An MBS is comprised of a portfolio of individual mortgages that are pack- aged together into a single security and sold to investors. The security is a coupon-bearing instrument, and it has a principal component as well. The funds used to pay the coupons of an MBS come directly from the monthly interest payments made by homeowners. The payments made by home- owners are passed through a servicing agent, who sends along appropriate payments directly to holders of the MBS. Accordingly, an MBS is sometimes called a pass-through security (orpass-thru), or an asset-backed securitysince its cash flows come from a bundle of assets (namely the home mortgages that are bundled together). An MBS also is sometimes called a securitized
Nominal Forward
Option adjusted
• Spread between a benchmark bond’s spot yield and a (non)benchmark bond’s forward yield.
• Spread is expressed in basis points.
• When the spot curve is flat, the forward curve and spot curve are equal to one another, and a nominal spread is equal to a forward spread.
• The difference in yield between a benchmark bond and a nonbenchmark bond.
• Spread is expressed in basis points.
• The two bonds have comparable maturity dates.
• Spread between a benchmark bond’s forward yield (typically without optionality) and a (non)benchmark bond’s forward yield (typically with optionality).
• Spread is expressed in basis points.
• When an OAS is calculated for a bond without optionality, and when the forward curve is of the same credit quality as the bond, the bond’s OAS is equal to its forward spread.
When an OAS is calculated for a bond with optionality, the bond’s OAS is equal to its forward spread if volatility is zero.
This particular type of OAS is also called a ZV spread (for zero volatility).
•When an OAS is calculated for a bond with optionality, if the spot curve is flat, then the bond’s OAS is equal to its forward spread as well as its nominal spread if volatility is zero.
FIGURE 4.14 Nominal, forward, and option-adjusted spreads.
asset, for the same reason. All else being equal, investors like the idea of a bond that is physically backed by (supported by) assets that they can ana- lyze and understand. In contrast with a more generic bond (debenture) that is backed by an issuer’s overall credit rating or general financial standing, an asset-backed security provides investors with things they can “touch and feel”—not in a literal sense, but in the sense of bringing some form and def- inition to what they are buying.4
When homeowners make their monthly mortgage payment, a portion of that payment goes to paying the interest on the mortgage and a portion goes to paying the principal. In the early phase of the typically 30-year mort- gage life, the largest portion of the monthly payment goes toward payment of interest. A growing portion of the monthly payment goes toward princi- pal, and in the same way that interest payments are passed along to MBS holders as coupons, principal payments are passed along to MBS holders as principal. Herein lies a key difference between a traditional bond and a tra- ditional pass-thru; the former pays 100 percent of its principal at maturity, while the latter pays out its principal over the life of the security as it is received and passed along to investors. Payments of principal and interest may not always be predictable; homeowners can refinance their mortgages if they want to, which involves paying down the principal remaining on their existing mortgage. This act of paying off a loan prior to its natural matu- rity (even if the purpose is to take on a new loan) is called prepaying, and prepaymentscan be attributable to many things, including a sudden decline in interest rates5(so that investors find it more cost-effective to obtain a new lower-cost loan), a natural disaster that destroys homes, changes in personal situations, and so forth.
Most MBSs are rated triple A. How is this possible unless every home- owner with a mortgage that is in the bundle has a personal credit rating that is comparable to a triple-A profile? One way to achieve this is by overcollat- eralizing(providing more collateralization than a 1:1 ratio of face value of security relative to underlying asset). The MBS is collateralized(backed by) mortgages. To overcollateralizean MBS, the originator of the MBS puts in more mortgages than the face value of the MBS. For example, if originators want to issue $10 million face amount of MBS that will be sold to investors, they put more than $10 million face amount of underlying mortgages into the
4Some larger investors do actively request and analyze detailed data underlying various asset-backed instruments.
