Securitization and Mortgage-Backed Securities

Chapter 11

Securitization and

Mortgage-Backed Securities

Securitization• Securitization refers to a process in which the

assets of a corporation or financial institution are pooled into a package of securities backed by the assets.

• The process starts when an originator, who owns the assets (e.g., mortgages or accounts receivable), sells them to an issuer.

• The issuer then creates a security backed by the assets called an asset-backed security or pass-through that he sells to investors.

Securitization• The securitization process often involves a third-

party trustee who ensures that the issuer complies with the terms underlying the asset-backed security.

• Many securitized assets are backed by credit enhancements, such as a third-party guarantee against the default on the underlying assets.

• The most common types of asset-backed securities are those secured by mortgages, automobile loans, credit card receivables, and home equity loans.

Securitization• By far the largest type and the one in which the

process of securitization has been most extensively applied is mortgages.

• Asset-backed securities formed with mortgages are called mortgage-backed securities, MBSs, or mortgage pass-throughs.

Mortgage-Backed Securities: Definition

• Mortgage-Backed Securities (MBS) or Mortgage Pass-Throughs (PT) are claims on a portfolio of mortgages.

• The securities entitle the holder to the cash flows from a pool of mortgages.

Mortgage-Backed Securities: Creation

• Typically, the issuer of a MBS buys a portfolio or pool of mortgages of a certain type from a mortgage originator, such as a commercial bank, savings and loan, or mortgage banker.

• The issuer finances the purchase of the mortgage portfolio through the sale of the mortgage pass-throughs, which have a claim on the portfolio's cash flow.

• The mortgage originator usually agrees to continue to service the loans, passing the payments on to the MBS holders.

Agency Pass-Throughs

• There are three federal agencies that buy certain types of mortgage loan portfolios (e.g., FHA- or VA-insured mortgages) and then pool them to create MBSs to sell to investors:– Federal National Mortgage Association (FNMA) – Government National Mortgage Association (GNMA) – Federal Home Loan Mortgage Corporation (FHLMC)

• Collectively, the MBSs created by these agencies are referred to as agency pass-throughs.

• Agency pass-throughs are guaranteed by the agencies, and the loans they purchase must be conforming loans, meaning they meet certain standards.


Government National Mortgage Association, GNMA• GNMA mortgage-backed securities or pass-throughs are

formed with FHA- or VA-insured mortgages.

• They are put together by an originator (bank, thrift, or mortgage banker), who presents a block of FHA and VA mortgages to GNMA.

• If GNMA finds them in order, they will issue a guarantee and assign a pool number that identifies the MBS that is to be issued.

• The originator will transfer the mortgages to a trustee, and then issue the pass-throughs, often selling them to investment bankers for distribution.


Government National Mortgage Association, GNMA

• The mortgages underlying GNMA’s MBSs are very similar (e.g., single-family, 30-year maturity, and fixed rate), with the mortgage rates usually differing by no more than 50 basis point from the average mortgage rate.

• GNMA does offer programs in which the underlying mortgages are more diverse.

• Note: Since GNMA is a federal agency, its guarantee of timely interest and principal payments is backed by the full faith and credit of the U.S. government -- the only MBS with this type of guarantee.


Federal Home Loan Mortgage Corporation, FHLMC• The FHLMC (Freddie Mac) issues MBSs that they refer

to as participation certificates (PCs).

• The FHLMC has a regular MBS (also called a cash PC), which is backed by a pool of either conventional, FHA, or VA mortgages that the FHLMC has purchased from mortgage originators.

• They also offer a pass-though formed through their Guarantor/Swap Program. In this program, mortgage originators can swap mortgages for a FMLMC pass-through.


Federal Home Loan Mortgage Corporation

• Unlike GNMA’s MBSs, Freddie Mac's MBSs are formed with more heterogeneous mortgages.

• Like GNMA, the Federal Home Loan Mortgage Corporation backs the interest and principal payments of its securities, but the FHLMC's guarantee is not backed by the U.S. government.


Federal National Mortgage Association, FNMA• FNMA (Fannie Mae) offers several types of pass-

throughs, referred to as FNMA mortgage-backed securities.

• Like FHLMC’s pass-throughs, FNMA’s securities are backed by the agency, but not by the government.

• Like the FHLMC, FNMA buys conventional, FHA, and VA mortgages, and offers a SWAP program whereby mortgage loans can be swapped for FNMA-issued MBSs.


Federal National Mortgage Association

• Like the FHLMC, FNMA's mortgages are more heterogeneous than GNMA's mortgages, with mortgage rates in some pools differing by as much as 200 basis points from the portfolio's average mortgage rate.

Conventional Pass-Throughs

• Conventional pass-throughs are sold by commercial banks, savings and loans, other thrifts, and mortgage bankers.

• These nonagency pass-throughs, also called private labels, are often formed with nonconforming mortgages; that is, mortgages that fail to meet size limits and other requirements placed on agency pass-throughs.


• The larger issuers of conventional MBSs include: – Citicorp Housing – Countrywide – Prudential Home – Ryland/Saxon – G.E. Capital Mortgage


• Conventional pass-throughs are often guaranteed against default through external credit enhancements, such as: – Guarantee of a corporation – Bank letter of credit – Private insurance from such insurers as the Financial

Guarantee Insurance Corporation (FGIC), the Capital Markets Assurance Corporation (CAPMAC), or the Financial Security Assurance Company (FSA)


• Some conventional pass-throughs are guaranteed internally through the creation of senior and subordinate classes of bonds with different priority claims on the pool's cash flows in the case some of the mortgages in the pool default.

• Example: A conventional pass-through, known as an A/B pass-through, consists of two types of claims on the underlying pool of mortgages - senior and subordinate. – The senior claim is backed by the mortgages, while the

subordinate claim is not. – The more subordinate claims sold relative to senior,

the more secured the senior claims.


• Conventional MBSs are rated by Moody's and Standard and Poor's.

• They must be registered with the SEC when they are issued.


• Most financial entities that issue private-labeled MBSs or derivatives of MBSs are legally set up so that they do not have to pay taxes on the interest and principal that passes through them to their MBS investors.

• The requirements that MBS issuers must meet to ensure tax-exempt status are specified in the Tax Reform Act of 1983 in the section on trusts referred to as Real Estate Mortgage Investment Conduits, REMIC.

• Private-labeled MBS issuers who comply with these provisions are sometimes referred to as REMICs.

Market

• Primary Market: Investors buy MBSs issued by agencies or private-label investment companies either directly or through dealers. Many of the investors are institutional investors. Thus, the creation of MBS has provided a tool for having real estate financed more by institutions.

• Secondary Market:– Existing MBS are traded by dealers on the

OTC

Cash Flows• Cash flows from MBSs are generated from the

cash flows from the underlying pool of mortgages, minus servicing and other fees.

• Typically, fees for constructing, managing, and servicing the underlying mortgages (also referred to as the mortgage collateral) and the MBSs are equal to the difference between the rates associated with the mortgage pool and the rates paid on the MBS (pass-through (PT) rate).

Cash Flows: Terms• Weighted Average Coupon Rate, WAC:

Mortgage portfolio's (collateral’s) weighted average rate.

• Weighted Average Maturity, WAM: Mortgage portfolio's weighted average maturity.

• Pass-Through Rate, PT Rate: Interest rate paid on the MBS; PT rate is lower than WAC -- the difference going to MBS issuer.

• Prepayment Rate or Speed: Assumed prepayment rate.

Prepayment• A number of prepayment models have been

developed to try to predict the cash flows from a portfolio of mortgages.

• Most of these models estimate the prepayment rate, referred to as the prepayment speed or simply speed, in terms of four factors: – Refinancing incentive

– Seasoning (the age of the mortgage)

– Monthly factors

– Prepayment burnout

PrepaymentRefinancing Incentive

• The refinancing incentive is the most important factor influencing prepayment.

• If mortgage rates decrease below the mortgage loan rate, borrowers have a strong incentive to refinance.

• This incentive increases during periods of falling interest rates, with the greatest increases occurring when borrowers determine that rates have bottomed out.

PrepaymentRefinancing Incentive

• The refinancing incentive can be measured by the difference between the mortgage portfolio's WAC and the refinancing rate, Rref.

• A study by Goldman, Sachs, and Company found that the annualized prepayment speed, referred to as the conditional prepayment rate, CPR, is greater the larger the positive difference between the WAC and Rref.

Prepayment

Seasoning

• A second factor determining prepayment is the age of the mortgage, referred to as seasoning.

• Prepayment tends to be greater during the early part of the loan, then stabilize after about three years. The figures on the next slide depicts a commonly referenced seasoning pattern known as the PSA model (Public Securities Association).

Prepayment

• PSA Model:

CPR (%)

Month30 3600

0 2.

6 0. 9 0.

30.

100 PSA50 PSA

150 PSA

Prepayment

Seasoning

• In the standard PSA model, known as 100 PSA, the CPR starts at .2% for the first month and then increases at a constant rate of .2% per month to equal 6% at the 30th month; then after the 30th month the CPR stays at a constant 6%. Thus for any month t, the CPR is

30tfi,06.CPR

,30tif,30

t06.CPR

Prepayment

Seasoning

• Note that the CPR is quoted on an annual basis.

