PSJ Model Guidebook. Prepared: March 2011 Revised: April 2016 Japan Securities Dealers Association PSJ Calculation Statistics Council

Transcription

1 PJ Model Guidebook Prepred: Mrch 0 Revised: April 06 Jpn ecurities Delers Assocition PJ Clcultion ttistics Council

2 Tble of Contents Forwrd to the English Lnguge Version... Forwrd to the Jpnese Lnguge Version... Chpter Purpose for Introducing the PJ Model... Chpter MB Prepyments... 6 ection cheduled Repyments nd Prepyments of Mortgges... 6 ection CPR nd MM... 8 ection Exmple of the Use of CPR nd MM with JHF MB... Chpter PJ Model tndrd Model... ection The Development Concept of the tndrd Model... ection Definitions... ection Process of Producing Csh Flows for JHF MB using the tndrd Model... 5 ection 4 Exmple of Appliction for Risk Mngement... Chpter 4 PJ Model Customized Model... 7 ection The Development Concept of the Customized Model... 7 ection Definitions... 8 ection Process of Producing Csh Flows for JHF MB using the Customized Model... 4 Afterword to the Jpnese Lnguge Version Appendix Mesures towrd the Estblishment of n Infrstructure for the MB Mrket in Jpn Appendix Formt for PJ Clcultion ttisticl Vlues Report: Averge Vlues... 54

3 The mendment in April 06 is s follows: Amendment Originl text 0 Deleted 0 With PJ clcultion sttisticl vlues, the PJ clcultion vlues reported by prticipting JDA member firms when interest rtes chnge re premised on prllel shift in the yield curve. As result, if the interest rte is negtive, the clcultion is done using 0%.

4 Forwrd to the English Lnguge Version In 006, the Jpn ecurities Delers Assocition (hereinfter referred to s the JDA ) begn to operte the Prepyment tndrd Jpn (PJ) model creted bsed on discussions by its Working Group on Jpn Version of the PA Model (hereinfter referred to s the WG ). In conjunction with tht event, JDA lso published the PJ Model Guidebook. The introduction of the PJ Model enbled mrket prticipnts to enjoy the convenience of using common price levels, spred vlutions, nd other fctors bsed on the sme expected csh flows, which improved pricing trnsprency in the mortgge bcked securities (MB) mrket. Currently, use of the PJ model s stndrd mesure for the prepyment rtes hs fully penetrted Jpn s MB mrket in both the primry nd secondry mrkets. brokerdelers prticipte in the PJ Clcultion ttistics Council set up to crry on the work of the WG, continuing to provide PJ clcultion dt to the mrket nd endevoring to mintin nd improve the convenience of the PJ model. In other relted events, the Jpnese government introduced preferentil tx tretment for non-resident holders of Jpnese municipl nd corporte bonds in June 00. It is hoped tht more mesures will be introduced in future to increse the prticiption of foreign investors in the domesticlly issued MB mrket. As with the Jpnese version of this guidebook, we hope tht use of the English version by cross border mrket prticipnts will contribute to the growth of the MB mrket in Jpn. Mrch 9, 0 JDA PJ Clcultion ttistics Council

5 Forwrd to the Jpnese Lnguge Version In November 005, fter receiving joint proposl from severl brokerdelers hndling mortgge bcked securities (MB) regrding introducing stndrd mesure for mrket prticipnts to use for prepyment rtes, the Jpn ecurities Delers Assocition (JDA), estblished Working Group on Jpn Version of the PA Model under its ecurities trtegy Bord nd begn delibertions. Over the ensuring period nd fter gret del of energetic discussion, the working group cme up with the PJ model. The ecurities trtegy Bord formlly pproved the introduction of this model on April 4, 006. Put simply, the PJ model is n esy-to-use mthemticl model for expressing MB prepyment scenrios. The model hs been rendered usble for lrge rnge of mrket prticipnts by gretly simplifying its form. Moreover, becuse the model ws designed to reflect the specil chrcteristics of the prepyment rte of MB, which re known to move in specific wy over time, it is reltively esy to express vriety of prepyment scenrios over certin timefrmes using stndrd mesure for mrket prticipnts. This guidebook ws creted with those coming into contct with the PJ model for the first time in mind. It ims to promote the widespred use of the model by providing s simple s possible explntions of the purpose for introducing the model, definitions, prcticl use of the model, nd other points. It is hoped tht growing use of the PJ model will fmilirize mny more mrket prticipnts with the prepyment rtes nd csh flow nlysis of MB, leding to greter ctivity in the MB secondry mrket nd contributing to improved mrket liquidity. April 4, 006 JDA Working Group on Jpn Version of the PA Model Plese refer to Appendix : Mesures towrd the Estblishment of n Infrstructure for the MB Mrket in Jpn

6 Chpter Purpose for Introducing the PJ Model In nlyzing the investment vlue of n MB issue, it is importnt to be ble to project contingent csh flows bsed on fixed ssumption of the prepyment rte. While certin portion of mrket prticipnts cn ssess the investment vlue of n MB issue on their own using complex prepyment models creted bsed on their own nlysis to estimte csh flows by projecting prepyment rte, not ll mrket prticipnts re cpble of doing so. Therefore, to pursue the further development of the MB mrket, wht is needed is common metric for prepyment rtes tht cn be used in prcticl terms by much lrger number of mrket prticipnts to nlyze investment vlue. To tht end, the working group hs creted the Prepyment tndrd Jpn model (PJ model). Produced s prt of efforts to develop the mrket infrstructure from the perspective of the role the securities industry should ply in Jpn s MB mrket, it is ment to serve s stndrd mesure for the chrcteristic prepyments of MB. The significnce of the introduction of the PJ model produced by the working group is s follows.. MB nd prepyments The mjor chrcteristic of MB finncil instruments is tht prepyments re mde to MB holders bsed on the pss-through of the prepyments mde to the underlying mortgge pool. Currently, the most widely used mesures for expressing prepyment rtes by mortgge pools nd prepyment rtes on MB re MM nd CPR 4. The former expresses the monthly prepyment rte for mortgge pools s percentge, while the ltter expresses it s n nnulized prepyment rte in percentge (in terms of ctul use, the CPR is the most commonly used mesure).. Importnce of prepyment rte in nlysis of investment vlue of MB From the point of view of mrket prticipnts, the determintion of ssumptions bout the prepyment rte is extremely importnt. Contrry to the fixed csh flows of regulr bullet bond tht is redeemed in lump sum t mturity, the nlysis of the investment vlue of the MB depends on the Acronym for Mortgge Bcked ecurities. The term is generlly used for housing lon (residentil mortgge lon) bcked securities or trust beneficiry rights. Housing lon bcked securities nd trust beneficiry rights re sometimes referred to s RMB (Residentil Mortgge Bcked ecurities) when it is necessry to distinguish them from CMB (Commercil Mortgge Bcked ecurities) which re secured by commercil property lons. ingle Monthly Mortlity 4 Conditionl Prepyment Rte or Constnt Prepyment Rte

7 contingent csh flows. Put in nother wy, if n ssumed prepyment rte is not used to project csh flows, the product cnnot be priced. It is possible for mrket prticipnts to nlyze the Jpn Housing Finnce Agency (JHF) s publicly nnounced historicl mortgge repyment dt nd other dt nd predict the CPR of n MB issue. Currently, ech mrket prticipnt must use its own methods bsed on nlysis to build complex model, estimte future CPR, nd use it to clculte nd evlute csh flows. In determining the prepyment rte trend mong MB, it is well known tht the CPR will vry in ccordnce with the interest rte climte. It lso hs been recognized through experience tht the CPR will follow certin trend over time from the origintion of the lon.. Necessity of mrket prticipnts using common stndrd in order to confer on prepyment rte for n MB issue As noted in. bove, ech of the mrket prticipnts will rrive t different trend for the future prepyment rtes of n MB issue. ince ech of the mrket prticipnts will come up with different evlutions for the csh flows even for the sme MB issue, these vritions will result in different prices even if the mrket prticipnts use the sme spred (discount curve) 5. Of course, these differing views of MB csh flows by mrket prticipnts re not problem in themselves. Nevertheless, becuse not ll of the mrket prticipnts re cpble of doing these clcultions, without common mesure in the MB mrket to enble comprison of these differing views of csh flow, mny investors will hve difficulties in nlyzing the investment vlue of MB. This condition could crete n obstcle to the future expnsion of the investor bse in the MB mrket. For tht purpose, it is necessry to hve stndrd prepyment model tht includes vritions in CPR over time. This model will serve s simple mesure of CPR tht cn be used prcticlly by mny more mrket prticipnts in their nlysis of MB investment vlue. With this thinking in mind, in 985, the Public ecurities Assocition, currently the ecurities Industry nd Finncil Mrkets Assocition (IFMA) introduced the Prepyment peed Assumption Model (PA model) in the United ttes. The model continues to be widely used by mrket prticipnts. 4. ignificnce of the introduction of the PJ model hould the PJ model become widely used by mrket prticipnts nd be commonly recognized by mrket prticipnts s stndrd mesure for MB 5 The spred is the difference between the yield curve for government bond pr yields, or swp rte, or other rte tht becomes the stndrd yield curve nd the yield curve of the MB. In discounting the vlue of the expected csh flows of the MB to their present vlues, it is norml to use yield curve tht includes certin spred on the stndrd yield curve (discount curve). 4

