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**Residential Mortgages and Mortgage-Backed Securities**

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**Mortgage-Backed Securities**

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**Mortgage-Backed Securities**

A mortgage originator with a pool of mortgages has the option of holding the portfolio, selling it, or selling it to be used to securitize a MBS issue or deal. Depending on the types of mortgages, the originator who sells mortgages to become a securitized asset can sell them to one of the three agencies (Fannie Mae, Ginnie Mae, or Freddie Mac) or to a private-sector conduit. As noted in Chapter 7, Fannie Mae and Freddie Mac are Government-sponsored enterprises (GSEs), whereas Ginnie Mae is a federal agency. In our discussion of MBSs, we will refer to all three as being agencies.

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**Mortgage-Backed Securities**

Agency MBSs are MBSs created by one of the agencies; they are collectively referred to as agency MBSs, Nonagenecy MBS are MBS created by private conduits; also called private labels.

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**Mortgage-Backed Securities**

Residential mortgages can be divided into prime and subprime mortgages. Prime mortgages include those that are both conforming (meet the agency’s underwriting standards) and nonconforming but still meeting credit quality standards. Subprime mortgages include those with low credit ratings.

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**Mortgage-Backed Securities**

Note: Typically, agency residential MBSs are created from conforming loans. In more recent periods, though, agency MBS issues backed by pools of lower quality mortgages were issued. All other mortgages that are securitized are nonagency MBS.

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**Mortgage-Backed Securities**

After the mortgages are sold to an agency or private conduit, the originator typically continues to service the loan for a service fee (that is, collect payments, maintain records, forward tax information, and the like). The service fee is typically a fixed percentage (25 to 100 basis points) of the outstanding balance. The originator can also sell the servicing to another party. Investors who buy the MBSs receive a pro rata share from the cash flow of the pool of mortgages.

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**Ginnie Mae Mortgage-Backed Securities**

Ginnie Mae (Government National Mortgage Association's (GNMA)) is a true federal agency. As such, the MBSs that it guarantees are backed by the full faith and credit of the U.S. government.

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**Ginnie Mae Mortgage-Backed Securities**

Creation Ginnie Mae MBSs are put together by a lender/originator (bank, thrift, or mortgage banker), who presents a block of mortgages that meets Ginnie Mae’s underwriting standards. If Ginnie Mae finds them in order, it will issue a guarantee and assign a pool number that identifies the MBS that is to be issued. The lender will then transfer the mortgages to a trustee, and then issue the pass-through securities as a Ginnie Mae pass-through security.

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**Ginnie Mae Mortgage-Backed Securities**

Features Ginnie Mae provides the guarantee, but does not issue the Ginnie Mae MBS. Thus, different from the standard MBS that is issued by the other agencies or a conduit, Ginnie Mae MBSs are issued by the lenders. The minimum denomination on a Ginnie Mae pass-through is $25,000 and the minimum pool is $1 million.

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**Ginnie Mae Mortgage-Backed Securities**

Types The mortgages underlying Ginnie Mae MBSs can be grouped into one of two Ginnie Mae MBS programs: Ginnie Mae I and Ginnie Mae II. The Ginnie Mae I program consists of MBSs backed by single-family and multifamily mortgage loans that have a fixed note rate and are sold by only one issuer. The Ginnie Mae II program consists of just single-family mortgage loans that can have either fixed or adjustable rates and have multiple issuers.

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**Fannie Mae and Freddie Mac Mortgage-Backed Securities**

Fannie Mae and Freddie Mac are Government-sponsored enterprises (GSE) initially created to provide a secondary market for mortgages. Today, there activities include not only the buying and selling of mortgages, but also creating and guaranteeing mortgage-backed pass-through securities, as well as buying MBSs.

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**Fannie Mae and Freddie Mac Mortgage-Backed Securities**

Note: Both GSEs are regulated by the Office of Federal Housing Enterprise Oversight (OFHEO) and both were placed in conservatorship in September 2008. Prior to being placed in conservatorship, the Fannie Mae and Freddie Mac MBSs were guarantee by each of the companies, but not the government. As part of the banking bailout in 2008, though, government backing was provided to their MBSs.

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**Fannie Mae and Freddie Mac Mortgage-Backed Securities**

Freddie Mac issues MBSs that it refers to as participation certificates (PCs). Freddie Mac and Fannie Mae have regular MBSs (also called a cash PC), which are backed by a pool of conforming mortgages that they have purchased from mortgage originators. They also offer a pass-though formed through their Guarantor/Swap Program. In this program, mortgage originators can swap mortgages for a Fannie Mae or Freddie Mac pass-through.

