Bac Cmo Primer

A Primer on Agency CMOs

Residential Mortgage Research

Sharad Chaudhary (704) 386 2135

Laurent Gauthier (212) 583 8209

Agency CMO Trading

Naveed Ameen

Steve Choran

Nick Letica

(212) 583 8340

December 2001

Residential Mortgage Research, Banc of America Securities, LLC.

Summary

n Market Overview

n Creating CMOs

n A Detailed Look at CMO Structures

n The Evolution of CMO Structures


n Market Overview

n Basic Conceptsn Growth of the Marketn Market Liquidityn Major Underwriters

n Creating CMOs




Basic Concepts

n A CMO (collateralized mortgage obligation) reallocates the pass-throughcash-flows from its underlying mortgage obligations to a series ofdifferent bond classes (called tranches) with varying maturitycharacteristics

n The mortgage obligations (or collateral) backing the CMO bond classesmay consist of mortgage pools, whole loans, or even other CMO bondclasses

n Agency CMOs are collateralized by Fannie Mae, Freddie Mac, or GinnieMae-issued pools. Credit risk is minimal for Agency CMOs since thesepools carry government (Ginnie Mae) or implied government (FannieMae, Freddie Mac) guarantees

n Non-Agency CMOs are not backed by these guarantees and thereforeare usually credit-enhanced and rated by the bond rating agencies

n Redirecting pass-through cash-flows to different bond classes isequivalent to redistributing the prepayment (interest-rate) and credit riskin these cash-flows. This redistribution can be achieved in a number ofdifferent ways and allows bonds to be tailored to the risk appetites ofinvestors


Growth of the Market

n In mid-1983 Freddie Mac issued the first CMO, and the market hasgrown rapidly since then with issuance typically averaging more than$100 billion a year. Over $300 billion Agency CMOs were issued in 1993

n The overall level of Agency CMO issuance usually tracks mortgage rateswith the highest rates of issuance corresponding to periods of heavyrefinancing activity

n The current interest rate environment is very favorable to Agency CMOissuance: production for 2001 is estimated above $250 billion

The Agency CMOmarket has grownsignificantly overthe past decade

Annual Issuance of Agency CMOs

0

50

100

150

200

250

300

35019

87

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

(es

t)

Issu

ance

($

bb

)

GNMA

FNMA

FHLMC


Outstanding Amount of Agency CMOs

0

100

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600

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800

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100019

87

1988

1989

1990

1991

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1994

1995

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1998

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2001

(est

)

Ou

tsta

nd

ing

($

bb

)

GNMA

FNMA

FHLMC

Market Liquidity

n The Agency CMO market consists of over $900bb in outstandingsecurities and is one of the largest sectors in the fixed-income universe

n CMOs issued by Freddie Mac and Fannie Mae constitute the lion’s shareof the market. Ginnie Mae CMOs also represent a significant portion ofthe market with nearly $90bb outstanding securities and strong investorsponsorship

A significant poolof Agency CMOswith customizedcharacteristics isavailable forinvestors


Major Agency and Non-Agency CMOUnderwriters

Bank of Americaplays a prominentrole in the Agencyand Non-AgencyCMO markets asan underwriterand market-maker

CMO Underwriting for Q1-Q3 2001

Dealer Rank Amount ($ bb)

UBS Warburg 1 46

Bear Sterns 2 46

Salomon Smith Barney 3 37

Credit Suisse First Boston 4 36

Lehman Brothers 5 36

Bank of America 6 29

Greenwich Capital 7 18

Goldman Sachs 8 17

Merrill Lynch 9 16

JP Morgan 10 7

Source: Bloomberg


n Market Overview

n Creating CMOs

n Cash-flow Structuring Methods: In Cash-flow Structuring Methods: IIn Analyzing CMO Classesn Payment Windows and Average Life