8 prepyment rtes tht tkes into ccount the clssic behvior of prepyments, which reflect the sesoning fctor by month, the working group considers tht it would hve the following significnce from the point of view of development nd expnsion of the MB mrket. It would become possible for mrket prticipnts to confer on the MB prepyment rte bsed on much more detiled set of prerequisites. When multiple brokerdelers nnounced their own projected pre-pyment rtes, inputting ech compny s projected prepyment rte into the PJ model would enble comprison of the differences in ech prepyment rte using common mesure. Providing simple function-bsed model s common pltform for mrket prticipnts would fcilitte evlution nd understnding of expected csh flows by trnsction counterprties, which cn be expected to broden the investment field for mrket prticipnts. In future, when n MB-secured CMO 6 mrket emerges in Jpn, it would be possible to structure products premised on common understnding of MB prepyment rtes, which cn be expected to llow wider rnge of product structures. The model would enble simpler nd more convenient wys to mnge MB risks using expected prepyment rtes. 6 An cronym for Collterlized Mortgge Obligtion. A generl term for rtificilly creted multiple clss finncil products secured by csh flows from residentil mortgge pools or MB (pss-through securities of residentil mortgge pools). CMOs cn be structured with wide rnge of risk profiles. 5

9 Chpter MB Prepyments In this chpter, we review the fundmentl thinking bout prepyments, specil nd importnt fctor in MB products. ection cheduled Repyments nd Prepyments of Mortgges Principl repyments on MB occur ccording to the principl repyments by the underlying mortgge pool. The two mjor resons for principl repyments re scheduled repyments nd prepyments.. cheduled repyments Bsed on the mortgge lon greement, monthly or semi-nnul repyment schedule is determined for mortgge lon. While principl nd interest equl repyment nd principl equl repyment methods re both vilble, generlly borrowers choose the former, in which the mount of monthly or semi-nnul repyment is fixed sum. ince the mount of the repyment nd the schedule re bsed on the mortgge lon greement, the mount of the lon, the interest rte, nd the term of the mortgge vry by individul mortgge lon. The plnned repyment determined by the greement is clled the scheduled repyment.. Prepyments cheduled repyments tke plce only ccording to the mortgge lon greement, but with mortgge lons, the borrower or the subrogtion rights holder hve the right to mke repyments hed of schedule. For tht reson, when considering the csh flows from MB secured by mortgge pool, it must be ssumed tht some principl pyments will occur hed of schedule. These erly principl repyments from the mortgge pool nd erly pyments from MB re termed prepyments. On mortgge lon level, the following re the two min types of prepyments of principl. () Advnce repyment The following re the two types of dvnce repyments tht borrower of mortgge lon my mke.. Prtil dvnce repyment In prtil dvnce repyment the mortgge lon debtor uses surplus funds, etc. to py bck portion of the lon hed of schedule. When prtil dvnce repyment is mde on mortgge lon, the repyment schedule must be reclculted for the remining principl. There re two wys in which the new schedule cn be mde: either the monthly or semi-nnul repyment mounts re kept the sme nd the period of the lon is shortened (hereinfter referred to s the term-reduction type ), or the period of the lon is kept the sme nd the monthly or semi-nnul repyment mounts re reduced (hereinfter referred to s the pyment-reduction type ). 6

10 b. Full dvnce repyment In full dvnce repyment, in ddition to using surplus funds, etc., the debtor my refinnce the lon or sell the residence nd move, resulting in full dvnce repyment of the outstnding lon blnce in lump sum. () ubrogtion, etc. When debtor becomes unble to mke scheduled repyments ccording to schedule, the following types of subrogtion my tke plce. However, becuse of the impct of pyment delinquencies, mortgge lon defults, subrogtion, nd other events on the csh flows of MB differs ccording to the structure of MB, the effect must be confirmed for individul products.. ubrogtion settlement by lon gurntee compny When the debtor is no longer ble to py the lon becuse heshe hs gone bnkrupt, etc., the lon gurntee compny repys the full mount of the outstnding lon on behlf of the debtor. b. ettlement with life insurnce proceeds When the debtor dies, the outstnding lon is fully repid using the proceeds from group life insurnce contrct under which the debtor ws insured. * In the cse of JHF MB In the cse of Jpn Housing Finnce Agency MB nd Government Housing Lon Corportion (GHLC) MB (together referred to below s JHF MB ) 7, the mortgge lon for which the unforeseen chnge in the repyment schedule hs occurred is removed from the underlying ssets nd ) replced with sound lons held by JHF in the cse of monthly MB issued during the GHLC er nd -series MB or ) JHF mkes prtil pyment of the principl of the MB in the mount of the removed lon in the cse of monthly MB issued by JHF. 7 Currently, JHF issues monthly MB secured by the mortgge pool it purchses monthly nd -series MB bcked by mortgges originted by GHLC. The Government Housing Lon Corportion (GHLC) is the predecessor of the Jpn Housing Finnce Agency (JHF). 7

11 ection CPR nd MM The pyment of MB principl occurs in ccordnce with the repyment of principl by the underlying mortgge pool. As previously mentioned, these lon pyments cn be roughly divided into scheduled repyments nd prepyments.. MM The ingle Monthly Mortlity (MM) indictes the monthly prepyments by the mortgge pool nd is the most bsic figure for clculting the prepyment rte. The detiled clcultion for MM is to divide the prepyment mounts incurred for the bse month by the scheduled principl blnce for the bse month (the principl blnce for the previous month less the scheduled repyments for the bse month). PPT PPT MM (%) = 00 = 00 (Formul --) O CO0 PP CO :Principl blnce of month previous to bse month 8 0 PP :cheduled repyments for bse month 9 PPT : Prepyments for bse month 0 O : cheduled principl blnce for the bse month ( = CO 0 PP ). CPR The ConditionlConstnt Prepyment Rte is the nnulized rte of the monthly clculted MM. The CPR is clculted using the following formul bsed on the MM. (%) MM CPR = 00 (Formul --) 00 Conversely, the MM cn be derived from the CPR by reversing the clcultion shown in (Formul --) bove, using the following formul. CPR MM (%) = 00 (Formul --) 00 8 CO: Current Outstnding 9 cheduled Principl Pyment 0 Prepyment cheduled Outstnding 8

12 . Long-term CPR The monthly CPR of mortgge pools differs by pool (smple group). Its term structure is determined bsed on such fctors s the nnul sesoning structure nd the Weighted Averge Lon Age (WALA) from the origintion of the lon. (Chrt --) Reltionship between WALA s derived from publicized dt from JHF nd CPR 60% 50% 40% CPR(%) 0% 0% 0% 0% Accrued 経過月数 Months (WALA) (WALA) (ource: Produced by WG bsed on historicl dt publicized by JHF) As result, the monthly CPR of n MB issue is not ctully uniform, it bsiclly vries every month. In order to express the expected time series of the monthly CPR s uniform CPR for descriptive purposes, the long term CPR (LTCPR) is used. Ordinrily, when Expected CPR is used regrding MB, it mens the LTCPR. Generlly, the LTCPR indicted by brokerdelers is figure clculted so tht the weighted verge life (WAL) of the MB derived using the CPR nd the WAL of the MB derived from the monthly CPR predicted with time series deduced using self-developed prepyment model re the sme. If you grph the LTCPR ginst WALA, it forms stright line prllel to the X xis. The LTCPR, therefore, cn be sid to be the simplest prepyment model for creting the expected csh flows of n MB issue with term structure. 9

13 (Chrt --) Reltionship between WALA nd LTCPR CPR(%) Accrued 経過月数 Months (WALA) (WALA) 0

