Now we will see how mortgage passthroughs securities backed by fixedrate mortgage loans with a long WAM can be used to create a structure called a collateralized mortgage obligation (CMO). Two types of bond classes that can be created within the structure is a floatingrate bond class and a fixedrate bond class with a short average life.
We will discuss CMOs issued by the three agencies that issue mortgage passthrough securities and CMOs issued by private entities.CMOs are also referred to as “paythroughs” or “multiclass passthroughs.” Because they are created so as to comply with a provision in the tax law called the Real Estate Mortgage Investment Conduit, or REMIC, they are also referred to as “REMICs.” Throughout this section we refer to these structures as simply CMOs. We will see similar paythrough or multiclass passthrough structures when we cover other assetbacked security structures in the next section.
Basic Principles of a CMO
By investing in a mortgage passthrough security an investor is exposed to prepayment risk. Furthermore, as explained earlier, prepayment risk can be divided into extension risk and contraction risk. Some investors are concerned with extension risk and others with contraction risk when they invest in a passthrough. An investor may be willing to accept one form of prepayment risk but seek to avoid the other. For example, a cash manager seeks a shortterm security and is concerned with extension risk. A portfolio manager who seeks a longterm security, and wants to avoid reinvesting unexpected principal prepayments due to refinancing of mortgages should interest rates drop, is concerned with contraction risk.
By redirecting how the cash flows of passthrough securities are paid to different bond classes that are created, securities can be created that have different exposure to prepayment risk. When the cash flows of mortgagerelated products are redistributed to different bond classes, the resulting securities are called CMOs. Simply put, CMOs set forth rules for dividing up cash flows among bond classes.
The basic principle is that redirecting cash flows (interest and principal) to different bond classes, called tranches, mitigates different forms of prepayment risk. It is never possible to eliminate prepayment risk. If one tranche in a CMO structure has less prepayment risk than the mortgage passthrough securities that are collateral for the structure, then another tranche in the same structure has greater prepayment risk than the collateral.
Agency Collateralized Mortgage Obligations
Issuers of CMOs are the same three entities that issue agency passthrough securities: Freddie Mac, Fannie Mae, and Ginnie Mae. However, Freddie Mac and Fannie Mae have used Ginnie Mae passthroughs as collateral for their own CMOs. CMOs issued by any of these entities are referred to as agency CMOs.
When an agency CMO is created it is structured so that even under the worst circumstances regarding prepayments, the interest and principal payments from the collateral will be sufficient to meet the interest obligation of each tranche and pay off the par value of each tranche. Defaults are ignored because the agency that has issued the passthroughs used as collateral is expected to make up any deficiency. Thus, the credit risk of agency CMOs is minimal. However, the guarantee of a government sponsored enterprise does not carry the full faith and credit of the U.S. government. Fannie Mae and Freddie Mac CMOs created from Ginnie Mae passthroughs effectively carry the full faith and credit of the U.S. government.
Types of Bond Classes
There have been a good number of products created in the CMO market that would be acceptable investments for shortterm investors. But there are also a good number that shortterm investors should avoid given the typical interest rate exposure a shortterm investor seeks.
SequentialPay Tranches
The first CMO was structured so that each tranche would be retired sequentially. Such structures are referred to as sequentialpay CMOs. To illustrate a sequentialpay CMO, we will use a hypothetical deal that wewill refer to as Deal 1. The collateral for Deal 1 is a hypotheticalpassthrough with a total par value of $400 million and the followingcharacteristics: (1) the passthrough coupon rate is 7.5%, (2) the WAC is8.125%, and (3) the WAM is 357 months. This is the same passthrough that we used in Exhibit to describe the cash flows of a passthroughbased on an assumed 165 PSA prepayment speed.
From this $400 million of collateral, four tranches are created. Their characteristics are summarized in Exhibit The total par value of the four tranches is equal to the par value of the collateral (i.e., the passthrough security). In this simple structure, the coupon rate is the same for each tranche and also the same as the collateral’s coupon rate.
