Frank J. Fabozzi, Ph.D., CFA

Adjunct Professor of Finance School of Management Yale University

David Yuen, CFA

Senior Vice President Portfolio Strategist/Risk Manager Franklin Templeton Investments

Real estate backed securities are securities backed by a pool (collection) of mortgage loans. Residential or commercial mortgages can be used as collateral for such securities. Real estate securities backed by residential mortgage loans include mortgage passthrough securities, stripped mortgage-backed securities, and collateralized mortgage obligations. Collectively we refer to these securities as mortgage-backed securities (MBS). In this chapter we describe those issued by either the Government National Mortgage Association (Ginnie Mae), the Federal National Mortgage Association (Fannie Mae), and the Federal Home Loan Mortgage Corporation (Freddie Mac). For the reasons described later in this chapter, these securities are referred to as agency MBS. In the next chapter, MBS not issued by one of these three entities are described. In Chapter 16 MBS backed by commercial mortgage loans are covered.

WHY IT IS IMPORTANT TO UNDERSTAND REAL ESTATE-BACKED SECURITIES

The U.S. mortgage market is the largest debt market in the world. A major innovation in the U.S. mortgage market has been the development of a wide range of mortgage designs from which borrowers can select. (We’ll discuss the major ones for residential mortgages later in this chapter.) Regardless of the type of mortgage design, as a stand alone investment mortgages typically have unattractive characteristics for both institutional and retail investors. From the perspective of investors, the major innovation in the mortgage market has been the development of securities backed by real estate mortgage loans-mortgage-backed securities or, more generally, real estate-backed securities. In this chapter and the two that follow, these securities are discussed.

An investor who is managing funds where the benchmark or “bogey” is a broad-based bond market index must be familiar with these securities because they represent a major component of the investment-grade bond market (i.e., market for bonds rated at least BBB-). To see this, consider one of the most popular bond indexes followed by institutional investors, the Lehman Brothers’ U.S. Aggregate Index. This index includes only investment-grade bonds and is composed of six sectors: Treasury, agency, mortgage passthrough, commercial mortgage-backed, asset-backed, and credit sectors. The mortgage passthrough sector includes securities guaranteed by Ginnie Mae, Fannie Mae, or Freddie Mac. These securities, which we describe later in this chapter, represent the largest sector of the index, constituting about 36%. Add to the mortgage passthrough sector the sector with securities backed by commercial mortgages of about 2% and the real estate-backed securities component increases to about 38% of the Lehman Brothers’ Aggregate Index.

The “mortgage sector” is defined by Lehman Brothers to consist of the mortgage passthrough sector and the commercial mortgage-backed sector. However, one more real estate component must be added: asset-backed securities (ABS) where the collateral is residential mortgages. The asset-backed sector is 2% of the index and includes securities backed by both real estate and non-real estate assets. Approximately 25% of the ABS sector is backed by residential real estate mortgages—specifically, home equity loan ABS and manufactured housing ABS, products that are described in the next chapter.

Consequently, a bond portfolio manager who is seeking to build a core portfolio to match the characteristics of the Lehman Brothers’ Aggregate Index must understand real estate-backed securities. Moreover, in constructing a portfolio, portfolio managers will depart from the characteristics of an index in order to enhance returns relative to the index. While there are a variety of strategies employed by active managers, one strategy is to look for securities that are not included in the index but are expected to outperform those securities in the index. There are opportunities to do this with real estate-backed securities. This can be done with securities issued by agencies that expose investors to minimal credit risk, called agency collateralized mortgage obligations, which we describe in this chapter. In addition, there are securities issued by private entities that provide return enhancement opportunities for investors willing to accept credit risk that are described in the next chapter.

The bottom line is that a bond portfolio manager seeking to build a core portfolio but who is unfamiliar with real estate-backed securities will be at a competitive disadvantage. Moreover, a portfolio manager who is unfamiliar with real estate-backed securities may miss opportunities to enhance return in products that are not part of the index.

MORTGAGES

We begin our discussion with the raw material for a mortgage-backed security-the mortgage loan. A mortgage loan, or simply mortgage, is a loan secured by the collateral of some specified real estate property, which obliges the borrower to make a predetermined series of payments. The mortgage gives the lender the right if the borrower defaults (i.e., fails to make the contracted payments) to “foreclose” on the loan and seize the property in order to ensure that the debt is paid off. The interest rate on the mortgage loan is called the mortgage rate or contract rate. Our focus is on residential mortgage loans.

An individual who wants to borrow funds to purchase a home will apply for a loan from a mortgage originator. The individual who seeks funds completes an application form that provides personal financial information, and pays an application fee; then the mortgage originator performs a credit evaluation of the applicant. The two primary factors in determining whether the funds will be lent are the (1) payment-to-income (PTI) ratio, and (2) the loan-to-value (LTV) ratio. The former is the ratio of monthly payments to monthly income and is a measure of the ability of the applicant to make monthly payments (both mortgage and real estate tax payments). The lower this ratio, the greater the likelihood that the applicant will be able to meet the required payments.

LTV is the ratio of the amount of the loan to the market (or appraised) value of the property. The lower this ratio, the greater the protection the lender has if the applicant defaults on the payments and the lender must repossess and sell the property. For example, if an applicant wants to borrow $150,000 on property with an appraised value of $200,000, the LTV is 75%. Suppose the applicant subsequently defaults on the mortgage. The lender can then repossess the property and sell it to recover the amount owed. But the amount that will be received by the lender depends on the market value of the property. In our example, even if conditions in the housing market are weak, the lender will still be able to recover the proceeds lent if the value of the property declines by $50,000. Suppose instead that the applicant wanted to borrow $180,000 for the same property. The LTV would then be 90%. If the lender had to sell the property because the applicant defaults, there is less protection for the lender.

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 also may take out mortgage insurance to guarantee the fulfillment of the borrower’s obligation. 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.

There are many types of mortgage designs available in the United States. A mortgage design is a specification of the interest rate, term of the mortgage, and manner in which the borrowed funds are repaid. Here we will discuss the three major ones. With an understanding of the features of these mortgages, securities backed by mortgages can be understood.

Fixed-Rate, Level-Payment, Fully Amortized Mortgage

The basic idea behind the design of the fixed-rate, level-payment, fully amortized mortgage is that the borrower pays interest and repays principal in equal installments over an agreed-upon period of time, called the maturity or term of the mortgage. 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:

1. interest of 1/12 of the annual interest rate times the amount of the outstanding mortgage balance at the beginning of the previous month, and
2. a repayment of a portion of the outstanding mortgage balance (principal).

