Choudhry. Fixed Income Securities Derivatives Handbook

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252 Selected Cash and Derivative Instruments

remainder of the term, as the outstanding balances become so small

that the scheduled principal payments are insigniﬁ cant.

FIGURE 14.3

shows the payment pattern for a single 9 percent, 30-year loan at 100

percent PSA.

FIGURE 14.2

Ratio of Interest to Principal Payments for a

Mortgage Pass-Through Security with 0 Percent CPR

Annual cash flow ($100 nominal)

Maturity (years)

Interest

Principal

FIGURE 14.3

Payment Ratio in a 100 Percent PSA Model

Annual cash flow ($100 nominal)

Maturity (years)

Interest

Principal

Securitization and Mortgage-Backed Securities 253

The prepayment volatility of a mortgage-backed bond depends on the

interest rates of the underlying mortgages. Volatility has been observed to

be highest when the mortgages’ rates are between 100 and 300 basis points

above current rates: at the bottom of this range, any fall in interest rates

tends to produce a sudden increase in reﬁ nancings and thus prepayments,

while at the top of the range, a rise in rates leads to a decrease in reﬁ nanc-

ings and prepayments.

The actual cash ﬂ ows of a mortgage pass-through depend, of course, on

the cash ﬂ ow patterns of the underlying mortgages. The projected monthly

payment for a level-paying ﬁ xed-rate mortgage is given by formula (14.8).

tmt

−

−+

()

−

⎡

⎣

⎢

⎤

⎦

⎥

(14.8)

where

= the projected monthly mortgage payment for month t

mt −1

= the projected mortgage balance at the end of month t - 1,

assuming that prepayments have occurred in the past

n = mortgage term, in months

r = annualized interest rate

The interest portion of the projected monthly mortgage payment,

is calculated using equation (14.9).

iM i

tmt

−1

(14.9)

where

i = the interest amount

Equation (14.9) states that the projected monthly interest payment can

be obtained by multiplying the mortgage balance at the end of the previous

month by the monthly interest rate. The expression for calculating the pro-

jected scheduled monthly principal payment for any month is (14.10).

pIi

ttt

=−

(14.10)

where

= the projected scheduled principal payment for the month t

The projected monthly principal prepayment, which is an expected

ﬁ gure only and not a model forecast, is given by (14.11).

254 Selected Cash and Derivative Instruments

pp SMM M p

ttmtt

=−

()

−1

(14.11)

where

= the projected monthly principal prepayment for month t.

Equations (14.9) through (14.11) calculate values for

❑ the projected monthly interest payment

❑ the projected scheduled monthly principal payment

❑ the projected monthly principal prepayment

Combining these values, as in (14.12), gives the total cash ﬂ ow that a

holder of a mortgage-backed bond receives in any month.

cf i p pp

tt t t

=+ +

(14.12)

where

= the cash ﬂ ow received in month t

Using a projected prepayment rate enables analysts to evaluate

mortgage-backed bonds. The original PSA benchmarks were based on

the observation that prepayment rates tend to stabilize after the ﬁ rst

thirty months of a mortgage and assumed a linear increase in these

rates. They do not reﬂ ect seasonal variations in prepayment patterns

nor the different behavior patterns of different types of mortgages.

The PSA benchmarks can be applied to assumptions about defaults to

produce the PSA standard default assumption (SDA) benchmark, which is

used to assess the potential default rate for a mortgage pool. This bench-

mark is used only for nonagency mortgage-backed bonds, since agency

securities are guaranteed by one of the three government or government-

sponsored agencies. The standard benchmark, 100 SDA, assumes that the

default rate in the ﬁ rst month of a mortgage is 0.02 percent and that the

rate increases in a linear fashion by 0.02 percentage points each month

until the thirtieth one, when it levels off at 0.60 percent. It remains at

0.60 percent until month 60, when it begins to fall to 0.03 percent until it

reaches 0.03 percent in month 120, remaining at that level for the rest of

the mortgage term. The other benchmarks have similar patterns.