Cash-flow Structuring Methods: I

n The cash-flows on a CMO bond class (tranche) are built byredistributing the principal (both scheduled and prepaid) and interestcash-flows on the underlying mortgage pools

n A number of different methods may be used to redirect these pass-through cash-flows:

Methods for Creating CMOs

Cash-flow Structuring Method Examples Characteristics

Direct transfer of Cashflows Passthrough The simplest security; most commonin non-agency CMOs

Sequential allocation of principal Sequentials Creates securities with a wide rangeof average lives

Allocation of principal dependingon prepayment speeds

PACs, TACs,Companions

Creates tranches with more or lessaverage life variability than collateral

Allocation of interest to payprincipal

Z-bonds,VADMs

Increases the average life stabilityacross the structure while increasingduration on the accrual tranche

Allocation of interest versusprincipal

IOs, POs Creates tranches with strongdirectionality with respect to interestrates

Indexing of coupon payments Floaters andInverse floaters

Creates securities that are sensitiveto both short-term factors (indexchanges) and long-term factors(prepayment rates)

CMOs cash-flowsare created by“slicing” up thepass-throughcash-flows on amortgage pool


Cash-flow Structuring Methods: II

n Cash-flow structuring methods can be further applied to the cash-flowsof the deal itself or to the cash-flows of a particular tranche in the deal

n For example, structuring methods to create Interest-only (IO) orPrincipal-only (PO) cash-flows can be applied at the deal level or at thetranche level

n at the deal level, IO-ettes can be created by stripping out a portion of thecoupon cash-flow to reduce the coupon on the entire deal

n At the tranche level, IOs and POs can be created by separating theinterest and principal from a specific tranche. For example, Support-IOsand Support-POs can be created from a Support tranche

n Structuring methods used to create Floater or Inverse Floater cash-flows are generally applied at the tranche level

n For example, PAC-Floaters and PAC-Inverse floaters can be createdfrom PAC tranches

Combiningdifferentstructuringmethods leads toa wide range ofstructures with avariety of riskprofiles


Analyzing CMO Classes

n Most CMO classes pay interest monthly on their current face amount.However, depending upon the allocation of cash-flows, a CMO classmay be locked out of principal for some time (the Lockout Period). ThePayment Window of a CMO class refers to the period in which principalpayments are received, for a given prepayment speed assumption

n The Weighted Average Life of a tranche measures the average time untilthe principal is paid, for a given prepayment speed assumption

n Average life variability looks at how average life changes whenprepayment assumptions are changed

n Keep in mind that the average life is an average of an entire paymentwindow, which may also widen or tighten as average life changes

n The OAS measure values the prepayment option embedded in CMObonds

n The option cost from the OAS model captures the variability of averagelife and duration on a CMO class, and values its potential negativeeffects. However, it does not take into account potential changes in theMortgage-LIBOR basis or uncertainty about prepayment assumptions

n Some CMO bonds are extremely sensitive to the model’s prepaymentassumptions

n OAS is generally a better measure of relative value for CMOs thanclassical measures such as yield spread

No single relative-value measurefully captures therisk/reward profileof a CMO class;OAS is the mostwidely used


Payment Windows And Average Life

n The legal maturity, or statedmaturity corresponds to thelast cash-flow date, assumingthere are no prepayments

n The payment window tells usthe time span between the firstprincipal cash-flow and the lastprincipal cash-flow on thesecurity, for a givenprepayment speed. When thepayment window starts in thefuture, we say the bond islocked-out

n The average life of a bond isthe average time until thebond’s principal is paid. It liesin the payment window

n For reasonable prepaymentassumptions, the paymentwindow gives a fairly accuraterepresentation of when thebond’s principal will be paid

n Shorter tranches typicallyshow less variability inaverage life and window sizethan longer tranches

Time (Months)

Principal Cash-flows on Sequentials at 20% CPR

$-

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

1 61 121 181 241 301

Time (Months)

Prin

cipa

l pay

men

t ($)