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 payment of the loan is made, the amount of the outstanding mortgage balance is zero (i.e., the mortgage is fully repaid or amortized).

To illustrate this mortgage design, consider a 30-year (360-month) $100,000 mortgage with a mortgage rate of 8.125%. The monthly mortgage payment would be $742.50. Exhibit 14.1 shows for selected months how each monthly mortgage payment is divided between interest and repayment of principal. 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 $65.42 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 repayment of principal. The $65.42 in month 1 reduces the mortgage balance. Notice that the last mortgage payment in month 360 is sufficient to pay off the remaining mortgage balance.

As Exhibit 14.1 clearly shows, the portion of the monthly mortgage payment applied to interest declines each month, and the portion applied to reducing the mortgage balance 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 fixed, an increasingly larger portion of the monthly payment is applied to reduce the principal in each subsequent month.

The monthly mortgage payment made by the borrower is not what the investor receives. This is because the mortgage must be serviced. The servicing fee is a portion of the mortgage rate. If the mortgage rate is 8.125% and the servicing fee is 50 basis points, then the investor receives interest of 7.625%. The interest rate that the investor receives is said to be the net interest or net coupon.

Prepayments and Cash Flow Uncertainty

Our illustration of the cash flows from a fixed-rate, level-payment, fully amortized mortgage assumes that the homeowner does not pay off any portion of the mortgage balance prior to the scheduled due date. But some homeowners do pay off all or part of their mortgage balance prior to the maturity date. Payments made in excess of the scheduled principal repayments are called prepayments. Later we will discuss factors that affect prepayments.

The effect of prepayments is that the amount and timing of the cash flows from a mortgage are not known with certainty. This risk is referred to as prepayment risk. For example, all that the investor in a $100,000, 8.125% 30-year mortgage knows is that as long as the loan is outstanding and the borrower does not default, interest will be received and the principal will be repaid at the scheduled date each month; then at the end of the 30 years, the investor would have received $100,000 in principal payments. What the investor does not know-the uncertainty-is for how long the loan will be outstanding, and therefore what the timing of the principal payments will be. This is true for all mortgage loans, not just fixed-rate, level-payment, fully amortized mortgages.

The majority of mortgages outstanding do not penalize the borrower for prepaying any part or all of the outstanding mortgage balance. In recent years, mortgage prepayment penalty mortgages (PPMs) have been originated. In a PPM there is a specified time period, called the “lockout period,” where partial prepayments above a specified amount will result in a prepayment penalty. (There is no penalty for prepayment due to the sale of property; only voluntary prepayments are penalized.) After the lockout period there are no penalties for prepayment. The motivation for the PPM is that it reduces prepayment risk for the lender during the lockout period. It does so by effectively making it more costly for the borrower to prepay in order to take advantage of a decline in mortgage rates. In exchange for this reduction in prepayment risk, the lender will offer a mortgage rate that is less than that of an otherwise comparable mortgage loan without a prepayment penalty.

Adjustable-Rate Mortgages

As the name implies, an adjustable-rate mortgage (ARM) has an adjustable or floating coupon instead of a fixed one. The coupon adjusts peri-odically—monthly, semiannually, or annually. Some ARMs even have coupons that adjust every three years or five years. The coupon formula for an ARM is specified in terms of a reference rate plus a quoted margin. The margin is typically 2% to 3%.

At origination, the mortgage usually has an initial rate for an initial period (teaser period) which is slightly below the rate specified by the coupon formula. This is called a “teaser rate” and makes it easier for first time home buyers to qualify for the loan. At the end of the teaser period, the loan rate is reset based on the coupon formula. Once the loan comes out of its teaser period and resets based on the coupon formula, it is said to be fully indexed.

To protect the homeowner from interest rate shock, there are caps or ceilings imposed on the coupon adjustment level. There are periodic caps and lifetime caps. The periodic cap limits the amount of coupon reset upward or downward from one reset period to another. The lifetime cap is the maximum absolute level for the coupon rate that the loan can reset to for the life of the mortgage.

The attributes needed to describe an ARM are the teaser rate, teaser period, index, margin, reset frequency, periodic cap, and lifetime cap. For example, a “6% 1-year CMT + 3% ARM with 2/12 caps” means the loan has a 6% coupon for the first year. It will reset the second year coupon to the then 1-year CMT index rate plus 3% on the anniversary date subject to the 2% periodic cap and 12% lifetime cap constraints. If the prevailing CMT rate is 4.8%, the coupon will simply reset to 7.8% (4.8% + 3%). If the prevailing CMT rate is 5.5%, the coupon can only reset to 8% (not 5.5% + 3%) because the 2% periodic cap only allows a maximum of 2% movement (plus or minus) in the coupon rate from one period to another. The 12% lifetime cap limits the coupon to 12% during the life of the loan.

Two categories of indices have been used in ARMs: (1) market determined rates and (2) calculated cost of funds for thrifts. The index will have an important impact on the performance of an ARM and its value. The most common market determined rates used are the 1-year, 3-year, or 5-year Constant Maturity Treasury (CMT), 3-month or 6-month London Interbank Offered Rate (LIBOR), and the 6-month CD rate.

The cost of funds index for thrifts is calculated based on the monthly weighted average interest cost for liabilities of thrifts. The most popular is the Eleventh Federal Home Loan Bank Board District Cost of Funds Index (COFI). About 25% of ARMs are indexed to this reference rate. The Eleventh District includes the states of California, Arizona, and Nevada. The cost of funds is calculated by first computing the monthly interest expenses for all thrifts included in the Eleventh District. The interest expenses are summed and then divided by the average of the beginning and ending monthly balance. The index value is reported with a one month lag. For example, June’s Eleventh District COFI is reported in July. The mortgage rate for a mortgage based on the Eleventh District COFI is usually reset based on the previous month’s reported index rate. For example, if the reset date is August, the index rate reported in July will be used to set the mortgage rate. Consequently, there is a two month lag by the time the average cost of funds is reflected in the mortgage rate. This obviously is an advantage to the borrower when interest rates are rising and a disadvantage to the investor. The opposite is true when interest rates are falling.

