CH-12 Agency Collateralized Mortgage Obligations and Stripped Mortgage-Backed Securities – Bond Markets, Analysis and Strategies : Book Guide

CHAPTER 12 AGENCY COLLATERALIZED MORTGAGE OBLIGATIONS AND STRIPPED MORTGAGE-BACKED SECURITIES CHAPTER SUMMARY In this chapter we discuss two derivative mortgage-backed securities products: collateralized mortgage obligations and stripped mortgage-backed securities. In the agency mortgage-backed securities markets, these securities are referred to as derivative mortgage products since they derive their cash flow from the underlying mortgage collateral with a pass-through security or a pool of pass-through securities. These mortgage products are issued by the same entities that issue agency pass-through securities: Ginnie Mae, Fannie Mae, and Freddie Mac. AGENCY COLLATERALIZED MORTGAGE OBLIGATIONS Collateralized mortgage obligations (CMOs) are bond classes created by redirecting the cash flows of mortgage-related products so as to mitigate prepayment risk. The mere creation of a CMO cannot eliminate prepayment risk; it can only transfer the various forms of this risk among different classes of bondholders. The bond classes created are commonly referred to as tranches. The principal payments from the underlying collateral are used to retire the tranches on a priority basis according to terms specified in the prospectus. All three entities that issue agency pass-through securities also issue CMOs, with Ginnie Mae being a late entry into the market, issuing its first CMO in 1994. The CMOs are not referred to not as CMOs by these issuers. They are referred to as REMICs or REMIC structures. REMIC means Real Estate Mortgage Investment Conduit and is a provision in the Tax Reform Act of 1986. Sequential-Pay Tranches The first CMO was created in 1983 and was structured so that each class of bond would be retired sequentially. Such structures are referred to as sequential-pay CMOs. A CMO is created by redistributing the cash flow (interest and principal) to the different tranches based on a set of payment rules. 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. Each tranche receives periodic 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 preceding tranche has been paid off. The principal pay-down window for a tranche is the time period between the beginning and the ending of the principal payments to that tranche. Tranches can 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 considerable variability of the average life for the tranches. 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 against extension risk. This protection must come from somewhere, so it comes from the other tranches. At the same time these other tranches are provided protection against contraction risk. Accrual Bonds 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 bond class is then used to speed up the pay down of the principal balance of earlier bond classes. Thus, the average lives for the nonaccrual tranches has shortened as a result of the inclusion of accrual tranche. The accrual bond has appeal to investors who are concerned with reinvestment risk. Because there are no coupon payments to reinvest, reinvestment risk is eliminated until all the other tranches are paid off. Floating-Rate Tranches Floating-rate tranches can be created from fixed-rate tranches by creating a floater and an inverse floater. We can select any of the tranches from which to create a floating-rate and an inverse-floating-rate tranche. We can even create these two securities for more than one of the four tranches or for only a portion of one tranche. Any reference rate can be used to create a floater and the corresponding inverse floater. There is an infinite number of ways to cut up the monetary value between the floater and inverse floater, and final partitioning will be driven by the demands of investors. Unlike a floating-rate note in the corporate bond market, whose principal is unchanged over the life of the instrument, the floater’s principal balance declines over time as principal payments are made. The principal payments to the floater are determined by the principal payments from the tranche from which the floater is created. Assume that the reference rate is the one-month LIBOR of 3.75%, then the coupon rate on the inverse floater takes the following form: K – L × (one-month LIBOR) where K is the cap or maximum coupon rate for the inverse floater and L is the multiple that determine the coupon rate for the inverse floater (L is referred to as the coupon leverage). If K is set at 28.50% and L at 3, then the coupon rate for the month is: 28.50% – 3(3.75%) = 17.25%. The higher the coupon leverage, the more the inverse floater’s coupon rate changes for a given change in one-month LIBOR. Inverse floaters with a wide variety of coupon leverages are available in the market. Participants refer to low-leverage inverse floaters as those with a coupon leverage between 0.5 and 2.1; medium-leverage as those with a coupon leverage higher than 2.1 but not exceeding 4.5; and high-leverage as those with a coupon leverage higher than 4.5. As in the case of the floater, the principal pay-down of an inverse floater will be a proportionate amount of the principal pay-down of the bond class from which it is created. Because the reference rate (e.g., one-month LIBOR) is always positive, the coupon rate paid to the floating rate bond class cannot be negative. If there are no restrictions placed on the coupon rate for the inverse floater, however, it is possible for the coupon rate for that bond class to be negative. To prevent this, a floor, or minimum, can be placed on the coupon rate. In many structures, the floor is set at zero. Once a floor is set for the inverse floater, a cap or ceiling is imposed on the floater. The cap for the floater and the inverse floater, the floor for the inverse floater, the coupon leverage, and the margin spread are not determined independently. Given four of these variables, the fifth will be determined. Planned Amortization Class Tranches The CMO innovations attracted institutional investors who had previously either avoided investing in mortgage-backed securities or allocated only a nominal portion of their portfolio to this sector of the fixed-income market. Potential demand for a CMO product with less uncertainty about the cash flow increased in the mid-1980s. In March 1987, the M.D.C. Mortgage Funding Corporation CMO Series 0 included a class of bonds referred to as stabilized mortgage reduction term (SMRT) bonds; another class in its CMO Series P was referred to as planned amortization class (PAC) bonds. The Oxford Acceptance Corporation III Series C CMOs included a class of bonds referred to as a planned redemption obligation (PRO) bonds. The greater predictability of the cash flow for these classes of bonds, now referred to exclusively as PAC bonds, occurs because there is a principal repayment schedule that must be satisfied. The greater certainty of the cash flow for the PAC bonds comes at the expense of the non-PAC classes, called support or companion bonds. It is these bonds that absorb the prepayment risk. Because PAC bonds have protection against both extension risk and contraction risk, they are said to provide two-sided prepayment protection. Creating a Series of PAC Bonds Although there is no assurance that the collateral will prepay between selected Public Securities Association (PSA) speeds, a PAC bond can be structured to assume that it will. The two speeds used to create a PAC bond are called the initial PAC collars (or initial PAC bands). Most CMO PAC structures have more than one class of PAC bonds. From a PAC bond, we can create other bonds with average lives that are stable and also where all average lives are either much shorter or longer. Even if prepayments are faster than the initial upper collar, there may be sufficient support bonds to assure the average life is unchanged. The degree of protection against extension risk increases for shorter PAC bonds. The effective collar can be wider than the initial collar for shorter PAC tranches. Planned Amortization Class Window A PAC window can be wide or narrow. The narrower a PAC window, the more it resembles a corporate bond with a bullet payment. PAC buyers appear to prefer tight windows, although institutional investors facing a liability schedule are generally better off with a window that more closely matches the liabilities. Investor demand dictates the PAC windows that issuers will create. Investor demand in turn is governed by the nature of investor liabilities. Effective Collars and Actual Prepayments The creation of a mortgage-backed security cannot make prepayment risk disappear. This is true for both a pass-through and a CMO. Thus the reduction in prepayment risk (both extension risk and contraction risk) that a PAC offers must come from somewhere. The prepayment protection comes from the support bonds. It is the support bonds that forego principal payments if the collateral prepayments are slow; support bonds do not receive any principal until the PAC bonds receive the scheduled principal repayment. This reduces the risk that the PAC bonds will extend. Similarly, it is the support bonds that absorb any