14 ection Exmple of the Use of CPR nd MM with JHF MB In this section, using JHF MB, we will explin in detil how the CPR nd MM re used in determining the csh flows from the MB expected prepyment rte.. Fctor nd cheduled Fctor The fctor sets the lon principl blnce of the mortgge pool securing the MB t the point of collection corresponding to issue dte of the MB s, with the outstnding lon principl blnce t collection point corresponding to ny point of time fter issue dte being or less. It is clculted using the following formul. CO F = (Formul --) OO F : Fctor CO :Outstnding lon principl blnce t collection point corresponding to ny given point in time OO :Outstnding lon principl blnce t collection point corresponding to issue dte of MB On the other hnd, with MB, the fctor sets the originl fce vlue of the MB t issue (hereinfter referred to s Originl Fce ) s, with the outstnding fce vlues t ny given point in time (hereinfter referred to s Current Fce ) being or less. The fctor is clculted using the following formul. Most MB in Jpn re structured using the senior portion of the mortgge pool fter removing the subordinted portion of lons or the overcollterliztion portion. However, it should be pointed out tht for MB tht utilize credit enhncement system with sequentil py for seniorsubordinted structure, the mortgge pool fctor nd the MB fctor will not be the sme. CF F = (Formul --) OF F : Fctor CF :Actul fce vlue blnce t ny given point in time 4 OF :Fce vlue blnce t point of issue of MB 5 OO: Originl Outstnding equentil py is pyment system where the underlying ssets hve been securitized into multiple clsses of securities for which the principl pyments from the underlying ssets re mde to ech clss in predetermined order. For exmple, if the securitized product hd three senior-sub trnches of A, B, nd C, principl pyments from the underlying ssets would ll go to trnche A until its principl ws completely returned, with principl pyments then shifting to trnche B nd finlly C. This type of pyment system is commonly seen with senior-sub MB in the privte sector. 4 CF: Current Fce 5 OF: Originl Fce

15 The formul cn be rrnged s follows to derive the current fce vlue blnce from the originl fce vlue blnce by multiplying by the fctor. CF = OF F (Formul --) The cheduled Fctor expresses the time series of monthly MB fctors if the underlying mortgge lons in the pool mke their principl pyments ccording to the repyment schedule (CPR is 0%). At the very lest, for regulr MB, the cheduled Fctor for the pool cut off dte 6 is mde public t the time of issue.. JHF MB Fctor In the cse of JHF MB, JHF designs its products so tht the Fctor of the underlying mortgge pool (entrusted mortgge pool) t the end of collection month is lwys the sme s the Fctor of the MB on the principl nd interest pyment dte of the corresponding collection month. In other words, lthough there will be difference in the clcultion process of the cheduled Fctor bsed on lon blnce for the entrusted mortgge pool or on the MB fce vlue blnce, since the principl repyments of the mortgge pool nd the principl pyments of the MB re lwys conducted on pro rt bsis, the fctors will lwys be the sme. However, it should be noted tht time lg cn occur in either the ctul collection of repyments from the mortgge or the principl nd interest pyments of the MB. For exmple, with the No. 9 GHLC MB issued on Februry 8, 006 (hereinfter referred to s the No.9 GHLC issue ), while the MB Fctor for the issue dte is, the Fctor for the entrusted mortgge pool is t the end of December 005. imilrly, the Fctor pplied on the No. 9 JHF issue principl nd interest pyment dte of Mrch 0, 006, corresponds to the Fctor of the entrusted mortgge pool t the end of Jnury 006. In other words, the Fctor pplied on the monthly principl nd interest pyment dte of JHF MB is the entrusted mortgge pool Fctor on the lst dy of the month two months previous to the principl nd interest pyment dte.. JHF MB cheduled Fctor When issuing JHF MB, JHF mkes public on its Web site the entrusted mortgge pool cheduled Fctor, the Actul Fctor for the issued MB, the Initil cheduled Fctor, nd the Rescheduled Fctor, which reclcultes the impct of prepyments nd lon replcements, etc. every six months following the issue. 6 Dte on which the lons to be included in the housing lon pool securing the MB re determined.

16 4. Method of clculting the expected principl pyment mounts of JHF MB bsed on expected CPR Using the expected CPR of JHF MB, the project principl pyment mounts cn be clculted. For the purposes of explining the process using mthemticl formul, we hve first put together list of the definitions of the nottions used in the following section (Plese see Tble --).

17 (Tble --) Definitions Used in this ection 0 : The bse monthly principl nd interest (P&I) pyment dte. The dte is the initil clcultion dte when the initil clcultion dte is the issue dte or P&I pyment dte. When the initil clcultion dte is not either of these dtes, the dte is the P&I pyment dte immeditely previous to the initil clcultion dte (provided tht when the initil clcultion dte flls before the first P&I pyment dte, the issue dte is used). : The number of months tht hve elpsed since the bse monthly P&I pyment dte ( =,,,Λ) : the th P&I pyment dte following the bse monthly P&I pyment dte. CPR : The expected CPR for P&I pyment dte MM : The expected MM for P&I pyment dte AF 0 : The ctul fctor 7 for JHF MB on the bse monthly P&I pyment dte 0 F 0 : The individul figures of the cheduled Fctor corresponding to the bse monthly P&I pyment dte 0 (provided, however, tht if there is no ltest cheduled Fctor equivlent to F 0, F 0 = AF 0 ) 8 mong the ltest publicly nnounced JHF scheduled fctors (the most recent of either the Initil cheduled Fctor nnounced t time of issue or the Rescheduled Fctor nnounced periodiclly fter issue). F : The individul figures of the cheduled Fctor corresponding to the P&I pyment dte mong the ltest publicly nnounced JHF scheduled fctors (the most recent of either the Initil cheduled Fctor nnounced t time of issue or the Rescheduled Fctor nnounced periodiclly fter issue). EF : The expected fctor corresponding to the P&I pyment dte 9 OF: Originl fce vlue CF 0 : The current fce vlue blnce of the bse monthly P&I pyment dte 0 ECF : Expected current fce vlue blnce corresponding to the P&I pyment dte 0 EP : Expected principl pyment mount fter considering prepyments corresponding to the P&I pyment dte. C: Coupon rte on JHF MB AI : Actul interest mount corresponding to the P&I pyment dte EI : Expected interest mount corresponding to the P&I pyment dte. ( ) 7 AF: Actul Fctor 8 F: cheduled Fctor 9 EF: Expected Fctor 0 ECF: Expected Current Fce EP: Expected Principl AI: Actul Interest EI: Expected Interest 4

18 () Clcultion of MM bsed on expected CPR First, using (Formul --), the expected MM for the next month is clculted using the expected CPR for the next month. CPR (%) MM = 00 (Formul --4) 00 For exmple, if the expected CPR for the next month ws 6%, the expected MM for the next month would be clculted in the following wy. Expected MM(%) corresponding to expected CPR6% 6 = 00 = 0.54(%) (Formul --4 ) 00 () Importnt ssumptions in deriving MB csh flows Here, we will explin importnt ssumptions tht re prerequisites to deriving expected csh flows for MB. When prepyment occurs in the mortgge pool (entrusted mortgges) securing the MB, it is expected to hve n impct on the principl blnce schedule (cheduled Fctor) bsed on the initil scheduled repyments due to the reduction of principl resulting from the full dvnce repyment or prtil dvnce repyment of the individul lons (the sme effect occurs with lon replcement). However, keeping trck of the chnges in the principl blnce schedule of individul lons in entrusted mortgge pool of multiple lons is impossible in prcticl terms. Therefore, the following ssumptions re generlly mde regrding the method of describing future principl csh flows (principl pyment mounts) tking into considertion prepyments from the entrusted mortgge pool. Assumptions Entrusted mortgge pool comprise innumerble, smll mortgges with csh flows bsed on the sme cheduled Fctor. 4 All of the debtors of the mortgges belonging to the entrusted mortgge pool will only choose to mke full or prtil (pyment-reduction type) dvnce repyments on principl (there will be no chnges in schedule from termreduction type prtil dvnce repyments or other resons). 5 4 In fct, the principl mounts nd scheduled repyments of individul mortgges in the mortgge pool vry, but this ssumption is mde for the ske of simplifying the clcultion. 5 In fct, debtors often choose to mke term-reduction type prtil repyments, but this ssumption is mde for the ske of simplifying the clcultion. 5