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**Fannie Mae and Freddie Mac Mortgage-Backed Securities**

Unlike Ginnie Mae, Fannie Mae’s and Freddie Mac's MBSs are formed with more heterogeneous mortgages. The minimum denomination on a Freddie Mac and Fannie Mae pass-through is $100,000 and their mortgage pools range up to several hundred million dollars.

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Nonagency MBS Nonagency pass-throughs or private labels are sold by commercial banks, investment banks, other thrifts, and mortgage bankers. As noted, nonagency pass-throughs are often formed with prime or subprime nonconforming mortgages. Larger issuers of nonagency MBSs include Citigroup, Bank of America, and G.E. Capital Mortgage.

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**Nonagency MBS Features**

Nonagency MBSs are often guaranteed against default through external credit enhancements, such as the guarantee of a corporation or a bank letter of credit or by private insurance from a monocline insurer. Many are also guaranteed internally through the creation of senior and subordinate classes of bonds with different priority claims on the pool's cash flows in the case some of the mortgages in the pool default. The more subordinate claims sold relative to the senior claims, the more secure the senior claims.

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**Nonagency MBS Features**

Nonagency MBSs are rated by Moody's and Standard and Poor's. They must be registered with the SEC when they are issued.

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**Nonagency MBS Features**

Most financial entities that issue private-label MBSs or derivatives of MBSs are legally set up so that they do not have to pay taxes on the interest and principal that passes through them to their MBS investors. The requirements that MBS issuers must meet to ensure tax-exempt status are specified in the Tax Reform Act of 1983 in the section on trusts referred to as Real Estate Mortgage Investment Conduits, REMIC. Private-labeled MBS issuers who comply with these provisions are sometimes referred to as REMICs.

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**Nonagency MBS Features**

Nonagency residential MBSs differ fundamentally from agency MBSs in that their cash flows are subject to default risk, whereas agency MBSs with their government and agency guarantees are considered default free.

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Cash Flows Cash flows from MBSs are generated from the cash flows from the underlying pool of mortgages, minus servicing and other fees. Typically, fees for constructing, managing, and servicing the underlying mortgages (also referred to as the mortgage collateral) and the MBSs are equal to the difference between the rates associated with the mortgage pool and the rate that is paid to the MBS investors (pass-through (PT) rate).

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Cash Flows: Terms Weighted Average Coupon Rate, WAC: Mortgage portfolio's (collateral’s) weighted average rate. Weighted Average Maturity, WAM: Mortgage portfolio's weighted average maturity. Pass-Through Rate, PT Rate: Interest rate paid on the MBS; PT rate is lower than WAC—the difference going to the MBS issuer. Prepayment Rate or Speed: Assumed prepayment rate.

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**Example Cash Flow from a MBS**

The next slide shows the monthly cash flows for a MBS issue constructed from a $100 million mortgage pool with the following features: Current balance = $100 million WAC = 8% WAM = 355 months PT rate = 7.5% Prepayment speed equal to 150% of the standard PSA model: PSA = 150

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Projected Cash Flows from an Agency MBS Issue Mortgage Portfolio = $100,000,000, WAC = 8%, WAM = 355 Months, PT Rate = 7.5%, Prepayment: 150 PSA

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**Cash Flow from a MBS Notes:**

The first month's CPR for the MBS issue reflects a 5-month seasoning in which t = 6, and a speed that is 150% greater than the 100 PSA. For the MBS issue, this yields a first month SMM of and a constant SMM of starting in month 25. The WAC of 8% is used to determine the mortgage payment and scheduled principal, whereas the PT rate of 7.5% is used to determine the interest. The monthly fees implied on the MBS issue are equal to % = (8% − 7.5%)/12 of the monthly balance.