principal payments in excess of the scheduled principal payment that are made. This reduces the contraction risk of the PAC bonds. Thus the key to the prepayment protection offered by a PAC bond is the amount of support bonds outstanding. If the support bonds are paid off quickly because of faster-than-expected prepayments, there is no longer any protection for the PAC bonds. The support bonds can be thought of as bodyguards for the PAC bondholders. When the bullets fly (i.e., prepayments occur) it is the bodyguards that get killed off first. The bodyguards are there to absorb the bullets. When all the bodyguards are killed off (i.e., the support bonds paid off with faster-than-expected prepayments), the PAC bonds must fend for themselves: they are exposed to all the bullets. Busted means that the prepayment protection is reduced. It is the term used in the CMO market when a PAC schedule is broken. The initial collars are not particularly useful in assessing the prepayment protection for a seasoned PAC bond. This is most important to understand, as it is common for CMO buyers to compare prepayment protection of PACs in different CMO structures, and conclude that the greater protection is offered by the one with the wider collar. This approach is inadequate because it is actual prepayment experience that determines the degree of prepayment protection as well as the expected future prepayment behavior of the collateral. The way to determine this protection is to calculate the effective collar for a seasoned PAC bond. An effective collar for a seasoned PAC is the lower PSA and the upper PSA that can occur in the future and still allow maintenance of the schedule of principal repayments. The effective collar changes every month. An extended period over which actual prepayments are below the upper range of the initial PAC collar will result in an increase in the upper range of the effective collar. This is because there will be more bodyguards around than anticipated. An extended period of prepayments slower than the lower range of the initial PAC collar will raise the lower range of the effective collar. This is because it will take faster prepayments to make up the shortfall of the scheduled principal payments not made plus the scheduled future principal payments. The PAC schedule may not be satisfied even if the actual prepayments never fall outside the initial collar. This may seem surprising because our previous analysis indicated that the average life would not change if prepayments are at either extreme of the initial collar. However, our previous analysis has been based on a single PSA speed for the life of the structure. Providing Greater Prepayment Protection for PACs There are two ways to provide greater protection for PAC bonds: lockouts and reverse PAC structures. One obvious way to provide greater protection for PAC bonds is to issue fewer PAC bonds relative to support bonds. Such a CMO structure with no principal payments to a PAC bond class in the earlier years is referred to as a lockout structure. A CMO structure requiring any excess principal payments to be made to the longer PAC bonds after all support bonds are paid off is called a reverse PAC structure. Other Planned Amortization Class Tranches The collateral can be used to create interest-only and principal-only tranches. These same types of bond classes can be created from a PAC bond. The difference between the bond classes described and those created from a PAC bond is simply the prepayment protection offered by the PAC structure. Targeted Amortization Class Bonds A targeted amortization class (TAC) bond resembles a PAC bond in that it also has a schedule of principal repayment. The difference between a PAC bond and a TAC bond is that the former has a wide PSA range over which the schedule of principal repayment is protected against contraction risk and extension risk. A TAC bond, in contrast, has a single PSA rate from which the schedule of principal repayment is protected. As a result, the prepayment protection afforded the TAC bond is less than that for a PAC bond. The creation of a bond with a schedule of principal repayments based on a single prepayment rate results in protection against contraction risk but not extension risk. Thus, whereas PAC bonds are said to have two-sided prepayment protection, TAC bonds have one-sided prepayment protection. Very Accurately Determined Maturity Bonds Accrual or Z bonds have been used in CMO structures as support for bonds called very accurately determined maturity (VADM) or guaranteed final maturity bonds. In this case the interest accruing (i.e., not being paid out) on a Z bond is used to pay the interest and principal on a VADM bond. Interest-Only and Principal-Only Tranches Stripped mortgage-backed securities are created by paying all the principal to one bond class and all the interest to another bond class. These two classes are referred to as the principal-only (PO) bond class and the interest only (IO) bond class. Notional Interest-Only In the earlier CMO deals, all of the excess interest between the coupon rate on the tranches and the coupon interest on the collateral were paid to an equity class referred to as the CMO residual. This is no longer the practice today. Instead, a tranche is created that receives the excess coupon interest. This tranche is called a notional interest only (IO) class and also referred to as a structured IO. The notional amount is the amount on which the interest payments will be determined, not the amount that will be paid to the holder of this bond. Mathematically, this notional amount is found as follows: notional amount for 7.5% IO = where excess interest = collateral coupon rate – tranche coupon rate. Support Bonds The support bonds—or bodyguards—are the bonds that provide prepayment protection for the PAC tranches. Consequently, they are exposed to the greatest level of prepayment risk. The support bond typically is divided into different bond classes. The support bond can even be partitioned so as to create support bond classes with a schedule of principal repayments. That is, support bond classes that are PAC bonds can be created. AGENCY STRIPPED MORTGAGE-BACKED SECURITIES Agency stripped mortgage-backed securities (SMBSs) are another example of derivative mortgage products. A SMBS is created by altering the distribution of principal and interest from a pro rata distribution to an unequal distribution. There are three types of SMBS: (1) synthetic-coupon pass-throughs, (2) interest-only/principal-only securities, and (3) CMO strips. There are three types of SMBS: (1) synthetic-coupon pass-throughs, (2) interest-only/principal-only securities, and (3) CMO strips. Synthetic-Coupon Pass-Throughs The first generation of SMBS were synthetic-coupon pass-throughs was where two securities were paid some interest and principal from a pass-through security but the distribution of interest or principal are not equal. The result is two securities with a synthetic coupon rate that is different from that of the underlying pass-through security from which they were created. Interest-Only/Principal-Only Strips In the synthetic coupon pass-throughs, at least some interest and principal is paid to the two securities created. In an interest-only (IO) security and principal-only (PO) security, all of the interest is allocated to the IO and the entire principal to the PO. These two SMBS are referred to as mortgage strips. The PO security is purchased at a substantial discount from par value. The yield an investor will realize depends on the speed at which prepayments are made. The faster the prepayments, the higher the yield the investor will realize. For the IO, there is no par value. In contrast to the PO investor, the IO investor wants prepayments to be slow. The reason is that the IO investor receives only interest on the amount of the principal outstanding. As prepayments are made, the outstanding principal declines, and less dollar interest is received. An interesting characteristic of an IO is that its price tends to move in the same direction as the change in mortgage rates. This effect occurs (1) when mortgage rates fall below the coupon rate, and (2) for some range of mortgage rates above the coupon rate. Collateralized Mortgage Obligation Strips One of the classes in a CMO structure can be a principal-only or an interest-only class. These are called CMO strips or structured IOs. KEY POINTS • Agency CMOs, referred to by the agencies that issue them as REMICs, are bond classes created by redirecting the cash flows of mortgage-related products (mortgage pass-through securities). • The creation of a CMO cannot eliminate prepayment risk; it can only redistribute the various forms of this risk among different classes of bonds called tranches. • The credit risk of an agency CMO carries the same credit risk as that of an agency pass-through security. • In a CMO, there are rules for the distribution of interest and principal from the collateral. • The first CMOs were structured so that each class of bond would be retired sequentially, and hence such structures are referred to as sequential-pay CMOs. The average life of the tranches differs from that of the collateral. • An