5This decline in interest rates gives value to the long call option that homeowners have embedded in their mortgage agreement; the option (or choice) to refinance the mortgage at a lower rate has economic value that is realized only by refinancing the existing mortgage to secure new and lower monthly payments.
bundle that comprises the MBS. Accordingly, if some homeowners happen to default on their mortgages, the excess supply of mortgages in the bundle will help to cover that event. Another way that MBS products are able to secure a triple-A rating is by virtue of their being supported by federal agencies. The three major agencies of the United States involved with supporting mortgages include Ginnie Mae, Fannie Mae, and Freddie Mac.6The key purpose of these governmental organizations is to provide assurance and confidence in the mar- ket for MBSs and other mortgage products.
Table 4.3 summarizes key differences between an MBS and a callable bond.
The most dramatic differences between MBSs and callable bonds are that the options embedded with the former are continuous while the single option embedded in the latter tends to be discrete, and the multiple options within an MBS can be triggered by many more variables.
Figure 4.15 shows how an MBS’s cash flows might look; none of the cash flow boxes is solid because none of them can be relied on with 100 percent certainty. While less-than-100% certainty might be due partly to the vagaries of what precisely is meant by saying that the federal agencies issu- ing these debt types are “supported by” the federal government, more of the uncertainty stems from the embedded optionality. Although it may very well be unlikely, it is theoretically possible that an investor holding a mortgage- backed security could receive some portion of a principal payment in one of the very first cash flows that is paid out. This would happen if a home-
6Ginnie Mae pass-thrus are guaranteed directly by the U.S. government regarding timely payment of interest and principal. Fannie Mae and Freddie Mac pass-thrus carry the guarantee of their respective agency only; however, both agencies can borrow from the Treasury, and it is not considered to be likely that the U.S.
government would allow any of these agencies to default.
TABLE 4.3 MBS versus Callable Bond Optionality
Mortgage Callable
Callability Continuous Discrete (sometimes continuous) Call period Immediately Eligible after the passage of some time Call trigger Level of yields Level of yields, other cost considerations
Homeowner defaults Homeowner sells property
for any reason Property is destroyed as
by natural disaster
owner decides or is forced to sell the home almost immediately after pur- chase and pays off the full principal of the loan. In line with what we would generally expect, principal payments will likely make their way more mean- ingfully into the mix of principal-coupon cash flows after some time passes (or, in the jargon of the marketplace, with some seasoning).
How can probabilities be assigned to the mortgage product’s cash flows over time? While we can take the view that we adopted for our callable debenture—that at the start of the game every uncertain cash flow has a 50/50 chance of being paid—this type of evenly split tactic may not be very practical or realistic for mortgage products. For example, a typical home mortgage is a 30-year fixed-rate product. This type of product has been around for some time, and some useful data have been collected to allow for the evaluation of its cash flows over a variety of interest rate and eco- nomic environments. In short, various patterns can and do emerge with the nature of the cash flows. Indeed, a small cottage industry has grown up for the creation and maintenance of models that attempt to divine insight into the expected nature of mortgage product cash flows. It is sufficient here merely to note that no model produces a series of expected cash flows from year 1 to year 30 with a 50/50 likelihood attached to each and every pay- out. Happily, this conforms to what we would expect from more of an intu- itive or common sense approach.
Given the importance of prepayment rates when valuing an MBS, sev- eral models have been developed to forecast prepayment patterns. Clearly, investors with a superior prepayment model are better equipped to identify fair market value.
In an attempt to impose a homogeneity across prepayment assumptions, certain market conventions have been adopted. These conventions facilitate trades in MBSs since respective buyers and sellers know exactly what assumptions are being used to value various securities.
O
+
p2 p1
Time Cash Flow
p4 p3
p6 p5
p8 p7
p719 p720
FIGURE 4.15 MBS cash flows over time.