• The monthly prepayment rate, referred to as the single monthly mortality rate, SMM, can be obtained given the annual CPR by using the following formula:

12/1]CPR1[1SMM

PrepaymentSeasoning

• The 100 PSA model is often used as a benchmark. The actual aging pattern will differ depending on where current mortgage rates are relative to the WAC.

• Analysts often refer to the applicable pattern as being a certain percentage of the PSA.

• For example:– If the pattern is described as being 200 PSA, then the

prepayment speeds are twice the 100 PSA rates.– If the pattern is described as 50 PSA, then the CPRs

are half of the 100 PSA rates (see figures on previous slide).

Prepayment

Seasoning• A current mortgage pool described by a 100 PSA

would have a annual prepayment rate of 2% after 10 months (or a monthly prepayment rate of SMM = .00168), and a premium pool described as a 150 PSA would have a 3% CPR (or SMM = .002535) after 10 months.

PrepaymentMonthly Factors

• In addition to the effect of seasoning, mortgage prepayment rates are also influenced by the month of the year, with prepayment tending to be higher during the summer months.

• Monthly factors can be taken into account by multiplying the CPR by the estimated monthly multiplier to obtain a monthly-adjusted CPR. PSA provides estimates of the monthly multipliers.

PrepaymentBurnout Factors

• Many prepayment models also try to capture what is known as the burnout factor.

• The burnout factor refers to the tendency for premium mortgages to hit some maximum CPR and then level off.

• For example, in response to a 2% decrease in refinancing rates, a pool of premium mortgages might peak at a 40% prepayment rate after one year, then level off at approximately 25%.

Cash Flow from a Mortgage Portfolio

• The cash flow from a portfolio of mortgages consists – Interest payments – Scheduled principal – Prepaid principal

Cash Flow from a Mortgage Portfolio: Example 1

• Example 1: Consider a bank that has a pool of current fixed rate mortgages that are – worth $100 million (Par, F)– yield a WAC of 8%, and – have a WAM of 360 months.


• For the first month, the portfolio would generate an aggregate mortgage payment of $733,765:

12/R))12/R(1/(11

Fp

12/R

))12/R(1/(11pF

))12/R(1(

pF

A

MA0

A

MA

0

M

1ttA0

765,733$

12/08.))12/08(.1/(11

000,000,100$p

360


• From the $733,765 payment, $666,667 would go towards interest and $67,098 would go towards the scheduled principal payment:

098,67$667,666$765,733$InterestpPaymentincipalPrScheduled

667,666$000,000,100$12

08.F

12

RInterest 0

A


• The projected first month prepaid principal can be estimated with a prepayment model. Using the 100% PSA model, the monthly prepayment rate for the first month (t = 1) is equal to SMM = .0001668:

0001668.]002.1[1SMM

002.06.30

1CPR

12/1


• Given the prepayment rate, the projected prepaid principal in the first month is found by multiplying the balance at the beginning of the month minus the scheduled principal by the SMM.

• Doing this yields a projected prepaid principal of $16,671 in the first month:

671,16$]098,67$000,000,100[$0001668.principalprepaid

]principalScheduledF[SMMprincipalprepaid 0


• Thus, for the first month, the mortgage portfolio would generate an estimated cash flow of $750,435, and a balance at the beginning of the next month of $99,916,231:

231,916,99$671,16$098,67$000,000,100$2MonthforBalanceBeginning

principalprepaidprincipalScheduledF2MonthforBalanceBeginning

435,750$671,16$098,67$666,666$CF

principalprepaidprincipalScheduledInterestCF

0


• In the second month (t = 2), the projected payment would be $733,642 with $666,108 going to interest and $67,534 to scheduled principal:

534,67$108,666$642,733$principalScheduled

108,666$)231,916,99($12

08.Interest

642,733$

12/08.))12/08(.1/(11

231,916,99$p

359


• Using the 100% PSA model, the estimated monthly prepayment rate is .000333946, yielding a projected prepaid principal in month 2 of $33,344:

344,33]534,67$231,916,99[$000333946.principalprepaid

000333946.]004.1[1SMM

004.06.30

2CPR

12/1


• Thus, for the second month, the mortgage portfolio would generate an estimated cash flow of $766,986 and have a balance at the beginning of month three of $99,815,353:

353,815,99$

344,33$534,67$231,916,99$3MonthforBalanceBeginning

986,766$344,33$534,67$108,666$CF


• The exhibit on the next slide summarizes the mortgage portfolio's cash flow for the first two months and other selected months.

• In examining the exhibit, two points should be noted:

1. Starting in month 30 the SMM remains constant at .005143; this reflects the 100% PSA model's assumption of a constant CPR of 6% starting in month 30.

2. The projected cash flows are based on a static analysis in which rates are assumed fixed over the time period.

Cash Flow from a Mortgage Portfolio: Example 1Period Balance Interest p Sch. Prin. SMM Prepaid Prin. CF

1000000001 100000000 666667 733765 67098 0.0001668 16671 7504352 99916231 666108 733642 67534 0.0003339 33344 7669863 99815353 665436 733397 67961 0.0005014 50011 7834094 99697380 664649 733029 68380 0.0006691 66664 7996945 99562336 663749 732539 68790 0.0008372 83294 8158336 99410252 662735 731926 69191 0.0010055 99892 8318177 99241170 661608 731190 69582 0.0011742 116449 84763923 94291147 628608 703012 74405 0.0039166 369010 107202324 93847732 625652 700259 74607 0.0040908 383607 108386625 93389518 622597 697394 74798 0.0042653 398017 109541126 92916704 619445 694420 74975 0.0044402 412234 110665327 92429495 616197 691336 75140 0.0046154 426250 111758628 91928105 612854 688146 75292 0.0047909 440059 112820429 91412755 609418 684849 75430 0.0049668 453653 113850230 90883671 605891 681447 75556 0.005143 467027 114847531 90341088 602274 677943 75669 0.005143 464236 114217932 89801183 598675 674456 75781 0.005143 461459 1135915

110 54900442 366003 451112 85109 0.005143 281916 733028111 54533417 363556 448792 85236 0.005143 280028 728820112 54168153 361121 446484 85363 0.005143 278148 724632113 53804641 358698 444188 85490 0.005143 276278 720466114 53442873 356286 441903 85617 0.005143 274417 716320115 53082839 353886 439631 85745 0.005143 272565 712195357 496620 3311 126231 122920 0.005143 1922 128153358 371778 2479 125582 123103 0.005143 1279 126861359 247395 1649 124936 123287 0.005143 638 125574360 123470 823 124293 123470 0.005143 0 124293

]incipalPrScheduledBalanceBeginning[SMMincipalPrepaidPr

Balance)08(.pincipalPrScheduled

)Balance)(12/08(.Interest

)12/08(.

))]12/08(.1/(1[1

BalancepPaymentMonthly

PeriodsmainingRe

Cash Flow from a MBS: Example 2

Example 2• The next exhibit shows the monthly cash

flows for a MBS issue constructed from a $100M mortgage pool with the following features– Current balance = $100M – WAC = 8%– WAM = 355 months – PT rate = 7.5%– Prepayment speed equal to 150% of the

standard PSA model: PSA = 150

Cash Flow from a MBS: Example 2Period Balance Interest p Scheduled SMM Prepaid Principal CF

100000000 Principal Principal1 100000000 625000 736268 69601 0.0015125 151147 220748 8457482 99779252 623620 735154 69959 0.0017671 176194 246153 8697733 99533099 622082 733855 70301 0.0020223 201148 271449 8935314 99261650 620385 732371 70627 0.0022783 225990 296617 9170025 98965033 618531 730702 70936 0.002535 250701 321637 9401686 98643396 616521 728850 71227 0.0027925 275262 346489 96301120 91641550 572760 684341 73398 0.0064757 592971 666369 123912821 90975181 568595 679910 73408 0.0067447 613101 686510 125510522 90288672 564304 675324 73399 0.0070144 632804 706204 127050823 89582468 559890 670587 73370 0.0072849 652066 725436 128532724 88857032 555356 665702 73321 0.0075563 670873 744194 129955025 88112838 550705 660671 73253 0.0078284 689211 762463 131316926 87350375 545940 655499 73164 0.0078284 683243 756406 130234627 86593968 541212 650368 73075 0.0078284 677322 750397 129160928 85843572 536522 645277 72986 0.0078284 671448 744434 128095729 85099137 531870 640225 72897 0.0078284 665621 738519 127038830 84360619 527254 635213 72809 0.0078284 659840 732649 125990331 83627969 522675 630240 72721 0.0078284 654106 726826 124950132 82901143 518132 625307 72632 0.0078284 648416 721049 123918133 82180094 513626 620411 72544 0.0078284 642772 715317 1228942

100 44933791 280836 366433 66874 0.0078284 351237 418111 698947101 44515680 278223 363564 66793 0.0078284 347965 414758 692981102 44100923 275631 360718 66712 0.0078284 344718 411430 687061103 43689493 273059 357894 66631 0.0078284 341498 408129 681188200 16163713 101023 166983 59225 0.0078284 126073 185298 286321201 15978416 99865 165676 59153 0.0078284 124623 183776 283641353 148527 928 50171 49181 0.0078284 778 49958 50887354 98569 616 49778 49121 0.0078284 387 49508 50124355 49061 307 49388 49061 0.0078284 0 49061 49368

]incipalPrScheduledBalanceBeginning[SMMincipalPrepaidPr

Balance)08(.pincipalPrScheduled

)Balance)(12/075(.Interest

)12/08(.