accrual tranche allows the creation of even shorter-term and longer-term average life tranches than in a sequential-pay CMO without the inclusion of an accrual tranche. • From any of the fixed-rate tranches, a floater and an inverse can be created. • An interest-only and a principal-only tranche can be created from a tranche. A notional IO is a tranche created from the difference between the collateral’s coupon interest and the total coupon interest paid to the tranches. • Despite the redistribution of prepayment risk with sequential-pay and accrual CMOs, there is still considerable prepayment risk. That is, there is still considerable average life variability for a given tranche. This problem has been mitigated by the creation of a planned amortization class tranche. This type of CMO tranche reduces average life variability. • The bonds included in a CMO structure that provide the better protection for PAC tranches are the support or companion tranches. There are various ways in which greater prepayment protection can be provided for some or all of the PAC bonds within a CMO structure. These include a lockout and a reverse PAC structure. • Targeted amortization class bonds are created so as to provide protection against contraction risk but not against extension risk. A reverse TAC also provides one-sided protection: protection against extension risk but not against contraction risk. A very accurately determined maturity bond also provides protection against extension risk. • Support bonds are the riskiest tranche within a CMO structure. From support bonds other types of bonds can be created. For example, a part of the support bonds can be carved up to create support bonds with a principal repayment schedule. Such bonds are referred to as PAC II or level II PAC bonds. • A stripped MBS is created by assigning distribution of principal and interest of the underlying pass-through security in unequal portions to two classes of bonds. The result is that the two bonds will have a different price/yield relationship from that of the underlying pass-through. • There are three types of SMBS: (1) synthetic-coupon pass-throughs, (2) interest-only/principal-only securities, and (3) CMO strips. ANSWERS TO QUESTIONS FOR CHAPTER 12 (Questions are in bold print followed by answers.) 1. How does a CMO alter the cash flow from mortgages so as to shift the prepayment risk across various classes of bondholders? Prepayment risk refers to the risk associated with the early unscheduled return of principal on a fixed-income security. Collateralized mortgage obligations (CMOs) redirect cash flows from a pass-through security to various bond classes making it possible to redistribute prepayment risk for investors who want to reduce their exposure to prepayment risk. Because the total prepayment risk of a pass-through will not be changed by altering the cash flows, other investors must be found who are willing to accept the unwanted prepayment risk. 2. What is the difference between a REMIC and a CMO? All three entities (Ginnie Mae, Fannie Mae, and Freddie Mac) that issue agency pass-through securities also issue CMOs, with Ginnie Mae being a late entry into the market, issuing its first CMO in 1994. The CMOs are not referred to not as CMOs by these issuers. They are referred to as REMICs or REMIC structures. REMIC means Real Estate Mortgage Investment Conduit and is a provision in the Tax Reform Act of 1986. This provision in the tax law allows the efficient creation of a CMO structure. Consequently, issuers, both agency and nonagency issuers, structure their CMO deals so as to qualify for REMIC tax treatment. Rather than referring to this multiclass mortgage structure as a CMO, the preference is to refer to it as a REMIC. 3. Answer the below questions. (a) “By creating a CMO, an issuer eliminates the prepayment risk associated with the underlying mortgages.” Do you agree with this statement? A CMO redirects cash flows making it possible to redistribute prepayment risk so that some investors reduce their prepayment risk exposure while others increase their prepayment risk exposure. Thus, one would agree with the statement that a CMO eliminates prepayment risk for certain investors, but would disagree with the statement that a CMO eliminates prepayment risk for all investors. (b) Wall Street often refers to CMOs as “customized securities.” Explain why. CMOs are “customized securities” in the sense that they can be tailor-made to satisfy the preferences of investors. For example, classes of bonds or tranches can be created which are customized or structured for individual and institutional investors to meet a particular prepayment risk that is desired. 4. In a discussion of the CMO market, the popular press sometimes refers to this sector of the mortgage-backed securities market as the riskiest sector and the pass-through sector as the safest sector. Comment. Collateralized mortgage obligations derive their cash flow from underlying mortgage collateral such as pass-throughs or a pool of whole loans. Thus, CMOs can be referred to as a derivative mortgage-backed securities product. The popular press does not always distinguish between the speculative and hedging nature of derivates but perceive derivatives as riskier due to greater variability in outcomes that often result. On the other hand, many pass-throughs are sponsored by government agencies and thus perceived as being safe. Thus, the popular press can erroneously mistake differences in overall or total risk when speaking of the CMO sector and the pass-through sector. The fact is CMOs are backed by pass-throughs and thus the total risk of each sector should be the same. 5. Explain the effect on the average lives of sequential-pay structures of including an accrual tranche in a CMO structure. The effect of an accrual tranche is to decrease the average lives of the other tranches at the expense of the accrual tranche. Background information on sequential-pay CMOs and more details on the effect of an accrual tranche are given below. The first CMO was created in 1983 and was structured so that each class (or tranche) of bond would be retired sequentially. Such structures are referred to as sequential-pay CMOs. A CMO is created by redistributing the cash flow—interest and principal—to the different tranches based on a set of payment rules. Each tranche receives periodic 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 preceding tranche has been paid off. Although the priority rules for the disbursement of the principal payments are known, the precise amount of the principal in each period is not. This will depend on the cash flow, and therefore principal payments, of the collateral, which depends on the actual prepayment rate of the collateral. An assumed PSA speed allows the cash flow to be projected. The principal pay-down window for a tranche is the time period between the beginning and the ending of the principal payments to that tranche. Tranches can 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. However, there is considerable variability of the average life for the tranches even though 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) can effectively protect the shorter-term tranches against extension risk. This protection must come from somewhere, so it comes from the other longer term tranches that benefit from being protected against contraction risk. 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 bond class is then used to speed up or pay down of the principal balance of earlier bond classes. Thus, the average lives for the other tranches become shorter because of the inclusion of the accrual bond. 6. What types of investors would be attracted to an accrual bond? The accrual bond has appeal to investors who are concerned with reinvestment risk. Because there are no coupon payments to reinvest, reinvestment risk is eliminated until all the other tranches are paid off. 7. Suppose that a tranche from which an inverse floater is created has an average life of five years. What will the average life of the inverse floater be? The coupon rate on the tranche from which two classes (floater and inverse floater) are created can support the aggregate interest payments that must be made to them. As in the case of the floater, the principal pay-down of an inverse floater will be a proportionate amount of the principal pay-down of bond class that created it. Thus, the floater and inverse floater will have a weighted average life equal to the average life of the tranche from which it is created. In equation form, we have: Average life = 5 years = (inverse floater’s weight)(X years) + (floater’s weight)(Y years) where X equals inverse floater’s average life in years and Y equals floater’s average life in years. Solving for X, we get: X years = . Let’s illustrate. Suppose that the floater and inverse floater are equally-weighted (each weight = ½). If so, then, we have: X years = =  (1/2)X years = 5 years – (1/2)(Y years)  (1/2)X years + (1/2)Y years = 5 years. Thus, the average life of the inverse floater would be 5 years. Now assume that the average life for the floater and inverse floater are equal (X = Y). Further solving gives: (1/2)X + (1/2)X = 5 years  X = 5 years and Y = 5 years. If we assume that 2X = Y, then we have: (1/2)X + (1/2)(2X) = 5  (3/2)X = 5  X = 3.33 years and Y = 6.67 years. Thus, the average life of the inverse floater would be 3.33 years. Similarly, we could show that if X = 2Y, then the average life of the inverse floater would be 6.67 years. 