The second most popular index is the National Cost of Funds Index, which covers all Federal Home Loan Bank districts. A third category is a calculated index based on market rates. An example would be the 12-month moving average of the 1-year Treasury bill rates.

Balloon Mortgages

In a balloon mortgage, the borrower is given long-term financing by the lender but at specified future dates the contract rate is renegotiated. Thus, the lender is providing long-term funds for what is effectively a short-term borrowing, how short depending on the frequency of the renegotiation period. Effectively it is a short-term balloon loan in which the lender agrees to provide financing for the remainder of the term of the mortgage. The balloon payment is the original amount borrowed less the amount amortized. Thus, in a balloon mortgage, the actual maturity is shorter than the stated maturity.

MORTGAGE PASSTHROUGH SECURITIES

Investing in mortgages exposes an investor to default risk and prepayment risk. A more efficient way is to invest in a mortgage passthrough security. This is a security created when one or more holders of mortgages form a pool (collection) of mortgages and sell shares or participation certificates in the pool. A pool may consist of several thousand or only a few mortgages. When a mortgage is included in a pool of mortgages that is used as collateral for a mortgage passthrough security, the mortgage is said to be securitized.

The cash flows of a mortgage passthrough security depend on the cash flows of the underlying mortgages. The cash flows consist of monthly mortgage payments representing interest, the scheduled repayment of principal, and any prepayments for all the mortgages in the pool.

Payments are made to security holders each month. Neither the amount nor the timing, however, of the cash flows from the pool of mortgages are identical to that of the cash flows passed through to investors. The monthly cash flows for a passthrough are less than the monthly cash flows of the underlying 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. The coupon rate on a passthrough, called the passthrough coupon rate, is less than the mortgage rate on the underlying pool of mortgage loans by an amount equal to the servicing fee and guarantee fee. Consequently, if there are 10,000 certificate issued, then the holder of one certificate is entitled to 1/10,000 of the cash flow from the pool of mortgages after adjusting for all fees.

The timing of the cash flows 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 amount of the mortgage balance outstanding. 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 mortgage balance outstanding.

Other features of mortgage passthrough securities vary by issuer. The key features of a passthrough will have an impact on its investment characteristics (particularly its prepayment characteristics). These general features are (1) the type of guarantee, (2) the mortgage design of the loans, and (3) the characteristics of the mortgage loans in a pool.

AGENCY PASSTHROUGHS

Mortgage passthroughs are classified into Government National Mortgage Association (Ginnie Mae), Federal National Mortgage Association (Fannie Mae), Federal Home Loan Mortgage Corporation (Freddie Mac), and private entity mortgage passthroughs. The first three are federal agencies which were described in Chapter 9. Ginnie Mae is a federally related institution while Fannie Mae and Freddie Mac are government sponsored enterprises (GSEs).

There are several practices in the market in referring to the mortgage passthroughs issued by these entities. Some market participants simply refer to them as “agency passthroughs.” Other market participants refer to the mortgage passthroughs issued by Ginnie Mae as “agency passthroughs” and those issued by the two GSEs as “conventional passthroughs” and then all three are referred to as “agency/conventional passthroughs.” In this chapter, mortgage passthroughs issued by Ginnie Mae, Fannie Mae, and Freddie Mac will be referred to as agency passthroughs.

For a mortgage to be included in the pool of mortgages that is the collateral for an agency passthrough, the loans must meet the criteria established by the agency. These criteria are referred to as “underwriting standards” and they are discussed in the next chapter. A mortgage that meets the underwriting standards is referred to as a “conforming loan” and obviously a loan that fails the underwriting standards is called a “nonconforming loan.” The different types of nonconforming loans are discussed in the next chapter.

Private entities are issuers of mortgage passthroughs that are not one of the federal agencies. They include commercial banks, savings and loan associations, investment banking firms, finance companies, and mortgage companies. The mortgage passthrough securities issued by private entities are referred to as “nonagency passthroughs.” The mortgages that back nonagency passthrough securities are nonconforming loans.

Default Risk

A Ginnie Mae passthrough-referred to by as a Ginnie Mae mortgage passthrough security (MBS)-is guaranteed by the full faith and credit of the U.S. government. That is, the investor will receive timely payment of interest and principal when it is due even if borrowers default on their loans. Thus, a Ginnie Mae MBS is viewed as risk-free in terms of default risk, just like Treasury securities.

Because Fannie Mae and Freddie Mac are GSEs, a mortgage passthrough that they issue is not guaranteed by the full faith and credit of the U.S. government. Market participants, however, view their mortgage passthroughs as having minimal credit risk. A passthrough issued by Fannie Mae—called a Fannie Mae mortgage-backed security (MBS)—is guaranteed with respect to the timely payment of interest and principal. A Freddie Mac passthrough—called a Freddie Mac participation certificate (PC)—can have one of two guarantees. One type of guarantee is where Freddie Mac guarantees the timely payment of interest and the eventual payment of principal. By “eventual” it is meant that the principal due will be paid when it is collected, but in no circumstance later than one year. The second type of guarantee is one in which Freddie Mac guarantees the timely payment of both interest and principal which the agency refers to as the Gold program. Freddie Mac now only issues Gold PCs.

Because of the guarantee provided by Ginnie Mae, Fannie Mae, and Freddie Mac, principal payment due to defaults are reported as a prepayment. For nonagency passthroughs, there is no explicit or implicit government guarantee. Instead, a private entity that wants to issue a mortgage-backed security must credit enhance the issue. The mechanisms for credit enhancement (internal and external) are explained in the next chapter.

Prepayment Conventions and Cash Flows

The cash flows of a mortgage passthrough are unknown because of prepayments. The only way to project cash flows is to make some assumptions about the prepayment rate over the life of the underlying mortgage pool. The prepayment rate is sometimes referred to as the speed. Two conventions have been used as a benchmark for prepayment rates: conditional prepayment rate and Public Securities Association prepayment benchmark.

Conditional Prepayment Rate

One convention for projecting prepayments and the cash flows of a passthrough assumes that some fraction of the remaining principal in the pool is prepaid each month for the remaining term of the mortgage. The prepayment rate assumed for a pool, called the conditional prepayment rate (CPR), is based on the characteristics of the pool (including its historical prepayment experience) and the current and expected future economic environment.