))]12/08(.1/(1[1

BalancepPaymentMonthly

Pe riodsma iningRe


Notes:• The first month's CPR for the MBS issue reflects a five-

month seasoning in which t = 6, and a speed that is 150% greater than the 100 PSA. For the MBS issue, this yields a first month SMM of .0015125 and a constant SMM of .0078284 starting in month 25.

• The WAC of 8% is used to determine the mortgage payment and scheduled principal, while the PT rate of 7.5% is used to determine the interest.

• The monthly fees implied on the MBS issue are equal to .04167% = (8% - 7.5%)/12 of the monthly balance.


• First Month’s Payment:

268,736$

12/08.))12/08(.1/(11

M100$p

355

WAC


• From the $736,268 payment, $625,000 would go towards interest and $69,601 would go towards the scheduled principal payment:

601,69$

)]000,000,100)($12/08[(.268,736$InterestpPaymentincipalPrScheduled

000,625$000,000,100$12

075.F

12

RInterest 0

A

RatePT WAC


• Using 150% PSA model and seasoning of 5 months the first month SMM = .0015125:

0015125.]018.1[1SMM

018.06.30

650.1CPR

12/1


• Given the prepayment rate, the projected prepaid principal in the first month is $151,147



sdifferenceroundingslightforAllow


• Thus, for the first month, the MBS would generate an estimated cash flow of $845,748 and a balance at the beginning of the next month of $99,779,252:

252,779,99$147,151$601,69$000,000,100$2MonthforBalanceBeginning

principalprepaidprincipalScheduledF2MonthforBalanceBeginning

748,845$147,151$601,69$000,625$CF


0



• Second Month: Payment, Interest, Scheduled Principal, Prepaid Principal, and Cash flow:

773,869$194,176$959,69$620,623$CF


154,735$

12/08.))12/08(.1/(11

252,779,99$p

354

959,69$)]252,779,99)($12/08[(.154,735$InterestpPaymentincipalPrScheduled

620,623$252,779,99$12

075.F

12

RInterest 0

A

0017671.]021.1[1SMM

021.06.30

750.1CPR

12/1




Market

• As noted, investors can acquire newly issued mortgage-backed securities from the agencies, originators, or dealers specializing in specific pass-throughs.

• There is also a secondary market consisting of dealers who operate in the OTC market as part of the Mortgage-Backed Security Dealers Association.

• These dealers form the core of the secondary market for the trading of existing pass-throughs.

Market

• Mortgage pass-throughs are normally sold in denominations ranging from $25,000 to $250,000, although some privately-placed issues are sold with denominations as high as $1 million.

Price Quotes

• The prices of MBSs are quoted as a percentage of the underlying MBS issue’s balance.

• The mortgage balance at time t, Ft, is usually calculated by the servicing institution and is quoted as a proportion of the original balance, F0.

• This proportion is referred to as the pool factor, pf:

0

tt F

Fpf

Price Quotes

• Example: A MBS backed by a mortgage pool originally worth $100M, a current pf of .92, and quoted at 95 - 16 (Note: 16 is 16/32) would have a market value of $87.86M:

M92$)M100($)92(.

F)pf(F 0tt

M86.87$)M92($)9550(.ValueMarket

Price Quotes

• The market value is the clean price; it does not take into account accrued interest, ai.

• For MBS, accrued interest is based on the time period from the settlement date (two days after the trade) and the first day of the next month.

• Example: If the time period is 20 days, the month is 30 days, and the WAC = 9%, then ai is $.46M:

M46.0$M92$12

09.

30

20ai

Price Quotes

• The full market value would be $88.32M:

M32.88$

M46.0$M86.87$ValueMktFull

Price Quotes

• The market price per share is the full market value divided by the number of shares.

• If the number of shares is 400, then the price of the MBS based on a 95 - 16 quote would be $220,800:

800,220$400

M32.88$shareperpriceMBS

Extension Risk

• Like other fixed-income securities, the value of a MBS is determined by the MBS's future cash flow (CF), maturity, default risk, and other features germane to fixed-income securities.

)R,CF(fV

)R1(

CFV

tMBS

M

1tt

tMBS

Extension Risk

• In contrast to other bonds, MBSs are also subject to prepayment risk.

• Prepayment affects the MBS’s CF.

• Prepayment, in turn, is affected by interest rates.

• Thus, interest rates affects the MBS’s CFs.

)R,CF(fVMBS

)R(fCF

Extension Risk

• With the CF a function of rates, the value of a MBS is more sensitive to interest rate changes than those bonds whose CFs are not.

• This sensitivity is known as extension risk.

Extension Risk

• If interest rates decrease, then the prices of MBSs, like the prices of most bonds, increase as a result of the lower discount rates.

• However, the decrease in rates will also augment prepayment speed, causing the earlier cash flow of the mortgages to be larger which, depending on the level of rates and the maturity remaining, could also contribute to increasing the MBS’s price.

Extension Risk

• Rate Decrease

MVratediscountlowerRif

bondsmostlike

orVCFsEarlierprepaymentIncreasesRif M

Extension Risk

• If interest rates increase, then the prices of MBSs will decrease as a result of higher discount rates and possibly the smaller earlier cash flow resulting from lower prepayment speeds.

Extension Risk

• Rate Increase

MVratediscountgreaterRif

orVCFsEarlierprepaymentDecreasesRif M

bondsmostlike

Average Life

• The average life of a MBS or mortgage portfolio is the weighted average of the security’s time periods, with the weights being the periodic principal payments (scheduled and prepaid principal) divided by the total principal:

T

1t principaltotal

tatreceivedprincipalt

12

1LifeAverage

Average Life

• The average life for the MBS issue with WAC = 8%, WAM = 355, PT Rate = 7.5%, and PSA = 150 is 9.18 years

years18.9

000,000,100$

061,49($355)153,246($2)748,220($1

12

1LifeAverage

Average Life

• The average life of a MBS depends on prepayment speed: – If the PSA speed of the $100M MBS issue

were to increase from 150 to 200, the MBS’s average life would decrease from 9.18 to 7.55, reflecting greater principal payments in the earlier years.

– If the PSA speed were to decrease from 150 to 100, then the average life of the MBS would increase to 11.51.

Average Life and Prepayment Risk

• For MBSs and mortgage portfolios, prepayment risk can be evaluated in terms of how responsive a MBS's or mortgage portfolio’s average life is to changes in prepayment speeds:

• A MBS with an average life that did not change with PSA speeds, in turn, would have stable principal payments over time and would be absent of prepayment risk.

PSA

LifeAverageriskprepayment

riskprepaymentZero0PSA

lifeAv

MBS Derivatives

• One of the more creative developments in the security market industry over the last two decades has been the creation of derivative securities formed from MBSs and mortgage portfolios that have different prepayment risk characteristics, including some that are formed that have average lives that are invariant to changes in prepayment rates.

• The most popular of these derivatives are – Collateralized Mortgage Obligations, CMOs – Stripped MBS

Collateralized Mortgage Obligations

• Collateralized mortgage obligations, CMOs, are formed by dividing the cash flow of an underlying pool of mortgages or a MBS issue into several classes, with each class having a different claim on the mortgage collateral and with each sold separately to different types of investors.

Collateralized Mortgage Obligations

• The different classes making up a CMO are called tranches or bond classes.

• There are two general types of CMO tranches:– Sequential-Pay Tranches – Planned Amortization Class Tranches, PAC

Sequential-Pay Tranches

• A CMO with sequential-pay tranches, called a sequential-pay CMO, is divided into classes with different priority claims on the collateral's principal.

• The tranche with the first priority claim has its principal paid entirely before the next priority class, which has its principal paid before the third class, and so on.

• Interest payments on most CMO tranches are made until the tranche's principal is retired.


• Example: A sequential-pay CMO is shown in the next exhibit.

• This CMO consist of three tranches, A, B, and C, formed from the collateral making up the $100M MBS in the previous example: F = $100M, WAM = 355, WAC = 8%, PT Rate = 7.5%, PSA = 150.

– Tranche A = $50M

– Tranche B = $30M

– Tranche C = $20M

Sequential-Pay Tranches• In terms of the priority disbursement rules:

– Tranche A receives all principal payment from the collateral until its principal of $50M is retired. No other tranche's principal payments are disbursed until the principal on A is paid.

– After tranche A's principal is retired, all principal payments from the collateral are then made to tranche B until its principal of $30M is retired.

– Finally, tranche C receives the remaining principal that is equal to its par value of $20M.

– Note: while the principal is paid sequentially, each tranche does receive interest each period equal to its stated PT rate (7.5%) times its outstanding balance at the beginning of each month.