8. This quotation is taken from a 1991 issue of BondWeek: First Interstate Bank of Texas will look into buying several different types of collateralized mortgage obligation tranches when it starts up its buy program sometime after the second quarter of 1991, according to Jules Pollard. V.P. Pollard said he will consider replacing maturing adjustable-rate mortgage pass-throughs with short companion tranches and planned amortization classes because the ARMs have become rich. . . . Pollard did not provide a dollar figure on the planned investments, which will be made to match fund the bank’s liabilities. When he does invest he said he prefers government guaranteed securities or those with implied guarantees. Answer the below questions. (a) Explain the types of securities that Pollard is buying and selling. Pollard wants to replace (or sell) adjustable-rate mortgage pass-throughs. Pollard wants to buy various types of CMO tranches. In particular, he wants “short companion” and “planned amortization” tranches. He prefers these tranches to be government guaranteed securities or those with implied guarantees. (b) Given the preference stated in the last sentence of the quotation, what issuers is he likely to prefer? What issuers would he reject? Given the last sentence, one would conclude that Pollard wants tranches backed by agency CMOs. In particular, he would want Ginny Mae, Freddie Mae, and Fannie Mae. He would reject any tranches backed by nonagency CMOs which are not (implicitly or explicitly) guaranteed by the government. More details as to what Pollard would prefer are given below. Pollard wants to replace (or sell) adjustable-rate mortgage pass-throughs. The type of security he no longer wants and the implications of this desire can include a mortgage pass-through security, or simply a pass-through. This is a security that results when one or more mortgage holders form a collection (pool) of mortgages and sell shares or participation certificates in the pool. The cash flow of a mortgage pass-through security depends on the cash flow of the underlying mortgages. The cash flow consists of monthly mortgage payments representing interest, the scheduled repayment of principal, and any prepayments. Payments are made to security holders each month. Neither the amount nor the timing, however, of the cash flow from the pool of mortgages is identical to that of the cash flow passed through to investors. Since Pollard owns adjustable-rate pass-throughs, he is currently free from inflation rate risk. This implies he thinks that interest rates may be falling and adjustable rate securities will pay lower cash flows in the future. Pollard wants to buy various types of CMO tranches. In particular, he wants “short companion” and “planned amortization” tranches. He prefers these tranches to be government guaranteed securities or those with implied guarantees. In particular, it appears that Pollard wants collateralized mortgage obligations (CMOs), which are bond classes created by redirecting the cash flows of mortgage-related products so as to mitigate prepayment risk for at least some classes. An accrual tranche can help overcome reinvestment rate risk if that is Pollard’s main concern. While Pollard appears to be concerned with interest rates falling, he may be more concerned with mitigating prepayment risk, in particular contraction risk. For example, when interest rates fall there is greater prepayment risk because borrowers will want to retire their debt quicker. Thus, he wants to avoid contraction risk. The mere creation of a CMO cannot eliminate prepayment risk; it can only transfer the various forms of this risk among different classes of bondholders. Pollard wants a “short companion” which indicates he wants a tranche where the principal is paid off early. This is not consistent with the notion that he believes interest rates are falling because the early pay-off means he would have to reinvest funds at a lower rate. Thus, we can eliminate this choice. Pollard’s other choice is “planned amortization” tranches (referred to as PAC tranches). PAC tranches can reduce prepayment risk in a manner desired by an investor’s preference. However, despite the redistribution of prepayment risk with sequential-pay and accrual CMOs, there is still considerable prepayment risk. That is, there is still considerable average life variability for a given tranche. This problem is mitigated by the PAC tranche. The greater predictability of the cash flow for PAC bonds occurs because there is a principal repayment schedule that must be satisfied. PAC bondholders have priority over all other classes in the CMO issue in receiving principal payments from the underlying collateral. The greater certainty of the cash flow for the PAC bonds comes at the expense of the non-PAC classes, called support bonds. It is these bonds that absorb the prepayment risk. Because PAC bonds have protection against both extension risk and contraction risk, they are said to provide two-sided prepayment protection. Given all of the above details and Pollard’s assumed desire to reduce prepayment risk, it appears that Pollard would choose a “planned amortization” tranche. In particular, he would want a PAC class that avoids contraction risk. If alleviating reinvestment rate risk is also a major concern, then Pollard could also choose some accrual tranches. Whatever his choice, Pollard would want a tranche backed by an agency CMO. 9. Describe how the schedule for a PAC tranche is created. The schedule for a PAC tranche is set so that there will be greater predictability of the cash flow through establishing a principal repayment schedule that must be satisfied. The schedule will be set so that PAC bondholders have priority over all other classes in the CMO issue in receiving principal payments from the underlying collateral. The greater certainty of the cash flow for the PAC bonds comes at the expense of the non-PAC classes, called support or companion bonds. It is these bonds that absorb the prepayment risk. Because PAC bonds have protection against both extension risk and contraction risk, they are said to provide two-sided prepayment protection. In setting the schedule, one specifies the amount of the collateral from the pass-through, a coupon rate, a WAC, and a WAM. Given two prepayment speeds (expressed in terms of PSA and called the initial PAC collars), the principal payment or PAC schedule is set. The principal payment consists of the regularly scheduled principal repayment plus prepayments for chosen collateral PSA speeds. The minimum principal payment for the PAC schedule is given by the lower PSA speed (called the lower collar). The characteristic of the collateral allows for the creation of a PAC bond, assuming that the collateral prepays over its life between the two speeds. A schedule of principal repayments that the PAC bondholders are entitled to receive (before any other bond class in the CMO) is specified. Although there is no assurance that the collateral will prepay between the two speeds, a PAC bond can be structured to assume that it will. The payment rules state (i) how to disburse periodic coupon interest to each tranche on the basis of the amount of principal outstanding at the beginning of the period, and (ii) how to disburse principal payments to tranches based on its schedule of principal repayments. The latter also states which tranches have priority with respect to current and future principal payments to satisfy the schedule. When one tranche is paid off completely, all principal payments are to be made to next tranche specified in the payment rules. Between the two PSA speeds, the average life for the PAC bond is stable. However, at slower or faster PSA speeds, the schedule is broken, and the average life changes, lengthening when the prepayment speed is less than the lower collar and shortening when it is greater than the upper collar. Even so, there is much greater variability for the average life of the support bond. Most CMO PAC structures have more than one class of PAC bonds. Given the prepayment speeds chosen, it is possible to make the average life for the multiple PAC bonds less than or greater than that if there was only one class of PAC bonds. 10. Explain the role of a support bond in a CMO structure. The support bond class in a CMO structure provides for the prepayment protection for the other bond classes. It is the support bonds that forego principal payments if the collateral prepayments are slow. Support bonds do not receive any principal until the PAC bonds receive the scheduled principal repayment. This reduces the risk that the PAC bonds will extend. Similarly, it is the support bonds that absorb any principal payments in excess of the scheduled principal payment that are made. This reduces the contraction risk of the PAC bonds. Thus the key to the prepayment protection offered by a PAC bond is the amount of support bonds outstanding. If the support bonds are paid off quickly because of faster-than-expected prepayments, there is no longer any protection for the PAC bonds. In fact, if the support bond is paid off, the structure is effectively reduced to a sequential-pay CMO. The support bonds can be thought of as bodyguards for the PAC bondholders. When the bullets fly (i.e., prepayments occur) it is the bodyguards that get killed off first. The bodyguards are there to absorb the bullets. When all the bodyguards are killed off (i.e., the support bonds paid off with faster-than-expected prepayments), the PAC bonds must fend for themselves: they are exposed to all the bullets. 