Guide to the REX Indices

Transcription

1 Guide o he REX Indices Version 3.12 Ocober 2017

2 Deusche Börse AG Version 3.12 Ocober 2017 Page 2 General Informaion In order o ensure he highes qualiy of each of is indices, Deusche Börse AG exercises he greaes care when compiling and calculaing fixed income indices on he basis of he rules se ou in his guide. However, Deusche Börse AG canno guaranee ha he various indices, or he various raios ha are required for index compilaion and compuaion purposes, as se ou in his guide, are always calculaed free of errors. Deusche Börse AG acceps no liabiliy for any direc or indirec losses arising from any incorrec calculaion of such indices or key figures. Decisions concerning he way is fixed income indices are calculaed, as well as regarding heir compilaion, are always aken by Deusche Börse AG o he bes of is knowledge and belief. Deusche Börse AG shall no be liable for any losses arising from such decisions. The fixed income indices of Deusche Börse AG do no represen a recommendaion for invesmen of whaever naure. In paricular, he compilaion and calculaion of he various indices shall no be consrued as a recommendaion of Deusche Börse AG o buy or sell individual securiies, or he baske of securiies underlying a given index.

3 Page 3 Conens 1 Key Feaures Index Concep Selecion of Inpu Daa Calculaion Basis Weighing Coupon Effec Publicaion Hisorical Daa Licensing Decision-Making Bodies 9 2 Calculaion REX REXP 15 3 Calculaion of REX Yields 18 4 Chaining in he Even of Changes in he Weighing Marix 19 5 Changes in Composiion Inclusion of new bonds Eliminaion of bonds 20 6 Excepional rules Handling of unforeseeable evens Consideraion of exreme economic siuaions and marke disrupions 21

4 Page 4 7 Your direc Line o Deusche Börse 22

5 Page 5 1 Key Feaures 1.1 Index Concep REX REXP All bond indices of Deusche Börse are based on he so-called noional bond concep. This means ha he characerisic feaures of synheic bonds and morgage bonds used, such as remaining erm and coupons, are mainained on a consan basis, hereby avoiding any unwaned changes in average coupons and average mauriies for he index porfolio. The bond indices hus represen he prices of bonds feauring an average coupon of percen and a consan remaining erm of 5.49 years. A sub-index is compued and published for each of he various mauriy windows ranging from one up o en years. In deail, Deusche Börse calculaes he following bond indices: The REX 1 index is compued on he basis of governmen bonds which are raded on he German bond marke, comprising all Federal governmen bonds ( Bundesanleihen ), Federal deb obligaions ( Bundesobligaionen ), and Treasury noes ( Bundesschazanweisungen ) wih a fixed coupon and remaining erm beween six monhs and 10.5 years, issued by he Federal Republic of Germany, he German Uniy Fund as well as he former Treuhandansal privaizaion agency. Though i represens jus a fracion of he oal ousanding volume of all domesic issuers his marke accouns for mos of he exchange urnover in bonds. The REX bond index is a weighed price average calculaed on he basis of synheic bonds wih a consan mauriy. I conains 30 bonds wih ineger mauriies of one up o en years and hree differen coupon ypes of 6 percen, 7.5 percen and 9 percen, respecively. The REXP performance index measures he overall resul on invesmens in he German bond marke, covering price changes and ineres income in line wih oal reurn indices which are well esablished inernaionally. Such indices measure he performance of a hypoheical porfolio wihou any wihdrawals nor injecions of cash. 1.2 Selecion of Inpu Daa The main index and is en sub-indices are compued once a day. The compuaion of he REX is based on reference prices (Bundesbank-Referenzpreise) from Xera Frankfur for all fixed-income Federal governmen bonds, Federal deb obligaions and Treasury noes wih a remaining erm beween six monhs and 10.5 years, issued by he Federal Republic of Germany, he German Uniy Fund and he former Treuhandansal privaizaion agency. The bonds require a specific minimum nominal amoun ousanding in order o be eligible for he REX indices. A presen, a minimum size of 500 million Euro is required. 1 REX and REXP are regisered rademarks of Deusche Börse AG