Par = $100M Rate = 7.5% A: Par = $50M Rate = 7.5% B: Par =$30M Rate = 7.5% C: Par = $20M Rate = 7.5%Period Collateral Collateral Collateral Tranch A A A Tranche B B B Tranche C C CMonth Balance Interest Principal Balance Interest Principal Balance Principal Interest Balance Principal Interest

100000000 50000000 30000000 20000000 01 100000000 625000 220748 50000000 312500 220748 30000000 0 187500 20000000 0 1250002 99779252 623620 246153 49779252 311120 246153 30000000 0 187500 20000000 0 1250003 99533099 622082 271449 49533099 309582 271449 30000000 0 187500 20000000 0 1250004 99261650 620385 296617 49261650 307885 296617 30000000 0 187500 20000000 0 1250005 98965033 618531 321637 48965033 306031 321637 30000000 0 187500 20000000 0 12500085 51626473 322665 471724 1626473 10165 471724 30000000 0 187500 20000000 0 12500086 51154749 319717 467949 1154749 7217 467949 30000000 0 187500 20000000 0 12500087 50686799 316792 464204 686799 4292 464204 30000000 0 187500 20000000 0 12500088 50222595 313891 460488 222595 1391 222595 30000000 237893 187500 20000000 0 12500089 49762107 311013 456802 0 0 0 29762107 456802 186013 20000000 0 12500090 49305305 308158 453144 0 0 0 29305305 453144 183158 20000000 0 12500091 48852161 305326 449515 0 0 0 28852161 449515 180326 20000000 0 12500092 48402646 302517 445915 0 0 0 28402646 445915 177517 20000000 0 125000

178 20650839 129068 222016 0 0 0 650839 222016 4068 20000000 0 125000181 19990210 124939 216625 0 0 0 0 0 0 19990210 216625 124939182 19773585 123585 214856 0 0 0 0 0 0 19773585 214856 123585183 19558729 122242 213101 0 0 0 0 0 0 19558729 213101 122242184 19345627 120910 211360 0 0 0 0 0 0 19345627 211360 120910353 148527 928 49958 0 0 0 0 0 0 148527 49958 928354 98569 616 49508 0 0 0 0 0 0 98569 49508 616355 49061 307 49061 0 0 0 0 0 0 49061 49061 307


• Given the assumed PSA of 150, the first month cash flow for tranche A consist of a principal payment (scheduled and prepaid) of $220,748 and an interest payment of $312,500:

[(.075/12)($50M) = $312,500]

• In month 2, tranche A receives an interest payment of $311,120 based on the balance of $49.779252M and a principal payment of $246,153.

Sequential-Pay Tranches• Based on the assumption of a 150% PSA speed, it takes

88 months before A's principal of $50M is retired.

• During the first 88 months, the cash flows for tranches B and C consist of just the interest on their balances, with no principal payments made to them.

• Starting in month 88, tranche B begins to receive the principal payment.

• Tranche B is paid off in month 180, at which time principal payments begin to be paid to tranche C.

• Finally, in month 355 tranche C's principal is retired.


Features of Sequential-Pay CMOs

• By creating sequential-pay tranches, issuers of CMOs are able to offer investors maturities, principal payment periods, and average lives different from those defined by the underlying mortgage collateral.

Sequential-Pay TranchesFeatures of Sequential-Pay CMOs

• Maturity:– Collateral's maturity = 355 months (29.58 years)– Tranche A’s maturity = 88 months (7.33 years)– Tranche B's maturity = 180 months (15 years) – Tranche C’s maturity = 355 months (29.58 years)

• Window: The period between the beginning and ending principal payment is referred to as the principal pay-down window:

– Collateral’s window = 355 months– Tranche A’s window = 87 months– Tranche B's window = 92 months – Tranche C's window =176 months

• Average Life:– Collateral's average = 9.18 years – Tranche A’s average life = 3.69 years– Tranche B’s average life = 10.71 years – Tranche C’s Average life = 20.59 years


Tranche Maturity Window Average LifeA 88 Months 87 Months 3.69 yearsB 179 Months 92 Months 10.71 yearsC 355 Months 176 Months 20.59 years

Collateral 355 Months 355 Months 9.18 years

Sequential-Pay Tranches• Note: A CMO tranche with a lower average life is still

susceptible to prepayment risk. • The average lives for the collateral and the three tranches

are shown below for different PSA models

• Note that the average life of each of the tranches still varies as prepayment speed changes.

PSA Collateral Tranche A Tranche B Tranche C50 14.95 7.53 19.4 26.81100 11.51 4.92 14.18 23.99150 9.18 3.69 10.71 9.18200 7.55 3.01 8.51 17.46300 5.5 2.26 6.03 12.82


• Note: Issuers of CMOs are able to offer a number of CMO tranches with different maturities and windows by simply creating more tranches.

Different Types of Sequential-Pay Tranches

• Sequential-pay CMOs often include traches with special features. These include:– Accrual Bond Trache– Floating-Rate Tranche– Notional Interest-Only Tranche

Accrual Tranche

• Many sequential-pay CMOs have an accrual bond class.

• Such a tranche, also referred to as the Z bond, does not receive current interest but instead has it deferred.

• The Z bond's current interest is used to pay down the principal on the other tranches, increasing their speed and reducing their average life.

Accrual Tranche

• Example: suppose in our preceding equential-pay CMO example we make tranche C an accrual tranche in which its interest of 7.5% is to paid to the earlier tranches and its principal of $20M and accrued interest is to be paid after tranche B's principal has been retired

• The next exhibit shows the principal and interest payments from the collateral and Tranches A, B, and Z.

Accrual TranchePar = $100M Rate = 7.5% A: Par = $50M Rate = 7.5% B: Par = $30M Rate = 7.5% Z: Par = $20M Rate = 7.5%

Period Collateral Collateral Collateral A A A B B B Z Z ZMonth Balance Interest Principal Balance Interest Principal Balance Principal Interest Bal.+Cum Int Principal Interest

100000000 50000000 30000000 20000000 01 100000000 625000 220748 50000000 312500 345748 30000000 0 187500 20000000 0 02 99779252 623620 246153 49654252 310339 371153 30000000 0 187500 20125000 0 03 99533099 622082 271449 49283099 308019 396449 30000000 0 187500 20250000 0 04 99261650 620385 296617 48886650 305542 421617 30000000 0 187500 20375000 0 05 98965033 618531 321637 48465033 302906 446637 30000000 0 187500 20500000 0 068 60253239 376583 540668 1878239 11739 665668 30000000 0 187500 28375000 0 069 59712571 373204 536352 1212571 7579 661352 30000000 0 187500 28500000 0 070 59176219 369851 532069 551219 3445 551219 30000000 105850 187500 28625000 0 071 58644150 366526 527821 0 0 0 29894150 652821 186838 28750000 0 072 58116329 363227 523605 0 0 0 29241329 648605 182758 28875000 0 0

122 36470935 227943 350111 0 0 0 1345935 475111 8412 35125000 0 0123 36120824 225755 347292 0 0 0 870824 472292 5443 35250000 0 0125 35429038 221431 341719 0 0 0 0 0 0 35429038 341719 221431126 35087319 219296 338966 0 0 0 0 0 0 35087319 338966 219296354 98569 616 49508 0 0 0 0 0 0 98569 49508 616355 49061 307 49061 0 0 0 0 0 0 49061 49061 307

Accrual Tranche• Since the accrual tranche's current interest of $125,000 is

now used to pay down the other classes' principals, the other tranches now have lower maturities and average lives.

• For example, the principal payment on tranche A is $345,748 in the first month ($220,748 of scheduled and projected prepaid principal and $125,000 of Z's interest); in contrast, the principal is only $220,748 when there is no Z bond.

• As a result of the Z bond, trache A's window is reduced from 87 months to 69 months and its average life from 3.69 years to 3.06 years.

Accrual Tranche

Tranche Window Average LifeA 69 Months 3.06 YearsB 54 Months 8.23 Years

Floating-Rate Tranche

• In order to attract investors who prefer variable rate securities, CMO issuers often create floating-rate and inverse floating-rate tranches.

• The monthly coupon rate on the floating-rate tranche is usually set equal to a reference rate such as the London Interbank Offer Rate, LIBOR, while the rate on the inverse floating-rate tranche is determined by a formula that is inversely related to the reference rate.


• Example: Sequential-pay CMO with a floating and inverse floating tranches

Tranche Par Value PT Rate

AFRIFRZ

$50M$22.5M$7.5M$20M

7.5%LIBOR +50BP

28.3 – 3 LIBOR7.5%

Total $100 7.5%• Note: The CMO is identical to our preceding CMO, except that

tranche B has been replaced with a floating-rate tranche, FR, and an inverse floating-rate tranche, IFR.


• The rate on the FR tranche, RFR, is set to the LIBOR plus 50 basis points, with the maximum rate permitted being 9.5%.

• The rate on the IFR tranche, RIFR, is determined by the following formula:

• This formula ensures that the weighted average coupon rate (WAC) of the two tranches will be equal to the coupon rate on tranche B of 7.5%, provided the LIBOR is less than 9.5%.

RIFR = 28.5 - 3 LIBOR

Floating-Rate Tranche• For example, if the LIBOR is 8%, then the rate on the FR

tranche is 8.5%, the IFR tranche's rate is 4.5%, and the WAC of the two tranches is 7.5%:

%5.7R25.R75.WAC

%5.4LIBOR35.28R

%5.8BP50LIBORR

%8LIBOR

IFRFR

IFR

FR

Notional Interest-Only Class

• Each of the fixed-rate tranches in the previous CMOs have the same coupon rate as the collateral rate of 7.5%.