11. What was the motivation for the creation of PAC bonds? The motivation for the creation of PAC bonds was to diminish the uncertainty in cash flows including prepayment risk. More details are supplied below. The CMO innovations attracted many institutional investors who had previously either avoided investing in mortgage-backed securities or allocated only a nominal portion of their portfolio to this sector of the fixed-income market. Although some traditional corporate bond buyers shifted their allocation to CMOs, a majority of institutional investors remained on the sidelines, concerned about investing in an instrument that they continued to perceive as posing significant prepayment risk because of the substantial average life variability, despite the innovations designed to reduce prepayment risk. Potential demand for a CMO product with less uncertainty about the cash flow increased in the mid-1980s because of two trends in the corporate bond market. First was the increased event risk faced by investors. The second trend was a decline in the number of AAA rated corporate issues. Traditional corporate bond buyers sought a structure with both the characteristics of a corporate bond (either a bullet maturity or a sinking fund type of schedule of principal repayment) and high credit quality. Although CMOs satisfied the second condition, they did not satisfy the first. In March 1987, the M.D.C. Mortgage Funding Corporation CMO Series 0 included a class of bonds referred to as stabilized mortgage reduction term bonds; another class in its CMO Series P was referred to as planned amortization class (PAC) bonds. The Oxford Acceptance Corporation III Series C CMOs included a class of bonds referred to as a planned redemption obligation bonds. The characteristic common to these three bonds is that if the prepayments are within a specified range, the cash flow pattern is known. The greater predictability of the cash flow for these classes of bonds, now referred to exclusively as PAC bonds, occurs because there is a principal repayment schedule that must be satisfied. PAC bondholders have priority over all other classes in the CMO issue in receiving principal payments from the underlying collateral. The greater certainty of the cash flow for the PAC bonds comes at the expense of the non-PAC classes, called support or companion bonds. It is these bonds that absorb the prepayment risk. Because PAC bonds have protection against both extension risk and contraction risk, they are said to provide two-sided prepayment protection. 12. Suppose that a savings and loan association has decided to invest in mortgage-backed securities and is considering the following two securities: (i) a Freddie Mac pass-through security with a WAM of 340 months or (ii) a PAC tranche of a Freddie Mac CMO issue with an average life of two years. Which mortgage-backed security would probably be better from an asset/liability perspective? Below we first describe the two choices in order to establish asset/liability possibilities. The first choice is a pass-through security. The cash flow of a mortgage pass-through security depends on the cash flow of the underlying mortgages. A weighted average maturity (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 outstanding. Freddie Mac issues a pass-through called a participation certificate (PC). In 1990, Freddie Mac introduced its Gold PC, which has stronger guarantees than other PCs it issues and will be the only type of PC issued in the future. Specifically, non-Gold PCs that have been issued are modified pass-throughs. This type of pass-through guarantees both interest and principal payments, but it guarantees only the timely payment of interest. The scheduled principal is passed through as it is collected, with a guarantee that the scheduled payment will be made no later than a specified date. The Freddie Mac pass-through still entails prepayment risk and uncertainty in cash flows that can be alleviated by creating CMOs. A CMO is the second choice. A CMO is a security backed by a pool of pass-throughs, whole loans, or stripped mortgage-backed securities. CMOs are structured so that there are several classes of bondholders with varying stated maturities. When there is more than one class of bondholders with the same level of credit priority, the structure is called a pay-through structure, as opposed to a pass-through structure in which there is only one class of bondholders at a given level of credit priority. The bond classes created are commonly referred to as tranches. The principal payments from the underlying collateral are used to retire the tranches on a priority basis according to terms specified in the prospectus. Despite the redistribution of prepayment risk with sequential-pay and accrual CMOs, there is still considerable prepayment risk. That is, there is still considerable average life variability for a given tranche. This problem has been mitigated by the creation of a planned amortization class (PAC) tranche. This type of CMO tranche reduces average life variability. The bonds included in a CMO structure that provide the better protection for PAC tranches are the support or companion tranches. There are various ways in which greater prepayment protection can be provided for some or all of the PAC bonds within a CMO structure. These include a lockout and a reverse PAC structure. From the above description, we see that both types are backed by the same mortgages and should share in the same credit risk. Thus, the savings and loan association can focus on matching assets and liabilities. There is a significant difference in terms of maturity between the two types. Thus, the savings and loan will choose the Freddie Mac pass-through security with a WAM of 340 months if their liabilities are closer to 340 than two years. The savings and loan will choose the PAC tranche of a Freddie Mac CMO issue with an average life of two years if their liabilities are closer to 24 months than 340 months. 13. Suppose that a PAC bond is created assuming prepayments speeds of 80 PSA and 350 PSA. If the collateral pays at 100 PSA over its life, what will this PAC tranche’s average life be? As illustrated in Exhibit 12-9, the average life for the PAC bond is stable at 7.26 years as long as the PSA speed is between the two designated prepayments speeds (i.e., between the lower and upper collars). However, at slower or faster PSA speeds than the two collar speeds, the schedule is broken with the average life changing. The average life lengthens when the prepayment speed is less than the lower collar and shortens when it is greater than the upper collar. 14. Suppose that $1 billion of pass-throughs is used to create a CMO structure with a PAC bond with a par value of $700 million and a support bond with a par value of $300 million. Answer the below questions. (a) Which of the following will have the greatest average life variability: (i) the collateral, (ii) the PAC bond, or (iii) the support bond? Why? The support bond will have the greatest average life variability because its purpose is to reduce variability in the cash flows, and thus the variability in the average life, of the PAC bonds. More details are given below. The average life variability for the collateral should lie between that for the PAC bond and the support bond because the PAC bond class and the support bond class are derived from the collateral. The support bond class is used to create a more stable average life for the PAC bond class. Support bondholders have less priority over all other classes in the CMO issue in receiving principal payments from the underlying collateral. It is the support bonds that forego principal payments if the collateral prepayments are slow; support bonds do not receive any principal until the PAC bonds receive the scheduled principal repayment. This reduces the risk that the PAC bonds will extend. On the other hand, it is the support bonds that absorb any principal payments in excess of the scheduled principal payment that are made. This reduces the contraction risk of the PAC bonds. The key to the prepayment protection offered by a PAC bond is the amount of support bonds outstanding. If the support bonds are paid off quickly because of faster-than-expected prepayments, there is no longer any protection for the PAC bonds. Because the stability for the PAC bond comes at the expense of the support bond, the support bond will have more variability in its average life than the PAC bond. Thus, in terms of greatest to least average life variability, we have: the support