19 Premised on these ssumptions, principl blnce without considering prepyment t the next P&I pyment dte cn be clculted from the principl blnce t the bse point nd cheduled Fctor t the next P&I pyment dte. Reducing this mount by the proportion tking into considertion the expected prepyment to be pplied on the next P&I pyment dte Expected, 00MM gives the expected principl blnce (ECF blnce) for the next P&I pyment dte. When the figure for the Actul or Expected Fctor differs from tht of the previously nnounced cheduled Fctor for sid month, bsed on the previously mentioned ssumptions, the fct tht the rtio of the cheduled Fctors of the bse month nd the next month will be the sme s the rtio of the Actul or Expected Fctor for the bse month nd the cheduled Fctor for the next month tht hs been djusted for the previous month s Actul or Expected Fctor cn be used to clculte the djusted cheduled Fctor for the next month. By repeting the process for ll following P&I pyment dtes, the expected principl blnces for ech future P&I pyment dte cn be clculted. By describing the expected principl blnces for ech P&I pyment dte in time series, the reduction in the outstnding principl blnce from the previous P&I pyment dte cn be clculted for ech P&I pyment dte nd used to describe principl csh flow tking into considertion prepyments. The detil process is introduced below. () Clculting the Expected Principl Blnce Now, bsed on the thinking bove in (), in order to determine the expected principl blnce (ECF), we first pply the expected MM for the next month, the Actul Fctor of the bse month, the cheduled Fctor of the bse month nd the next month to determine the Expected Fctor for the next month. F = MM EF AF0 (Formul --5) F0 00 * The following clcultion method is used to determine the Expected Fctor for the second month hed using the Expected Fctor for the first month hed nd the Expected MM of the second month hed. F = MM EF EF (Formul --6) F 00 Next, ccording to (Formul --), the expected principl blnce for the next month cn be determined by multiplying the initil fce vlue blnce of the MB by the Expected Fctor for the next month clculted bove. ECF = OF EF (Formul --7) * When clculting the expected principl blnce for two months hed, the following formul is used. ECF = OF (Formul --8) EF 6

20 (4) Clculting Expected Csh Flows In ddition, by multiplying the initil fce vlue blnce by the difference between the Actul Fctor of the bse month nd the Expected Fctor of the next month (the sme s subtrcting the expected fce vlue blnce for the next month from the Current Fce Vlue blnce of the bse month), the Expected Principl Prepyment Amount for the next month cn be determined. EP ( AF ) OF 0 EF = (Formul --9) * When clculting the Expected Principl Prepyment Amount for two months hed, the following formul is used. EP = OF ( EF EF ) (Formul --0) Finlly, using the Current Fce Vlue Blnce for the bse month s bse, you cn determine the interest pyment mount for the next month (ince the Current Fce Vlue for the bse month is decided, the next month s interest pyment is fixed figure). AI = OF AF C (Formul --) 0 * Only in the cse of the first interest pyment dte, the in the bove formul is the ctul number of dys from the issue dte to the first interest pyment dte (Counting only one of strt dte or end dte)65. * When determining the Expected Interest Pyment mount for two months hed, the formul becomes the following (the Current Fce Vlue for the next month is n expected figure, therefore, so is the interest rte mount for two months hed). EI = OF EF C (Formul --) In this mnner, following (Formul --5), (Formul --6), (Formul --7), nd (Formul --8), the monthly Expected Fctor nd the Expected Current Fce Vlue blnce cn be successively determined using the monthly cheduled Fctor. By using (Formul --9) nd (Formul --0) to clculte monthly expected principl pyment mounts nd (Formul --), nd (Formul --) to clculte monthly expected interest pyment mounts, the expected csh flows cn be derived using the Expected CPR for JHF MB. An ctul exmple of the time series of the bove process is shown in (Chrt --), while exmples of the ctul clcultions re shown in (Chrt --) nd in (Chrt --4). 7

21 (Chrt --) Process for Deriving JHF MB Csh Flows Using Expected CPR Expected P&I Dte Expected MM Expected Fctor CPR AF (Actul) 0 CPR CPR (%) MM = CPR CPR (%) MM = CPR CPR (%) MM = F = MM EF AF0 F 00 0 F = MM EF EF F 00 F = MM EF EF F 00 CPR F CPR (%) MM = 00 = MM 00 EF EF F 00 * The formul for determining the Expected Fctor does not tke into considertion the 0% Clen Up Cll 6 ttched to JHF MB. When expressing expected csh flows tking into considertion the 0% Clen Up Cll, it must be replced with the following formul. F MM EF (Formul --) F 00 EF = 0 ( EF 0. ) = EF EF ( > 0.) P&I Dte 0 Expected Current Fce Expected Principl Expected Interest Amount Vlue Blnce Pyment Amount CF (Actul) ECF = OF EF EP = OF ( AF0 EF ) AI = OF AF0 C * (Actul) ECF OF EF = EP OF ( EF EF ) = OF EP OF ( EF ) ECF EF = EI = OF EF C EF = OF EF C = EI ECF = OF EF EP = OF ( EF EF ) EI = OF EF C * When is the issue dte, is replced with the ctul number of dys from the issue 0 dte to the first interest pyment dte (Counting only one of strt dte or end dte)65. * * * * 6 When the outstnding blnce of JHF MB flls below 0% of the issue mount, s the issuer, JHF hs the right to mke n erly redemption in the full mount (0% Clen Up Cll). JHF cn exercise this right s of the P&I pyment dte following the P&I pyment dte on which the Current Fce Vlue Blnce of the JHF MB flls to 0% or less of the Initil Fce Vlue Amount (Fctor flls to 0. or less) 8

22 (Chrt --) Actul exmple of derivtion of csh flows for No. 9 GHLC MB (.84% coupon rte; Februry 8, 006 issue dte; Mrch 0, 006 initil P&I pyment dte; billion initil fce vlue mount). Does not tke into considertion the 0% Clen Up Cll nd uses LTCPR of 5.5% s the Expected CPR. (Mrch 0, 006 initil clcultion dte) * The bove clcultions hve not djusted for frctions nd interest pyments flling on holidys hve not been tken into ccount. 9

23 (Chrt --4) Actul exmple of derivtion of csh flows for No. 9 GHLC MB (.84% coupon rte; Februry 8, 006 issue dte; Mrch 0, 006 initil P&I pyment dte; billion initil fce vlue mount). Tkes into considertion the 0% Clen Up Cll nd uses LTCPR of 5.5% s the Expected CPR. (Mrch 0, 006 initil clcultion dte) * The bove clcultions hve not djusted for frctions nd interest pyments flling on holidys hve not been tken into ccount. 0

24 Chpter PJ Model tndrd Model In this chpter, we cover the development concept, definitions, nd method of use for the PJ model (stndrd model) creted by the JDA. ection The Development Concept of the tndrd Model While the use of the stndrd model is not necessrily limited to JHF MB, the continuous growth in issunce by the JH MB suggests it will become centrl product in Jpn s MB mrket. In ddition, given tht t this point in time the dt provided by JHF is the only dt on mortgge lons prepyments tht is vilble to ll mrket prticipnts, the working group decided tht it ws pproprite to crete stndrd model with the bsic form of the speed of prepyments determined using dt mde public by JHF becuse mrket prticipnts would gree with this method. The stndrd model ws developed for the purpose of providing common mesure for mrket prticipnts to be used for determining expected csh flows (premised on expected CPR) of JHF MB. For the mesure to be shred by mrket prticipnts, the working group decided tht its form must be simple (few prmeters) not complicted. Therefore, in deciding the form of the model, the working group used s reference the PA model introduced to the MB mrket in the United ttes for the sme resons nd ging fctors (chnges in the CPR over the durtion of lons), etc., tht could be observed from the historicl dt on prepyment provided by JHF. Discussion bout the form of the stndrd model in the working group during the process of deciding its form focused on the following three points. () The CPR t zero months (Initil CPR) () The number of months until the CPR becme fixed (number of sesoning months) () The level t which the CPR becme fixed (flt CPR) 7 If the bove points () to () were vrible for the stndrd model, premised on use with JHF MB, it would increse the number of prmeters of the model, possibly creting brrier to its prcticl use (shring mong mrket prticipnts or clcultion of sttisticl figures etc.). In considertion of tht point, the working group decided to use predetermined () initil CPR nd () sesoning months, giving priority to improving the ese of use of the model by utilizing only the verticl movement of the flt CPR to express the speed of prepyments. 7 It ws decided tht introducing burnout would not work well with the PJ model becuse stndrd form would not be possible since the impct of burnout depends on the pth interest rtes tke. Burnout is phenomenon where even if interest rtes fll providing n incentive for greter prepyments, the CPR does not rise nd my fll. One exmple of this phenomenon is when mortgge pool tht hs lredy experienced rise in CPR following reduction in interest rtes in the pst resists increses in its CPR when experiencing new declines in interest rtes.