The CPR is an annual prepayment rate. To estimate monthly prepayments, the CPR must be converted into a monthly prepayment rate, commonly referred to as the single-monthly mortality rate (SMM). A formula can be used to determine the SMM for a given CPR:

SMM = 1 - (1 - CPR)^1/12

Suppose that the CPR used to estimate prepayments is 6%. The corresponding SMM is:

SMM = 1 - (1 - 0.06)^1/12 = 1 - (0.94)^0.08333 = 0.005143

An SMM of w% means that approximately w% of the remaining mortgage balance at the beginning of the month, less the scheduled principal payment, will prepay that month. That is,

Prepayment for month t = SMM × (Beginning mortgage balance for month t - Scheduled principal payment for month t)

For example, suppose that an investor owns a passthrough in which the remaining mortgage balance at the beginning of some month is $290 million. Assuming that the SMM is 0.5143% and the scheduled principal payment is $3 million, the estimated prepayment for the month is:

0.005143 × ($290,000,000 - $3,000,000) = $1,476,041

PSA Prepayment Benchmark

The Public Securities Association (PSA) prepayment benchmark is expressed as a monthly series of CPRs. The PSA benchmark assumes that prepayment rates are low for newly originated mortgages and then will speed up as the mortgages become seasoned.

The PSA benchmark assumes the following prepayment rates for 30-year mortgages:

1. a CPR of 0.2% for the first month, increased by 0.2% per year per month for the next 30 months when it reaches 6% per year, and
2. a 6% CPR for the remaining years.

This benchmark, referred to as “100% PSA” or simply “100 PSA,” is mathematically expressed as follows:

if t ≤ 30 the CPR = 6% t/30
if t > 30 then CPR = 6%

where t is the number of months since the mortgage originated.

Slower or faster speeds are then referred to as some percentage of PSA. For example, 50 PSA means one-half the CPR of the PSA benchmark prepayment rate; 150 PSA means 1.5 times the CPR of the PSA benchmark prepayment rate; 300 PSA means three times the CPR of the benchmark prepayment rate. A prepayment rate of 0 PSA means that no prepayments are assumed.

The CPR is converted to an SMM using the formula given above. For example, assuming 165 PSA the SMMs for month 20 after the mortgage is originated is calculated as follows:

CPR = 6% (20/30) = 4% = 0.04

165 PSA = 1.65 (0.04) = 0.066

SMM = 1 - (1 - 0.066)^1/l2 = 0.005674

Notice that the SMM assuming 165 PSA is not just 1.65 times the SMM assuming 100 PSA. It is the CPR that is a multiple of the CPR assuming 100 PSA.

For months 31 to 360, the CPR is 6% at 100 PSA and the CPR and SMM for each month for 165 PSA is

165 PSA = 1.65 (0.06) = 0.099

SMM = 1 - (1 - 0.099)^1/l2 = 0.00865

Note: Since the WAM is 357 months, the underlying mortgage pool is seasoned an average of 3 months. Therefore, the CPR for month 27 is 1.65 × 6%.

Illustration of Monthly Cash Flow Construction

We now show how to construct a monthly cash flow for a hypothetical passthrough given a PSA assumption. For the purpose of this illustration, the underlying mortgages for this hypothetical passthrough are assumed to be fixed-rate, level-payment, fully amortized mortgages with a weighted average coupon (WAC) rate of 8.125%. It will be assumed that the passthrough rate is 7.5% with a weighted average maturity (WAM) of 357 months.

Exhibit 14.2 shows the cash flow for selected months assuming 165 PSA. The cash flow is broken down into three components: (1) interest (based on the passthrough rate), (2) the regularly scheduled principal repayment, and (3) prepayments based on 165 PSA.

Column (2) gives the outstanding mortgage balance at the beginning of the month. It is equal to the outstanding balance at the beginning of the previous month reduced by the total principal payment in the previous month. Column (3) shows the SMM for 165 PSA. Two things should be noted in this column. First, for month 1, the SMM is for a passthrough that has been seasoned 3 months because the WAM is 357. The total monthly mortgage payment is shown in Column (4). Notice that the total monthly mortgage payment declines over time as prepayments reduce the mortgage balance outstanding. There is a formula to determine what the monthly mortgage balance will be for each month given prepayments but we will not present that formula here. Column (6) gives the regularly scheduled principal repayment. This is the difference between the total monthly mortgage payment [the amount shown in Column (4)] and the gross coupon interest for the month. The gross coupon interest is 8.125% multiplied by the outstanding mortgage balance at the beginning of the month, then divided by 12.

The prepayment for the month is reported in Column (7). The prepayment is found using the formula given above. For example, in month 100, the beginning mortgage balance is $170,142,350, the scheduled principal payment is $244,953, and the SMM at 165 PSA is 0.00865. Therefore, the prepayment is:

0.00865 × ($170,142,350 - $244,953) = $1,469,612

The difference between $1,469,591 shown in Column (7) and the prepayment of $1,469,612 computed above is simply due to the rounding of the SMM shown in the exhibit to save space.

The total principal payment reported in Column (8) is the sum of Columns (6) and (7). Finally, the projected monthly cash flow for this passthrough is shown in this last column. The monthly cash flow is the sum of the interest paid to the passthrough investor [Column (5)] and the total principal payments for the month [Column (8)].

Factors Affecting Prepayment Behavior

A prepayment model is a statistical model that is used to forecast prepayments. It begins by modeling the statistical relationships among the factors that are expected to affect prepayments. The four main factors that affect prepayment behavior are (1) prevailing mortgage rate, (2) characteristics of the underlying mortgage pool, (3) seasonal factors, and (4) general economic activity.

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 more the contract rate exceeds the prevailing mortgage rate, 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, such as title insurance and origination points, will vary proportionately with the amount to be financed. Other costs, such as the application fee and legal expenses, are typically fixed. 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.

Other secondary factors affecting prepayments include:

• Loan-to-Value Ratio—High LTV loans prepay slower, everything else being equal, because there is not sufficient equity to refinance. Low LTV loans with lots of equity also trigger cash-out refinancing.
• Debt Consolidation—Sufficient equity also allows for debt consolidation, i.e. refinance into a higher balance mortgage loan to pay off car loans and credit card debts.
• Loan Size—Low balance loans prepay slower because the fixed portion of the refinancing cost becomes a bigger hurdle as a percentage of the loan size.
• Regional economy—Improving regional economy triggers housing turnover activity.
• Homeowners’ credit—Improving economy improves homeowners’ credit in general. During a recession, homeowners’ credit deteriorates (e.g., unemployment) and they cannot refinance even if mortgage rates are low.
• Proliferation of new mortgage loan types—A 30-year mortgagee does not have to refinance into another 30-year mortgage. Given the popularity of ARMs, balloons, and hybrids (fixed for a period then converts to an ARM), which generally offer lower rates in a steep yield curve environment, a 30-year borrower can refinance into these products while a 30-year to 30-year refinancing is not economical.