There is no reason why this must be so, and, in fact, typically the coupon rate varies by tranche. Specifically, if the yield curve is upwardsloping, the coupon rates of the tranches will usually increase with average life.
Now remember that a CMO is created by redistributing the cash flow—interest and principal—to the different tranches based on a set of payment rules. The payment rules at the bottom of Exhibit set forth how the monthly cash flow from the passthrough (i.e., collateral) is to be distributed among the four tranches. There are separate rules for the payment of the coupon interest and the payment of principal, the principal being the total of the regularly scheduled principal payment and any prepayments.
Deal 1: A Hypothetical FourTranche Sequential Pay Strucutre
Payment rules:
1. For payment of periodic coupon interest: Disburse periodic coupon interest to each tranche on the basis of the amount of principal outstanding at the beginning of the period.
2. For disbursement of principal payments: Disburse principal payments to tranche
A until it is completely paid off. After tranche A is completely paid off, disburse principal payments to tranche B until it is completely paid off. After tranche B is completely paid off, disburse principal payments to tranche C until it is completely paid off. After tranche C is completely paid off, disburse principal payments to tranche D until it is completely paid off.
In Deal 1, each tranche receives periodic coupon interest payments based on the amount of the outstanding balance. The disbursement of the principal, however, is made in a special way. A tranche is not entitled to receive principal until the entire principal of the tranche before it has been paid off. More specifically, tranche A receives all the principal payments until the entire principal amount owed to that tranche, $194,500,000, is paid off; then tranche B begins to receive principal and continues to do so until it is paid the entire $36,000,000. Tranche C then receives principal, and when it is paid off, tranche D starts receiving principal payments.
While the payment 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 monthly cash flow to be projected. Exhibit shows the monthly cash flow (interest, regularly scheduled principal repayment, and prepayments) assuming 165 PSA. Assuming that the collateral does prepay at 165 PSA, the cash flows available to all four tranches of Deal 1 will be precisely the cash flows shown in Exhibit
To demonstrate how the payment rules for Deal 1 work, Exhibit shows the cash flow for selected months assuming the collateral prepays at 165 PSA. For each tranche, the exhibit shows: (1) the balance at the end of the month, (2) the principal paid down (regularly scheduled principal repayment plus prepayments), and (3) interest. In month 1, the cash flow for the collateral consists of a principal payment of $709,923 and interest of $2.5 million (0.075 times $400 million divided by 12).
The interest payment is distributed to the four tranches based on the amount of the par value outstanding. So, for example, tranche A receives $1,215,625 (0.075 times $194,500,000 divided by 12) of the $2.5 million. The principal, however, is all distributed to tranche A.
Therefore, the cash flow for tranche A in month 1 is $1,925,548. The principal balance at the end of month 1 for tranche A is $193,790,076 (the original principal balance of $194,500,000 less the principal payment of $709,923). No principal payment is distributed to the three other tranches because there is still a principal balance outstanding for tranche A. This will be true for months 2 through 80.
After month 81, the principal balance will be zero for tranche A.For the collateral the cash flow in month 81 is $3,318,521, consisting of a principal payment of $2,032,196 and interest of $1,286,325. At the beginning of month 81 (end of month 80), the principal balance for tranche A is $311,926. Therefore, $311,926 of the $2,032,196 of the principal payment from the collateral will be disbursed to tranche A.
After this payment is made, no additional principal payments are made to this tranche as the principal balance is zero. The remaining principal payment from the collateral, $1,720,271, is disbursed to tranche B.According to the assumed prepayment speed of 165 PSA, tranche B then begins receiving principal payments in month 81.
Monthly cash flow for selected months fro deal 1 assuming 165 PSA
(concluded)
Average life for the colleteral and teh four tranches of deal 1
Exhibit shows that tranche B is fully paid off by month 100,when tranche C begins to receive principal payments.Tranche C is not fully paid off until month 178, at which time tranche D begins receiving the remaining principal payments. The maturity (i.e., the time until the principal is fully paid off) for these four tranches assuming 165 PSA is 81 months for tranche A, 100 months for tranche B, 178 months for tranche C, and 357 months for tranche D.