One commonly used method to proxy prepayment speeds is the constant prepayment rate(CPR). A CPR is the ratio of the amount of mortgages pre- paid in a given period to the total amount of mortgages in the pool at the beginning of the period. That is, the CPR is the percentage of the principal outstanding at the beginning of a period that will prepay over the follow- ing period. For example, if the CPR for a given security in a particular month is 10.5, then the annualized percentage of principal outstanding at the begin- ning of the month that will repay during the month is 10.5 percent. As the name implies, CPR assumes that prepayment rates are constant over the life of the MBS.
To move beyond the rather limiting assumption imposed by a CPR—
that prepayments are made at a constant rate over the life of an MBS—the industry proposed an alternative measure, the Public Securities Association (PSA) model. The PSA model posits that any given MBS will prepay at an annualized rate of 0.2 percent in the first month that an MBS is outstand- ing, and prepayments will increase by 0.2 percent per month until month 30. After month 30, it is assumed that prepayments occur at a rate of 6 per- cent per year for all succeeding months.
Generally speaking, the PSA model provides a good description of pre- payment patterns for the first several years in the life of an MBS and has proven to be a standard for comparing various MBSs. Figure 4.16 shows theoretical principal and coupon cash flows for a 9 percent Ginnie Mae MBS at 100 percent PSA. When an MBS is quoted at 100 percent PSA, this means that prepayment assumptions are right in line with the PSA model, above.
An MBS quoted at 200 percent PSA assumes prepayment speeds that are twice the PSA model, and an MBS quoted at 50 percent PSA assumes a slower prepayment pattern.
140 120
100 80 40 20
$1,000s
60 120 180 240 300 360
Month Interest
Principal 9% 30-year Ginnie Mae, 100% PSA
FIGURE 4.16 The relationship between pay-down of interest and principal for a pass- thru.
Another important concept linked to MBS is that of average life. As depicted in Figure 4.17, average life is the weighted average time to the return of a dollar of principal. It is often used as a measure of the investment life of an MBS and is typically compared against a Treasury with a final matu- rity that approximates the average life of the MBS. In short, it is a way to help fence in the nature of MBS cash flows to allow for some comparabil- ity with non-pass-thru type structures.
Since the principal or face value of an MBS is paid out over the life of the MBS and not in one lump sum at maturity, this is reflected in the price formula provided below. Accordingly, as shown, the MBS price formula has anFvariable alongside every Cvariable. Further, every Cand every Fhas its own unique probability value.
where
p1probability-weighted first coupon
p2probability-weighted first receipt of principal p3probability-weighted second coupon
p4probability-weighted second receipt of principal, . . . and so forth.
Cp5&Fp6
11Y>223 . . .$1,000 Price Cp1&Fp2
11Y>221 Cp3&Fp4 11Y>222
25 20 15 10 5
10 20 30 40 50 60 70
Prepayment rate (%) Average life
(years)
FIGURE 4.17 Average life vs. prepayment rate.
“Probability-weighted coupon” means the statistical likelihood of receiv- ing a full coupon payment (equivalent to 100 percent of FtimesC). As prin- cipal is paid down from par, the reference amount of coupon payment declines as well (so that when principal is fully paid down, a coupon pay- ment is equal to zero percent of FtimesC,or zero).
“Probability-weighted principal” means the statistical likelihood of receiving some portion of principal’s payment.
As is the case with a callable debenture, the initial price of an MBS is par, and YC. However, unlike our callable debenture, there is no formal lockout period with an MBS. While we might informally postulate that prob- ability values for Fshould be quite small in the early stages of an MBS’s life (where maturities can run as long as 15 or 30 years), this is merely an edu- cated guess. The same would be true for postulating that probability values forCshould be quite large in the early stages of an MBS’s life. Because an MBS is comprised of an entire portfolio of short call options (with each one linked to an individual mortgage), in contrast with the single short option embedded in a callable debenture, the modeling process for CandFis more complex; hence the existence and application of simplifying benchmark mod- els, as with the CPR approach.