Average Life

The stated maturity of a mortgage passthrough is an inappropriate measure because of principal repayments over time. Instead, market participants calculate an average life which is the average time to receipt of principal payments (scheduled principal payments and projected prepayments), calculating as follows:

where T is the last month that principal is expected to be received.

Then the average life is found as follows:

The average life of a passthrough depends on the PSA prepayment assumption. To see this, the average life is shown below for different prepayment speeds for the passthrough we used to illustrate the cash flows in Exhibit 14.2:

Contraction Risk and Extension Risk

An investor who owns passthrough securities does not know what the cash flows will be because that depends on prepayments. As noted earlier, this risk is called prepayment risk. However, prepayment risk can be divided into two risks, contraction risk and prepayment risk. We will explain these two risk by means of the following example.

Suppose an investor buys a 10% coupon mortgage passthrough at a time when the prevailing mortgage rate is 10%. Suppose further that the expected average life for this mortgage passthrough is 9 years based on a prepayment rate of 110 PSA. Let’s consider what will happen to prepayments if mortgage rates decline to, say, 6%. The borrower will have an incentive to prepay all or part of the mortgage resulting in a shortening of the average life of the security from what it was expected to be when the security was purchased. For example, the market might expect that the prepayment speed will increase to 200 PSA resulting in a decrease in the average life to 6 years. The disadvantage to the investor is that the funds received from the prepayments will have to be reinvested at lower interest rates. This risk that the average life of the security will be shortened, forcing the investor to reinvest at lower interest rates, is referred to as contraction risk.

Now let’s look at what happens if mortgage rates rise to 14%. Prepayments can be expected to slow down because homeowners will not refinance or partially prepay their mortgages resulting in an increase in the expected average life. For example, the market might expect the prepayment rate to decrease to 75 PSA, which would result in an average life of 12 years. Unfortunately, it is in a rising interest rate environment when investors want prepayments to speed up so that they can reinvest the principal received at the higher market interest rate. This adverse consequence of rising mortgage rates is called extension risk.

Therefore, prepayment risk encompasses contraction risk and extension risk. Prepayment risk makes passthrough securities unattractive for certain individuals and financial institutions to hold for purposes of accomplishing their investment objectives. Some individuals and institutional investors are concerned with extension risk and others with contraction risk when they purchase a passthrough security. Is it possible to alter the cash flows of a passthrough to reduce the contraction risk or extension risk for institutional investors? This can be done as we will see when we discuss collateralized mortgage obligations.

Trading and Settlement Procedures

Agency passthroughs are identified by a pool prefix and pool number provided by the agency. The prefix indicates the type of passthrough. For example, a pool prefix of 20 for a Freddie Mac PC means that the underlying pool consists of conventional mortgages with an original maturity of 15 years. A pool prefix of AR for a Ginnie Mae MBS means that the underlying pool consists of adjustable-rate mortgages. The pool number indicates the specific mortgages underlying the passthrough and the issuer of the passthrough.

There are specific rules established by the Bond Market Association (previously the Public Securities Association) for the trading and settlement of mortgage-backed securities. Our discussion here is limited to agency passthrough securities.

Many trades occur while a pool is still unspecified and therefore no pool information is known at the time of the trade. This kind of trade is known as a “TBA” (to be announced) trade. In a TBA trade the two parties agree on the agency type, the agency program, the coupon rate, the face value, the price, and the settlement date. The actual pools underlying the agency passthrough are not specified in a TBA trade. However, this information is provided by the seller to the buyer before delivery. There are trades where more specific requirements are established for the securities to be delivered, for example, a Freddie Mac Gold with a coupon rate of 7.0% and a WAC between 7.5% and 7.7%. There are also specified pool trades wherein the actual pool numbers to be delivered are specified.

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:

Price × Par value × Pool factor

For example, if the parties agree to a price of 92 for $1 million par value for a passthrough with a pool factor of 85, then the dollar price paid by the buyer in addition to accrued interest is:

0.92 × $1,000,000 × 0.85 = $782,000

Trades settle according to a delivery schedule established by the BMA. This schedule is published quarterly with information regarding delivery for the next six months. Each agency and program settles on a different day of the delivery month.

By 3 p.m. eastern standard time two business days before the settlement date, the seller must furnish information to the buyer about pools that will be delivered. This is called the 48-hour rule. The date that this information must be given is called the notification date or call-out date. Two parties can agree to depart from BMA guidelines and settle at any time.

When an investor purchases, say, $1 million GNMA 7s on a TBA basis, the investor can receive up to three pools. Three pools can be delivered because the BMA has established guidelines for standards of delivery and settlement of mortgage-backed securities, under which our hypothetical TBA trade permits three possible pools to be delivered. The option of what pools to deliver is left to the seller, as long as selection and delivery satisfy the BMA guidelines.

There are many seasoned issues of the same agency with the same coupon rate outstanding at a given point in time. For example, there are more than 30,000 pools of 30-year Ginnie Mae MBSs outstanding with a coupon rate of 7%. 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 7s? 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 are for generic passthroughs. A particular pool purchased may have a materially different prepayment speed from the generic. Moreover, when an investor purchases a passthrough without specifying a pool number, the seller can deliver the worst-paying pools as long as the pools delivered satisfy good delivery requirements.

In a TBA trade, the BMA delivery standards permit an under-or overdelivery tolerance of $100 per million traded or 0.01%. This means that if $1 million of par value is sold at par, the seller may deliver to the buyer passthroughs with a par value anywhere between $999,900 and $1,000,100. This delivery option used to be a benefit to the seller when the delivery variance was as large as 3%. To understand why, suppose that interest rates decline between the trade date and the settlement date. The value of passthroughs will rise, and therefore it will be beneficial for the seller to deliver less than $1 million. The opposite is true if interest rates rise between the trade date and the settlement date: the seller will deliver the maximum permissible. That delivery option is effectively removed by the current 0.01% variance allowance.