25 Detils re s follows: Form of tndrd Model () Although the historicl dt on prepyments provided by JHF suggests certin initil CPR could be determined, giving priority to setting speed of pyment tht is esy to use, the initil CPR hs been set t 0%. () The number of sesoning months lies between five to six yers ccording to the historicl dt. As result, 5 yers (60 months) hs been chosen s round nd esy-to-understnd number. () As vrible number, the flt CPR s 00% hs not been set s in the U.. PA model, but llowed to express prepyment rte bsed on the point t which the CPR becomes level on grph.

26 ection Definitions. Nme of model nd overview of functionl form The stndrd model shll be generlly known s the PJ model. The functionl form sets CPR of 0% for n MB issue (or mortgge pool) in the lon origintion month (WALA is 0 months). After initition, the CPR rises fixed rtio monthly, reching CPR of r% fter 60 months, fter which the CPR follows fixed pth t r%. This form is termed r%pj. The ctul method of expression of the speed of prepyment would be, for exmple if the flt CPR ws 8%, 8%PJ.. Formul definitions As previously mentioned, the PJ model hs n initil CPR of 0% nd sesoning period of 60 months. Therefore, if the r%pj hs CPR t n ge (WALA) of m months (CPR m ), it cn be expressed s the following formul. r CPR m = min m, r 60 (%) ( 0) r (Formul --) Conversely, bsed on the PJ model (tndrd Model), the vlue PJm (%) tht gives the instntneous velocity for the Actul CPR (R%) when WALA is m months cn be expressed s follows. PJ m (%) = R m 60 ( m 60) (Formul --) PJ m (%) = R ( m > 60) * For the ge in months (WALA), m, we use the WALA t the point of the monthly pyment collection on the mortgge pool underlying the MB. With JHF MB, the WALA is listed in the Entrusted Cndidte Mortgges Relted Dt nd the Entrusted Mortgges Relted Dt from the point of issue strting with the issue priced in Februry 006 (GHLC Monthly MB No. 40). In ddition, beginning with the publicly reported portion in Februry 006, the updted WALA is listed in the Fctors nd Other Monthly Dt. This mens tht in future, the monthly WALA figures used re one month greter thn the publicly nnounced updted WALA for the ppliction month.

27 (Chrt --) PJ Model (tndrd Model) CPR 標準モデルの Pth of tndrd CPRパスModel (CPR) % % % 0% 9% 8% 7% 6% 5% 4% % % % 0% %PJ 6%PJ %PJ (WALA( WALA 加重平均経過月数 (months) )) Cse of %PJ CPR0% t 0 months WALA (weighted verge lon ge) CRP lter rises t the sme rte per month to rech % t 60 months CPR remins flt t % from 60 months onwrd Cse of 6%PJ CPR0% t 0 months WALA CRP lter rises t the sme rte per month to rech 6% t 60 months CPR remins flt t 6% from 60 months onwrd Cse of %PJ CPR0% t 0 months WALA CRP lter rises t the sme rte per month to rech % t 60 months CPR remins flt t % from 60 months onwrd 4

28 ection Process of Producing Csh Flows for JHF MB using the tndrd Model In this section, we introduce the method of producing csh flows using the PJ model (stndrd model) introduced in the previous section bsed on the informtion on the entrusted mortgge pool provided by JHF. Fundmentlly, s ws explined in ection, 4. of the previous chpter (chpter ), the usul method for deriving expected csh flows for JHF MB using the expected CPR is to reduce the Expected Principl Blnce not tking prepyments into ccount for ech month by the reduction fctor fter considering the expected prepyment rte Expected nd tke the 00MM difference between the previous month s blnce nd the current month s blnce to be the principl csh flow (principl pyment mount) fter tking into ccount prepyments. Here, we will discuss the redjustment of JHF MB csh flow production process nd clcultion method for Weighted Averge Life (WAL) premised on use of the PJ model (stndrd model).. Informtion ssocited with entrusted mortgges provided by JHF To begin with, let us confirm the dt tht cn be ccessed when deriving future csh flows for JHF MB. As relted mterils, there is vriety of dt vilble on the cheduled Fctor on issunce of JHF MB. In ddition, strting with the GHLC Monthly MB No. 40 issue, the weighted verge lon ge (WALA) bsed on the lon greements very importnt for the PJ model is now vilble. 8 At the point of producing this guidebook, even fter the issue of JHF MB, JHF is continuing to provide the following informtion in its Fctors nd Other Monthly Dt on the web site. 8 For the first to the 9 th GHLC MB issues nd the first five -series MB issues, the definition for the weighted verge period ws the difference between the Initil lon period nd the remining period weighted by the remining blnce of ech lon, which is different from the WALA used by the PJ model. In order to use the PJ model with these issues, it is necessry to pply the WALA reported publicly in Fctors nd Other Monthly Dt. On the other hnd, for other issues, the most recent of the WALA given in the Entrusted Mortgge Relted Dt mde public on issunce or the WALA given in the Fctors nd Other Monthly Dt is used. 5

29 (Tble --) Fctors nd Other Monthly Dt Initil cheduled Fctor Rtio of ech GHLC MB nd JHF MB on blnce scheduled t issunce (clculted bsed on rtio in the principl blnce of underlying mortgges by ssuming no prepyment, replcement, nor chnge in the lon repyment method). More specificlly, the rtio is quoted in eight decimls s result of rounding it off to five deciml plces. The issunce mount is ssumed to be in the clcultion. Fctor (Actul) Rtio of ech GHLC MB nd JHF MB in terms of ctul outstnding blnce t ech month fter monthly repyment (or expected monthly repyment officilly nnounced) Weighted Averge Coupon or WAC (%) Averge coupon rte of underlying mortgge pool bcking ech GHLC MB nd JHF MB s weighted by the blnce of ech lon WAC = Σ [coupon rte x lon blnce] Σ lon blnce Weighted Averge Mturity or WAM (yers) Averge yers to mturity of underlying mortgge pool bcking ech GHLC MB nd JHF MB s weighted by the blnce of ech lon WAM = Σ [yers to mturity x lon blnce] Σ lon blnce Conditionl Prepyment Rte or CPR (%) Annulized prepyment rte of ech month CPR = - ( - prepyment mount for ech month lon blnce net of scheduled lon principl collection mount for the month) Rescheduled Fctor Rtio of ech GHLC MB nd JHF MB on blnce scheduled fter the ctul lon collection by then ( replcement or prtil cncelltion)(clculted bsed on rtio in the principl blnce of underlying mortgges by ssuming no prepyment, replcement, nor chnge in the lon repyment method) Weighted Averge Lon Age or WALA (months) Replcement or Prtil Cncelltion Rte (long-term delinquency,%) Replcement or Prtil Cncelltion Rte (other thn long-term delinquency,%) (ource: JHF web site Averge lon ge for the underlying mortgge pool bcking ech GHLC MB nd JHF MB s weighted by the blnce of ech lon Blnce of new replced or prtilly cncelled lons net of clims in rrers t end of period (lons tht re four months in rrers) blnce of lons net of clims in rrers t end of period (monthly rte) Blnce of new replced or prtilly cncelled lons net of clims in rrers t end of period (other thn lons tht re four months in rrers) blnce of lons net of clims in rrers t end of period (monthly rte) 6