Prepayment Models

The PSA standard benchmark discussed in the previous section assumes cer-

tain prepayment rates and can be used to calculate the prepayment proceeds

of a mortgage. It is not, strictly speaking, a prepayment model, because it

Securitization and Mortgage-Backed Securities 255

cannot be used to estimate actual prepayments of a mortgage pool. A pre-

payment model does attempt to do this, by modeling the statistical relation-

ships between the various factors that affect the level of prepayment. These

factors are the current mortgage rate, the characteristics of the mortgages

in the pool, seasonal inﬂ uences, and the general business cycle.

The prevailing mortgage interest rate and its spread above or below the

original contract rate are probably the most important factors in deter-

mining the level of prepayment, since they inﬂ uence borrowers’ decisions

about reﬁ nancing their mortgages. If the current rate is materially below

the original one, for instance, borrowers will prepay their loans. Because

the mortgage rate reﬂ ects the general bank base rate at the time, the level

of market interest rates has the greatest impact on mortgage prepayment

levels. The current mortgage rate also affects housing prices: when mort-

gages are seen as “cheap,” people are more likely to purchase homes, driv-

ing prices up. This rate has an impact on how likely it is that people will

repay early. The pattern followed by mortgage rates since the original loan

also has an impact on prepayments, a phenomenon known as reﬁ nancing

burnout. Presumably, the point is that if mortgage rates have been trend-

ing consistently downward for a long period, everyone who can reﬁ nance

will have done so, so the prepayment rate slows.

The housing market and mortgage activity also appear to follow seasonal

patterns. Spring and summer see the strongest action, winter the weakest.

Generally, mortgage activity reﬂ ects the economic cycle. An economy

that is performing strongly will see increasing levels of borrowing. How-

ever, as the economy picks up, this brings the risk of higher inﬂ ation,

such that interest rates need to be raised by the Federal Reserve to cool

the economy. This inﬂ uences mortgage activity and also paradoxically sees

higher repayments, as people seek to come out of debt. However, if the

slowdown is not graduated, but turns into a recession, prepayment activ-

ity falls off as people are not able to repay early. The various factors have

been combined to calculate expected prepayment levels. Fabozzi (1997),

for example, cites equation (14.13), which a U.S. investment bank uses to

calculate expected prepayments.

(14.13)

Monthly prepayment rate Refinancing Incentive Season mul=

()

× ttiplier

Month multiplier Burnout

()

Collateralized Mortgage Securities

Collateralized mortgage obligations, which were described earlier, account

for a large segment of the U.S. debt capital market. The majority of CMOs

are issued by government-sponsored agencies. They thus have Treasury

256 Selected Cash and Derivative Instruments

bond credit quality, but they offer signiﬁ cantly higher yields—a combina-

tion that makes the instruments attractive to a range of institutional inves-

tors, as does the ability to tailor their characteristics to speciﬁ c investment

needs. This section reviews some of the newer CMO structures.

The CMO market in the United States experienced rapid growth

during the 1990s. According to the securitization newsletter Asset-Backed

Alert, a high of $324 billion in the securities was issued in 1993; by 1998,

this ﬁ gure had fallen to just under $100 billion. The growth of the market

brought with it a range of new structures. To meet the demands of bond-

holders desiring lower exposure to prepayment risk, for example, planned

amortization classes, or PACs, and targeted amortization classes, TACs,

were introduced. Very accurately deﬁ ned maturity, or VADM, bonds,

which are guaranteed not to extend beyond a stated date, were created to

remove the uncertainty concerning the term of mortgage-backed bonds.

In the United Kingdom and certain overseas markets, mortgage-backed

bonds pay ﬂ oating-rate coupons, and the desire of foreign investors to

have something similar in the U.S. domestic market led to the creation of

bonds with coupons linked to LIBOR.

Originally, mortgage-backed bonds were created from individual un-

derlying mortgages. CMOs created in this manner are known as whole

loan. In contrast, the mortgages underlying agency-issued CMOs have

already been pooled and securitized, usually as pass-throughs. Whole-loan

CMOs are thus based on cash ﬂ ows from an entire pool of individual

mortgages rather than on a pass-through security formed from this pool.

As with agency CMOs, however, the underlying mortgages in a whole-

loan pool generally have the same risk, maturity, and interest rate.