Dollar Rolls

In the MBS market, a special type of collateralized loan has developed because of the characteristics of these securities and the need of dealers to borrow these securities to cover short positions. This arrangement is called a dollar roll because the dealer is said to “roll in” securities borrowed and “roll out” securities when returning the securities to the portfolio manager.

As with a repo agreement, it is a collateralized loan that calls for the sale and repurchase of a security. Unlike a repo agreement, the dealer who borrows the securities need not return the identical security. That is, the dealer need only return a “substantially identical security.” This means that the security returned by the dealer that borrows the security must match the coupon rate and security type (i.e., issuer and mortgage collateral). This provides flexibility to the dealer. In exchange for this flexibility, the dealer provides 100% financing. That is, there is no over collateralization or margin required. Moreover, the financing cost may be cheaper than in a repo because of this flexibility. Finally, unlike in a repo, the dealer keeps the coupon and any principal paid during the period of the loan.

Determination of the Financing Cost

Determination of the financing cost is not as simple as in a repo. The key elements in determining the financing cost, assuming that the dealer is borrowing securities/lending cash, are:

1. the sale price and the repurchase price
2. the amount of the coupon payment
3. the amount of the principal payments due to scheduled principal payments
4. the projected prepayments of the security sold (i.e., rolled in to the dealer)
5. the attributes of the substantially identical security that is returned (i.e., rolled out by the dealer)
6. the amount of under-or overdelivery permitted

Let’s look at these elements. In a repo agreement, the repurchase price is greater than the sale price, the difference representing interest and is called the drop. In the case of a dollar roll, the repurchase price need not be greater than the sale price. In fact, in a positively sloped yield curve environment (i.e., long-term rates exceed short-term rates), the repurchase price will be less than the purchase price. The reason for this is the second element, the coupon payment. The dealer keeps the coupon payment.

The third and fourth elements involve principal repayments. The principal payments include scheduled principal and prepayments. As with the coupon payments, the dealer retains the principal payments during the period of the agreement. A gain will be realized by the dealer on any principal repayments if the security is purchased by the dealer at a discount and a loss if purchased at a premium. Because of prepayments, the principal that will be paid is unknown and, as will be seen, represents a risk in the determination of the financing cost.

The fifth element is another risk since the effective financing cost will depend on the attributes of the substantially identical security that the dealer will roll out (i.e., the security it will return to the lender of the securities) at the end of the agreement. Finally, as explained earlier, there are delivery tolerances-that is, permissible under—or overdelivery permitted.

To illustrate how the financing cost for a dollar roll is calculated, suppose that a portfolio manager enters into an agreement with a dealer in which it agrees to sell $10 million par value (i.e., unpaid aggregate balance) of Ginnie Mae 8s at 101^7/32 and repurchase substantially identical securities a month later at 101 (the repurchase price). The drop is therefore 7/32. While under-or overdelivery is permitted, we will assume that $10 million par value will be delivered to the dealer by the portfolio manager and the same amount of par value will be returned to the portfolio manager by the dealer. Since the sale price is 101^7/32, the portfolio manager will receive in cash $10,121,875 (101.21875 × $10 million). At the repurchase date, the portfolio manager can repurchase substantially identical securities for 101 or $10,100,000. Therefore, the portfolio manager can sell the securities for $10,121,875 and buy them back for $10,100,000. The difference-which is the drop-is $21,875.

To offset this, the portfolio manager forfeits the coupon interest during the period of the agreement to the dealer. Since the coupon rate is 8%, the coupon interest forfeited is $66,666 (8% × $10 million/12). The dealer is also entitled to any principal repayments, both regularly scheduled and prepayments. Since the dealer purchases the securities from the portfolio manager at $101^7/32, any principal repayments will result in a loss of $1^7/32 per $100 of par value of principal repaid. From the portfolio manager’s perspective, this is a benefit and effectively reduces the financing cost. While the regularly scheduled amount can be determined, prepayments must be projected based on some PSA speed. In our illustration, for simplicity let’s assume that the regularly scheduled principal payment for the month is $6,500 and the prepayment is projected to be $20,000 based on some PSA speed. Since $1^7/32 is lost per $100 par value repaid, the dealer loses $79 due to the regularly scheduled principal payment (1^7/32 × $6,500/100) and $244 from prepayments (1^7/32 × $20,000/100).

The monthly financing cost is then:

The financing cost as calculated, 5.27%, must be compared with alternative financing opportunities. For example, funds can be borrowed via a repo agreement using the same Ginnie Mae collateral. In comparing financing costs, it is important that the dollar amount of the cost be compared to the amount borrowed. For example, in our illustration we annualized the cost by multiplying the monthly rate by 12. The convention in other financing markets may be different for annualizing. Moreover, it is not proper to compare financing costs of other alternatives without giving recognition to the risks associated with a dollar roll.

Because of the unusual nature of the dollar roll transaction as a collateralized borrowing vehicle, it is only possible to estimate the financing cost. From our illustration, it can be seen that when the transaction prices are above par value, then the speed of prepayments affects the financing cost. The maximum financing cost can be determined by assuming no prepayments. In this case, the total financing cost would be $244 greater or $44,712. This increases the annual financing cost from 5.27% to 5.29%, or 2 basis points. In practice, a portfolio manager can perform sensitivity analysis to determine the effect of prepayments on the financing cost.

STRIPPED MORTGAGE-BACKED SECURITIES

A mortgage passthrough distributes the cash flow from the underlying pool of mortgages on a pro rata basis to the security holders. A stripped mortgage-backed security (stripped MBS) is created by altering that distribution of principal and interest from a pro rata distribution to an unequal distribution. In the most common type of stripped mortgage-backed securities, all the interest is allocated to one class-the interest only class-and all the principal to the other class-the principal-only class.

Principal-Only Securities

A principal-only security, also a called the PO or a principal-only mortgage strip, is purchased at a substantial discount from par value. The return an investor realizes depends on the speed at which prepayments are made. The faster the prepayments, the higher the investor’s return. For example, suppose there is a mortgage pool consisting only of 30-year mortgages with $400 million in principal, and that investors can purchase POs backed by this mortgage pool for $175 million. The dollar return on this investment will be $225 million. How quickly that dollar return is recovered by PO investors determines the actual return that will be realized. 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 holder. 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.

Interest-Only Securities

An interest-only security, also called an IO or an interest-only mortgage strip, has no par value. In contrast to the PO investor, the IO investor wants prepayments to be slow because the IO investor receives interest only on the amount of the principal outstanding. When prepayments are made, less dollar interest will be received as the outstanding principal declines. In fact, if prepayments are too fast, the IO investor may not recover the amount paid for the IO even if the security is held to maturity.