Tranche BTranche D

Legal maturity on B

Legal maturity on D

Window on B

Window on D

Avg Life on B Avg Life on D

Principal Cash-flows on Sequentials at 10% CPR

$-

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

1 61 121 181 241 301

Prin

cipa

l pay

men

t ($)

Tranche BTranche D

Window on B

Window on D

Legal maturity on B

Legal maturity on D

Avg Life on B Avg Life on D

Both the averagelife and windowsize of a bond areimportant inassessing itscharacteristics


n Market Overview

n Creating CMOs


n Passthroughn Sequentialsn PACs and Supportsn TACs and Supportsn Z-Bonds and VADMsn Floatersn Interest-Only and Principal-Onlyn The Effect of a Structure’s Couponn The Effect of the Underlying Collateraln The Effect of Changes in Collateral Refinancing Incentive



A Typical Mortgage Pass-ThroughPayment Structure

n A pass-through MBS transfers principal and net interest payment to theinvestor

n Prepayments significantly affect the pass-through’s cash-flow profileand shortens its average life relative to the scheduled payments

The pass-throughchannels allprincipal andinterest paymentsto the investor

Principal and Interest Payment on a 30-year Mortgage with no Prepayments

0

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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Years

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)

Principal

Interest

Principal and Interest Payment on a 30-year Mortgage with Prepayments

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Interest


Sequentials: Payment Structure

n All the principal cash-flows from the underlying collateral are allocatedto one tranche at a time. When that tranche pays off, the next tranchereceives all the principal payments and so on. In other words, thetranches in the CMO are sequentially allocated principal payments

n Principal payments are therefore segmented into different average-lifesecurities. However, the average life of these securities can changedepending on prepayments

n By convention, average lives are calculated at a Pricing Speed (aconstant prepayment speed assumption used to calculate yields fromprices)

n The graphs demonstrate how the underlying collateral’s propensity torefinance directly impacts the cash-flows from a Sequential class

Sequentials areamong thesimplest CMOstructures

Principal Cashflows on a Sequential Structure at 100 PSA

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

1 61 121 181 241 301

Time (Months)

Prin

cipa

l pay

men

t ($)

Tranche A

Tranche B

Tranche CTranche D

Principal Cashflows on a Sequential Structure at 200 PSA

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

1 61 121 181 241 301

Time (Months)

Prin

cipa

l pay

men

t ($)

Tranche A

Tranche B

Tranche CTranche D


Sequentials: Relative Value

n The collateral’s prepayment risk is not evenly distributed across thedifferent sequential classes

Sequentials retainmost of thecollateral’snegativeconvexity whileoffering a widerange of durations

Typical Relative Value Indications for Sequentials

Bond Average Life Option Cost

Effective Duration

Effective Convex.

Remarks

2-year 35 1.0 -1.5 The smaller option cost is generally due to the lack of collateral seasoning

5-year 65 3.0 -2.0 Very similar to collateral at issuance

10-year 75 5.0 -2.0 This tranche gets the cash-flows that on average are the most prone to refinancings

20-year 60 9.0 -1.0 The slightly lower option cost is due to burnout on underlying collateral

Collateral 65 3.8 -1.6


PACs and Supports: Payment Structure

n A PAC (Planned Amortization Class) maintains the same principalredemption schedule across a range of prepayment rates and thereforeoffers protection against prepayment risk

n Support (or Companion) classes allow the PAC to maintain itsredemption schedule by absorbing faster than expected prepaymentsand contributing principal cash-flows if prepayments are slower thanexpected

n The range of prepayment speeds for which the PACs can meet theirschedule, called the PAC band, depends on the size of the PACs relativeto the supports

n The wider the PAC band, the fewer the PACs in the structure

A substantialportion of thecollateral’sprepayment risk isdiverted from thePACs to theSupport bonds

Principal Cashflows on a PAC / Companion Structure at 100 PSA

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

1 61 121 181 241 301

Time (Months)

Prin

cipa

l pay

men

t ($)