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. So, for example, for tranche A, the principal pay down window would be month 1 to month 81 assuming 165 PSA. For tranche B it is from month 81 to month 100. In confirmation of trades involving CMOs, the principal pay down window is specified in terms of the initial month that principal is expected to be received based on an assumed PSA speed to the final month that principal is expected to be received.
Let’s look at what has been accomplished by creating the CMO. First,earlier we saw that the average life of the passthrough is 8.76 years,assuming a prepayment speed of 165 PSA. Exhibit reports the averagelife of the collateral and the four tranches assuming different prepayment speeds. Notice that the four tranches have average lives that are both shorter and longer than the collateral, thereby attracting investors who have a preference for an average life different from that of the collateral.
There is still a major problem: there is considerable variability of the average life for the tranches. We’ll see how this can be tackled later on. However, there is some protection provided for each tranche against prepayment risk. This is because prioritizing the distribution of principal(i.e., establishing the payment rules for principal) effectively protects the shorterterm tranche A in this structure against extension risk.Thisprotection must come from some where—it comes from the three other tranches. Similarly, tranches C and D provide protection against extension risk for tranche B. At the same time, tranches C and D benefit because they are provided protection against contraction risk, the protection coming from tranches A and B.
Accrual Tranches
In Deal 1, the payment rules for interest provide for all tranches to be paid interest each month. In many sequentialpay CMO structures, atleast 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 zerocoupon bond). The interest that would have been paid to the accrual tranche is then used to speedup pay down of the principal balance of earlier tranches.
To see this, consider Deal 2, a hypothetical CMO structure with thesame collateral as Deal 1 and with four tranches, each with a couponrate of 7.5%. The difference is in the last tranche, Z, which is an accrual tranche. The structure for Deal 2 is shown in Exhibit
A Hypothetical FourTranche Sequential Pay Strucutre with an Accural bond class
Payment rules:
1. For payment of periodic coupon interest: Disburse periodic coupon interest to tranches A, B, and C on the basis of the amount of principal outstanding at the beginning of the period. For tranche Z, accrue the interest based on the principal plus accrued interest in the previous period. The interest for tranche Z is to be paid to the earlier tranches as a principal paydown.
2. For disbursement of principal payments: Disburse principal payments to tranche
A until it is completely paid off. After tranche A is completely paid off, disburse principal payments to tranche B until it is completely paid off. After tranche B is completely paid off, disburse principal payments to tranche C until it is completely paidoff. After tranche C is completely paid off, disburse principal payments to tranche Z until the original principal balance plus accrued interest is completely paid off.
It can be shown that the expected final maturity for tranches A, B,and C will shorten as a result of the inclusion of tranche Z. The final payout for tranche A is 64 months rather than 81 months; for tranche Bit is 77 months rather than 100 months; and for tranche C it is 112 months rather than 178 months. The average lives for tranches A, B,and C are shorter in Deal 2 compared to Deal 1 because of the inclusion of the accrual tranche. For example, at 165 PSA, the average lives are as follows:
The reason for the shortening of the nonaccrual tranches is that the interest that would be paid to the accrual tranche is being allocated to the other tranches.Tranche Z in Deal 2 will have a longer average life than tranche D in Deal 1. These shorter term average life tranches are more attractive to cash managers than the deal without an accrual tranche.
FloatingRate Tranches
Now let’s see how a floatingrate tranche can be created from a fixedrate tranche. This is done by creating a floater and an inverse floater. Wewill illustrate the creation of a floater and an inverse floater tranche using the hypothetical CMO structure Deal 2, which is a four tranche sequentialpay structure with an accrual tranche. We can select any of the tranches from which to create a floater tranche and an inverse floater tranche. In fact, we can create these two securities for more than one of the four tranches or for only a portion of one tranche.