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Cash Flow from a MBS First Month’s Payment:

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Cash Flow from a MBS From the $736,268 payment, $625,000 would go towards interest and $69,601 would go towards the scheduled principal payment:

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Cash Flow from a MBS Using 150% PSA model and seasoning of 5 months the first month SMM = :

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Cash Flow from a MBS Given the prepayment rate, the projected prepaid principal in the first month is $151,147

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Cash Flow from a MBS Thus, for the first month, the MBS would generate an estimated cash flow of $845,748 and a balance at the beginning of the next month of $99,779,252:

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Cash Flow from a MBS Second Month: Payment, Interest, Scheduled Principal, Prepaid Principal, and Cash flow:

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Market As noted, investors can acquire newly issued mortgage-backed securities from the agencies, originators, or dealers specializing in specific pass-through. There is also a secondary market consisting of dealers who operate in the OTC market as part of the Mortgage-Backed Security Dealers Association. These dealers form the core of the secondary market for the trading of existing pass-through.

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Market MBSs are normally sold in denominations ranging from $25,000 to $250,000, although some privately-placed issues are sold with denominations as high as $1 million.

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Price Quotes The prices of MBSs are quoted as a percentage of the underlying MBS issue’s balance. The mortgage balance at time t, Ft, is usually calculated by the servicing institution and is quoted as a proportion of the original balance, F0. This proportion is referred to as the pool factor, pf:

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Price Quotes Example: A MBS backed by a mortgage pool originally worth $100 million Current pf of 0.92 quoted at (Note: 16 is 16/32) The current balance, Ft, would be $92 million and the market value would be $87.86 million:

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Price Quotes Note: The market value is the clean price; it does not take into account accrued interest. For MBS, accrued interest is based on the time period from the settlement date (typically two days after the trade) and the first day of the next month.

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Price Quotes Example: If the time period is 20 days, the month is 30 days, and the WAC = 9%, then the accrued interest is $460,000: The full market value (clean price plus accrued interest) would be $88,320,000:

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Price Quotes The market price per share is the full market value divided by the number of shares. Example: If the number of shares is 400, then the price of the MBS based on a quote would be $220,800:

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Extension Risk Like other fixed-income securities, the value of a MBS is determined by the MBS's future cash flow (CF), maturity, default risk, and other features germane to fixed-income securities.

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Extension Risk In contrast to other bonds, MBSs are also subject to prepayment risk. Prepayment affects the MBS’s CF. Prepayment, in turn, is affected by interest rates.

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Extension Risk Thus, interest rates affects the MBS’s CFs:

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Extension Risk With the CF a function of rates, the value of a MBS is more sensitive to interest rate changes than those bonds whose CFs are not. This sensitivity is known as extension risk.

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Extension Risk If interest rates decrease, then the prices of MBSs, like the prices of most bonds, would increase as a result of the lower discount rates. However, the decrease in rates will also augment prepayment speed, causing the earlier cash flow of the mortgages to be larger which, depending on the level of rates and the maturity remaining, could also contribute to increasing the MBS’s price.

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Extension Risk Rate Decrease

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Extension Risk If interest rates increase, then the prices of MBSs will decrease as a result of higher discount rates and possibly the smaller earlier cash flow resulting from lower prepayment speeds.

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Extension Risk Rate Increase

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Average Life The average life of a MBS or mortgage portfolio is the weighted average of the security’s time periods, with the weights being the periodic principal payments (scheduled and prepaid principal) divided by the total principal:

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Average Life The average life for the MBS issue with WAC = 8%, WAM = 355, PT Rate = 7.5%, and PSA = 150 is 9.18 years

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**Average Life The average life of a MBS depends on prepayment speed:**

If the PSA speed of the $100 million MBS issue were to increase from 150 to 200, the MBS’s average life would decrease from 9.18 to 7.55, reflecting greater principal payments in the earlier years. If the PSA speed were to decrease from 150 to 100, then the average life of the MBS would increase to

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**Average Life and Prepayment Risk**

For MBSs and mortgage portfolios, prepayment risk can be evaluated in terms of how responsive a MBS's or mortgage portfolio’s average life is to changes in prepayment speeds:

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**Average Life and Prepayment Risk**

A MBS with an average life that did not change with PSA speeds, in turn, would have stable principal payments over time and would be absent of prepayment risk.

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MBS Derivatives

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MBS Derivatives One of the more creative developments in the security market industry over the last three decades has been the creation of derivative securities formed from MBSs and mortgage portfolios that have different prepayment risk characteristics, including some that are formed that have average lives that are invariant to changes in prepayment rates. The most popular of these derivatives are Collateralized Mortgage Obligations, CMOs Stripped MBS

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**Collateralized Mortgage Obligations**

Collateralized mortgage obligations, CMOs, are formed by dividing the cash flow of an underlying pool of mortgages or a MBS issue into several classes, with each class having a different claim on the mortgage collateral and with each sold separately to different types of investors.