Companion PSA 100

PAC 80-250

Principal Cashflows on a PAC / Companion Structure at 200 PSA

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

1 61 121 181 241 301

Time (Months)

Prin

cipa

l pay

men

t ($)

Companion PSA 200PAC 80-250


PACs and Supports: Relative Value

n PACs are generally sliced into smaller tranches with distinct average-life characteristics

n The structuring technology used to create PAC and Support cash-flowscan also be applied recursively at the tranche level

n Applied to the support bonds, it creates PAC IIs and PAC IIIsn Applied to the PACs, it creates Super-PACs and Sub-PACs

PACs offer a widerange ofdurations, alongwith betterconvexitycharacteristicsthan Sequentials

Typical Relative Value Indications for PACs and Supports


EffectiveDuration

Effective Convex.

Remarks

2-year PAC 10 1.5 -0.7

5-year PAC 35 2.5 -2.0

10-year PAC 50 4.5 -1.6

20-year PAC 35 7.5 -0.5

All the PACs have a smaller option cost than collateral

Shorter PACs benefit from lower refinancings like sequentials

2-year Support 135 2.7 -3.0


10-year Support 100 5.3 -1.3


The shortest support bonds have the greatest option cost and negative convexity, because their principal schedule can vary significantly



TACs and Supports: Payment Structure

n TACs (Targeted Amortization Classes) offer protection only againstfaster prepayments

n They are similar to PACs with a lower band equal to the pricing speedn For prepayments slower than the pricing speed, the principal payments

on a TAC extend in a manner similar to a Sequential class

n TAC Supports extend less than PAC Supports when prepayments slowdown and behave similarly to PAC Supports when prepayments rise

TACs offerasymmetricprotection againstprepayments

Principal Cashflows on a TAC / Support Structure at 200 PSA

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

1 61 121 181 241 301

Time (Months)

Prin

cipa

l pay

men

t ($)

TAC Support

TAC 250

Principal Cashflows on a TAC / Support Structure at 100 PSA

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

1 61 121 181 241 301

Time (Months)

Prin

cipa

l pay

men

t ($)

TAC SupportTAC 250


TACs and Supports: Relative Value

n As with PACs, TACs can be segmented and offer a wide range ofaverage-lives and durations

n The option cost on TACs is about 15-25bps more than on similaraverage life PACs and about 5-10bps less than on Sequentials

TACs are morestable thanSequentials butless stable thanPACs. This isexhibited in theiroption-adjustedcharacteristics

Typical Relative Value Indications for TACs and Supports


Effective Duration

Effective Convex.

Remarks

2-year TAC 25 1.5 -1.0

5-year TAC 60 3.0 -2.2

10-year TAC 60 5.5 -1.5

Short TACs have little optionality, while longer TACs have option costs similar to collateral

20-year Support 92 5.5 -2.2 Long TAC Supports have optional characteristics similar to long PAC Supports



Z-Bonds and VADMs: Payment Structure

n Z-bonds are initially locked out of interest and principal payments. Theinterest payments due on the principal balance of the class areallocated to other tranches and the Z gets credit for these payments byaccreting principal. Once the classes before the Z are fully paid down,the Z class begins to receive principal and interest

n Interest payments on the Z may be allocated to:

n Sequential classes;n Specific tranches called VADMs (Very Accurately Defined Maturities).

VADMs generally benefit from very stable average-life profiles;n Or to other tranches to retire them earlier

Z-bonds tend tostabilize averagelives in astructure. VADMscan be structuredto benefit fromthis increasedstability

Principal Cashflows on a Z-Bond / Accrual Structure at 100 PSA

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

1 61 121 181 241 301

Time (Months)

Prin

cipa

l pay

men

t ($)

Tranche A

Tranche B

Tranche CTranche Z

Principal Cashflows on a Z-Bond / Accrual Structure at 200 PSA

$-

$100,000

$200,000

$300,000

$400,000

$500,000

$600,000

$700,000

$800,000

$900,000

$1,000,000

1 61 121 181 241 301

Time (Months)