In this case, we created a floater and an inverse floater from tranche C. The par value for this tranche is $96.5 million, and we create two tranches that have a combined par value of $96.5 million. We refer to this CMO structure with a floater and an inverse floater as Deal 3. It has five tranches, designated A, B, FL, IFL, and Z, where FL is the floatingrate tranche and IFL is the inverse floatingrate tranche. Exhibit describes Deal 3. Any reference rate can be used to create a floater and the corresponding inverse floater. The reference rate selected for settingthe coupon rate for FL and IFL in Deal 3 is 1month LIBOR. The principal paydown for the floater and inverse floater is proportionate to the amount of the principal paydown of tranche C.
A Hypothetical FiveTranche Sequential Pay Strucutre with Floater,Inverse Floater,and Accural tranches
Payment rules:
1. For payment of periodic coupon interest: Disburse periodic coupon interest to tranches A, B, FL, and IFL on the basis of the amount of principal outstanding at the beginning of the period. For tranche Z, accrue the interest based on the principal plus accrued interest in the previous period. The interest for tranche Z is to be paid to the earlier tranches as a principal paydown. The maximum coupon rate for FL is 10%;the minimum coupon rate for IFL is 0%.
2. For disbursement of principal payments: Disburse principal payments to tranche
A until it is completely paid off. After tranche A is completely paid off, disburse principal payments to tranche B until it is completely paid off. After tranche B is completely paid off, disburse principal payments to tranches FL and IFL until they are completely paid off. The principal payments between tranches FL and IFL should be made in the following way: 75% to tranche FL and 25% to tranche IFL. After tranches FL and IFL are completely paid off, disburse principal payments to tranche Z until the original principal balance plus accrued interest is completely paid off.The amount of the par value of the floater tranche will be some portion of the $96.5 million. There are an infinite number of ways to cut upthe $96.5 million between the floater and inverse floater, and final partitioning will be driven by the demands of investors. In Deal 3, we made the floater from $72,375,000 or 75% of the $96.5 million. Therefore, for every $100 of principal received in a month, the floater receives $75 and the inverse floater receives $25. The coupon rate on the floater is set at 1month LIBOR plus 50 basis points. So, for example, if LIBOR is 3.75% at the coupon reset date, the coupon rate on the floater is 3.75% + 0.5%, or4.25%. There is a cap on the coupon rate for the floater.
Unlike the floaters discussed earlier whose principal is unchanged over the life of the instrument, the floater’s principal balance declines over time as principal repayments are made. The principal payments to the floater are determined by the principal payments from the tranche from which the floater is created. In Deal 3, this is tranche C.
Since the floater’s par value is $72,375,000 of the $96.5 million, the balance is the inverse floater. Assuming that 1month LIBOR is the reference rate, the coupon reset formula for an inverse floater takes the following form:
K − L × (1month LIBOR)
In Deal 3, K is set at 28.50% and L at 3. Thus, if 1month LIBOR is
3.75%, the coupon rate for the month is:
28.50% − 3 × (3.75%) = 17.25%
K is the cap or maximum coupon rate for the inverse floater. In Deal
3, the cap for the inverse floater is 28.50%.
The L or multiple in the coupon reset formula for the inverse floater is called the “coupon leverage.” The higher the coupon leverage, the more the inverse floater’s coupon rate changes for a given change in 1month LIBOR. For example, a coupon leverage of 3 means that a 1basis point change in 1month LIBOR will change the coupon rate on the inverse floater by 3 basis points.
Because 1month LIBOR is always positive, the coupon rate paid tothe floatingrate tranche 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 tranche to be negative. To prevent this, a floor, or minimum, is 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 is imposed on the floater. In Deal 3, a floor of zero is set for the inverse floater. The floor results in a cap for the floater of 10%.
As noted earlier, inverse floaters have substantial price volatility,a point that was unfortunately not recognized by some cash or shortduration managers who purchased them in anticipation of a decline in interest rates.