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 because the combined price volatility of the IO and PO must be equal to the price volatility of the passthrough.

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.

Trading and Settlement Procedures for Stripped Mortgage-Backed Securities

The trading and settlement procedures for stripped mortgage-backed securities are similar to those set by the BMA for agency passthroughs described in the previous section. The specifications are in the types of trades (TBA versus specified pool), calculations of the proceeds, and the settlement dates.

IOs and POs are extreme premium and discount securities and consequently are very sensitive to prepayments, which are driven by the specific characteristics (GWAC, WAM, geographic concentration, average loan size) of the underlying loans. The TBA delivery option on IOs and POs has an economic value and this value is hard to quantify. Therefore, almost all secondary trades in IOs and POs are on a specified pool basis rather than on a TBA basis.

All IOs and POs are given a trust number. For instance, FNMA Trust 1 is a IO/PO trust backed by specific pools of FNMA 9% mortgages. FNMA Trust 2 is backed by FNMA 10% mortgages. FNMA Trust 23 is another IO/PO trust backed by FNMA 10% mortgages. The value of Trust 23 PO may be higher or lower than the value of Trust 2 PO depending on the perceived prepayment behavior of Trust 23 relative to that of Trust 2 based on the GWAC, WAM, and geographical concentration of the two specific trusts. Therefore, an investor must specify which trust he or she is buying.

Since the transactions are on a specified trust basis, they are also done based on the original face amount. For example, suppose an investor agrees to buy $10 million original face of Trust 23 PO for August settlement. At the time of the transaction, the August factor need not be known; however, there is no ambiguity in the amount to be delivered because the seller does not have any delivery option. The seller has to deliver $3 million current face amount if the August factor turns out to be 0.30 and the seller needs to deliver $2.5 million current face amount if the August factor turns out to be 0.25.

The total proceeds of a PO trade are calculated the same way as with a passthrough trade except that there is no accrued interest. For example, suppose a buyer and a seller agree to trade $10 million original face of Trust 23 PO at 75-08 for settlement on August 25. The proceeds for the trade are calculated as follows assuming an August trust factor of 0.25:

The market trades IOs based on notional principal. The proceeds include the price on the notional amount and the accrued interest. For example, suppose a buyer and a seller agree to trade $10 million original notional face of Trust 23 IO at 33-20 for settlement on August 25. The proceeds for the trade are calculated as follows assuming an August factor of 0.25:

Agency passthrough trades settle according to a delivery schedule established by the BMA. Stripped mortgage-backed securities trades follow the same delivery schedule.

AGENCY COLLATERALIZED MORTGAGE OBLIGATIONS

Some institutional investors are concerned with extension risk and others with contraction risk when they invest in a mortgage passthrough. This problem can be mitigated by redirecting the cash flows of mortgage passthrough securities to different bond classes, called tranches, so as to create securities that have different exposure to prepayment risk and, therefore, different risk/return patterns than the passthrough securities from which the tranches were created. A CMO is an example of a paythrough structure.

When the cash flows of pools of mortgage passthroughs are redistributed to different bond classes, the resulting securities are called collateralized mortgage obligations (CMO). 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 and thus broaden the appeal of mortgage-backed products to bond investors.

Rather than list the different types of tranches that can be created in a CMO structure, we will show how the tranches can be created. This will provide an illustration of financial engineering. Although there are many different types of CMOs that have been created, we will only look at three of the key innovations in the CMO market: sequential-pay tranches, accrual tranches, and planned amortization class bonds. Two other important tranches that are not illustrated here are the floating-rate tranche and inverse floating-rate tranche.

Sequential-Pay CMOs

A sequential-pay CMO is structured so that each class of bond (i.e., tranche) is retired sequentially. To illustrate a sequential-pay CMO, we discuss CMO-1, a hypothetical deal made up to illustrate the basic features of the structure. The collateral for this hypothetical CMO is a mortgage passthrough with a total par value of $400 million and the following characteristics: (1) the security’s 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 mortgage passthrough that we used earlier in this chapter to describe the cash flow of a passthrough based on some PSA assumption.

Payment rules:

1. For payment of monthly coupon interest: Disburse monthly coupon interest to each tranche on the basis of the amount of principal outstanding at the beginning of the month.
2. For disbursement of principal payments: Disburse principal payments to tranche A until it is completely paid off. After tranche A is completely paid off, disburse principal payments to tranche B until it is completely paid off. After tranche B is completely paid off, disburse principal payments to tranche C until it is completely paid off. After tranche C is completely paid off, disburse principal payments to tranche D until it is completely paid off.

From this $400 million of collateral, four bond classes or tranches are created. Their characteristics are summarized in Exhibit 14.3. The total par value of the four tranches is equal to the par value of the collateral (i.e., the mortgage passthrough). 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 14.3 describe how the cash flow from the mortgage passthrough (i.e., collateral) is to be distributed to the four tranches. There are separate rules for the payment of the coupon interest and the payment of principal, the principal being the total of the regularly scheduled principal payment and any prepayments.

In CMO-1, each tranche receives monthly coupon interest payments based on the amount of the outstanding balance at the beginning of the month. The disbursement of the principal, however, is made in a special way. A tranche is not entitled to receive principal until the entire principal of the tranche has been paid off. More specifically, tranche A receives all the principal payments until the entire principal amount owed to that tranche, $194,500,000, is paid off; then tranche B begins to receive principal and continues to do so until it is paid the entire $36,000,000. Tranche C then receives principal, and when it is paid off, tranche D starts receiving principal payments.

Although the priority 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, on the principal payments of the collateral, which will depend on the actual prepayment rate of the collateral. An assumed PSA speed allows the cash flow to be projected. Exhibit 14.2 shows the cash flow (interest, regularly 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 CMO-1 will be precisely the cash flow shown in Exhibit 14.2.

To demonstrate how the priority rules for CMO-1 work, Exhibit 14.4 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 (regularly scheduled principal repayment plus prepayments), and (3) interest. In month 1, the cash flow for the collateral consists of principal payment of $709,923 and interest 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.

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 $2,032,196 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 disbursed to tranche B. According to the assumed prepayment speed of 165 PSA, tranche B then begins receiving principal payments in month 81.

