the average life formula instead of principal.

All IOs and POs are given a trust number. For instance, Fannie Mae Trust 1 is a IO/PO trust backed by specific pools of Fannie Mae 9% mortgages. Fannie Mae Trust 2 is backed by Fannie Mae 10% mortgages. Fannie Mae Trust 23 is another IO/PO trust backed by Fannie Mae 10% mortgages. Therefore, a portfolio manager must specify which trust he or she is buying.

The total proceeds of a PO trade are calculated the same way as with a passthrough trade except that there is no accrued interest. The market trades IOs based on notional principal. The proceeds include the price on the notional amount and the accrued interest.

The underlying mortgage loans for nonagency securities can be for any type of real estate property. There are securities backed by 1- to 4-single family residential mortgages with a first lien (i.e., the lender has a first priority or first claim) on the mortgaged property. There are nonagency securities backed by other types of single family residential loans. These include home equity loan-backed securities and manufactured housing-loan backed securities. Our focus in this section is on nonagency securities in which the underlying loans are first-lien mortgages for 1- to 4-single-family residential properties.

As with an agency mortgage-backed security, the servicer is responsible for the collection of interest and principal. The servicer also handles delinquencies and foreclosures. Typically, there will be a master servicer and subservicers. The servicer plays a key role. In fact, in assessing the credit risk of a nonagency security, rating companies look carefully at the quality of the servicers.

The loan-to-value ratio (LTV) is the ratio of the amount of the loan to the market value or appraised value of the property. The lower the LTV, the greater the protection afforded the lender. For example, an LTV of 0.90 means that if the lender has to repossess the property and sell it, the lender must realize at least 90% of the market value in order to recover the amount lent. An LTV of 0.80 means that the lender only has to sell the property for 80% of its market value in order to recover the amount lent.¹³⁰ Empirical studies of residential mortgage loans have found that the LTV is a key determinant of whether a borrower will default: the higher the LTV, the greater the likelihood of default.

As mentioned earlier in this chapter, a nonconforming mortgage loan is one that does not conform to the underwriting standards established by any of the agencies. Typically, the loans for a nonagency security are nonconforming mortgage loans that fail to qualify for inclusion because the amount of the loan exceeds the limit established by the agencies. Such loans are referred to as jumbo loans. Jumbo loans do not necessarily have greater credit risk than conforming mortgages.

Loans that fail to qualify because of the first two underwriting standards expose the lender to greater credit risk than conforming loans. There are specialized lenders who provide mortgage loans to individuals who fail to qualify for a conforming loan because of their credit history. These specialized lenders classify borrowers by credit quality. Borrowers are classified as A borrowers, B borrowers, C borrowers, and D borrowers. A borrowers are those that are viewed as having the best credit record. Such borrowers are referred to as prime borrowers. Borrowers rated below A are viewed as subprime borrowers. However, there is no industry-wide classification system for prime and subprime borrowers.

The major difference between agency and nonagency securities has to do with guarantees. With a nonagency security there is no explicit or implicit government guarantee of payment of interest and principal as there is with an agency security. The absence of any such guarantee means that the investor in a nonagency security is exposed to credit risk. The nationally recognized statistical rating organizations rate nonagency securities.

Because of the credit risk, all nonagency securities are credit enhanced. By credit enhancement it means that additional support against defaults must be obtained. The amount of credit enhancement needed is determined relative to a specific rating desired for a security rating agency. There are two general types of credit enhancement mechanisms: external and internal. We describe each of these types of credit enhancement in the next chapter where we cover asset-backed securities.

There are two types of CMBS deal structures that have been of primary interest to bond investors: (1) multiproperty single borrower and (2) multiproperty conduit. Conduits are commercial-lending entities that are established for the sole purpose of generating collateral to securitize.

CMBS have been issued outside the United States. The dominant issues have been U.K. based (more than 80% in 2000) with the primary property types being retail and office properties. Starting in 2001, there was dramatic increase in the number of CMBS deals issued by German banks. An increasing number of deals include multi-country properties. The first pan-European securitization was Pan European Industrial Properties in 2001.¹³¹

While fundamental principles of assessing credit risk apply to all property types, traditional approaches to assessing the credit risk of the collateral differs between CMBS and nonagency mortgage-backed securities and real estate-backed securities that fall into the asset-backed securities sector described in Chapter 11 (those backed by home equity loans and manufactured housing loans). For mortgage-backed securities and asset backed securities in which the collateral is residential property, typically the loans are lumped into buckets based on certain loan characteristics and then assumptions regarding default rates are made regarding each bucket. In contrast, for commercial mortgage loans, the unique economic characteristics of each income-producing property in a pool backing a CMBS require that credit analysis be performed on a loan-by-loan basis not only at the time of issuance, but monitored on an ongoing basis.

Regardless of the type of commercial property, the two measures that have been found to be key indicators of the potential credit performance is the debt-to-service coverage ratio and the loan-to-value ratio.

The debt-to-service coverage ratio (DSC) is the ratio of the property’s net operating income (NOI) divided by the debt service. The NOI is defined as the rental income reduced by cash operating expenses (adjusted for a replacement reserve). A ratio greater than 1 means that the cash flow from the property is sufficient to cover debt servicing. The higher the ratio, the more likely that the borrower will be able to meet debt servicing from the property’s cash flow.

For all properties backing a CMBS deal, a weighted average DSC ratio is computed. An analysis of the credit quality of an issue will also look at the dispersion of the DSC ratios for the underlying loans. For example, one might look at the percentage of a deal with a DSC ratio below a certain value.

As explained in Section VI.A, in computing the LTV, the figure used for “value” in the ratio is either market value or appraised value. In valuing commercial property, it is typically the appraised value. There can be considerable variation in the estimates of the property’s appraised value. Thus, analysts tend to be skeptical about estimates of appraised value and the resulting LTVs reported for properties.

The rating agencies will require that the CMBS transaction be retired sequentially, with the highest-rated bonds paying off first. Therefore, any return of principal caused by amortization, prepayment, or default will be used to repay the highest-rated tranche.

Interest on principal outstanding will be paid to all tranches. In the event of a delinquency resulting in insufficient cash to make all scheduled payments, the transaction’s servicer will advance both principal and interest. Advancing will continue from the servicer for as long as these amounts are deemed recoverable.

Losses arising from loan defaults will be charged against the principal balance of the lowest-rated CMBS tranche outstanding. The total loss charged will include the amount previously advanced as well as the actual loss incurred in the sale of the loan’s underlying property.