Prin

cipa

l pay

men

t ($)

Tranche A

Tranche B

Tranche CTranche Z


Z-Bonds: Relative Value

n Since Z-bonds start paying interest only after the sequentials and/orVADMs have been paid down, they resemble zero-coupon bonds (fromwhich they draw their name). In particular, a Z-bond is characterized by:

n Long durationn Increased convexity

n Z-bonds can be structured out of PAC cash-flows, instead ofsequentials, and are then called Z-PACs

Sequential Z-bonds typicallyhave much longerdurations andmore moderatenegativeconvexitycompared tocollateral Typical Relative Value Indications for Sequentials and Z Structures


Eff. Duration

Eff. Convex.

Remarks

2-year Sequential 35 1.0 -1.4



The sequentials in this structure have slightly lower option costs than those in a structure without Z

20-year Z-Bond 75 13.0 -1.0 The duration on the Z is significantly longer than on a similar average-life sequential



VADMs: Relative Value

n Since they get their principal from the interest payments on theoutstanding balance of the Z, VADMs (especially the short ones) arevirtually insensitive to variations in prepayments

The very lowoption costs onVADMs show theyare generallymuch more stablethan PACs orTACs

Typical Relative Value Indications for Sequential-pay/Z-bond structures with VADM Tranches


Eff. Duration

Eff. Convex.

Remarks




The option cost on the sequentials are 1-10bps greater than in the case of a structure with no VADMs

20-year Z -Bond 70 12.5 -0.9 The characteristics of the Z are very similar to the structure with no VADMs

2-year VADM 2 1.7 -0.1

5-year VADM 15 3.2 -0.9

10-year VADM 45 4.6 -1.2

The VADMs have extremely low option costs, reflecting their low average life variability



Floaters: Payment Structure

n Any fixed-rate paying bond can be sliced into a floater and an inversefloater

n Fixed-rate interest payments can be transformed into a capped floaterand an inverse floater

n Fixed-rate interest = Floater + Inverse Floatern The cap on the floater comes from the implicit floor on the inverse floater (no

negative interest)n For example

$50mm 8% =$25mm (LIBOR + 1%, cap at 16%)+ $25mm (15% - LIBOR, floor at zero)

n The floater generally benefits from attractive characteristics (reducedexposure to prepayment risk, moderate negative convexity)

n The inverse floater is more leveraged relative to prepayments, and isconsidered a “mortgage derivative”

n Agency CMO floaters are most often indexed off 1-month LIBOR, butother indices are available in the market, such as COFI


Floaters: Relative Value

n Floaters have short durations and attractive convexity (slightly negativeor sometimes positive)

Floaters haveattractive featuressince they are notvery sensitive toprepayments

Typical Relative Value Indications for CMO Floaters

Bond characteristics OptionCost

Eff.Duration

Eff.Convex.

Remarks

Strip 6% Floater, L+50bps capped

at 8.5%

51 1.1 -0.5 The strip floater amortizes likea passthrough. It benefits froma small option cost relative tocollateral, and very moderatenegative convexity

Intermediate 6% PAC Floater,

L+50bps capped at 8.5%

27 0.3 -0.5 The PAC floater is a verystable bond, with riskcharacteristics similar to a veryshort VADM (but with a longeraverage life)

Short 6% Support Floater,


65 2.0 1.6

Intermediate 6% Support Floater,


65 2.4 -2.9

Support floaters are moreleveraged relative toprepayments. They arebetween plain sequentials andPACs in terms of option costand risk


Interest-Only and Principal-Only:Payment Structure

n Stripping interest and principal payments from the cashflows on a CMOtranche creates an IO (which get the interest) and a PO (which get theprincipal). IOs are the ultimate premium cash-flow, while POs are theultimate discount cash-flow

n The value of these securities greatly depends on prepayments

n Faster prepayments reduce the total amount of interest paid out, whichis bad for IOs

n Slower prepayments mean that PO holders receive their cashflows later,which is bad for them