Exhibit 14.4 shows that tranche B is fully paid off by month 100, when tranche C now 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.

Let’s look at what has been accomplished by creating the CMO. First, the average life for the mortgage passthrough is 8.76 years, assuming a prepayment speed of 165 PSA. On page 361 is 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 tackled 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.

Accrual Bonds

In CMO-1, the payment rules for interest provide for all tranches to be paid interest each month. In many sequential-pay CMO structures, at least one tranche does not receive current interest. Instead, the interest for that tranche would accrue and be added to the principal balance. Such a bond class is commonly referred to as an accrual tranche, or a Z bond (because the bond is similar to a zero-coupon bond). The interest that would have been paid to the accrual tranche is then used to speed up paying down the principal balance of earlier tranches.

To see this, consider CMO-2, a hypothetical CMO structure with the same collateral as CMO-1 and with four tranches, each with a coupon rate of 7.5%. The structure is shown in Exhibit 14.5. The difference is in the last tranche, Z, which is an accrual bond.

Payment rules:

1. For payment of monthly coupon interest: Disburse monthly coupon interest to tranches A, B, and C on the basis of the amount of principal outstanding at the beginning of the month. For tranche Z, accrue the interest based on the principal plus accrued interest in the previous month. The interest for tranche Z is to be paid to the earlier tranches as a principal pay down.
2. For disbursement of principal payments: Disburse principal payments to tranche A until it is completely paid off. After tranche A is completely paid off, disburse principal payments to tranche B until it is completely paid off. After tranche B is completely paid off, disburse principal payments to tranche C until it is completely paid off. After tranche C is completely paid off, disburse principal payments to tranche Z until the original principal balance plus accrued interest is completely paid off.

Let’s look at month 1 and compare it to month 1 in Exhibit 14.4 based on 165 PSA. The principal payment from the collateral is $709,923. In CMO-1, this is the principal paydown for tranche A. In CMO-2, 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 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 inclusion of the accrual tranche results in a shortening of the expected final maturity for tranches A, B, and C. 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 112 rather than 178 months. The average lives for tranches A, B, and C are shorter in CMO-2 compared to CMO-1 because of the inclusion of the accrual bond. For example, at 165 PSA, the average lives are as follows:

The reason for the shortening of the nonaccrual tranches is that the interest that would be paid to the accrual bond is being allocated to the other tranches. Tranche Z in CMO-2 will have a longer average life than tranche D in CMO-1. Thus, shorter-term tranches and a longer-term tranche are created by including an accrual bond. The accrual bond appeals 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.

Planned Amortization Class Tranches

In a planned amortization class (PAC) CMO structure, if prepayments are within a specified range, the cash flow pattern is known for those tranches identified as PAC tranches. The greater predictability of the cash flow for PAC tranches occurs because there is a principal repayment schedule that must be satisfied. PAC tranches have priority over all other tranches in the CMO structure in receiving principal payments from the underlying collateral. The greater certainty of the cash flow for the PAC tranches comes at the expense of the non-PAC tranches, called the support tranches or companion tranches. It is the support tranches that absorb the prepayment risk.

To illustrate how to create a PAC tranche, we will use as collateral the $400 million mortgage passthrough with a coupon rate of 7.5%, a WAC of 8.125%, and a WAM of 357 months. The second column of Exhibit 14.6 shows the principal payment (regularly 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 mortgage passthrough prepays at 300 PSA.

The last column of Exhibit 14.6 gives the minimum principal payment if the collateral speed is 90 PSA or 300 PSA for months 1 to 349. (After month 346, 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 $508,169.52 if the collateral prepays at 90 PSA and $1,075,931.20 if the collateral prepays at 300 PSA. Thus, the minimum principal payment is $508,169.52, as reported in the last column of Exhibit 14.6. In month 103, the minimum principal payment is also the amount if the prepayment speed is 90 PSA, $1,446,761, compared to $1,458,618.04 for 300 PSA. In month 104, however, a prepayment speed of 300 PSA would produce a principal payment of $1,433,539.23, which is less than the principal payment of $1,440,825.55 assuming 90 PSA. So, $1,433,539.23 is reported in the last column of Exhibit 14.6. In fact, from month 104 on, the minimum principal payment is the one that would result assuming a prepayment speed of 300 PSA.

Payment rules:

1. For payment of monthly coupon interest: Disburse monthly coupon interest to each tranche on the basis of the amount of principal outstanding at the beginning of the month.
2. For disbursement of principal payments: Disburse principal payments to tranche P based on its schedule of principal repayments. Tranche P has priority with respect to current and future principal payments to satisfy the schedule. Any excess principal payments in a month over the amount necessary to satisfy the schedule for tranche P are paid to tranche S. When tranche S is completely paid off, all principal payments are to be made to tranche P regardless of the schedule.

If the collateral prepays at any speed between 90 PSA and 300 PSA, the minimum principal payment would be the amount reported in the last column of Exhibit 14.6. 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 11 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 constant speed between 90 PSA and 300 PSA. A schedule of principal repayments that the PAC bondholders are entitled to receive before any other bond class in the CMO is specified. The monthly schedule of principal repayments is as specified in the last column of Exhibit 14.6, which shows the minimum principal payment. Although there is no assurance that the collateral will prepay between these two speeds, a PAC bond can be structured to assume that it will.

Exhibit 14.7 shows a CMO structure, CMO-3, created from the $400 million, 7.5% coupon mortgage 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.

The average life for the PAC tranche and the support tranche in CMO-3, assuming various actual prepayment speeds, is shown here:

Notice that between 90 PSA and 300 PSA, the average life for the PAC tranche is stable at 7.26 years. However, at slower or faster PSA speeds, the schedule is broken, and the average life changes, lengthening when the prepayment speed is less than 90 PSA and shortening when it is greater than 300 PSA. Even so, there is much greater variability for the average life of the support tranche. The average life variability for the support tranche is substantial.

Most CMO structures that have a PAC typically have more than one PAC tranche. The tranches are created by carving up a PAC tranche into a series of sequential-pay PAC tranches.

SUMMARY

In this chapter we have focused on the agency sector of the mortgage-backed securities market. The securities included in this sector are agency passthrough securities, agency stripped mortgage-backed securities, and agency collateralized mortgage obligations. We have explained the raw material for the securities (i.e., the mortgage loans), the structure of the securities, trading and settlement procedures, and the risks associated with these securities.