• Many CMOs, though, are structured with tranches that have different rates. When CMOs are formed this way, an additional tranche, known as a notional interest-only (IO) class, is often created.

• This tranche receives the excess interest on the other tranches’ principals, with the excess rate being equal to the difference in the collateral’s PT rate minus the tranches’ PT rates.


• Example: A sequential-pay CMO with a Z bond and notional IO tranche is shown in the next exhibit.

• This CMO is identical to our previous CMO with a Z bond, except that each of the tranches has a coupon rate lower than the collateral rate of 7.5% and there is a notional IO class.


• The notional IO class receives the excess interest on each tranche's remaining balance, with the excess rate based on the collateral rate of 7.5%.

• In the first month, for example, the IO class would receive interest of $87,500:

500,87$000,25$500,62$Interest

000,000,30$12

065.075.000,000,50$

12

06.075.Interest

Notional Interest-Only ClassCollateral: Par = $100M Rate = 7.5% Tranche A: Par = $50M Rate = 6% Tranche B: Par = $30M Rate = 6.5% Tranche Z: Par = $20M Rate = 7% Notional Par = $15.333M

Period Collateral Collateral Collateral A A A Notional B B B Notional Z Z Z Notional NotionalMonth Balance Interest Principal Balance Interest Principal Interest Balance Principal Interest Interest Balance Principal Interest Interest Total CF

100000000 50000000 0.06 0.015 30000000 0.065 0.01 20000000 0 0.07 0.0051 100000000 625000 220748 50000000 250000 345748 62500 30000000 0 162500 25000 20000000 0 0 0 875002 99779252 623620 246153 49654252 248271 371153 62068 30000000 0 162500 25000 20125000 0 0 0 870683 99533099 622082 271449 49283099 246415 396449 61604 30000000 0 162500 25000 20250000 0 0 0 866044 99261650 620385 296617 48886650 244433 421617 61108 30000000 0 162500 25000 20375000 0 0 0 861085 98965033 618531 321637 48465033 242325 446637 60581 30000000 0 162500 25000 20500000 0 0 0 8558170 59176219 369851 532069 551219 2756 551219 689 30000000 105850 162500 25000 28625000 0 0 0 2568971 58644150 366526 527821 0 0 0 0 29894150 652821 161927 24912 28750000 0 0 0 2491272 58116329 363227 523605 0 0 0 0 29241329 648605 158391 24368 28875000 0 0 0 24368

122 36470935 227943 350111 0 0 0 0 1345935 475111 7290 1122 35125000 0 0 0 1122123 36120824 225755 347292 0 0 0 0 870824 472292 4717 726 35250000 0 0 0 726124 35773533 223585 344494 0 0 0 0 398533 398533 2159 332 35375000 -54038 206354 14740 15072125 35429038 221431 341719 0 0 0 0 0 0 0 0 35429038 341719 206669 14762 14762126 35087319 219296 338966 0 0 0 0 0 0 0 0 35087319 338966 204676 14620 14620127 34748353 217177 336235 0 0 0 0 0 0 0 0 34748353 336235 202699 14478 14478353 148527 928 49958 0 0 0 0 0 0 0 0 148527 49958 866 62 62354 98569 616 49508 0 0 0 0 0 0 0 0 98569 49508 575 41 41355 49061 307 49061 0 0 0 0 0 0 0 0 49061 49061 286 20 20


• The IO class is described as paying 7.5% interest on a notional principal of $15,333,333.

• This notional principal is determined by summing each tranche's notional principal.

• A tranche's notional principal is the number of dollars that makes the return on the tranche's principal equal to 7.5%.


• The notional principal for tranche A is $10,000,000, for B, $4,000,000, and for Z, $1,333,333, yielding a total notional principal of $15,333,333:

333,333,15$incipalPrNotionalTotal

333,333,1$075.

)07.075)(.000,000,20($principalNotionals'Z

000,000,4$075.

)065.075)(.000,000,30$principalNotionals'B

000,000,10$075.

)06.075)(.000,000,50($principalNotionals'A

Planned Amortization Class, PAC

• A CMO with a planned amortization class, PAC, is structured such that there is virtually no prepayment risk.

• In a PAC-structured CMO, the underlying mortgages or MBS (i.e., the collateral) is divided into two general tranches: – The PAC (also called the PAC bond) – The support class (also called the support

bond or the companion bond)


• The two tranches are formed by generating two monthly principal payment schedules from the collateral:

– One schedule is based on assuming a relatively low PSA speed – lower collar.

– The other schedule is based on assuming a relatively high PSA speed – upper collar.

• The PAC bond is then set up so that it will receive a monthly principal payment schedule based on the minimum principal from the two principal payments.


• The PAC bond is designed to have no prepayment risk provided the actual prepayment falls within the minimum and maximum assumed PSA speeds.

• The support bond, on the other hand, receives the remaining principal balance and is therefore subject to prepayment risk.


• To illustrate, suppose we form PAC and support bonds from the $100M collateral that we used to construct our sequential-pay tranches:

– Underlying MBS = $100M, WAC = 8%, WAM = 355 months, and PT rate = 7.5%

• To generate the minimum monthly principal payments for the PAC, assume:

– Minimum speed of 100% PSA; lower collar = 100 PSA

– Maximum speed of 300% PSA; upper collar = 300 PSA


• The next exhibit shows the cash flows for the PAC, collateral, and support bond. The exhibit shows:

– In columns 2 and 3 the principal payments (scheduled and prepaid) for selected months at both collars.

– In the fourth column the minimum of the two payments.

• For example, in the first month the principal payment is $170,085 for the 100% PSA and $374,456 for the 300% PSA; thus, the principal payment for the PAC would be $170,085.

Planned Amortization Class, PACPeriod Pac Pac Pac Pac Pac Collateral Collateral Collateral Collateral Support Support Support SupportMonth Low PSA Pr high PSA Pr Min. Principal Int CF Balance Interest Prncipal CF Principal Balance Interest CF

100 300 0.075 100000000 Col Pr - PAC Pr 0.0751 170085 374456 170085 398606 568692 100000000 625000 220748 845748 50662 36222970 226394 2770562 187135 425190 187135 397543 584678 99779252 623620 246153 869773 59018 36172308 226077 2850953 204125 475588 204125 396374 600499 99533099 622082 271449 893531 67324 36113290 225708 2930324 221048 525572 221048 395098 616147 99261650 620385 296617 917002 75568 36045966 225287 3008565 237895 575064 237895 393716 631612 98965033 618531 321637 940168 83742 35970398 224815 30855798 381871 386139 381871 135237 517108 45780181 286126 424898 711025 43028 24142190 150889 19391699 380032 379499 379499 132851 512349 45355283 283471 421491 704962 41993 24099163 150620 192613

100 378204 372970 372970 130479 503449 44933791 280836 418111 698947 45141 24057170 150357 195498101 376384 366552 366552 128148 494700 44515680 278223 414758 692981 48205 24012029 150075 198281102 374575 360242 360242 125857 486099 44100923 275631 411430 687061 51188 23963824 149774 200962201 235460 61932 61932 19312 81245 15978416 99865 183776 283641 121844 12888435 80553 202396202 234395 60806 60806 18925 79731 15794640 98716 182266 280982 121460 12766592 79791 201251203 233336 59699 59699 18545 78244 15612374 97577 180768 278345 121069 12645131 79032 200101204 232283 58611 58611 18172 76783 15431606 96448 179282 275729 120671 12524062 78275 198946205 231235 57542 57542 17806 75348 15252325 95327 177807 273134 120265 12403392 77521 197786206 230193 56492 56492 17446 73938 15074517 94216 176344 270560 119852 12283127 76770 196622354 124660 2559 2559 32 2591 98569 616 49508 50124 46948 93517 584 47533355 124203 2493 2493 16 2509 49061 307 49061 49368 46568 46568 291 46859

Par = 63777030 Par = 36222970


• Note: For the first 98 months, the minimum principal payment comes from the 100% PSA model, and from month 99 on the minimum principal payment comes from the 300% PSA model.


• Based on the 100-300 PSA range, a PAC bond can be formed that would promise to pay the principal based on the minimum principal payment schedule shown in the exhibit.

• The support bond would receive any excess monthly principal payment.


• The sum of the PAC's principal payments is $63.777M. Thus, the PAC can be described as having:

– Par value of $63.777M – Coupon rate of 7.5%– Lower collar of 100% PSA – Upper collar of 300% PSA

• The support bond, in turn, would have a par value of $36.223M ($100M - $63.777M) and pay a coupon of 7.5%.


• The PAC bond has no prepayment risk as long as the actual prepayment speed is between 100 and 300.

• This can be seen by calculating the PAC's average life given different prepayment rates.

• The next exhibit shows the average lives for the collateral, PAC bond, and support bond for various prepayment speeds ranging from 50% PSA to 350% PSA.