30 . Process of producing csh flows using the PJ model (stndrd model) Using the dt introduced in. bove, we will show the clcultion method for future csh flows of JHF MB tking into ccount prepyments (using PJ model). First, since the explntion will use equtions, we hve first put together list of the definitions of the nottions used in the following section (Plese see Tble --). (Tble --) Definitions Used in this ection 0 : The bse monthly principl nd interest (P&I) dte. The dte is the initil clcultion dte when the initil clcultion dte is the issue dte or P&I pyment dte. When the initil clcultion dte is not either of these dtes, the dte is pyment the P&I pyment dte immeditely previous to the initil clcultion dte.(provided tht when the initil clcultion dte flls before the first P&I pyment dte, the issue dte is used). : The number of months tht hve elpsed since the bse monthly P&I pyment dte ( =,, ) : the th P&I pyment dte following the bse monthly P&I pyment dte. L : The period from the clcultion dte to the P&I pyment dte. M: The WALA for the bse monthly P&I pyment dte 0 (noted in. bove) CPR : The expected CPR for P&I pyment dte MM : The expected MM for P&I pyment dte AF 0 : The ctul fctor for JHF MB on the bse monthly P&I pyment dte 0. F 0 : The individul figures of the cheduled Fctor corresponding to the bse monthly P&I pyment dte 0 (provided, however, tht if there is no ltest cheduled Fctor equivlent to F 0, F 0 = AF 0 ) mong the ltest publicly nnounced JHF scheduled fctors (the most recent of either the Initil cheduled Fctor nnounced t time of issue or the Rescheduled Fctor nnounced periodiclly fter issue). F : The individul figures of the cheduled Fctor corresponding to the P&I pyment dte mong the ltest publicly nnounced JHF scheduled fctors (the most recent of either the Initil cheduled Fctor nnounced t time of issue or the Rescheduled Fctor nnounced periodiclly fter issue). EF : The expected fctor corresponding to the P&I pyment dte OF: Originl fce vlue CF 0 : The current fce vlue blnce of the bse monthly P&I pyment dte 0 ECF : Expected current fce vlue blnce corresponding to the P&I pyment dte EP : Expected principl pyment mount fter considering prepyments corresponding to the P&I pyment dte. C: Coupon rte on JHF MB AI : Actul Interest mount corresponding to the P&I pyment dte EI : Expected interest mount corresponding to the P&I pyment dte ( ) 7

31 () Clcultion of WALA In order to describe csh flows using the PJ model, the first step is to decide the WALA for the future principl nd interest (P&I) pyment dtes of the JHF MB. As stted in the definitions bove, if the Bse Monthly P&I Pyment Dte is the issunce dte, the WALA (months) note in the Entrusted Mortgge Pools Relted Dt publicly reported t the time of issunce is the WALA M for the Bse Monthly P&I Pyment Dte 0 for the initil clcultion dte (the present or strting point for the clcultion of csh flows to be described). If the Bse Monthly P&I Pyment Dte is some other P&I pyment dte fter the issunce dte, the WALA (months) for sid P&I pyment dte listed in Fctors nd Other Monthly Dt is used. Moreover, s the WALA for the next P&I pyment dte fter the Bse Monthly P&I Pyment Dte 0 is M+ nd M+ for nd so on, the WALA for the P&I pyment dte " "(the th P&I pyment dte from the Bse Monthly P&I pyment dte) will be "M + ". (Tble --) An exmple of the clcultion of WALA (The shded portion of Column H in the following tble gives the clculted WALA figures) for future P&I pyment dtes when the Bse Monthly P&I Pyment Dte is Mrch 006 () The clcultion of the respective CPR for ech WALA Next, we will explin how to describe the expected CPR for ech month using the PJ model (stndrd model) bsed on the WALA for ech future P&I pyment dte s determined in the bove tble. For exmple, in determining the expected CPR from the PJ model given the WALA figures determined bove, for r%pj, the CPR (%) nd MM (%) for WALA M+α would be determined s follows. r CPR (%) = min ( M + ), r (Formul --) 60 CPR (%) MM = 00 (Formul --) 00 8

32 () Clculting JHF MB csh flows reflecting CPRs bsed on the PJ model When the expected CPRs for ech P&I pyment dte hve been determined s noted in () ccording to the expected PJ speed (r%pj), the process of producing csh flows is the sme s from ection, 4. () onwrd in Chpter. An exmple of the time series of the csh flow clcultion process is shown in (Chrt --4), while exmples of the ctul clcultions re shown in (Chrt - -5) nd in (Chrt --6). 9

33 (Chrt --4) Clcultion Process for JHF MB Csh Flows Using Expected PJ peed (r%pj) P&I Dte WALA Expected CPR Expected MM 0 M - - r CPR M + CPR (%) = min ( M + ), r (%) MM = r CPR (%) MM = r CPR CPR (%) = min M +, r (%) MM = M CPR (%) = min ( M + ), r M ( ) + r CPR M + CPR (%) = min ( M + ), r (%) MM = P&I Dte Expected Fctor Expected Current Fce Vlue Blnce 0 AF (Actul) 0 CF (Actul) 0 F = MM * EF AF0 ECF = OF EF F0 00 F = MM * EF EF ECF = OF EF F 00 F = MM * EF EF ECF = OF EF F 00 F = MM * EF EF ECF = OF EF F 00 * When expressing expected csh flows tking into considertion the 0% Clen Up Cll, the formul must be replced with tht in (formul --). P&I Dte Expected Principl Pyment Amount Expected Interest Amount EP = OF ( AF0 EF ) AI = OF AF C (Definite vlue) EP OF ( EF EF ) EP OF ( EF ) 0 = EI = OF EF C EF = OF EF C = EI EP = OF ( EF EF ) EI = OF EF C * When is the issue dte, is replced with the ctul number of dys from the issue 0 dte to the first interest pyment dte (Counting only one of strt dte or end dte)65. 0

34 (Chrt --5) Actul exmple of derivtion of csh flows for No. 9 GHLC MB (.84% coupon rte; Februry 8, 006 issue dte; Mrch 0, 006 initil P&I pyment dte; billion initil fce vlue mount). Does not tke into considertion the 0% Clen Up Cll nd uses n expected PJ speed (7.0%PJ). (Mrch 0, 006 initil clcultion dte) * The bove clcultions hve not djusted for frctions nd interest pyments flling on holidys hve not been tken into ccount. ince the (expected) WAL of the JHF MB bsed on the principl csh flow (expected principl pyment mounts) is the timing (WAL of ech P&I pyment dte from the clcultion dte to the repyment of principl) rising from principl pyments on ech P&I dte weighted by the principl pyment mounts on ech P&I dte, it is clculted using the following formul. ( WAL(yers) = EP L )+( EP L )+...+( EP L )+... (Formul --) OF AF 0 In the cse of (Chrt --5) (Initil clcultion dte: Mrch 0, 006), WAL = 0.46 yers.

35 (Chrt --6) Actul exmple of derivtion of csh flows done for No. 9 GHLC MB (.84% coupon rte; Februry 8, 006 issue dte; Mrch 0, 006 initil P&I pyment dte; billion initil fce vlue mount). Tkes into considertion the 0% Clen Up Cll nd uses n expected PJ speed (7.0%PJ). (Mrch 0, 006 initil clcultion dte) * The bove clcultions hve not djusted for frctions nd interest pyments flling on holidys hve not been tken into ccount. When the WAL is clculted using (Formul --) bsed on the exmple of (Chrt --6), WAL = 9.99 yers, demonstrting tht tking the 0% Clen Up Cll into ccount reduces the WAL.

36 ection 4 Exmple of Appliction for Risk Mngement In this chpter, we explin one exmple of methods of using the PJ model to mnge risk on JHF MB. However, we cution reders tht the following explntion is just one exmple of risk mngement pproches for reference purposes nd JDA nd the WG do not consider it the best method of risk mngement. We encourge ech investor to tke responsibility for determining their own method of risk mngement for JHF MB.. Appliction of PJ sttisticl clcultion figures Along with the introduction of the PJ model, JDA hs begun: () reporting PJ clcultions by mjor brokerdelers (In ddition to the PJ clcultion figures premised on the current interest rte environment, the PJ clcultion figures for shifts of 50bp, 00bp, 00bp, nd 00bp bove nd below the mrket interest rte (yield curve) re reported) nd () clculting sttisticl vlues (medin, verge, etc.) for the PJ clcultion figures received from brokerdelers nd publicly nnouncing them. The publicly reported PJ Clcultion ttisticl Vlues 9 re expected to, to certin extent, remove or verge out the differences nd individul chrcteristics of the prepyment models used by ech compny. Bsed on tht ssumption, JHF MB hve the following specil chrcteristics, bsed on which it is nticipted tht it will be possible to evlute the sensitivity of JHF MB prices to mrket rtes while reflecting these nd other chrcteristics under certin ssumptions. () Cll risk (incresed prepyments or shortening of weighted verge life when interest rtes re flling) (b) Extension risk (decresed prepyments or lengthening of weighted verge life when interest rtes re rising) (c) Negtive convexity (feture of verge life nd durtion shortening when interest rtes re flling, preventing prices from rising, nd verge life nd durtion lengthening when interest rtes re rising, ccelerting price declines) rising from the effect of () nd (b) on price chnges.. Exmple of clcultion of expected JHF MB prices for yield curve chnges For exmple, s shown below, when predicting chnges in PJ vlues bsed on level chnges in the yield curve, the first step is to use the following type of process to clculte the expected price of JHF MB when the level of the yield curve chnges. 9 For detils on the system for reporting PJ clcultion sttisticl vlues, plese see Appendix ; for view the reporting formt, plese see Appendix.