bond, the collateral, and the PAC bond. (b) Which of the following will have the least average life variability: (i) the collateral, (ii) the PAC bond, or (iii) the support bond? Why? The PAC bond will have the least average life variability because its payment schedule is structured to achieve stability in the cash flows and thus reduce variability in the average life. More details are given below. The average life variability for the collateral should lie between that for the PAC bond class and the support bond class because the PAC bonds and support bonds are derived from the collateral. The support bond class is used to create a more stable average life for the PAC bond class. PAC bondholders have priority over all other classes in the CMO issue in receiving principal payments from the underlying collateral. This gives a lower variability in its average life. Thus, in terms of least to greatest average life variability, we have: the PAC bond, the collateral, and the support bond. 15. Suppose that the $1 billion of collateral in Question 14 was divided into a PAC bond with a par value of $800 million and a support bond with a par value of $200 million. Will the PAC bond in this CMO structure have more or less protection than the PAC bond in Question 14? The PAC bond in the structure of $800 million versus $200 million will have less protection that $700 million versus $300 million. This is because $300 million support is greater than $200 million support. Also, the $300 million has a less amount of PAC bonds to support ($700 million versus $800 million). In general, more supports bonds will offer greater protection. This is because the key to the prepayment protection offered by a PAC bond is the amount of support bonds outstanding. If the support bonds are paid off quickly because of faster-than-expected prepayments, there is no longer any protection for the PAC bonds. In fact, if the support bond is paid off, the structure is effectively reduced to a sequential-pay CMO. The support bonds can be thought of as bodyguards for the PAC bondholders. When the bullets fly (i.e., prepayments occur) it is the bodyguards that get killed off first. The bodyguards are there to absorb the bullets. When all the bodyguards are killed off (i.e., the support bonds paid off with faster-than-expected prepayments), the PAC bonds must fend for themselves: they are exposed to all the bullets. 16. Suppose that $1 billion of pass-throughs is used to create a CMO structure with a PAC bond with a par value of $700 million (PAC I), a support bond with a schedule (PAC II) with a par value of $100 million, and a support bond without a schedule with a par value of $200 million. Answer the below questions. (a) Will the PAC I or PAC II have the smaller average life variability? Why? The PAC II will have greater average life variability. This is because the primary function of PAC II is to support PAC I bonds by allowing them to have more stable cash flows and thus less average life variability. More details are given below. A support bond can be partitioned so as to create support bond classes with a schedule of principal repayments. That is, support bond classes that are PAC bonds can be created. In a structure with a PAC bond and a support bond with a PAC schedule of principal repayments, the former is called a PAC I bond or level I PAC bond and the latter a PAC II bond or level II PAC bond. Although PAC II bonds have greater prepayment protection than the support bond classes without a schedule of principal repayments, the prepayment protection is less than that provided PAC I bonds. (b) Will the support bond without a schedule or the PAC II have the greater average life variability? Why? The support bond without a schedule will have greater average life variability. This is because they support more stable cash flows, and thus smaller average life variability, for PAC II bonds. 17. In a CMO structure with several PAC bonds, explain why, when the support bonds are paid off, the structure will be just like a sequential-pay CMO. The PAC bonds and support bonds are formed from the sequential-pay CMO. If the support bonds are paid off earlier than expected, then the structure reverts to a sequential-pay CMO. More details on the sequential-pay structure are supplied below. The first CMO was created in 1983 and was structured so that each class of bond would be retired sequentially. Such structures are referred to as sequential-pay CMOs. The payment rules dictate that each tranche receives periodic coupon interest payments based on the amount of the outstanding balance at the beginning of the month. However, the disbursement of the principal is made in a special way. A tranche is not entitled to receive principal until the entire principal of the preceding tranche has been paid off. More specifically, the first tranche receives all the principal payments until the entire principal amount owed to that bond class is paid off; then the next tranche begins to receive principal and continues to do so until it is paid off in entirety. This process continues until the last tranche is paid off. Tranches that are paid off later have greater maturities and thus greater average lives. Although the priority rules for the disbursement of the principal payments are known, the precise amount of the principal in each period is not. This will depend on the cash flow, and therefore principal payments, of the collateral, which depends on the actual prepayment rate of the collateral. An assumed PSA speed allows the cash flow to be projected. The principal pay-down window for a tranche is the time period between the beginning and the ending of the principal payments to that tranche. Tranches can 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. 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 (which is paid off first) in this structure against extension risk. This protection must come from somewhere, so it comes from the tranches where the principal is paid off later. These tranches benefit because they are provided protection against contraction risk. 18. Suppose that for the first four years of a CMO, prepayments are well within the initial PAC collar. What will happen to the effective upper collar? If the prepayments are well within the initial PAC collar, this means that there are more bodyguards (i.e., support bonds) around than was expected when the PAC was structured at the initial collar. This will result in an increase in the upper range of the effective collar. More details are supplied below. The initial collars are not particularly useful in assessing the prepayment protection for a seasoned PAC bond. This is most important to understand, as it is common for CMO buyers to compare prepayment protection of PACs in different CMO structures, and conclude that the greater protection is offered by the one with the wider collar. This approach is inadequate because it is actual prepayment experience that determines the degree of prepayment protection and the expected future prepayment behavior of the collateral. The way to determine this protection is to calculate the effective collar for a seasoned PAC bond. An effective collar for a seasoned PAC is the lower and the upper PSA that can occur in the future and still allow maintenance of the schedule of principal repayments. The effective collar changes every month. An extended period over which actual prepayments are below the upper range of the initial PAC collar will result in an increase in the upper range of the effective collar. This is because there will be more bodyguards around than anticipated. An extended period of prepayments slower than the lower range of the initial PAC collar will raise the lower range of the effective collar. This is because it will take faster prepayments to make up the shortfall of the scheduled principal payments not made plus the scheduled future principal payments. The PAC schedule may not be satisfied even if the actual prepayments never fall outside the initial collar. This is because single PSA speed does not necessarily hold for the life of the structure. Finally, any prepayment speeds faster than the collar jeopardize satisfaction of the principal repayment schedule and increase extension risk. This does not mean that the schedule will be busted—the term used in the CMO market when a PAC schedule is broken. It does mean that the prepayment protection is reduced. 