POs are stronglybullish, while IOsare stronglybearish. They canbe used to createsynthetic coupons

Interest Flow at Different Prepayment Speeds

0

100,000

200,000

300,000

400,000

500,000

600,000

700,000

1 61 121 181 241 301

PSA 200

PSA 100

Principal Flow at Different Prepayment Speeds

0

200,000

400,000

600,000

800,000

1,000,000

1,200,000

1 61 121 181 241 301

PSA 200

PSA 100


The Effect of the Structure’s Coupon

n By stripping out PO or IO cashflows, the coupon on a CMO tranche canbe artificially increased or decreased. The characteristics of the bondare significantly affected

n a higher coupon generally shortens duration and widens spreadn a lower coupon generally lengthens durations and tightens spread

CMOs can have adifferent couponfrom theunderlyingcollateral

Comparison of a CMO’s Characteristics Depending on its Coupon


Eff.Duration

Eff.Convex.

Remarks

5% coupon 75 -0.2 -1.5

6% coupon 95 -1.2 -0.8

7% coupon 114 -2.2 0.0

IO 2818 -110.2 80.6

Front Sequentialoff 6s

PO -28 5.2 -5.5

For the short sequential, alower coupons extendsduration and significantlydecreases option cost. Sincethe IO on this shortsequential has a positiveconvexity, lowering thecoupon does not improveconvexity.

5% coupon 60 5.6 -2.3

6% coupon 90 3.3 -3.4

7% coupon 119 1.2 -4.3

IO 1219 -50.1 -27.7

Locked-out 5-yearSequential off 6s

PO -116 20.9 4.6

The effect of a lower couponon the intermediatesequential is even stronger:option cost decreases fromabout 120bps to 60bps.Convexity is also improvedby the lower coupon.


The Effect of the Underlying Collateral

n Keeping the same structure, changing the underlying collateral’scharacteristics impacts the bond’s risk measures

n We make such a comparison with PACs, which have stable cashflowsunder a wide range of scenarios

The underlyingcollateralcontributes verysignificantly to aCMO’scharacteristics Comparison of a CMO’s Characteristics Depending on its Underlying Collateral


Eff.Duration

Eff.Convex.

Remarks

6.80 WAC 42 0.4 -2.2

7.30 WAC 76 -0.4 -2.6

7.80 WAC 95 -1.3 0.0

Front PAC (100-300PSA bands), 6%coupon

15-yr collat 52 0.1 -1.8

Increasing the underlying WACshortens duration (fasterprepayments), but it does notnecessarily improve convexity.Indeed, the bond’s dollar pricewill be lower, rather than highersince the net coupon isunchanged. Option cost alsoincreases with WAC

6.80 WAC 70 1.9 -1.6

7.30 WAC 88 1.6 -0.2

7.80 WAC 114 2.3 -0.3

Locked-out PAC(100-300 PSAbands), 6% coupon

15-yr collat 71 1.3 -1.4

With the longer PAC, weobserve a similar pattern. Theimprovement in convexity ishelped in this case by the largerdegree of burnout that will havebeen experienced by thecollateral over the life of thebond


The Effect of Changes in CollateralRefinancing Incentive

n The level of refinancing incentive incurred by collateral directly affectsits option cost. In the example below, the collateral’s option cost variesfrom 40bps to 120bps

n The more prepayment protection is offered by a structure, the lowest itsoption cost

n The spread between the option cost on these PACs and on collateral isrelatively constant over a wide range of refinancing incentives

As refinancingincentiveschange, theoption cost onCMOs issignificantlyaffected

Option Cost on Structures as a Function of Collateral Refinancing Incentive

0

20

40

60

80

100

120

140

-100 -80 -60 -40 -20 0 20 40 60 80 100

Interest Rate Shift (bps)