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**Collateralized Mortgage Obligations**

The different classes making up a CMO are called tranches or bond classes. There are two general types of CMO tranches: Sequential-Pay Tranches Planned Amortization Class Tranches, PAC

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**Sequential-Pay Tranches**

A CMO with sequential-pay tranches, called a sequential-pay CMO, is divided into classes with different priority claims on the collateral's principal. The tranche with the first priority claim has its principal paid entirely before the next priority class, which has its principal paid before the third class, and so on. Interest payments on most CMO tranches are made until the tranche's principal is retired.

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**Sequential-Pay Tranches**

Example: A sequential-pay CMO is shown in Slide 59. This CMO consist of three tranches, A, B, and C, formed from the collateral making up the $100 million MBS in the previous example: F = $100 million, WAM = 355, WAC = 8%, PT Rate = 7.5%, PSA = 150. Tranche A = $50 million Tranche B = $30 million Tranche C = $20 million

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**Sequential-Pay Tranches**

Priority Disbursement Rules: Tranche A receives all principal payment from the collateral until its principal of $50 million is retired. No other tranche's principal payments are disbursed until the principal on A is paid. After tranche A's principal is retired, all principal payments from the collateral are then made to tranche B until its principal of $30 million is retired. Finally, tranche C receives the remaining principal that is equal to its par value of $20 million. Although the principal is paid sequentially, each tranche does receive interest each period equal to its stated PT rate (7.5%) times its outstanding balance at the beginning of each month.

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Cash Flows from Sequential-Pay CMO Collateral: Balance = $100m, WAM = 355 Months, WAC = 8%, PT Rate = 7.5%, Prepayment: 150 PSA, Tranches: A: $50 million, B = $30 million, C = $20 million

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**Sequential-Pay Tranches**

Given the assumed PSA of 150, the first month cash flow for tranche A consist of a principal payment (scheduled and prepaid) of $220,748 and an interest payment of $312,500: Interest = (.075/12)($50,000,000) = $312,500 In month 2, tranche A receives an interest payment of $311,120 based on the balance of $49,779, 252 and a principal payment of $246,153.

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**Sequential-Pay Tranches**

Based on the assumption of a 150% PSA speed, it takes 88 months before A's principal of $50M is retired. During the first 88 months, the cash flows for tranches B and C consist of just the interest on their balances, with no principal payments made to them. Starting in month 88, tranche B begins to receive the principal payment. Tranche B is paid off in month 180, at which time principal payments begin to be paid to tranche C. Finally, in month 355 tranche C's principal is retired.

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**Sequential-Pay Tranches**

Features of Sequential-Pay CMOs By creating sequential-pay tranches, issuers of CMOs are able to offer investors maturities, principal payment periods, and average lives different from those defined by the underlying mortgage collateral.

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**Sequential-Pay Tranches**

Features of Sequential-Pay CMOs Maturity: Collateral's maturity = 355 months (29.58 years) Tranche A’s maturity = 88 months (7.33 years) Tranche B's maturity = 180 months (15 years) Tranche C’s maturity = 355 months (29.58 years) Window: The period between the beginning and ending principal payment is referred to as the principal pay-down window: Collateral’s window = 355 months Tranche A’s window = 87 months Tranche B's window = 92 months Tranche C's window =176 months Average Life: Collateral's average = 9.18 years Tranche A’s average life = 3.69 years Tranche B’s average life = years Tranche C’s Average life = years

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**Sequential-Pay Tranches**

Features of Sequential-Pay CMOs A CMO tranche with a lower average life is still susceptible to prepayment risk. The average life of each of the tranches still varies as prepayment speed changes.

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**Sequential-Pay Tranches**

Note: Issuers of CMOs are able to offer a number of CMO tranches with different maturities and windows by simply creating more tranches.

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**Different Types of Sequential-Pay Tranches**

Sequential-pay CMOs often include tranches with special features. These include: Accrual Bond Tranche Floating-Rate Tranche Notional Interest-Only Tranche

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**Accrual Tranche Many sequential-pay CMOs have an accrual bond class.**

Such a tranche, also referred to as the Z bond, does not receive current interest but instead has it deferred. The Z bond's current interest is used to pay down the principal on the other tranches, increasing their speed and reducing their average life.