6 Page 6 In he even of suspensions, he reference price of he previous day is aken insead. 1.3 Calculaion Basis All indices of Deusche Börse are based on he same reference dae (30 December 1987) o he exen possible, hus faciliaing direc comparison beween he various indices. The base value of he REXP as well as he various performance sub-indices for he mauriy windows of one up o en years is se a a level of 100. The REX indices do no ake a base value, insead, hey are always compued on he basis of average prices. Accordingly, a REX of 100 corresponds o a bond feauring an average yield of 7.44 percen and a remaining erm of 5.49 years. 1.4 Weighing All bond indices of Deusche Börse are based on he sandardized weighing scheme se ou below: Weigh Weighed Mauriy 6% 7.5% 9% Toal coupon 1 year years years years years years years years years years Toal * * weighed average coupon

7 Page 7 For he purpose of compuing weighs, he iniial sep aken was he analysis of he yield curve developmen since In his conex, all exising Federal governmen bonds and Federal deb obligaions excluding floaing-rae issues were aken ino accoun in order o idenify he various yield cycles beween ineres rae lows (beginning of 1969 and 1978; 1986 hrough 1987) and ineres rae peaks (1974, 1981, 1990). Analysis has been exclusively carried ou on he basis of enire yield cycles o avoid any influences due o differen issuer behavior in he respecive ineres rae peaks and roughs. Securiies were grouped by he en mauriy and hree coupon classes and weighed according o he share of he respecive classes in he oal number of bonds ousanding. The various classes have been aggregaed as follows: Coupon less han or equal o 6.5% coupon greaer han 6.5% bu less han 8.0% coupon greaer han or equal o 8.0% 1-year erm mauriies ranging from 0.5 o 1.49 years 10-year erm mauriy ranging from 9.5 o 10.5 years The weighing was compued shorly before he launch of he REX and is subjec o annual review. Since hen, such review has given no cause for any re-weighing. 1.5 Coupon Effec As for he REX and REXP, he so-called coupon effec is aken ino accoun, resuling from he fac ha ineres income from bonds is subjec o axaion while realized price gains remain ax-exemp. This is why privae invesors subjec o a high degree of ax progression end o prefer bonds wih a low coupon. Thus, he mere exisence of differen coupons may lead o differen yields (prices). Unlike similar index conceps, he coupon effec inheren o he REX is calculaed in line wih he corresponding yield curve (cf. secion for a deailed descripion of he underlying regression).

8 Page Publicaion The REX index as well as is respecive sub-indices are calculaed once every exchange rading. Index Alpha ISIN REX TOTAL (PRICE INDEX) REX DE REX 1-YEAR REX1 DE REX 2-YEAR REX2 DE REX 3-YEAR REX3 DE REX 4-YEAR REX4 DE REX 5-YEAR REX5 DE REX 6-YEAR REX6 DE REX 7-YEAR REX7 DE REX 8-YEAR REX8 DE REX 9-YEAR REX9 DE REX 10-YEAR REX0 DE REX TOTAL (PERFORMANCE INDEX) REXP DE REX 1-YEAR REXA DE REX 2-YEAR REXB DE REX 3-YEAR REXC DE REX 4-YEAR REXD DE REX 5-YEAR REXE DE REX 6-YEAR REXF DE REX 7-YEAR REXG DE REX 8-YEAR REXH DE REX 9-YEAR REXI DE REX 10-YEAR REXJ DE REX 6% COUPON (PRICE INDEX) RX60 DE REX 7.5% COUPON RX75 DE REX 9% COUPON RX90 DE REX 6% COUPON (PERFORMANCE INDEX) RP60 DE REX 7.5% COUPON RP75 DE REX 9% COUPON RP90 DE