Whole-loan CMOs also differ from agency bonds in the size of the

underlying mortgages: those backing agency bonds are limited to a stated

maximum size and so tend to be smaller than the ones backing whole-loan

CMOs, which may include jumbo loans. Another difference between

whole-loan and agency CMOs concerns compensating interest. Virtually

all mortgage-backed securities pay principal and interest monthly, on a

ﬁ xed coupon date. The underlying mortgages, however, may be paid off

on any day of the month. Agency-issued securities guarantee their bond-

holders interest payments for the complete month, even if the underlying

mortgage has been paid off ahead of the coupon date and so has not gen-

erated any interest for that month. Whole-loan CMOs do not offer this

guarantee. Holders of these bonds may thus receive less than one month’s

interest on the coupon date. Some issuers, though not all, will make a

compensating interest payment to bondholders to cover the shortfall.

Following Sundaresan (1997, page 389), the primary features of

CMOs in the U.S. market may be summarized as follows:

Securitization and Mortgage-Backed Securities 257

❑ Credit quality. CMOs issued by U.S. government agencies have

the same guarantee against default as agency pass-through securities and

so may be considered risk-free. They therefore do not require any form of

credit insurance or credit enhancement. Whole-loan CMOs do not carry

a government guarantee and are rated by credit rating agencies. Most of

them have triple-A ratings, either because their mortgage pools generate

cash ﬂ ows well in excess of what is required to service the interest obliga-

tions of all tranches, or because of the high quality of the issuing vehicles

or through some credit enhancement. CMOs also tend to be signiﬁ cantly

overcollateralized.

❑ Interest frequency. The notes usually pay semiannual or quarterly

coupons. The underlying mortgages, however, pay interest monthly or

almost daily. The cash generated between coupon dates is reinvested at

money market rates. The preferred reinvestment vehicle is a guaranteed in-

vestment contract (GIC), but only a few banks and insurance companies

offer GICs, so most issuers settle for money market accounts. However,

the providers of GICs will usually accept much smaller deposits, some-

times as little as $100,000, than are required for interbank deposits, which

are another option for investing the excess cash.

❑ Cash ﬂ ow proﬁ le. CMOs’ proﬁ les are based on an assumed

prepayment rate, known as the pricing speed, which reﬂ ects current market

expectations for prepayment levels and market interest rates.

❑ Maturity. Originally, virtually all CMOs were created from un-

derlying mortgage collateral with 30-year stated maturities. During the

1990s, issues were formed from shorter-dated collateral, including 5- to

7-year and 15- to 20-year mortgages. Still, most CMOs have long terms.

❑ Trading conventions. CMOs trade on a yield basis, as opposed to

a price basis, and are usually quoted as a spread over the yield of the Trea-

sury security with the most similar maturity. Like their cash ﬂ ows, CMOs’

yields are based on assumed prepayment rates. CMOs are settled on a T+3

basis. Agency issues are cleared via an electronic book-entry system run

by the Federal Reserve, known as Fedwire; whole-loan issues are cleared

using either physical delivery or by electronic transfer. New issues of

CMOs settle from one to three months after the initial offer date.

CMOs have two basic structures: sequential pay and planned amortiza-

tion class, or PAC.

Sequential Pay

One of the demands that drove the design of CMOs was for mortgage-

backed bonds with a wider range of maturities. Most CMO structures

redirect principal payments sequentially to individual tranches, according

258 Selected Cash and Derivative Instruments

to each one’s stated maturity. That is, principal payments go to the tranche

with the shortest stated maturity until it is completely redeemed and are

then allocated to the next maturity class, continuing in this manner until

all the bonds in the structure are retired. Sequential-pay CMOs are attrac-

tive to a wide range of investors, particularly those with shorter investment

horizons, because they can purchase only the CMO class whose maturity

terms meet their requirements. Investors with longer investment horizons

are protected from prepayment risk in the early years of the issue, when

principal payments are used to pay off the shorter-dated tranches.

FIGURE 14.4 shows a typical generic CMO sequential structure. The

collateral cash ﬂ ows are allocated to each tranche in speciﬁ ed order. The

ﬁ rst tranche is allotted both its coupon and any prepayments. The remain-

ing tranches receive only their coupon payments until the ﬁ rst one is fully

retired.