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**Accrual Tranche Example:**

Suppose in our preceding sequential-pay CMO example we make tranche C an accrual tranche in which its interest of 7.5% is to paid to the earlier tranches and its principal of $20 million and accrued interest is to be paid after tranche B's principal has been retired Slide 69 shows the principal and interest payments from the collateral and Tranches A, B, and Z.

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Cash Flows From Sequential-Pay CMO with Z Tranche Collateral: Balance = $100M, WAM = 355 Months, WAC = 8%, PT Rate = 7.5%, Prepayment: 150 PSA, Tranches: A: $50M, B = $30M, C = $20M

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**Accrual Tranche Features**

Since the accrual tranche's current interest of $125,000 is now used to pay down the other classes' principals, the other tranches now have lower maturities and average lives. For example, the principal payment on tranche A is $345,748 in the first month ($220,748 of scheduled and projected prepaid principal and $125,000 of Z's interest); in contrast, the principal is only $220,748 when there is no Z bond. As a result of the Z bond, tranche A's window is reduced from 87 months to 69 months and its average life from 3.69 years to 3.06 years.

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**Floating-Rate Tranche**

In order to attract investors who prefer floating-rate securities, CMO issuers often create floating-rate and inverse floating-rate tranches. The monthly coupon rate on the floating-rate tranche is usually set equal to a reference rate such as the London Interbank Offer Rate, LIBOR, while the rate on the inverse floating-rate tranche is determined by a formula that is inversely related to the reference rate.

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**Floating-Rate Tranche**

Example: Sequential-pay CMO with a floating and inverse floating tranches Note: The CMO is identical to the preceding CMO, except that tranche B has been replaced with a floating-rate tranche, FR, and an inverse floating-rate tranche, IFR. Tranche Par Value PT Rate A FR IFR Z $50 million $22.5 million $7.5 million $20 million 7.5% LIBOR + 50bp 28.3 – 3 LIBOR Total $100 million

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**Floating-Rate Tranche**

The rate on the FR tranche, RFR, is set to the LIBOR plus 50 basis points, with the maximum rate permitted being 10%. The rate on the IFR tranche, RIFR, is determined by the following formula: This formula ensures that the weighted average coupon rate (WAC) of the two tranches will be equal to the coupon rate on tranche B of 7.5%, provided the LIBOR is less than 9.5%. RIFR = − 3 LIBOR

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**Floating-Rate Tranche**

Example: If the LIBOR is 8%, then the rate on the FR tranche is 8.5%, the IFR tranche's rate is 4.5%, and the WAC of the two tranches is 7.5%:

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**Notional Interest-Only Class**

Each of the fixed-rate tranches in the previous CMOs have the same coupon rate as the collateral rate of 7.5%. Many CMOs are structured with tranches that have different rates. When CMOs are formed this way, an additional tranche, known as a notional interest-only (IO) class, is often created. The notional interest-only tranche receives the excess interest on the other tranches’ principals, with the excess rate being equal to the difference in the collateral’s PT rate minus the tranches’ PT rates.

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**Notional Interest-Only Class**

Example: A sequential-pay CMO with a Z bond and notional IO tranche is shown in the next slide. This CMO is identical to the previous CMO with a Z bond, except that each of the tranches has a rate lower than the collateral rate of 7.5% and there is a notional IO class.

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Sequential-Pay CMO with Notional IO Tranche Collateral: Balance = $100m, WAM = 355 Months, WAC = 8%, PT Rate = 7.5%, Prepayment: 150 PSA, Tranches: A: $50m, B = $30m, Z = $20m, Notional IO = $ m

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**Notional Interest-Only Class**

The notional IO class receives the excess interest on each tranche's remaining balance, with the excess rate based on the collateral rate of 7.5%. In the first month, for example, the IO class would receive interest of $87,500:

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**Notional Interest-Only Class**

The IO class is described as paying 7.5% interest on a notional principal of $15,333,333. This notional principal is determined by summing each tranche's notional principal. A tranche's notional principal is the number of dollars that makes the return on the tranche's principal equal to 7.5%.