37 (Tble -4-) Expected PJ Vlues nd JHF MB Prices for Level Chnges (±α%) in Yield Curve Yield Curve Level Chnge 0 α% ±0%(No Chnge) + α % Expected PJ vlue PJ α PJ 0 PJ +α Expected csh flow { ( )} N α i { ( )} N i 0 i { ( )} N i= +α i i Present vlue of expected csh flow CF = CF PV PV α 0 CF = JHF MB ccrued interest c c c Expected price of JHF P α ( = PV α c) P ( = PV0 c) P α = PV+ MB α % PV + α 0 + ( α c) :Absolute figure indicting degree of chnge in level of yield curve. CF ( i) :The expected csh flow of the JHF MB for ll P&I pyment 0 = { } N i dtes when the yield curve does not chnge ( CF 0 ( i) is the expected csh flow for the i th P&I pyment dte fter the initil clcultion dte. { CF ( i) } N is the expected csh flows from the 0 i= CF 0( ) CF 0( ) CF 0( ) CF 0 ( N ) series of ech P&I pyment dte. N is the lst P&I pyment dte fter the initil clcultion dte). CF ( i) : Expected csh flow of the JHF MB for ll P&I pyment dtes α = when the yield curve level shifts α%. CF ( i) : Expected csh flow of the JHF MB for ll P&I pyment dtes +α = when the yield curve level shifts + α%. { } N i { } N i () The expected csh flow for the JHF MB for the current yield curve { CF ( i) } N is derived from the expected PJ vlue, PJ 0 i= 0, for the current yield curve (the expected PJ vlue when there is no yield curve chnge). () The spred ( pd ) to the benchmrk interest rte for the JHF MB is derived using the csh flow { CF ( i) } N derived in (), the JHF MB mrket 0 i= price P (nd the present vlue PV 0 0 of { CF ( i) } N derived using 0 P ) nd the i= 0 current yield curve. 0 Deleted PV: Present Vlue Accrued Interest When the mrket price for the JHF MB is vilble, there re two typicl methods of determining the spred on the JHF MB benchmrk interest rte from the expected csh flows for the JHF MB nd the yield curve. They re ) to determine the IRR from the mrket vlue nd expected csh flows, nd then define the difference between the IRR nd the mrket rte for the specific term of the WAL of the JHF MB (=benchmrk rte) s the spred for the JHF MB or ) to determine n interest rte spred for yield curve tht equlizes the mrket vlue nd the vlue of the present vlue of the JHF MB derived from the expected csh flows for ech P&I pyment dte nd the discount fctor for ech P&I pyment dte less ccrued interest nd define the difference between the yield curve nd the overll yield curve (benchmrk rte) s the spred. (Plese note tht the impliction of the spred will chnge depending on the benchmrk rte chosen). 4

38 () The expected csh flows for ech chnge in the level of the yield curve { CF ( i) } N, α { CF ( i) } N re derived bsed on the expected PJ vlues i= +α i= PJ, α PJ for ± α% chnges in the yield curve. + α (4) From the { CF ( i) } N α { CF ( i) } N derived in (), produce yield curves for i= +α i= ech post level chnge yield curve by dding the pd given in (). Using these yield curves clculte the present vlues PV, α PV for the expected + α csh flows. 4 (5) The vlues give by subtrcting the ccrued interest c from the PV α PV clculted in (4) re the expected JHF MB prices +α P, α P for the + α ± α% degree of level chnges in the yield curves. When clculting the expected price of JHF MB fter chnge in the level of the yield curve bsed on the bove process using the PJ clcultion sttisticl vlues of the JDA, it is importnt to ensure tht the ssumption of the chnge ( ± α% ) in the yield curve does not result in negtive interest rte ( negtive interest rte is deemed to be 0%). In other words, for α% chnge in interest rte level, chnges in interest rtes less thn α % in yield curve must not rech α%. Also be wre tht the expected price in the bove clcultion exmple is bsed on the ssumption tht the spred ( pd ) to the JHF MB benchmrk rte will not chnge even if the yield curve chnges.. Method of clcultion of MB effective durtion nd effective convexity Effective durtion ( Eff. Dur ± ) nd effective convexity ( α Eff. Cvx ± ) indicte the α chnge in expected csh flows in ccordnce with the degree of level chnge ( ± α% ) in the mrket yield curve. They re clculted using the following formule. PV α PV+ α Eff. Dur± α = PV0 ( α00) (Formul -4-) PV+ α + PV α PV0 Eff. Cvx± α = 00 PV α00 (Formul -4-) 0 ( ) 4 When the spred to the JHF MB benchmrk interest rte is vilble, there re two typicl methods of determining the present vlue of the expected csh flows from the yield curve. They re ) to determine present vlue where the interest rte for the specific term of the WAL of the JHF MB (=benchmrk rte) plus the spred for the JHF MB will equl the IRR from the mrket vlue nd expected csh flows, nd then define the difference between the IRR of the expected csh flows or ) to determine the present vlue of the expected csh flows of JHF MB bsed on the expected csh flows for ech P&I pyment dte nd their corresponding discount fctors fter clculting the discount fctor for ech P&I pyment dte bsed on the yield curve consisting of the overll yield curve (=benchmrk interest rte) plus the JHF MB spred. (Plese note tht the impliction of the spred will chnge depending on the benchmrk rte chosen). 5

39 The vlue of effective durtion nd effective convexity will fluctute with the set vlue for the ssumed degree of chnge ( ± α% ) in the yield curve. Therefore, when using these vlues s risk indictors, it is necessry to determine nd confirm the expected degree ( ± α% ) of interest rte chnge. 4. Exmple of the clcultion of effective durtion nd effective convexity For reference, we show below n exmple of the clcultion of the effective durtion nd effective convexity for the clcultion of the expected price of JHF MB with degree ( α % = 0.5% ) of chnge in the yield curve of ±50bp(±0.5%). We emphsize tht this is only n exmple, JDA or the working group do not recommend tht the clcultion of risk indictors be bsed on degree of level chnge of ±50bp. (Tble -4-) Chnges in Expected Price Due to Chnges in Yield Curve (exmple) Yield curve level chnge -0.5% ±0 +0.5% MB expected price Eff. Dur ± 50 bp = ( 0.500) (Formul -4-) Eff. Cvx ± 50 bp = (Formul -4-4) ( ) 6

40 Chpter 4 PJ Model Customized Model In this chpter, we cover the development concept, definitions, nd method of use for the PJ model (customized model) creted by the JDA. ection The Development Concept of the Customized Model The customized model ws conceived for use in cses where the stndrd model could not dequtely express the prepyment speed. The model hs been designed to llow djustments to fit the ttributes of individul pools. pecificlly, the model is expected to be pplied when wnting to express the prepyment speed in little more dvnced form thn the stndrd model or for securitiztion dels, etc. for highly individulistic privte sector mortgge lons. While the customized model is equivlent to the stndrd model in tht, in covering ll MB (or mortgge lon pools), it uses the bsic form of the CPR rising from the lon origintion point for specific number of months (WALA), from which point on the CPR becomes fixed. However, in the ttributes of the ech MB (or mortgge lon pool) the ) initil CPR nd ) number of sesoning months cn be djusted. It is possible tht, when estblishing prepyment scenrios for use in pricing MB other thn JHF MB t the point of issunce, there will be cses where it is inpproprite to use the customized model to express expected prepyment scenrios. The working group hs no intention of requiring the use of the customized model in such cses. When use of the customized model is inpproprite, we believe tht prepring other prepyment scenrios in ccordnce with the specil ttributes of individul MB nd using them to nlyze investment vlue should continue to be llowed. On the other hnd, regrding the form of the prepyment scenrios used to nlyze the investment vlue of individul MB other thn JHF MB, even though it would only fll within certin rnge, we believed tht hving uniform mesure vilble for use s mrket prctice would lend such dvntges s voiding perception disgreements regrding prepyments in individul trnsctions, etc. nd contributing to smooth discussions of prepyment scenrios. 7