Planned Amortization Class Tranches
A planned amortization class (PAC) bond is one in which a schedule of principal payments is set forth in the prospectus. The PAC bondholders have priority over all other bond classes in the structure with respect tothe receipt of the scheduled principal payments. While there is no assurance that the principal payments will be actually realized so as to satisfy the schedule, a PAC bond is structured so that if prepayment speeds are within a certain range of prepayment speeds, the collateral will generate sufficient principal to meet the schedule of principal payments.1
Structure with one PAC bond andone support bond
Payment rules:
1. For payment of periodic coupon interest: Disburse periodic coupon interest to each tranche on the basis of the amount of principal outstanding at the beginning of the period.
2. For disbursement of principal payments: Disburse principal payments to tranche P based on its schedule of principal repayments. Tranche P has priority with respect to current and future principal payments to satisfy the schedule. Any excess principal payments in a month over the amount necessary to satisfy the schedule for tranche P are paid to tranche S. When tranche S is completely paid off, all principal payments are to be made to tranche P regardless of the schedule.
The greater certainty of the cash flow for the PAC bonds comes at the expense of the nonPAC classes, called the support or companion tranches. It is these tranches that absorb the prepayment risk. Because PAC bonds have protection against both extension risk and contraction risk, they are said to provide “twosided” prepayment protection.
Exhibit shows a CMO structure, Deal 4, created from the $400 million 7.5% coupon passthrough with a WAC of 8.125% and a WAM of 357 months. There are just two tranches in this structure: a 7.5% coupon PAC bond created assuming 90 to 300 PSA with a par value of $243.8 million, and a support bond with a par value of $156.2 million.
The two speeds used to create a PAC bond are called the initial PAC collars (or initial PAC bands). For Deal 4, 90 PSA is the lower collar and 300 PSA the upper collar.
Exhibit reports the average life for the PAC bond and the support bond in Deal 4 assuming various actual prepayment speeds. Notice that between 90 PSA and 300 PSA, the average life for the PAC bond is stable at 7.26 years. However, at slower or faster PSA speeds the schedule is broken and the average life changes, lengthening when the prepayment speed is less than 90 PSA and shortening when it is greater than 300 PSA. Even so, there is much greater variability for the average life of the support bond.
Most CMO PAC structures have more than one class of PAC bonds.
Exhibit shows six PAC bonds created from the single PAC bond inDeal 4. We will refer to this CMO structure as Deal 5. Information about this CMO structure is provided in Exhibit .The total par value of the six PAC bonds is equal to $243.8 million, which is the amount of the single PAC bond in Deal 4.
Average life for PAC bond and support bond in deal 4 assuming various prepayments speeds
Structure with six PAC bonds and one support bond
Payment rules:
1. For payment of periodic coupon interest: Disburse periodic coupon interest to each tranche on the basis of the amount of principal outstanding at the beginning of the period.
2. For disbursement of principal payments: Disburse principal payments to tranches PA to PF based on their respective schedules of principal repayments. Tranche PA has priority with respect to current and future principal payments to satisfy the schedule. Any excess principal payments in a month over the amount necessary to satisfy the schedule for tranche PA are paid to tranche S. Once tranche PA is completely paid off, tranche PB has priority, then tranche PC, etc. When tranche S is completely paid off, all principal payments are to be made to the remaining PAC tranches in order of priority regardless of the schedule.
Average life for PAC bond and support bond in deal 5 assuming varioius prepayment speeds
Exhibit shows the average life for the six PAC bonds and the support bond in Deal 5 at various prepayment speeds. From a PAC bond in Deal 4 with an average life of 7.26, we have created six PAC bonds with an average life as short as 2.58 years (PA) and as long as 16.92 years (PF) if prepayments stay within 90 PSA and 300 PSA.
As expected, the average lives are stable if the prepayment speed is between 90 PSA and 300 PSA. Notice that even outside this range the average life is stable for several of the shorter PAC bonds. For example, PAC PA is stable even if prepayment speeds are as high as 400 PSA. For the PAC PB, the average life does not vary when prepayments are between 90 PSA and 350 PSA. Why is it that the shorter the PAC, the more protection it has against faster prepayments?