Average LifePSA Collateral PAC Support50 14.95 7.90 21.50

100 11.51 6.98 19.49150 9.18 6.98 13.05200 7.55 6.98 8.55250 6.37 6.98 5.31300 5.50 6.98 2.91350 4.84 6.34 2.71


Note:• The PAC bond has an average life of 6.98 years

between 100% PSA and 300% PSA; its average life does change, though, when prepayment speeds are outside the 100-300 PSA range.

• In contrast, the support bond's average life changes as prepayment speed changes.

• Changes in the support bond's average life due to changes in speed are greater than the underlying collateral's responsiveness.

Other PAC-Structured CMOs

• The PAC and support bond underlying a CMO can be divided into different classes. Often the PAC bond is divided into several sequential-pay tranches, with each PAC having a different priority in principal payments over the other.

• Each sequential-pay PAC, in turn, will have a constant average life if the prepayment speed is within the lower and upper collars.

• In addition, it is possible that some PACs will have ranges of stability that will increase beyond the actual collar range, expanding their effective collars.

Other PAC-Structured CMOs

• A PAC-structured CMO can also be formed with PAC classes having different collars.

• Some PACs are formed with just one PSA rate. These PACs are referred to as targeted amortization class (TAC) bonds.

• Different types of tranches can also be formed out of the support bond class. These include sequential-pay, floating and inverse-floating rate, and accrual bond classes.

Stripped MBS

• Stripped MBSs consist of two classes:

1. Principal-only (PO) class that receives only the principal from the underlying mortgages.

2. Interest-only (IO) class that receives just the interest.

Principal-Only Stripped MBS

• The return on a PO MBS is greater with greater prepayment speed.

• For example, a PO class formed with $100M of mortgages (principal) and priced at $75M would yield an immediate return of $25M if the mortgage borrowers prepaid immediately. Since investors can reinvest the $25M, this early return will have a greater return per period than a $25M return that is spread out over a longer period.

Principal-Only Stripped MBS• Because of prepayment, the price of a PO MBS tends to

be more responsive to interest rate changes than an option-free bond.

• That is, if interest rates are decreasing, then like the price of most bonds, the price of a PO MBS will increase. In addition, the price of a PO MBS is also likely to increase further because of the expectation of greater earlier principal payments as a result of an increase in prepayment caused by the lower rates.

PO

PO

Vratediscountlower)2(

R

Vreturnprepayment)1(


• In contrast, if rates are increasing, the price of a PO MBS will decrease as a result of both lower discount rates and lower returns from slower principal payments.

PO

PO

Vratediscountgreater)2(

R



• Thus, like most bonds, the prices of PO MBSs are inversely related to interest rates, and, like other MBSs with embedded principal prepayment options, their prices tend to be more responsive to interest rate changes.

0R

VPO

Interest-Only Stripped MBS

• Cash flows from an I0 MBS come from the interest paid on the mortgages portfolio’s principal balance.

• In contrast to a PO MBS, the cash flows and the returns on an IO MBS will be greater, the slower the prepayment rate.

Interest-Only Stripped MBS• If the mortgages underlying a $100M, 7.5% MBS with PO

and IO classes were paid off in the first year, then the IO MBS holders would receive a one-time cash flow of $7.5M:

• If $50M of the mortgages were prepaid in the first year and the remaining $50M in the second year, then the IO MBS investors would receive an annualized cash flow over two years totaling $11.25M:

• If the mortgage principal is paid down $25M per year, then the cash flow over four years would total $18.75M:

$11.25M = (.075) ($100M) + (.075)($100M-$50M)

$18.75M = (.075)($100M) + (.075)($100M-$25M) + (.075)($75M-$25M) + (.075)($50M-$25M))

$7.5M = (.075)($100M)

Interest-Only Stripped MBS• Thus, IO MBSs are characterized by an inverse

relationship between prepayment speed and returns: the slower the prepayment rate, the greater the total cash flow on an IO MBS.

• Interestingly, if this relationship dominates the price and discount rate relation, then the price of an IO MBS will vary directly with interest rates.

0R

Vthen,effectnd2effectst1If

Vratediscountgreater)2(

R


IO

IO

IO

IO and PO Stripped MBS

• An example of a PO MBS and an IO MBS are shown in next exhibit.

• The stripped MBSs are formed from collateral with

– Mortgage Balance = $100M– WAC = 8% – PT Rate = 8%– WAM = 360 – PSA = 100

IO and PO Stripped MBSPeriod Collateral Collateral Collateral Collateral Collateral Collateral Stripped StrippedMonth Balance Interest Scheduled Prepaid Total CF PO IO

100000000 Principal Principal Principal1 100000000 666667 67098 16671 83769 750435 83769 6666672 99916231 666108 67534 33344 100878 766986 100878 6661083 99815353 665436 67961 50011 117973 783409 117973 6654364 99697380 664649 68380 66664 135044 799694 135044 6646495 99562336 663749 68790 83294 152084 815833 152084 663749

100 58669646 391131 83852 301307 385159 776290 385159 391131101 58284486 388563 83977 299326 383303 771866 383303 388563200 27947479 186317 97308 143234 240542 426858 240542 186317201 27706937 184713 97453 141996 239449 424162 239449 184713358 371778 2479 123103 1279 124382 126861 124382 2479359 247395 1649 123287 638 123925 125574 123925 1649360 123470 823 123470 0 123470 124293 123470 823

IO and PO Stripped MBS

• The table shows the values of the collateral, PO MBS, and IO MBS for different discount rate and PSA combinations of 8% and 150, 8.5% and 125, and 9% and 100.

• Note: The IO MBS is characterized by a direct relation between its value and rate of return.

Discount PSA Value of Value of Value ofRate PO IO Collateral8% 150 $54,228,764 $47,426,196 $101,654,960

8.50% 125 $49,336,738 $49,513,363 $98,850,1019.00% 100 $44,044,300 $51,795,188 $95,799,488

Other Asset-Backed Securities

• MBSs represent the largest and most extensively developed asset-backed security. A number of other asset-backed securities have been developed.

• The three most common types are those backed by

– Automobile Loans

– Credit Card Receivables

– Home Equity Loans

• These asset-backed securities are structured as pass-throughs and many have tranches.


Automobile Loan-Backed Securities• Automobile loan-backed securities are often referred to

as CARS (certificates for automobile receivables).

• The automobile loans underlying these securities are similar to mortgages in that borrowers make regular monthly payments that include interest and a scheduled principal.

• Like mortgages, automobile loans are characterized by prepayment. For such loans, prepayment can occur as a result of car sales, trade-ins, repossessions and subsequent resales, wrecks, and refinancing when rates are low.

• Some CARS are structured as PACS.


Automobile Loan-Backed Securities

• CARS differ from MBSs in that – they have much shorter lives – their prepayment rates are less influenced by

interest rates than mortgage prepayment rates– they are subject to greater default risk.


Credit-Card Receivable-Backed Securities• Credit-card receivable-backed securities are

commonly referred to as CARDS (certificates for amortizing revolving debts).

• In contrast to MBSs and CARS, CARDS investors do not receive an amortorized principal payment as part of their monthly cash flow.


Credit-Card Receivable-Backed Securities• CARDS are often structured with two periods:

– In one period, known as the lockout period, all principal payments made on the receivables are retained and either reinvested in other receivables or invested in other securities.

– In the other period, known as the principal-amortization period, all current and accumulated principal payments are paid.


Home Equity Loan-Backed Securities• Home-equity loan-backed securities are referred

to as HELS.

• They are similar to MBSs in that they pay a monthly cash flow consisting of interest, scheduled principal, and prepaid principal.

• In contrast to mortgages, the home equity loans securing HELS tend to have a shorter maturity and different factors influencing their prepayment rates.

Websites

• For more information on the mortgage industry, statistics, trends, and rates go to www.mbaa.org

• Mortgage rates in different geographical areas can be found by going to www.interest.com.

• For historical mortgage rates go to http://research.stlouisfed.org/fred2 and click on “Interest Rates.”

http://www.mbaa.org/

http://www.interest.com/

http://research.stlouisfed.org/fred2

Websites

• Agency information: www.fanniemae.com, www.ginniemae.gov, www.freddiemac.com

• For general information on MBS go to www.ficc.com

• For information on the market for mortgage-backed securities go to www.bondmarkets.com and click on “Research Statistics and “Mortgage-Backed Securities.” For information on links to other sites click on “Gateway to Related Links.”

• For information on the market for asset-backed securities go to www.bondmarkets.com and click on “Research Statistics and “Asset-Backed Securities.”

http://www.fanniemae.com/

http://www.ginniemae.gov/

http://www.freddiemac.com/

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Evaluating Mortgage-Backed Securities

Monte Carlo Simulation

• Objective: Determine the MBS’s theoretical value • Steps:1. Simulation of interest rates: Use a binomial interest rate

tree to generate different paths for spot rates and refinancing rates.

2. Estimate the cash flows of a mortgage portfolio, MBS, or tranche for each path given a specified prepayment model based on the spot rates

3. Determine the present values of each path.

4. Calculate the average value – theoretical value.

Step 1: Simulation of Interest Rate • Determination of interest rate paths from a binomial

interest rate tree.• Example:

– Assume three-period binomial tree of one-year spot rates (S) and refinancing rates, (Rref) where:

– With three periods, there are four possible rates after three periods (years) and there are eight possible paths.