41 ection Definitions. Nme of model nd overview of functionl form The functionl form sets CPR of i% for MB (or mortgge pool) in the lon origintion month (WALA is 0 months). After initition, the CPR rises fixed rtio monthly, reching CPR of r% fter n months, fter which the CPR follows fixed pth (i%, n months re fixed numbers). This form is termed r%pji-n nd the customized model is known s the PJi-n model. More concretely, CPR pth where the CPR for n MB issue (or mortgge pool) in the lon origintion month (WALA is 0 months) ws %, fter which the CPR rose fixed rtio per month until it reched 8% fter 40 months, following which the prepyment rte remined constnt t 8% would be expressed s 8%PJ-40 nd the customized model would be known s the PJ-40 model.. Formul definitions In the customized model, if the r%pji-n hs CPR t n ge (WALA) of m months (CPR m ), it cn be expressed s the following formul. ( r i) (%) = min m + i r ( i) CPR m, n ( r i) CPR m = mx m + i, r n (%) ( i) r (Formul 4--) r < (Formul 4--) * When expressing the expected prepyment scenrios in the nlysis of the prepyments of MB, we expect tht (Formul 4--) will minly be used. (Formul 4--) describes the sitution where with n initil point of CPR i% when WALA is 0 months, the CPR drops by fixed rtio monthly until it reches r% when WALA is n months. While this is necessry form under the definitions of the customized model, we expect there is little possibility it will be ctully used to express expected prepyment scenrios for MB. Conversely, bsed on the PJi-n model, the vlue PJi-n (m) tht gives the instntneous velocity for the Actul CPR (R%) when WALA is m months cn be expressed s follows. ( ) ( R i) n m (%) = n i ( n) m n( m) (%) R ( n) PJi + PJi = m (Formul 4--) m > (Formul 4--4) * For exmple, expressing instntneous velocity on continuous bsis for the monthly Actul CPR of individul MB fter their issue by using the PJ-40 model tht ws used s the pricing model t the time of origintion will require the seprte use of (Formul 4--) or (Formul 4--4) depending on the WALA for the Actul CPR level. pecificlly, if the Actul CPR t the WALA 0 month point is % nd the Actul CPR t the WALA 0 month point is 0.5%, etc., (Formul 4--) is used, with the former giving n instntneous velocity of 6%PJ-40 nd the ltter one of -%PJ-40 bsed on the PJ-40 model. However, for n Actul CPR t the WALA 50 month point of 6%, (Formul 4--4) would be used, giving n instntneous velocity of 6%PJ-40. 8

42 (Chrt 4--) PJ Model (Customized Model) カスタマイズド モデルの CPR Pth of Customized CPRパス Model (CPR) % % % 0% 9% 8% 7% 6% 5% 4% % % % 0% -% -% -% -4% %PJ-40 9%PJ-40 6%PJ-80 %PJ %PJ-80 (WALA( WALA 加重平均経過月数 (months) )) Cse of %PJ-40 (Initil CPR%sesoning 40 months) CPR% t 0 months WALA (weighted verge lon ge) CRP lter rises t the sme rte per month to rech % t 40 months CPR remins flt t % from 40 months onwrd Cse of 9%PJ-40 (Initil CPR%sesoning 40 months) CPR% t 0 months WALA CRP lter rises t the sme rte per month to rech 9% t 40 months CPR remins flt t 9% from 40 months onwrd Cse of 6%PJ-80 (Initil CPR%sesoning 80 months) CPR% t 0 months WALA CRP lter rises t the sme rte per month to rech 6% t 80 months CPR remins flt t 6% from 80 months onwrd Cse of %PJ-80 (Initil CPR%sesoning 80 months) CPR% t 0 months WALA CRP lter rises t the sme rte per month to rech % t 80 months CPR remins flt t % from 80 months onwrd 9

43 Cse of -%PJ-80 (Initil CPR%sesoning 80 months) CPR% t 0 months WALA CRP lter flls t the sme rte per month to rech -% t 80 months CPR remins flt t -% from 80 months onwrd * Plese understnd tht lthough there is only smll likelihood tht scenrio where the PJ vlue is minus would hve ctul use in predicting MB prepyments, we hve gone to the trouble of giving n exmple ) to clrify the definition of the customized model nd ) to mke clrify the concept tht minus vlues cn occur when using the MB Actul CPR to clculte bck to the instntneous velocity. For exmple, with n Actul CPR of 0.5% t WALA of 0 months, the PJ-80 model will give instntneous velocity of -%PJ

44 ection Process of Producing Csh Flows for JHF MB using the Customized Model In this section, we introduce the method of producing csh flows using the customized model bsed on the informtion on the Entrusted mortgge pool provided by JHF. Fundmentlly, the bsic method for deriving expected csh flows using the customized model is the sme s for the stndrd model s explined in Chpter, ection,. The only difference is tht s the prepyment model chnges, the clcultion process for the prepyment rte for WALA chnges with the customized model. Therefore, in preprtion for the following explntion, we first give the definitions of the nottions used in Chpter, ection,. To void overlp in the explntion, we sk you to, s necessry, refer to the pproprite portion of Chpter, ection,. () Clcultion of WALA WALA is clculted using the sme method s in Chpter, ection,. () Clcultion of WALA. () The clcultion of the respective CPR for ech WALA Next, we will explin how to describe the expected CPR for ech month using the previously mentioned customized model bsed on the WALA for ech future P&I pyment dte s determined in () bove. For exmple, in determining the expected CPR from the customized model given the reltionship with the described WALA formuls, for r%pji-n, the CPR (%) nd MM (%) for WALA M+α would be determined s follows. ( r i) CPR (%) = min, r (Formul 4--) n (%) 00 CPR MM = (Formul 4--) 00 ( M + ) + i () Clculting JHF MB csh flows reflecting CPRs bsed on the customized model From here, like the stndrd model, the process of producing csh flows is the sme s from ection, 4. () onwrd in Chpter. An exmple of the time series of the csh flow clcultion process is shown in (Chrt 4--), while exmples of the ctul clcultions re shown in (Chrt 4- -) nd (Chrt 4--). 4

45 (Chrt 4--) Clcultion Process for JHF MB Csh Flows Using Expected PJ peed (r%pji-n) * With the exception of expected CPR, ll clcultions re exctly the sme s with the stndrd model. P&I Dte WALA Expected CPR Expected MM 0 M - - ( ) M + r i CPR CPR (%) = min ( M + ) + i, r (%) MM = 00 n 00 M + M + ( r i) CPR CPR (%) = min ( M + ) + i, r (%) MM = 00 n 00 ( r i) CPR CPR (%) = min ( M + ) + i, r (%) MM = 00 n 00 M + ( r i) CPR CPR (%) = min ( M + ) + i, r (%) MM = 00 n 00 P&I Dte Expected Fctor Expected Current Fce Vlue Blnce 0 AF (Actul ) 0 CF (Actul ) 0 F = MM * EF AF0 ECF = OF EF F0 00 F = MM * EF EF ECF = OF EF F 00 F = MM * EF EF ECF = OF EF F 00 F = MM * EF EF ECF = OF EF F 00 * When expressing expected csh flows tking into considertion the 0% Clen Up Cll, the formule must be replced with those in (formul --). P&I Dte Expected Principl Pyment Amount Expected Interest Amount EP = OF ( AF0 EF ) AI = OF AF C (Definite vlue) EP OF ( EF EF ) EP OF ( EF ) 0 = EI = OF EF C EF = OF EF C = EI EP = OF ( EF EF ) EI = OF EF C * When is the issue dte, is replced with the ctul number of dys from the issue 0 dte to the first interest pyment dte (Counting only one of strt dte or end dte)65. 4

46 (Chrt 4--) Actul exmple of derivtion of csh flows for No. 9 GHLC MB (.84% coupon rte; Februry 8, 006 issue dte; Mrch 0, 006 initil P&I pyment dte; billion initil fce vlue mount). Does not tke into considertion the 0% Clen Up Cll nd uses n expected speed (6.5%PJ-50) bsed on the PJ-50 model. (Mrch 0, 006 initil clcultion dte) * The bove clcultions hve not djusted for frctions nd interest pyments flling on holidys hve not been tken into ccount. Weighted Averge Life (WAL) Clcultion (Initil clcultion dte Mrch 0, 006) using (Formul --) gives WAL = 0.4 yers. 4

47 (Chrt 4--) Actul exmple of derivtion of csh flows for No. 9 GHLC MB (.84% coupon rte; Februry 8, 006 issue dte; Mrch 0, 006 initil P&I pyment dte; billion initil fce vlue mount). Tkes into considertion the 0% Clen Up Cll nd uses n expected speed (6.5%PJ-50) bsed on the PJ-50 model. (Mrch 0, 006 initil clcultion dte) * The bove clcultions hve not djusted for frctions nd interest pyments flling on holidys hve not been tken into ccount. Weighted Averge Life (WAL) Clcultion (Initil clcultion dte Mrch 0, 006) using (Formul --) gives WAL = 9.9 yers. 44