Op

tio

n C

ost

(b

ps)

Collateral

PAC (100-250)

Super PAC (100-500)

PAC-2 (100-250)


n Market Overview

n Creating CMOs



n The Changing Aspects of CMO Structuresn The Evolution of a Bond’s Average Lifen Sequentials and Collateraln PACs and Supportsn The PAC Band Driftn PAC-2s and PAC-1 Supportsn Directed Accretion and Zsn No VADM Band Drift


The Changing Aspects of CMOStructures

n Bond structures are strongly affected by the bonds’ relative balances.Prepayment protection or leverage always comes down to how large thesupporting tranche is compared to the protected tranche

n As prepayments come in, fast or slow, some bonds are paid down fasteror slower than projected at pricing speed. This affects the entirestructure, and changes the protection or leverage on the bonds

n These evolutions take place in addition to the evolution of collateralitself. As mortgages season, their prepayment characteristics alsochange, sometimes in a dramatic way

n OAS is the only approach that can at the same time take into accountthe path-dependent behavior of the collateral and of the structures

CMO structuresevolve throughtime, mostly as afunction of thecollateral’sprepayments


The Evolution of a Bond’s Average Life

n A bond’s payment window’s shape conditions the way its average lifewill decrease across time

n When the bond is not paying back principal (during the lock-out periodfor example), its average life at a given assumed prepayment speeddecreases in parallel with time

n When the bond is paying principal, its average life decreases moreslowly than time

The average lifeconvergestowards thebeginning of thepayment windowat first, and thentowards maturity

The Evolution of Average Life on a Bond

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 10 20 30 40 50 60 70 80

Time in months

Rem

ain

ing

Ave

rag

e L

ife

(yea

rs)

Payment window

Avg life Maturity


Sequentials and Collateral

n As expected future prepayments change, the anticipated average life onthe bonds also changes

n Relative to their underlying collateral, sequentials have more potentialfor relative variations in average life

n However, short sequentials extend much less than collateral in absoluteterms and long sequentials shorten much less than collateral

Average Life Profiles on Sequentials vs Mortgage Collateral

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Life PSA Assumption

Ave

rag

e L

ife (

year

s)

Collateral

Sequentials 1 to 4


PACs and Supports

n PACs offer a flat average life profile for a range of prepayment speedassumptions

n Typically, shorter PACs have less potential variations in average liferelative to longer PACs, in absolute terms

n Average lives on support bonds are the most variable within the PACranges they are supporting

PACs offer stableaverage livesrelative tosequentials andcollateral

Average Life Profiles on PACs (100-300 PSA bands) and Supports

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Life PSA Assumption

Ave

rag

e lif

e (y

ears

)

Front PAC

Intermediate PAC

Long PAC

Front PAC support

Intermediate PAC support

Long PAC support


Potential Band Drift on a PAC

0

100

200

300

400

500

600

700

800

900

1000

Aug

-01

Oct

-01

Dec

-01

Feb-

02

Apr

-02

Jun-

02

Aug

-02

Oct

-02

Dec

-02

Feb-

03

Apr

-03

Jun-

03

Aug

-03

Oct

-03

Dec

-03

Feb-

04

Apr

-04

Jun-

04

Aug

-04

Oct

-04

Time into the future

PS

A B

and

Bands at 5% CPR

Bands at 20% CPR

PAC Average Life Profile

0

2

4

6

8

10

12

14

16

0 100 200 300 400 500 600

Life PSA Speed Assumption

Ave

rage

life

(ye

ars)

Original profile

After 15 months at 5% CPR

After 15 months at 20% CPR

The PAC Band Drift

n The outstanding balance onthe PAC support bondsdecays differently dependingon the prepaymentexperience of the collateral

n When prepayments are fast,the lower PAC bandincreases and the upper banddecreases, since there is lessand less support to absorbvery fast or very slowprepayments in the future

n When prepayments are slow,the support tranche’s sizeincreases relative to thePAC’s. It increases the upperband, providing a betterprepayment protection.However, the lower banddoes not decrease, since thesupport needs to be paiddown