At this stage we have pretty much defined the two extremes of option- ality with fixed income products in the U.S. marketplace. However, there are gradations of product within these two extremes. For example, there are PACs, or planned amortization class securities.
Much like a Thanksgiving turkey, an MBS can be carved up in a vari- ety of ways. At Thanksgiving, some people like drumsticks and others pre- fer the thigh or breast. With bonds, some people like predictable cash flows while others like a higher yield that comes with products that behave in less predictable ways. To satisfy a variety of investor appetites, MBS pass-thrus can be sliced in a variety of ways. For example, classesof MBS can be cre- ated. Investors holding a Class A security might be given assurances that they will be given cash distributions that conform more to a debenture than a pass-thru. Investors in a Class B security would have slightly weaker assur- ances, those in a Class C security would have even weaker assurances, and so forth. As a trade-off to these levels of assurances, the class yield levels would be progressively higher.
A PAC is a prime example of a security type created from a pool of mort- gages. What happens is that the cash flows of an MBS pool are combined such that separate bundles of securities are created. What essentially distin- guishes one bundle from another is the priority given for one bundle to be assured of receiving full and timely cash flows versus another bundle.
For simplicity, let us assume a scenario where a pool of mortgages is assembled so as to create three tranches of cash flow types. In tranche 1, investors would be assured of being first in line to receive coupon cash flows
generated by the underlying mortgages. In tranche 2, investors would be sec- ond in line to receive coupon cash flows generated by the underlying mort- gages. If homeowners with mortgages in this pool decide to pay off their mortgage for whatever reason, then over time tranche 2 investors would not expect to receive the same complete flow of payouts relative to tranche 1 investors. If only for this reason, the tranche 2 investors should not expect to pay the same up-front price for their investment relative to what is paid by tranche 1 investors. They should pay less. Why? Because tranche 2 investors do not enjoy the same peace of mind as tranche 1 investors of being kept whole (or at least “more whole”) over the investment horizon. And finally, we have tranche 3, which can be thought of as a “residual” or “clean- up” tranche. The tranche 3 investors would stand last in line to receive cash flows, only after tranche 1 and tranche 2 investors were paid. And consis- tent with the logic presented above for tranche 2, tranche 3 investors should not expect to pay the same up-front price for their investment as tranche 1 or 2 investors; they should pay less.
Note that tranche 1 investors are not by any means guaranteed of receiv- ing all cash flows in a complete and timely matter; they only are the first in line as laying priority to complete and timely cash flows. In the unlikely event that every mortgage within the pool were to be paid off at precisely the same time, then each of the three tranches would simply cease to exist. This com- ment helps to reinforce the idea that tranche creation does not create new cash flows where none existed previously; tranche creation simply reallocates existing cash flows in such a way that at one end of a continuum is a security type that at least initially looks and feels like a more typical bond while at the other end is a security type that exhibits a price volatility in keeping with its more uncertain place in the pecking order of all-important cash flow receipts.
This illustration is a fairly simplified version of the many different ways in which products can be created out of mortgage pools. Generally speak- ing, PAC-type products are consistent with the tranche 1 scenario presented.
Readers can refer to a variety of texts to explore this kind of product cre- ation methodology in considerable detail. From PACs to TACs to A, B, C, and Z tranches (and much, much more), there is much to keep an avid mort- gage investor occupied.
Figure 4.18 applies the PAC discussion to our cash flow diagram.
Notice that the cash flow boxes in the early part of the PAC’s life are drawn in with solid lines. PACs typically come with preannounced lockout periods. Here, lockout refers to that period of time when the PAC is pro- tected from not receiving complete and timely cash flow payments owing to option-related phenomena. The term of lockouts varies, though is generally 5 to 10 years. Again, the PAC is protected in this lockout period because it stands first in line to receive cash flows out of the mortgage pool. Many times a PAC is specified as being protected only within certain bandwidths of