To understand why this is so, remember that there are $156.2 million in support bonds that are protecting the $85 million of PAC PA.
Thus, even if prepayments are faster than the initial upper collar, there may be sufficient support bonds to assure the satisfaction of the schedule.
In fact, as can been from Exhibit , even if prepayments are 400 PSA over the life of the collateral, the average life is unchanged.
Now consider PAC PB. The support bonds are providing protection for both the $85 million of PAC PA and $93 million of PAC PB. As can be seen from Exhibit , prepayments could be 350 PSA and the average life is still unchanged. From Exhibit it can be seen that the degree of protection against extension risk increases the shorter the PAC. Thus, while the initial collar may be 90 to 300 PSA, the effective collar is wider for the shorter PAC tranches.
PAC Floaters Given a series of PAC bonds, any of the tranches can be carved up to make a floater and an inverse floater. The advantage of the PAC floater compared to a sequentialpay floater is that there is two sided prepayment protection and therefore the uncertainty of the average life is less. The tradeoff is that this greater prepayment protection is not free. All other factors constant, the margin over the same reference rate offered on a PAC floater will be less than that on a sequentialpay floater and/or the cap will be the lower.
Effective Collars and Actual Prepayments As we have emphasized, the creation of an MBS cannot make prepayment risk disappear. This is true for both a passthrough and a CMO. Thus, the reduction in prepayment risk (both extension risk and contraction risk) that a PAC bond offers must come from somewhere.
The prepayment protection comes from the support bonds. It is the support bonds that have principal payments deferred 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 payments 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 fasterthanexpected prepayments, then there is no longer any protection for the PAC bonds. In fact, in Deal 5, if the support bond is paid off, the structure is effectively reduced to a sequentialpay CMO. In such cases, the schedule is unlikely to be maintained, and the structure is referred to as a busted PAC.
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 first. The bodyguards are there to absorb the bullets. Once all the bodyguards are killed off (i.e., the support bondspaid off with fasterthanexpected prepayments), the PAC bonds mustfend for themselves: they are exposed to all the bullets.
With the bodyguard metaphor for the support bonds in mind, let’s consider two questions asked by buyers of PAC bonds:
1. Will the schedule of principal repayments be satisfied if prepayments are faster than the initial upper collar?
2. Will the schedule of principal repayments be satisfied as long as prepayments stay within the initial collar?
Let’s address the first question. The initial upper collar for Deal 4 is 300 PSA. Suppose that actual prepayments are 500 PSA for seven consecutive months.Will this disrupt the schedule of principal repayments?
The answer is: it depends!
There are two pieces of information we will need to answer this question.
First, when does the 500 PSA occur? Second, what has been the actual prepayment experience up to the time that prepayments are 500 PSA? For example, suppose six years from now is when the prepayments reach 500 PSA, and also suppose that for the past six years the actual prepayment speed has been 90 PSA every month. What this means is that there are more bodyguards (i.e., support bonds) around than was expected when the PAC was structured at the initial collar. In establishing the schedule of principal repayments, it is assumed that the bodyguards would be killed off at 300 PSA. But the actual prepayment experience results in them being killed off at only 90 PSA. Thus, six years from now when the 500 PSA is assumed to occur, there are more bodyguards than expected. Thus, a 500 PSA for seven consecutive months may have no effect on the ability of the schedule of principal repayments to be met.
In contrast, suppose that the actual prepayment experience for the first six years is 300 PSA (the upper collar of the initial PAC collar). In this case, there are no extra bodyguards around. As a result, any prepayment speeds faster than 300 PSA, such as 500 PSA in our example, jeopardize satisfaction of the principal repayment schedule and increase contraction risk. What this means is that the prepayment protection is reduced.
It should be clear from these observations that 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 initial collars. This approach is in adequate because it is actual prepayment experience that determines the degree of prepayment protection going forward, 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 PAC bond. An effective collar for a 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.