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**Notional Interest-Only Class**

The notional principal for tranche A is $10,000,000, for B, $4,000,000, and for Z, $1,333,333, yielding a total notional principal of $15,333,333:

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**Planned Amortization Class, PAC**

A CMO with a planned amortization class, PAC, is structured such that there is virtually no prepayment risk. In a PAC-structured CMO, the underlying mortgages or MBS (i.e., the collateral) is divided into two general tranches: The PAC (also called the PAC bond) The support class (also called the support bond or the companion bond)

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**Planned Amortization Class, PAC**

The two tranches are formed by generating two monthly principal payment schedules from the collateral: One schedule is based on assuming a relatively low PSA speed – lower collar. The other schedule is based on assuming a relatively high PSA speed – upper collar. The PAC bond is then set up so that it will receive a monthly principal payment schedule based on the minimum principal from the two principal payments.

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**Planned Amortization Class, PAC**

The PAC bond is designed to have no prepayment risk provided the actual prepayment falls within the minimum and maximum assumed PSA speeds. The support bond, on the other hand, receives the remaining principal balance and is therefore subject to prepayment risk.

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**Planned Amortization Class, PAC**

Example PAC and support bond formed from the $100 million collateral with WAC = 8%, WAM = 355 months, and PT rate = 7.5% Minimum monthly principal payments for the PAC generated using 100 and 300 collars: Lower Collar = 100 PSA: Minimum speed of 100% PSA Upper Collar = 300 PSA: Maximum speed of 300% PSA

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**Planned Amortization Class, PAC**

The next slide shows the cash flows for the PAC, collateral, and support bond. The exhibit shows: In columns 2 and 3 the principal payments (scheduled and prepaid) for selected months at both collars. In the fourth column the minimum of the two payments. For example, in the first month the principal payment is $170,085 for the 100% PSA and $374,456 for the 300% PSA; thus, the principal payment for the PAC would be $170,085.

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PAC And Support Bonds PAC formed 100 and 300 PSA Model Collateral: Balance = $100m, WAM = 355 Months, WAC = 8%, PT Rate = 7.5%, Prepayment: 150 PSA

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**Planned Amortization Class, PAC**

Note: For the first 98 months, the minimum principal payment comes from the 100% PSA collar, and from month 99 on the minimum principal payment comes from the 300% PSA collar.

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**Planned Amortization Class, PAC**

Based on the PSA range, a PAC bond can be formed that would promise to pay the principal based on the minimum principal payment schedule shown in the exhibit. The support bond would receive any excess monthly principal payment.

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**Planned Amortization Class, PAC**

The sum of the PAC's principal payments is $ million. Thus, the PAC can be described as having: Par value of $ million Coupon rate of 7.5% Lower collar of 100% PSA Upper collar of 300% PSA The support bond, in turn, would have a par value of $ million ($100 million − $ million) and pay a coupon of 7.5%.

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**Planned Amortization Class, PAC**

The PAC bond has no prepayment risk as long as the actual prepayment speed is between 100 and 300. This can be seen by calculating the PAC's average life given different prepayment rates. The next exhibit shows the average lives for the collateral, PAC bond, and support bond for various prepayment speeds ranging from 50% PSA to 350% PSA.

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**Planned Amortization Class, PAC**

The average lives for the collateral, PAC bond, and support bond for various prepayment speeds ranging from 50% PSA to 350% PSA.

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**Planned Amortization Class, PAC**

Features: The PAC bond has an average life of 6.98 years between 100% PSA and 300% PSA; its average life does change, though, when prepayment speeds are outside the PSA range. In contrast, the support bond's average life changes as prepayment speed changes. Changes in the support bond's average life due to changes in speed are greater than the underlying collateral's responsiveness.

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**Other PAC-Structured CMOs**

The PAC and support bonds can be divided into different classes. Often the PAC bond is divided into several sequential-pay tranches, with each PAC having a different priority in principal payments over the other. Each sequential-pay PAC, in turn, will have a constant average life if the prepayment speed is within the lower and upper collars. In addition, it is possible that some PACs will have ranges of stability that will increase beyond the actual collar range, expanding their effective collars.

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**Other PAC-Structured CMOs**

A PAC-structured CMO can also be formed with PAC classes having different collars. Some PACs are formed with just one PSA rate. These PACs are referred to as targeted amortization class (TAC) bonds. Different types of tranches can also be formed out of the support bond class. These include sequential-pay, floating and inverse-floating rate, and accrual bond classes.

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**Stripped MBS Stripped MBSs consist of two classes:**

Principal-only (PO) class that receives only the principal from the underlying mortgages. Interest-only (IO) class that receives just the interest.