1.1/19091.d

1.1u

%6S0

1.1/19091.d

1.1u

%8R ref0

Step 1: Binomial Tree for Spot and Refinancing Rates

%00.8R

%00.6Sref0

0

u = 1.10, d = .9091

2728.7R

4546.5Srefd

d

800.8R

600.6Srefu

u

680.9R

260.7Srefuu

uu

6117.6R

9588.4Srefdd

dd

00.8R

00.6Srefud

ud

0107.6R

5080.4Srefddd

ddd

2728.7R

4546.5Srefudd

udd

800.8R

600.6Srefuud

uud

648.10R

9860.7Srefuuu

uuu

Step 1: Interest Rate Paths

Path 1 Path 2

Path 3 Path 4

6.0000%5.45464.95884.5080

6.0000%5.45464.95885.4546

6.0000%5.45466.00005.4546

6.0000%6.60006.00005.4546

Path 5 Path 6 Path 7 Path 8

6.0000%5.45466.00006.6000

6.0000%6.60006.00006.6000

6.0000%6.60007.26006.6000

6.0000%6.60007.26007.9860

Step 2: Estimating Cash Flows

• The second step is to estimate the cash flow for each interest rate path.

• The cash flow depends on the prepayment rates assumed.

• Most analysts use a prepayment model in which the conditional prepayment rate (CPR) is determined by the seasonality of the mortgages, and by a refinancing incentive that ties the interest rate paths to the proportion of the mortgage collateral prepaid.


• To illustrate, consider a MBS formed from a mortgage pool with a par value of $1M, WAC = 8%, and WAM = 10 years.

• To fit this example to the three-year binomial tree assume that – the mortgages in the pool all make annual cash flows

(instead of monthly) – all have a balloon payment at the end of year 4 – the pass-through rate on the MBS is equal to the WAC

of 8


• The mortgage pool can be viewed as a four-year asset with a principal payment made at the end of year four that is equal to the original principal less the amount paid down.

• As shown in the next exhibit, if there were no prepayments, then the pool would generate cash flows of $149,029M each year and a balloon payment of $688,946 at the end of year 4.

Step 2: Estimating Cash Flows• Mortgage Portfolio:

– Par Value = $1M, WAC = 8%, WAM = 10 Yrs, – PT Rate = 8%, Balloon at the end of the 4th Year

Year Balance P Interest Scheduled Principal

Cash Flow

1234

$1,000,000$930,971$856,419$775,903

$149,029$149,029$149,029$149,029

$80,000$74,478$68,513$62,072

$69,029$74,552$80,516$86,957

$149,029$149,029$149,029$837,975

975,837$072,62$903,775$

Interest)4yr(BalanceCF

975,837$029,149$946,688$

pBalloonCF

946,688$957,86$903,775$

)4yr(prin.Sch)4yr(BalanceBalloon

4

4


• Such a cash flow is, of course, unlikely given prepayment. A simple prepayment model to apply to this mortgage pool is shown in next exhibit.


• The prepayment model assumes: 1. The annual CPR is equal to 5% if the mortgage pool rate is at

a par or discount (that is, if the current refinancing rate is equal to the WAC of 8% or greater).

2. The CPR will exceed 5% if the rate on the mortgage pool is at a premium.

3. The CPR will increase within certain ranges as the premium increases.

4. The relationship between the CPRs and the range of rates is the same in each period; that is, there is no seasoning factor.


Range X = WAC – Rref

CPR

X 0 0.0% < X 0.5% 0.5% < X 1.0% 1.0% < X 1.5% 1.5% < X 2.0% 2.0% < X 2.5% 2.5% < X 3.0% X > 3.0%

5%10%20%30%40%50%60%70%


• With this prepayment model, cash flows can be generated for the eight interest rate paths.

• These cash flows are shown in Exhibit A (next two slides).

Exhibit APath 1 1 2 3 4 5 6 7 8 9 10 11

Year RrefBalance WAC Interest Sch. Prin. CPR Prepaid Prin. CF Z1,t-1 Zt0 Value Prob.

1 0.072728 1000000 0.08 80000 69029 0.20 186194 335224 0.080000 0.080000 310392 0.52 0.066117 744776 0.08 59582 59641 0.30 205540 324764 0.074546 0.077270 279846 0.53 0.060107 479594 0.08 38368 45089 0.40 173802 257259 0.069588 0.074703 207255 0.54 260703 0.08 20856 281560 0.065080 0.072289 212972

Value = 1010465 0.125

Path 2 1 2 3 4 5 6 7 8 9 10 11


1 0.072728 1000000 0.08 80000 69029 0.20 186194 335224 0.080000 0.080000 310392 0.52 0.066117 744776 0.08 59582 59641 0.30 205540 324764 0.074546 0.077270 279846 0.53 0.072728 479594 0.08 38368 45089 0.20 86901 170358 0.069588 0.074703 137245 0.54 347604 0.08 27808 375413 0.074546 0.074664 281461

Value = 1008945 0.125

Path 3 1.000000 2 3 4 5 6 7 8 9 10 11


1 0.072728 1000000 0.08 80000 69029 0.20 186194 335224 0.080000 0.080000 310392 0.52 0.080000 744776 0.08 59582 59641 0.05 34257 153480 0.074546 0.077270 132253 0.53 0.072728 650878 0.08 52070 61192 0.20 117937 231200 0.080000 0.078179 184465 0.54 471749 0.08 37740 509489 0.074546 0.077270 378301

Value = 1005411 0.125

Path 4 1 2 3 4 5 6 7 8 9 10 11


1 0.088000 1000000 0.08 80000 69029 0.05 46549 195578 0.080000 0.080000 181091 0.52 0.080000 884422 0.08 70754 70824 0.05 40680 182258 0.086000 0.082996 155393 0.53 0.072728 772918 0.08 61833 72666 0.20 140050 274550 0.080000 0.081996 216742 0.54 560202 0.08 44816 605018 0.074546 0.080129 444494

Value = 997720 0.125

Exhibit APath 5 1 2 3 4 5 6 7 8 9 10 11


1 0.072728 1000000 0.08 80000 69029 0.20 186194 335224 0.080000 0.080000 310392 0.52 0.080000 744776 0.08 59582 59641 0.05 34257 153480 0.074546 0.077270 132253 0.53 0.088000 650878 0.08 52070 61192 0.05 29484 142747 0.080000 0.078179 113892 0.54 560202 0.08 44816 605018 0.086000 0.080129 444494

Value = 1001031 0.125

Path 6 1 2 3 4 5 6 7 8 9 10 11


1 0.088000 1000000 0.08 80000 69029 0.05 46549 195578 0.080000 0.080000 181091 0.52 0.080000 884422 0.08 70754 70824 0.05 40680 182258 0.086000 0.082996 155393 0.53 0.088000 772918 0.08 61833 72666 0.05 35013 169512 0.080000 0.081996 133820 0.54 665240 0.08 53219 718459 0.086000 0.082996 522269

Value = 992574 0.125

Path 7 1 2 3 4 5 6 7 8 9 10 11


1 0.088000 1000000 0.08 80000 69029 0.05 46549 195578 0.080000 0.080000 181091 0.52 0.096000 884422 0.08 70754 70824 0.05 40680 182258 0.086000 0.082996 155393 0.53 0.088000 772918 0.08 61833 72666 0.05 35013 169512 0.092600 0.086188 132277 0.54 665240 0.08 53219 718459 0.086000 0.086141 516247

Value = 985008 0.125

Path 8 1 2 3 4 5 6 7 8 9 10 11


1 0.088000 1000000 0.08 80000 69029 0.05 46549 195578 0.080000 0.080000 181091 0.52 0.096000 884422 0.08 70754 70824 0.05 40680 182258 0.086000 0.082996 155393 0.53 0.106480 772918 0.08 61833 72666 0.05 35013 169512 0.092600 0.086188 132277 0.54 665240 0.08 53219 718459 0.099860 0.089590 509741

Value = 978502 0.125

Wt. Value $997,457


Path 1• The cash flows for path 1 (the path with three

consecutive decreases in rates) consist of – $335,224 in year 1 (interest = $80,000, scheduled

principal = $69,029.49, and prepaid principal = $186,194.10, reflecting a CPR of .20)

– $324,764 in year 2, with $205,540 being prepaid principal (CPR = .30)

– $257,259 in year 3, with $173,802 being prepaid principal (CPR = .40)

– $251,560 in year 4

• The year 4 cash flow with the balloon payment is equal to the principal balance at the beginning of the year and the 8% interest on that balance.