19. Consider the following CMO structure backed by 8% collateral: Tranche Par Amount (in millions) Coupon Rate (%) A $300 6.50% B $250 6.75% C $200 7.25% D $250 7.75% Suppose that a client wants a notional IO with a coupon rate of 8%. Calculate the notional amount for this notional IO. Notice that for this structure the notional amount for the IO class is shown in the table below as $121,875,000 for a coupon rate of 8.0%. This is an IO class, so there is no par amount. The amount shown is the amount on which the interest payments will be determined, not the amount that will be paid to the holder of this bond. Therefore, it is called a notional amount. Let’s look at how the notional amount is determined. Consider first tranche A. The par value is $300 million and the coupon rate is 6.5%. Because the collateral’s coupon rate is 8%, the excess interest is 150 basis points. Therefore, an IO with a 1.5% coupon rate and a notional amount of $300 million can be created from tranche A. As seen below, this is equivalent to an IO with a notional amount of $56.25 million and a coupon rate of 8%. Mathematically, this notional amount is found as follows: notional amount for 8% IO = where excess interest = collateral coupon rate – tranche coupon rate. For example, for tranche A, excess interest = 0.080 – 0.065 = 0.015 and the tranche’s par value = $300,000,000. Inserting in these values in our equation gives: notional amount for 8% IO = = $56,250,000. Similarly, from tranche B with a par value of $250 million, the excess interest is 125 basis points. Therefore, an IO with a coupon rate of 1.25% and a notional amount of $250 million can be created. As seen below, this is equivalent to creating an IO with a notional amount of $39,620,500 million and a coupon rate of 8%. For example, for tranche B, excess interest = 0.080 – 0.0675 = 0.0125 and tranche’s par value = $250,000,000. Inserting in these values in our equation gives: notional amount for 8% IO = = = $39,062,500. Similarly, from tranche C with a par value of $200 million, the excess interest is 75 basis points, and therefore an IO with a coupon rate of 0.75% and a notional amount of $200 million can be created. As seen below, this is equivalent to creating an IO with a notional amount of $18,750,000 million and a coupon rate of 8%. For example, for tranche C, excess interest = 0.080 – 0.0725 = 0.0075 and tranche’s par value = $200,000,000. Inserting in these values gives: notional amount for 8% IO = = = $18,750,000. Similarly, from tranche D with a par value of $250 million, the excess interest is 25 basis points, and therefore an IO with a coupon rate of 0.25% and a notional amount of $250 million can be created. As seen below, this is equivalent to creating an IO with a notional amount of $7,812,500 million and a coupon rate of 8%. For example, for tranche D, excess interest = 0.080 – 0.0775 = 0.0025 and tranche’s par value = $250,000,000. Inserting in these values in our equation gives: notional amount for 8% IO = = = $7,812,500. The above amounts are summarized in the following table for all four tranches. Tranche Par Amount Excess Interest (%) Notional Amount for an 8% Coupon Rate IO A $300,000,000 1.50% $ 56,250,000 B $250,000,000 1.25% $ 39,062,500 C $200,000,000 0.75% $ 18,750,000 D $250,000,000 0.25% $ 7,812,500 Notional Amount for an 8.0% IO $ 21,875,000 20. An issuer is considering the following two CMO structures. The first structure is: Structure I Tranche Par Amount (in millions) Coupon Rate (%) A $150 6.50% B $100 6.75% C $200 7.25% D $150 7.75% E $100 8.00% F $500 8.50% Tranches A to E are a sequence of PAC I’s and F is the support bond. The second structure is: Structure II Tranche Par Amount (in millions) Coupon Rate (%) A $150 6.50% B $100 6.75% C $200 7.25% D $150 7.75% E $100 8.00% F $200 8.25% G $300 ? Tranches A to E are a sequence of PAC I’s, F is a PAC II, and G is a support bond without a PAC schedule. Answer the below questions. (a) In structure II, tranche G is created from tranche F in structure I. What is the coupon rate for tranche G assuming that the combined coupon rate for tranches F and G in structure II should be 8.5%? We can solve for tranche G by using the following weighted average formula: 8.5% = ($200/$500)(8.25%) + ($300/$500)(?). Using algebra, simplifying, and rearranging, we get: ? = [8.5% – (0.4)8.25%] / 0.6 = [8.5% – 3.3%] / 0.6 = 8.6667%. Thus, tranche G has a coupon rate of about 8.67%. (b) What is the effect on the value and average life of tranches A to E by including the PAC II in structure II? It has no effect since it is formed from tranche F. Together tranches F and G in Structure II have a value and an average life equal to that of tranche F in Structure I. (c) What is the difference in the average life variability of tranche G in structure II and tranche F in structure II? Tranche F in Structure II is formed to give more stable cash flows and thus a lower variability in average life than found in tranche F in Structure I. This lower variability in average life comes at the expense of the support tranche or tranche G which has a higher average life than tranche F. 21. Answer the below questions. (a) What is the role of a lockout in a CMO structure? The role of a lockout in a CMO structure is to provide greater prepayment protection to all PAC bonds. More details are given below. One obvious way to provide greater protection for PAC bonds is to issue fewer PAC bonds relative to support bonds. A CMO structure with no principal payments to a PAC bond class in the earlier years is referred to as a lockout structure. A lockout structure provides greater prepayment protection to all PAC bonds in the CMO structure. One way to provide greater prepayment protection to only some PAC bonds is to alter the principal payment rules for distributing principal when all the support bonds have been paid off. For example, when the support bond is paid off, the structure can be made to effectively become a sequential-pay structure. To provide greater protection to a PAC bond, the payment rules after all support bonds have been paid off can be specified so that any principal payments in excess of the scheduled amount will be paid to the last PAC bond. Thus this PAC bond is exposed to greater contraction risk, which provides the other five PAC bonds with more protection against contraction risk. The principal payment rules would also specify that when the support bond and last PAC bond are paid off, all principal payments in excess of the scheduled amounts to earlier tranches are to be paid to the next-to-last PAC bond. (b) Explain why in a reverse PAC bond structure the longest average life bond can turn out to be effectively a support bond if all the support bonds in the structure are paid off. By definition, the support bonds—or bodyguards—are the bonds that provide prepayment protection for the PAC tranches. In a reverse PAC bond structure, the longest average life bond performs the same function as a support bond. For example, a CMO structure requiring any excess principal payments to be made to the longer PAC bonds after all support bonds are paid off is called a reverse PAC structure. By requiring the longer PAC bonds receive any excess principal, these bonds are effectively performing the same function as the support bonds. 22. Answer the below questions. (a) What type of prepayment protection is afforded a TAC bond? A targeted amortization class (TAC) bond resembles a PAC bond in that both have a schedule of principal repayment. The difference between a PAC bond and a TAC bond is that the former has a wide PSA range over which the schedule of principal repayment is protected against contraction risk and extension risk. A TAC bond, in contrast, has a single PSA rate from which the schedule of principal repayment is protected. As a result, the prepayment protection afforded the TAC bond is less than that for a PAC bond. (b) What type of prepayment protection is afforded a reverse TAC bond? If mortgage rates rise, the price of any bond will decline. But pass-throughs will decline more because the higher rates will tend to slow down the rate of prepayment. This is just the time when investors want prepayments to speed up so that they can reinvest the prepayments at the higher market interest rate. This adverse consequence of rising mortgage rates is called extension risk. Some institutional investors are interested in protection against extension risk but are willing to accept contraction risk. This is the opposite protection from that sought by the buyers of TAC bonds. The structures created to provide such protection are referred to as reverse TAC bonds. (c) What type of prepayment protection is afforded a VADM? Accrual or Z bonds have been used in CMO structures as support for bonds called very accurately determined maturity (VADM) or guaranteed final maturity bonds. In this case the interest accruing (i.e., not being paid out) on a Z bond is used to pay the interest and principal on a VADM bond. This effectively provides protection against extension risk even if prepayments slow down, because the interest accruing on the Z bond will be sufficient to pay off the scheduled principal and interest on the VADM bond. Thus the maximum final maturity can be determined with a high degree of certainty. If prepayments are high, resulting in the supporting Z bond being paid off faster, however, a VADM bond can shorten. A VADM is similar in character to a reverse TAC. For structures with similar collateral, however, a VADM bond offers greater protection against extension risk. Moreover, most VADMs will not shorten significantly if prepayments speed up. Thus they offer greater protection against contraction risk compared with a reverse TAC with the same underlying collateral. Compared with PACs, VADM bonds have greater absolute protection against extension risk, and though VADM bonds do not have as much protection against contraction risk, the structures that have included these bonds are such that contraction risk is generally not significant. 