9 Page Hisorical Daa The ime series lised below are available for indices of Deusche Börse: Index Prices Availabiliy REX and 10 mauriy indices (1 10 years) Daily closing prices from 1988 REX and 10 mauriy indices (1 10 years) End-of-monh prices from 1967 REXP and 10 mauriy indices 1 10 years daily closing prices from 1988 REXP and 10 mauriy indices 1 10 years end-of-monh prices from Licensing The indices are regisered rademarks of Deusche Börse AG and herefore proeced agains unlawful usage inside and ouside Germany. Exchanges, banks and invesmen companies may, however, apply o Deusche Börse AG for licenses o use hese indices as underlying insrumens for derivaive insrumens. The sandardized licensing agreemen grans he licensee he righ o use all indices for any number of insrumens, wih he license fee se according o he acual usage. For enquiries regarding he licensing of price daa and indices please conac Deusche Börse AG. 1.9 Decision-Making Bodies The Working Commiee for Bond Indices advises Deusche Börse on all issues relaed o such indices, recommending measures which are necessary in order o ensure he relevance of he index range and he correcness and ransparency of he index calculaion process. However, any decisions on he composiion of and possible modificaions o all hese indices are exclusively aken by he Board of Deusche Börse.

10 Page 10 2 Calculaion 2.1 REX Calculaion of yields The marke prices of all Federal governmen bonds, Federal deb obligaions and Treasury noes issued by he Federal Republic of Germany, he German Uniy Fund and he former Treuhandansal privaizaion agency are used o compue he yields according o he ACT/ACT mehod. For he purpose of yield calculaion, all fuure paymens are discouned o he acual value dae. The mehod provides for exponenial discouning of no only he number of enire paymen periods, bu also he broken (parial) paymen period. n Coupon Redempion (1) Price i 1 i n R R R = Discoun ineres rae (equals he yield of a bond) Afer ransformaion pursuan o he summaion formula for geomeric series: 1 (2) P S q f*a * C a C a * q n 1 N q 1 q n whereby: P = Marke price for he bond S = Accrued ineres C = Coupon (nominal ineres rae) in percen a = Number of ineres periods per annum n = Number of ousanding enire ineres periods f = Pro-raa firs ineres period up o he nex coupon dae N = Nominal value q = 1 + r, whereby: r = yield

11 Page 11 The required yield (r) is he resul of: r (3) q Formula (2) comprises he following feaures: Several coupon daes in he course of he year are aken ino accoun hrough facor a (e.g. for a semi-annual coupon: a = 2). In his case, he annual yield (R) is obained from he period yield (r) as follows: (4) R 100*(q a 1 ) If a = 1 hen: R = r The paymen of ineres does no sar on he day of purchase, bu only when he respecive amouns are acually being charged or credied, respecively. Since he value dae (VD) is wo bank business days afer he purchase dae, public holidays hroughou he year mus be observed as well. Ineres calculaions are based on he ACT/ACT day coun mehod. The pro-raa firs ineres period up o he nex coupon dae (CD) is as follows: (5) f (CD VD)/ ACT. whereby: ACT = number of calendar days of he respecive year. Paricular aenion is o be paid o he fac ha he buyer (seller) of a bond does no only pay (receive) he marke price, bu also he accrued ineres. Since formula (2) canno be explicily resolved o show he yield, such yield has o be approximaed on an ieraive basis. The period yield (r) in formula (2) is herefore calculaed using he discree Newon ieraion mehod. Insead of an exac derivaive, his mehod uses an approximaion hereof by means of a so-called quoien of differences.

12 Page 12 The saring value for deermining he yield (r) is he value which, according o he mehod of simple yield compuaion, is esablished by he following rule-of-humb: (6) q 0 1 N P C m P 100 or N P C m r 0 P whereby: m = Remaining erm in years (m = n + f) The value obained in his way is insered ino formula (2). The yield is deemed o be exacly calculaed if one of he following crieria is fulfilled: a) If he differenial amoun of successive yield values corresponds o (F(q )-F(q -1)) <= 0, , changes are considered o be oo small. b) If he funcion value (in absolue erms) equals F(q ) <= 0, , he desired level of accuracy has been reached. The derivaive of he yield funcion is calculaed as a quoien of differences wih an incremen of = As long as he above crieria are no fulfilled, he subsequen value o be insered is esablished as follows: (7) q 1 q F *Fq q Fq Calculaion of he yield curve srucure A yield curve is calculaed on he basis of yields esablished in (1) for each remaining erm and coupon. The following regression deermines he area which minimizes he sum of square deviaions: (8) Yield (r) of a bond b 1 b 2 *m b 3 *m b 4 *m b 5 * ln (m) b 6 *C b 7 *C