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**Principal-Only Stripped MBS**

The return on a PO MBS is greater with greater prepayment speed. For example, a PO class formed with $100 million of mortgages (principal) and priced at $75 million would yield an immediate return of $25 million if the mortgage borrowers prepaid immediately. Since investors can reinvest the $25 million, this early return will have a greater return per period than a $25 million return that is spread out over a longer period.

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**Principal-Only Stripped MBS**

Because of prepayment, the price of a PO MBS tends to be more responsive to interest rate changes than an option-free bond.

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**Principal-Only Stripped MBS**

If interest rates are decreasing, then like the price of most bonds, the price of a PO MBS will increase. In addition, the price of a PO MBS is also likely to increase further because of the expectation of greater earlier principal payments as a result of an increase in prepayment caused by the lower rates.

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**Principal-Only Stripped MBS**

If rates are increasing, the price of a PO MBS will decrease as a result of both lower discount rates and lower returns from slower principal payments.

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**Principal-Only Stripped MBS**

Thus, like most bonds, the prices of PO MBSs are inversely related to interest rates, and, like other MBSs with embedded principal prepayment options, their prices tend to be more responsive to interest rate changes.

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**Interest-Only Stripped MBS**

Cash flows from an I0 MBS come from the interest paid on the mortgages portfolio’s principal balance. In contrast to a PO MBS, the cash flows and the returns on an IO MBS will be greater, the slower the prepayment rate.

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**Interest-Only Stripped MBS**

If the mortgages underlying a $100 million, 7.5% MBS with PO and IO classes were paid off in the first year, then the IO MBS holders would receive a one-time cash flow of $7.5 million: If $50 million of the mortgages were prepaid in the first year and the remaining $50 million in the second year, then the IO MBS investors would receive an annualized cash flow over two years totaling $11.25 million: If the mortgage principal is paid down $25 million per year, then the cash flow over four years would total $18.75 million: $7.5m = (.075)($100m) $11.25m = (.075) ($100m) + (.075)($100m − $50m) $18.75m = (.075)($100m) + (.075)($100m − $25m) + (.075)($75m − $25m) + (.075)($50m − $25m)

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**Interest-Only Stripped MBS**

Thus, IO MBSs are characterized by an inverse relationship between prepayment speed and returns: the slower the prepayment rate, the greater the total cash flow on an IO MBS.

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**Interest-Only Stripped MBS**

Note: If inverse relationship between prepayment speed and returns dominates the price and discount rate relation, then the price of an IO MBS will vary directly with interest rates.

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IO and PO Stripped MBS An example of a PO MBS and an IO MBS are shown in the next slide. The stripped MBSs are formed from collateral with Mortgage Balance = $100 million WAC = 8% PT Rate = 8% WAM = 360 PSA = 100

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Projected Cash Flows for Stripped PO and IO Collateral: Mortgage Portfolio = $100 million, WAC = 8%, WAM = 360 Months, Prepayment: 100% PSA

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IO and PO Stripped MBS The table shows the values of the collateral, PO MBS, and IO MBS for different discount rate and PSA combinations of 8% and 150, 8.5% and 125, and 9% and 100. Note: The IO MBS is characterized by a direct relation between its value and rate of return. Price Sensitivity Discount PSA Value of Rate PO IO Collateral 8.00% 150 $54,228,764 $47,426,196 $101,654,960 8.50% 125 $49,336,738 $49,513,363 $98,850,101 9.00% 100 $44,044,300 $51,795,188 $95,799,488

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**Evaluating Mortgage-Backed Securities**

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**Evaluating Mortgage-Backed Securities**

Like all securities, MBSs can be evaluated in terms of their characteristics. With MBSs, such an evaluation is more complex because of the difficulty in estimating cash flows due to prepayment. One approached used to evaluate MBS and CMO tranches is yield analysis.

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Yield Analysis Yield analysis involves calculating the yields on MBSs or CMO tranches given different prices and prepayment speed assumptions or alternatively calculating the values on MBSs or tranches given different rates and speeds.

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**Yield Analysis Example**

Suppose an institutional investor is interested in buying a MBS issue that has a par value of $100 million, WAC = 8%, WAM = 355 months, and a PT rate of 7.5%. The value, as well as average life, maturity, duration, and other characteristics of this security would depend on the rate the investor requires on the MBS and the prepayment speed she estimates.