Planned Amortization Class

The ﬁ rst CMO with a PAC structure was issued in 1986, in response to

a demand for less interest-rate-sensitive mortgage-backed structures that

was sparked by a period of sustained falls in market rates. PAC structures

are designed to reduce prepayment risk and the volatility of the weighted

average life measure, which is related to the prepayment rate. PAC CMOs

have principal-payment schedules that are unaffected by changes in pre-

payment rates. These schedules, similar to those of corporate-bond sinking

funds, are based on the minimum amounts of principal cash ﬂ ow that will

be produced by the underlying mortgage pool at two different prepayment

rates. These rates together deﬁ ne a range known as a PAC band.

PAC bands are deﬁ ned by prepayment rates set at a low and a high

PSA standard—for example, 50 percent PSA and 250 percent PSA. This

FIGURE 14.4

Generic CMO Sequential Structure

AVERAGE LIFE

TRANCHE PRINCIPAL COUPONS (YEARS) YIELD

A 100 7.00% 2.5 2-year benchmark plus 80 bps

B 250 7.00% 5 5-year benchmark plus 100 bps

C 75 7.00% 10 10-year benchmark plus 120 bps

Z 75 7.00% 20 30-year benchmark plus 150 bps

Securitization and Mortgage-Backed Securities 259

constrains the amount of principal repayment: in the early years of the

issue, the lower standard serves as a ﬂ oor for the minimum principal re-

ceived, while later in the bond’s life the payment schedule is constrained

by the upper PSA standard. The total principal cash ﬂ ows under the PAC

schedule determine the value of PACs in an issue.

In the PAC structure, the uncertainty of principal payments is directed

to another class of security, i.e., another tranche in the CMO, known as

the companion, or support, class. When prepayment rates are high, com-

panion issues support the main PACs by absorbing any principal prepay-

ments that are in excess of the PAC schedule; when the rate falls, the com-

panion amortization is delayed if principal prepayments are not sufﬁ cient

to reach the minimum stipulated by the PAC band. Accordingly, when

prepayment rates are high, the companions’ average life shortens; when

rates are low, their average life lengthens. Within the set of PACs and the

set of companions, the principal cash ﬂ ows can be allotted sequentially, as

in the sequential-pay structure.

PACs exhibit lower price volatility than other mortgage securities.

When the prepayment rates are within the PAC band, their prices are

fairly stable; when rates move outside the band, volatility increases by a

smaller amount than for non-PAC bonds, because the prepayment risk

is transferred to the companions. For this reason, PAC issues trade at

lower spreads to the Treasury yield curve than do other issues with similar

maturities. The companion bonds are always priced at a wider spread than

the PACs, reﬂ ecting their higher prepayment risk.

Within the CMO structure may be some PAC bonds with less prepay-

ment risk than others, known as Type II and Type III PACs. A Type II PAC

has a narrower band than a standard PAC, thus reducing prepayment risk.

If prepayment rates remain within their narrower bands, Type II PACs

trade like standard PACs; if rates move outside their bands, the extra cash

ﬂ ow is redirected to the companions only if the rates move above the range.

Otherwise, there is no excess and the companion amortization is delayed.

Type II PACs are second in priority to the standard PACs and so trade at a

higher yield. If prepayment rates remain high for an extended period and

all the companions are redeemed, the Type II PACs take over the function

of companion and, with it, the higher prepayment risk. Type III PACs

function like Type II PACs, but their band ranges are even tighter.

The upper and lower limits of a PAC band may “drift” during the

life of the CMO, regardless of actual prepayment rates. This drift results

from the interaction of actual cash prepayments with the bands and from

changes in the collateral balance and in the ratio between the nominal

values of the PACs and the companions. The type of drift and its impact

depend on the prepayment rate, as illustrated in the following scenarios:

260 Selected Cash and Derivative Instruments

❑ The prepayment rate lies within the current band. If this situa-

tion continues, the upper limit will rise, since prepayments have been be-

low the maximum level, leaving more companion issues to receive future

prepayments. The lower limit rises as well, because prepayments have been

above the minimum level, resulting in less collateral to generate future

principal payments. The upper limit, though, tends to rise more quickly

than the lower one, widening the range.