Calculations for CF for Path 1:• $335,224 in year 1: • Interest = $80,000 • scheduled principal = $69,029.49 • prepaid principal = $186,194.10, reflecting a CPR of .20

224,335$194,186$029,69$000,80$CF

194,186$)029,69$000,000,1($20.principalprepaid

029,69$000,80$029,149$principalscheduled

000,80$)000,000,1($08.erestint

029,149$

08.)08.1/(1(1

000,000,1$p

1

10



Calculations for CF for Path 1:• $324,764 in year 2: • Interest = $59,582 • scheduled principal = $59,641 • prepaid principal = $205,540, reflecting a CPR of .30

764,324$540,205$641,59$582,59$CF

540,205$)641,59$776,744($30.principalprepaid


582,59$)776,744($08.erestint

223,119$

08.)08.1/(1(1

776,744$p

776,744$)194,186$029,69($000,000,1$Balance

2

9



Calculations for CF for Path 1:• $257,259 in year 3: • Interest = $38,368 • scheduled principal = $45,089 • prepaid principal = $173,802, reflecting a CPR of .40

259,257$802,173$089,45$368,38$CF

802,173$)089,45$594,479($40.principalprepaid


368,38$)594,479($08.erestint

456,83$

08.)08.1/(1(1

594,479$p

594,479$)540,205$641,59($776,744$Balance

3

8



Calculations for CF for Path 1:• $281,560 in year 4: • The year 4 cash flow with the balloon payment is equal to

the principal balance at the beginning of the year and the 8% interest on that balance.

560,281$856,20$703,260$CF

856,20$)703,260($08.erestint

703,260$)802,173$089,45($594,479$Balance

4



Path 8

• In contrast, the cash flows for path 8 (the path with three consecutive interest rate increases) are smaller in the first three years and larger in year 4, reflecting the low CPR of 5% in each period.

Step 3: Valuing Each Path

• Like any bond, a MBS or CMO tranche should be valued by discounting the cash flows by the appropriate risk-adjusted spot rates.

• For a MBS or CMO tranche, the risk-adjusted spot rate, zt, is equal to the riskless spot rate, St, plus a risk premium.

• If the underlying mortgages are insured against default, then the risk premium would only reflect the additional return needed to compensate investors for the prepayment risk they are assuming.

• As noted in Chapter 4, this premium is referred to as the option-adjusted spread (OAS).


• If we assume no default risk, then the risk-adjusted spot rate can be defined as

where: k = OAS

ttt kSz


• The value of each path can be defined as

where:• i = ith path• zM = spot rate on bond with M-year maturity• T = maturity of the MBS

TT

T3

3

32

2

2

1

1T

1MM

M

MPathi )z1(

CF

)z1(

CF

)z1(

CF

z1

CF

)z1(

CFV


• For this example, assume the option-adjusted spread is 2% greater than the one-year, risk-free spot rates.


Binomial Tree for

Discount Rates

8%

%6.8

7 4546%.

6 9588%.

8%

9 26%.

8 6%.

9 9860%.

7 4546%.

65080%.Z10 Z11 Z12 Z13


• From these current and future one-year spot rates, the current 1-year, 2-year, 3-year, and 4-year equilibrium spot rates can be obtained for each path by using the geometric mean:

1)z1()z1()z1(z M/11M,11110M


• The set of spot rates z1, z2, z3, and z4 needed to discount the cash flows for path 1 would be:

072289.1)06508.1)(069588.1)(074546.1()08.1(

1)z1)(z1)(z1()z1(z

074703.1)069588.1)(074546.1()08.1(

1)z1)(z1()z1(z

07727.1)074546.1()08.1(

1)z1()z1(z

08.z

4/1

4/1131211104

3/1

3/11211103

2/1

2/111102

1


• Using these rates, the value of the MBS following path 1 is $1,010,465:

465,010,1$)072289.1(

560,281$

)074703.1(

259,257$

)07727.1(

764,324$

08.1

224,335$V

432Path

1

The spot rates and values of each of the eight paths areshown in columns 9 and 10 of Exhibit A.

Step 4: Theoretical Path

• The theoretical value of the MBS is defined as the average of the values of all the interest rate paths:

• In this example, the theoretical value of the MBS issue is $997,457 or 99.7457% of its par value (see bottom of Exhibit A).

N

1i

pathiV

N

1V

Step 4: Theoretical Path

• The theoretical value along with the standard deviation of the path values are useful measures in evaluating a MBS or CMO tranche relative to other securities.

• A MBS's theoretical value can also be compared to its actual price to determine if the MBS is over or underpriced.

• For example, if the theoretical value is 98% of par and the actual price is at 96%, then the mortgage security is underpriced, '$2 cheap', and if it is priced at par, then it is considered overpriced, '$2 rich.'

Option-Adjusted Spread

• Instead of determining the theoretical value of the MBS or tranche given a path of spot rates and option-adjusted spreads, analysts can use a Monte Carlo simulation to estimate the mortgage security's rate of return given its market price.


• Since the security's rate of return is equal to a riskless spot rate plus the OAS (assuming no default risk), many analysts use the simulation to estimate just the OAS.

• From the simulation, the OAS is determined by finding that OAS that makes the theoretical value of the MBS equal to its market price.


• This spread can be found by iteratively solving for the k that satisfies the following equation:

T

1MM

M)N(

M)N(T

1MM

M)2(

M)2(T

1MM

M)1(

M)1(

)kS1(

CF

)kS1(

CF

)kS1(

CF

N

1icePrMarket

where: N = number of paths

Effective Duration and Convexity

• Effective duration and convexity can be used with a binomial tree to measure the duration of a MBS.

ratesinincreasesmallawithassociatedpriceP

ratesindecreasesmallawithassociatedpriceP

:where

20

0

0 )y()P(

)P(2PPConvexity;

y)P(2

PPDuration

Effective Duration and Convexity

• Steps for using the binomial tree to estimate duration and convexity:

1. Take yield curve estimated with bootstrapping and value the MBS (theoretical value), P0, using the calibration approach.

2. Let the yield curve estimated with bootstrapping decrease by a small amount and then estimate the price of the MBS using the calibration approach -- P-.

3. Let the yield curve estimated with bootstrapping increase by a small amount and then estimate the price of the MBS using the calibration approach -- P+.

4. Calculate effective duration and convexity.

20

0

0 )y()P(

)P(2PPConvexity;

y)P(2

PPD

Yield Analysis

• Yield analysis involves calculating the yields on MBSs or CMO tranches given different prices and prepayment speed assumptions or alternatively calculating the values on MBSs or tranches given different rates and speeds.

Yield Analysis

• For example, suppose an institutional investor is interested in buying a MBS issue that has a par value of $100M, WAC = 8, WAM = 355 months, and a PT rate of 7.5%.

• The value, as well as average life, maturity, duration, and other characteristics of this security would depend on the rate the investor requires on the MBS and the prepayment speed she estimates.

Yield Analysis

• If the investor’s required return on the MBS is 9% and her estimate of the PSA speed is 150, then she would value the MBS issue at $93,702,142.

• At that rate and speed, the MBS would have an average life of 9.18 years. Whether a purchase of the MBS issue at $93,702,142 to yield 9% represents a good investment depends, in part, on rates for other securities with similar maturities, durations, and risk, and in part, on how good the prepayment rate assumption is.

• For example, if the investor felt that the prepayment rate should be 100% PSA and her required rate with that level of prepayment is 9%, then she would price the MBS issue at $92,732,145 and the average life would be 11.51 years.

Yield Analysis

• In general, for many institutional investors the decision on whether or not to invest in a particular MBS or tranche depends on the price the institution can command.

• For example, based on an expectation of a 100% PSA, our investor might conclude that a yield of 9% on the MBS would make it a good investment. In this case, the investor would be willing to offer no more than $92,732,145 for the MBS issue.

Yield Analysis

• One common approach used in conducting a yield analysis is to generate a matrix of different yields by varying the prices and prepayment speeds.

• The next exhibit shows the different values for our illustrative MBS given different required rates and different prepayment speeds.

• Using this matrix, an investor could determine, for a given price and assumed speed, the estimated yield, or determine, for a given speed and yield, the price. Using this approach, an investor can also evaluate for each price the average yield and standard deviation over a range of PSA speeds.

Yield and Vector Analysis

Mortgage Portfolio = $100M, WAC = 8%, WAM = 355 Months, PT Rate = 7.5

Rate/PSA 50 100 150

7%8%9%

10%

Average Life

Rate7%8%9%

10%

Value$106,039,631$98,251,269$91,442,890$85,457,483

14.95

VectorMonth Range: PSA

1-50: 20051-150: 250

151-250: 150251-355: 200

Value$103,729,227$98,893,974$94,465,328$90,395,704

Value$105,043,489$98,526,830$92,732,145$87,554,145

11.51


1-50: 20051-150: 300

151-250: 350251-355: 400

Value$103,473,139$98,964,637$94,794,856$90,929,474

Value$104,309,207$98,732,083$93,702,142$89,146,871

9.18


1-50: 20051-150: 150

151-250: 100251-355: 50

Value$104,229,758$98,756,37093,826,05389,,364,229

Yield Analysis

• One of the limitations of the above yield analysis is the assumption that the PSA speed used to estimate the yield is constant during the life of the MBS.

• In fact, such an analysis is sometimes referred to as static yield analysis.

• In practice, prepayment speeds change over the life of a MBS as interest rates change in the market.

Vector Analysis

• A more dynamic yield analysis, known as vector analysis, can be used.

• In applying vector analysis, PSA speeds are assumed to change over time.

• In the above case, a matrix of values for different rates can be obtained for different PSA vectors formed by dividing the total period into a number of periods with different PSA speeds assumed for each period.

• A vector analysis example is also shown at the bottom of the last exhibit.

Securitization and Mortgage-Backed Securities

Economy & Finance

Transcript of Securitization and Mortgage-Backed Securities