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Yield Analysis If the investor’s required return on the MBS is 9% and her estimate of the PSA speed is 150, then she would value the MBS issue at $93,702,142. At that rate and speed, the MBS would have an average life of 9.18 years. Whether a purchase of the MBS issue at $93,702,142 to yield 9% represents a good investment depends, in part, on rates for other securities with similar maturities, durations, and risk, and in part, on how good the prepayment rate assumption is. For example, if the investor felt that the prepayment rate should be 100% PSA and her required rate with that level of prepayment is 9%, then she would price the MBS issue at $92,732,145 and the average life would be years.

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Yield Analysis In general, for many institutional investors the decision on whether or not to invest in a particular MBS or tranche depends on the price the institution can command. For example, based on an expectation of a 100% PSA, our investor might conclude that a yield of 9% on the MBS would make it a good investment. In this case, the investor would be willing to offer no more than $92,732,145 for the MBS issue.

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Yield Analysis One common approach used in conducting a yield analysis is to generate a matrix of different yields by varying the prices and prepayment speeds. The next slide shows the different values for our illustrative MBS given different required rates and different prepayment speeds. Using this matrix, an investor could determine, for a given price and assumed speed, the estimated yield, or determine, for a given speed and yield, the price. Using this approach, an investor can also evaluate for each price the average yield and standard deviation over a range of PSA speeds.

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**Yield and Vector Analysis Mortgage Portfolio = $100M, WAC = 8%, WAM = 355 Months, PT Rate = 7.5%**

Rate/PSA 50 100 150 7% 8% 9% 10% Average Life Rate Value $106,039,631 $98,251,269 $91,442,890 $85,457,483 14.95 Vector Month Range: PSA 1-50: 200 51-150: 250 : 150 : 200 $103,729,227 $98,893,974 $94,465,328 $90,395,704 $105,043,489 $98,526,830 $92,732,145 $87,554,145 11.51 51-150: 300 : 350 : 400 $103,473,139 $98,964,637 $94,794,856 $90,929,474 $104,309,207 $98,732,083 $93,702,142 $89,146,871 9.18 51-150: 150 : 100 : 50 $104,229,758 $98,756,370 93,826,053 89,,364,229

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Yield Analysis One of the limitations of the above yield analysis is the assumption that the PSA speed used to estimate the yield is constant during the life of the MBS. In fact, such an analysis is sometimes referred to as static yield analysis. In practice, prepayment speeds change over the life of a MBS as interest rates change in the market.

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Vector Analysis A more dynamic yield analysis, known as vector analysis, can be used. In applying vector analysis, PSA speeds are assumed to change over time. In the above case, a matrix of values for different rates can be obtained for different PSA vectors formed by dividing the total period into a number of periods with different PSA speeds assumed for each period. A vector analysis example is also shown at the bottom of the last exhibit slide.

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**Web Sites MBS Price Information: Wall Street Journal**

Go to “Market,” “Bonds, Rates, & Credit Markets,” and “Mortgage-Backed Securities, CMO.” Investinginbonds.com MBS Price Index: The Merrill Lynch Mortgage-Backed Securities (MBS) Index is a statistical composite tracking the overall performance of the mortgage-backed securities market over time. The index includes U.S. dollar-denominated 30-year, 15-year and balloon pass-through mortgage securities. Go to click “MBS/ABS Market At-A-Glance.”

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**Web Sites Agency MBS Prospectus and other information:**

Fannie Mae Information and Prospectus: Use Advance Search to find a MBS and its pool number: Go to Fannie Mae: Site Map; Mortgage-Backed Securities; “More Search Options.” Or go to Use pool number to find information on Fannie Mae MBS Information includes: Prospectus and Common Pool Information

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**Web Sites Agency MBS Prospectus and other information:**

Ginnie Mae Information and Prospectus: Go to Ginnie Mae: To find pool number, look for “Multiple Issue Pool Number” found under “Issuer” To find prospectus on MBS, look for “REMIC Offering Circulars” under “Investors” Or go to

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**Web Sites Agency MBS Prospectus and other information:**

Freddie Mae Information on types of MBS Go to “Mortgage Securities”

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**Web Sites For Moody’s information on MBS: www.moodys.com**

Search for structured finance, historical performance, and structured finance default studies.

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**Web Sites Office of Federal Housing Enterprise Oversight: www.ficc.com**

Office of Federal Housing Enterprise Oversight: Rating Agencies

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Chapter 3 Measuring Yield.

Chapter 3 Measuring Yield.

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