23. Answer the below questions. (a) What is a PO security? What is an IO security? In early 1987, stripped MBS began to be issued where all the interest is allocated to one class (the IO class) and the entire principal to the other class (the PO class). The IO class receives no principal payments. IOs and POs are referred to as mortgage strips. Additional details for POs and IOs are discussed below. The PO security is purchased at a substantial discount from par value. The yield an investor will realize depends on the speed at which prepayments are made. The faster the prepayments, the higher the yield the investor will realize. For example, suppose that there is a pass-through backed by 30-year mortgages with $400 million in par value and that investors can purchase POs backed by this pass-through 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 yield that will be realized. In the extreme case, if all the 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 keep their houses for 30 years and make no prepayments, the $225 million will be spread out over 30 years, which will result in a lower yield for PO investors. The price of the PO can be expected to change as mortgage rates in the market change. When mortgage rates decline below the coupon 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 price of a PO will increase when mortgage rates decline. When mortgage rates rise above the coupon rate, prepayments are expected to slow down. The cash flow deteriorates (in the sense of its taking longer to recover principal repayments). Coupled with a higher discount rate, the price of a PO will fall when mortgage rates rise. When an IO is purchased there is no par value. In contrast to the PO investor, the IO investor wants prepayments to be slow. The reason is that the IO investor receives only interest on the amount of the principal outstanding. As prepayments are made, the outstanding principal declines, and less dollar interest is received. In fact, if prepayments are too fast, the IO investor may not recover the amount paid for the IO. (b) How is the price of an interest-only security expected to change when interest rates change? The price of an interest-only security (IO) can move in various directions depending on the direction of the change in interest rates and also the change relative to the coupon rate. Details on the precise expectations of IO price changes are supplied below. If mortgage rates decline below the coupon rate, prepayments on the interest-only security (IO) are expected to accelerate. This results in a deterioration of the expected cash flow for an IO. Although the cash flow will be discounted at a lower rate (causing an increase in the IO price), the net effect is typically a decline in the price of an IO. If mortgage rates rise above the coupon rate, the expected cash flow improves but the cash flow is discounted at a higher interest rate (causing a decrease in the IO price). The net effect may be either a rise or a 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. This effect occurs (i) when mortgage rates fall below the coupon rate, and (ii) for some range of mortgage rates above the coupon rate. An example of this effect can be seen in Exhibit 12-19, which shows for various mortgage rates the price of (i) a 9% pass-through, (ii) a PO created from this pass-through, and (iii) an IO created from this pass-through. Notice that as mortgage rates decline below 9%, the price of the pass-through does not respond much. This is the negative convexity (or price compression) property of pass-throughs. For the PO security, the price falls monotonically as mortgage rates rise. For the IO security, at mortgage rates above approximately 11%, the price declines as mortgage rates rise; as mortgage rates fall below about 11%, the price of an IO falls as mortgage rates decline. Both POs and IOs display substantial price volatility when mortgage rates change. The greater price volatility of the IO and PO compared with the pass-through from which they were created can be seen by the steepness of a tangent line to the curves at any given mortgage rate. 24. Suppose that 8% coupon pass-throughs are stripped into two classes. Class X-1 receives 75% of the principal and 10% of the interest. Class X-2 receives 25% of the principal and 90% of the interest. Answer the below questions. (a) What type of MBS would this be? The stripped MBS described in the question is a synthetic-coupon pass-through with each class receives an unequal distribution of principal and interest. More details are given below. Stripped mortgage-backed securities (MBSs), introduced by Fannie Mae in 1986, are another example of derivative mortgage products. A pass-through divides the cash flow from the underlying pool of mortgages on a pro rata basis across the security holders. A stripped MBS is created by altering the distribution of principal and interest from a pro rata distribution to an unequal distribution. Some of the securities thus created will have a price/yield relationship that is different from the price/yield relationship of the underlying mortgage pool. There are three types of stripped MBS: (i) synthetic-coupon pass-throughs, (ii) interest-only/principal-only securities, and (iii) CMO strips. The first generation of stripped mortgage-backed securities is called synthetic-coupon pass-throughs. This is because the unequal distribution of coupon and principal results in a synthetic coupon rate that is different from that of the underlying collateral. In the example above, each class receives an unequal distribution of coupon and principal. Thus, they are synthetic-coupon pass-throughs. (b) What is the synthetic coupon rate on Class X-1? Class X-1 receives 10% or 0.10 of the interest. Because the coupon rate is 8%, it effectively will receive 0.1(8%) = 0.80%. More details are supplied below concerning the relationship between yield and price that Class X-1 investors can expect. A stripped MBS is created by altering the distribution of principal and interest from a pro rata distribution to an unequal distribution. Some of the securities thus created will have a price/yield relationship that is different from the price/yield relationship of the underlying mortgage pool. Class X-1 receives 75% of the principal and 10% of the interest. Thus, it is more like a PO which is purchased at a substantial discount from par value. The yield an investor will realize on a PO depends on the speed at which prepayments are made. The faster the prepayments, the higher the yield the investor will realize. For example, suppose that there is a pass-through backed by 30-year mortgages with $400 million in par value and that investors can purchase POs backed by this pass-through 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 yield that will be realized. In the extreme case, if all the 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 keep their houses for 30 years and make no prepayments, the $225 million will be spread out over 30 years, which will result in a lower yield for PO investors. (c) What is the synthetic coupon rate on Class X-2? Class X-2 receives 25% of the principal and 90% or 0.9 of the interest. Because the coupon rate is 8%, it effectively will receive 0.9(8%) = 7.2%. More details are supplied below concerning the relationship between yield and price that Class X-2 investors can expect. A stripped MBS is created by altering the distribution of principal and interest from a pro rata distribution to an unequal distribution. Some of the securities thus created will have a price/yield relationship that is different from the price/yield relationship of the underlying mortgage pool. Class X-2 receives 25% of the principal and 90% of the interest. Thus, it is more like an IO, which when purchased has no par value. In contrast to the PO investor, the IO investor wants prepayments to be slow. The reason is that the IO investor receives only interest on the amount of the principal outstanding. As prepayments are made, the outstanding principal declines, and less dollar interest is received. In fact, if prepayments are too fast, the IO investor may not recover the amount paid for the IO thus realizing a low effective yield. Exhibit 12-19 shows for various mortgage rates the price of (i) a 9% pass-through, (ii) a PO created from this pass-through, and (iii) an IO created from this pass-through. Notice that as mortgage rates decline below 9%, the price of the pass-through does not respond much. This is the negative convexity (or price compression) property of pass-throughs. For the PO security, the price falls monotonically as mortgage rates rise. For the IO security, at mortgage rates above approximately 11%, the price declines as mortgage rates rise; as mortgage rates fall below about 11%, the price of an IO falls as mortgage rates decline. Both POs and IOs display substantial price volatility when mortgage rates change. The greater price volatility of the IO and PO compared with the pass-through from which they were created can be seen by the steepness of a tangent line to the curves at any given mortgage rate. Solution Manual for Bond Markets, Analysis and Strategies Frank J. Fabozzi 9780132743549, 9780133796773