PAC bands do notremain the sameover the life of abond, they tend todrift away


PAC-2s and PAC-1 Supports

n PAC-2s are carved out of PAC-1 supports, and offer more stablecharacteristics than PAC-1 support bonds

n The supports of the PAC-2s (which also support PAC-1s) are extremelysensitive to prepayments

Average Life Profiles on PAC 2s (150-250 PSA bands) and Supports

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Life PSA Assumption

Ave

rage

life

(ye

ars)

Front PAC-2Intermediate PAC-2

Long PAC-2Front PAC-1 supportIntermediate PAC-1 supportLong PAC-1 support

Long Support for the PAC 2


Directed Accretion and Zs

n When the accrued interest from Z tranches is directed to the sequentialsthat precede it, they benefit from a more stable average life profile

n For very fast prepayments, accretion-directed sequentials and nonaccretion-directed sequentials behave similarly

n For slow prepayments, the accretion-directed sequentials benefit from alower average life extension, since in this case the Z tranche generatesmore interest payments, which are channeled to the sequentials

Average Life Profiles on Plain Sequentials vs Accretion-directed Sequentials

0

5

10

15

20

25

0 100 200 300 400 500 600

Life PSA Assumption

aver

age

Lif

e (y

ears

)

Non-accreted intermediate sequential

Accreted intermediate sequential

Non-accreted front sequential

Accreted front sequential

Final Z tranche


Average Life Profiles on VADMs

0

1

2

3

4

5

6

0 100 200 300 400 500 600 700 800 900 1000

Life PSA Assumption

Ave

rage

life

(ye

ars)

Short VADM

Intermediate VADM

5-year VADM

Intermediate VADM after 2 years at 50% CPR

5-year VADM after 2 years at 50% CPR

No VADM Band Drift

n VADMs derive their cash-flow stability from the interest payment on theZ tranche, and not from a schedule

n This makes them much less sensitive to whipsaw prepayment scenariosn Whether prepayments have been fast or slow, VADMs always benefit

from a strong extension protection, since the Z tranche is always presentto support them

AlthoughsometimesVADMs look likePACs, they aremuch moreprotected againstchanges inprepayments


Disclaimer

n This report is for information purposes only and is based on information available to the public fromsources believed to be reliable, but no representation is made that it is accurate or complete, and noinformation herein should be relied upon as such. Opinions and projections found in this reportreflect our opinion as of the report date and are subject to change without notice. This report isneither intended nor should be considered as an offer to sell, or solicitation or basis for any contract,for the purchase of, any security, loan or other financial product. Banc of America Securities LLC, itsaffiliates, Bank of America Corporation and their respective directors, officers and employees, fromtime to time may maintain a long or short position in, act as a market maker for, or purchase or sell aposition in, securities, loans or other financial products mentioned herein, or of the entities referredto herein, or related investment securities or products. Banc of America Securities LLC or itsaffiliates may have acted as manager or co-manager for a public offering of securities of companiesmentioned herein. Banc of America Securities LLC or its affiliates may be performing, haveperformed or seek to perform investment banking, advisory, banking or other services for anycompany mentioned herein. Certain securities in this report may not have been registered under theSecurities Act of 1933 as amended (the "Securities Act") and may not be offered or sold except in atransaction pursuant to SEC Rule 144A, Regulation S or otherwise exempt from or not subject to theregistration requirements of the Securities Act. Past performance of securities, loans or otherfinancial instruments is not indicative of future performance. This report may not be circulated orreproduced without prior written permission from Banc of America Securities LLC. Furtherinformation on any security mentioned herein may be available upon request. Banc of AmericaSecurities LLC is a subsidiary of Bank of America Corporation and is a member of NYSE, NASD andSIPC.

n © 2001 Banc of America Securities LLC.

Bac Cmo Primer

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