It is important to understand that the PAC schedule may not be satisfied even if the actual prepayments never fall outside of the initial collar. This may seem surprising since our previous analysis indicated that the average life would not change if prepayments are at either extreme of the initial collar. However, recall that all of our previous analysis has been based on a single PSA speed for the life of the structure. If we vary the PSA speed over time rather than keep it constant over the life of the CMO, we can see what happens to the effective collar if the prepayments are at the initial upper collar for a certain number of months. For example, if one computed the average life two years from now for the PAC bond in Deal 4 assuming that prepayments are 300 PSA for the first 24 months, one would find that the average life is stable at six years if the prepayments for the following months are between 115 PSA and 300 PSA.
That is, the effective PAC collar is no longer the initial collar. Instead, the lower collar has shifted upward. This means that the protection from year 2 on is for 115 PSA to 300 PSA, a narrower band than initially, even though the earlier prepayments did not exceed the initial upper collar.
Support Bonds
The support bonds are the bonds that provide prepayment protection for the PAC tranches. Consequently, support tranches expose investors to the greatest level of prepayment risk. Because of this, investors must be particularly careful in assessing the cash flow characteristics of support bonds to reduce the likelihood of adverse portfolio consequences due to prepayments.
To see this, consider a shortterm, 7% coupon support bond issued by Freddie Mac (Class BA, Series 2279) in January 2001. Exhibit presents a Bloomberg Security Description screen for this security. This support bond makes coupon payments monthly on the fifteenth day of each month. Let’s analyze this support bond’s exposure to prepayment risk using Bloomberg’s PT (Price Table) function in Exhibit.Suppose at current interest rates, the underlying mortgage collateral prepays at 210 PSA and the security’s current price is 10007. Note at the bottom of the screen, given a prepayment speed of 210 PSA, the average life is 0.22 years. If we shock the current U.S. Treasury yield curve by ±100, 200, 300 basis points, respectively, and feed those shocks into a prepayment model, what will happen to the prepayment speed of the collateral and the average life of this support bond? As can be seen from the Price Table, if interest rates rise, prepayment speeds will decrease and the security’s average life will extend from 0.22 years to 7.17 years for a 100 basis point upward parallel shift in the yield curve. Of course, this is a concern to an investor who thought that they were purchasing a money market type instrument. Correspondingly, if interest rate decline, prepayment speeds will increase such that the security’s average life will shorten.
The support bond typically is divided into different tranches. All the tranches we have discussed earlier are available, including sequentialpay support tranches and floater and inverse floater support tranches. The support bond can even be partitioned so as to create support tranches with a schedule of principal payments. That is, support tranches that are PAC bonds can be created. In a structure with a PAC bond and a support bond with a PAC schedule of principal payments, 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 or scheduled bond. While PAC II bonds have greater prepayment protection than the support tranches without a schedule of principal repayments, the prepayment protection is less than that provided PAC I bonds.
Bloomberg security description screen for a Freddic Mac support bond
Bloomberg price table screen
There is more that can be done with the PAC II bond. A series of PAC IIs can be created just as we did with the PACs in Deal 5. PAC IIs can also be used to create any other type of bond class, such as a PAC II floater and inverse floater, for example. The support bond without a principal repayment schedule can be used to create any type of bond class. In fact, a portion of the nonPAC II support bond can be given a schedule of principal repayments. This bond class would be called a PAC III bond or a Level III PAC bond. While it provides protection against prepayments for the PAC I and PAC II bonds and is therefore subject to considerable prepayment risk, such a bond class has greater protection than the support bond class without a schedule of principal repayments.


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Global Money Markets Tutorial
Money Market Calculations
U.s. Treasury Bills
Agency Instruments
Corporate Obligations:commercial Paper Andmediumterm Notes
Debt Obligations Offinancial Institutions
Floatingrate Securities
Repurchase And Reverse Repurchase Agreements
Shortterm Mortgagebacked Securities
Shortterm Assetbacked Securities
Futures And Forward Rate Agreements
Swaps And Caps/floors
Asset And Liability Management
Bank Regulatory Capital
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