❑ The prepayment rate lies above the band. If this continues, the

number of companions available to receive faster prepayments will fall, and

the band will narrow, its upper and lower limits converging completely when

all the companion bonds have been redeemed. At that point, the PAC will

trade as a conventional sequential-pay security until it is redeemed.

❑ The prepayment rate lies below the band. The upper limit will

drift upward, because more companion bonds are available to receive a

greater level of prepayments in the future; the lower band may also rise by

a small amount. This type of drift is relatively rare, however, since PACs

have the highest priority of all classes in a CMO structure until the pay-

ment schedule is back on track.

Band drift occurs over time and is sometimes not noticeable. Signiﬁ -

cant changes in the band levels only take place if the prepayment rate is

outside the band for a prolonged period. Prepayment rates that move out-

side the bands for short spells do not have any effect on the bands.

Targeted Amortization Class

Targeted amortization class, or TAC, bonds were created to cater to inves-

tors who require prepayment protection but at a higher yield than would

be available with a PAC. Essentially, a TAC is a PAC whose “band” con-

sists of only one standard prepayment rate. Like PACs, TACs amortize

principal according to a schedule when the actual prepayment rate accords

with this standard and, when the rate moves above it, use the extra princi-

pal amounts to pay off companion bonds. They differ from PACs mainly

in taking on extra prepayment risk when prepayments fall below the rate

required to maintain the payment schedule, extending the issue’s average

life. Because one element of the PAC band is removed, TACs trade at a

higher yield.

The preference for TACs over PACs is a function of the prevailing

interest rate environment. When current rates are low or are expected to

fall, there is a risk of prepayments increasing, reducing the average life of

the bond. In this scenario, investors may be willing to forgo the protection

against an extension in the bond’s average life provided by PACs, deeming

it unlikely to be required, and take the extra yield offered by the TAC.

Securitization and Mortgage-Backed Securities 261

Z-Class Bonds

The Z-class, or Z, bond ranks below all other classes in the CMO’s struc-

ture and pays no cash ﬂ ows for part of its life, functioning essentially like

a zero-coupon bond (hence its name). When the CMO is issued, the Z

bond, also known as an accrual, or accretion, bond, has a relatively small

nominal value. At the start of its life, it pays out cash ﬂ ows on a monthly

basis, as determined by its coupon. However, when the Z bond itself is

not receiving principal payments, its cash ﬂ ows are used to retire some

of the principal of the other classes in the structure. In their place, the

bond receives credits, which increase its face value by the amount of the

forgone coupon. As a result, its principal amount is higher at the end of

its life than at the start. When all classes of bond ahead of the Z bond

have been retired, the Z bond itself starts to pay out principal and inter-

est cash ﬂ ows.

In a conventional sequential-pay structure, the other classes in the

CMO receive some of their principal prepayments from the Z bond,

which lowers their average-life volatility. Z bonds are an alternative for

investors who might otherwise purchase Treasury zero-coupon bonds.

Like zero coupons, these bonds have no reinvestment risk, but they have

higher yields than Treasury strips with similar average lives.

Interest-Only and Principal-Only Classes

As noted earlier, stripped mortgage-backed securities, or stripped bonds,

are created by splitting the cash ﬂ ows payable by a pool of mortgages into

interest and principal payments and assigning the two different streams to

two different classes of bonds: interest-only, or IO, and principal-only, or

PO, bonds.

The PO bond is similar to a zero-coupon in that it is issued at a

discount to par value. The PO bondholder’s return is a function of the

rapidity at which prepayments are made; the quicker the prepayment, the

higher the return. This is like the buyer of a zero-coupon bond receiving

the maturity payment ahead of the redemption date. The highest possible

return for the bondholder would occur if all the mortgages were prepaid

the instant after the PO bond was bought. A low return occurs if all the

mortgages are held until maturity, so that there are no prepayments.

The price of a PO bond ﬂ uctuates with mortgage interest rates. As noted

earlier, the majority of mortgages are ﬁ xed-rate loans. If mortgage rates fall

below the PO bond’s coupon rate, the volume of prepayments should in-

crease as the individuals holding the underlying loans reﬁ nance them,

speeding the stream of payments to the bondholder. The PO’s price will

rise both because of the faster cash ﬂ ows and because the ﬂ ows are now dis-

counted at a lower rate. The opposite happens when mortgage rates rise.