13 Page 13 whereby: m = Remaining erm (m = n + f) C = Coupon in percen b 1...b 7 = Regression coefficiens (published daily). The exchange applies he householder mehod o calculae he regression parameers. Wihin he framework of his procedure, he parameers b 1...b 7 (uniform for every bond) are compued in such a way ha he sum of square adjusmen errors is minimized Eliminaion of ouliers: In order o avoid daa and/or ransmission errors, a ool for he eliminaion of ouliers has been incorporaed. Tha way, he acual yield curve srucure can be replicaed quie precisely. The eliminaion of ouliers is carried ou on he basis of wo crieria. A securiy is considered o represen an oulier if: I.) diff perc r a * sq whereby: r diff = Square error of he respecive securiy in relaion o he yield curve (square difference beween he acual and he heoreical yield of he respecive securiy) perc a = 10 sq = Average aggregae square error II.) P - P 1 whereby: P = Marke price for he bond P = Esimaed marke price/ mid-marke average based on bid and ask quoes for he bond.

14 Page 14 Afer he eliminaion of ouliers, a renewed regression is implemened for he remaining securiies, and he final regression coefficiens b 1...b 7 are compued Calculaion of he 30 synheic index bonds By enering he regression coefficiens b 1...b 7 ino he regression formula, yields for he ineger erm periods (one up o en years) and he respecive coupons (6 percen, 7.5 percen and 9 percen) are deermined. For example, according o formula (8) he yield wih respec o a erm of hree years and a coupon of 9 percen is calculaed as follows: r b 1 b 2 * 3 b 3 * 3 b 4 * 3 b 5 * ln( 3) b 6 * 9 b 7 * 9 whereby: b 1...b 7 = Regression coefficiens These yields are hen convered ino he prices (P) of noional bonds. Formula (2) has already been solved for he price. Addiionally, he formula is shorened since he following applies o noional bonds: As only ineger mauriy periods are aken ino accoun, he pro-raa firs ineres period (f) equals zero. Accordingly, he accrued ineres (S) is zero as well. The nominal value (N) of such noional bonds is 100. The number of ineres periods per annum (a) equals one. This avoids accrued ineres issues, and he number of cash flows is reduced o a maximum of en paymen daes. The shorened formula looks as follows: (9) P C* qn q 1 q n Weighing of synheic bonds and summaion of weighed prices The fourh sep is o muliply he price of each noional bond P jk wih a erm of j (= 1 o 10) and a coupon of k (= 1 o 3) by is corresponding weigh Q jk. As for he calculaion of weighs, please refer o secion 1.4. The oal of he 30 weighed prices deermines he overall REX index:

15 Page 15 (10) 10 3 REX K * P *Q j1 k 1 jk jk and 30 (11) REX K * P *Q i 1 i i The REX j group indices for bonds wih a remaining erm of j are compued as follows: 3 (12) P Q k1 jk* jk REX K * j j 3 Q k1 jk whereby: K j = Chaining facor (for he ime being: = 1) P jk = Price of he bond wih remaining erm j and coupon k Q jk = Weigh of he bond wih remaining erm j and coupon k. 2.2 REXP The iniial calculaion of he REX was based on he end of January Anybody who had invesed DEM 100 in he REX index on ha day could dispose of DEM as per 30 December 1987 (subjec o monhly reinvesmen of he respecive coupon income). For harmonizaion purposes, i was decided ha he base dae of he REXP index was o coincide wih ha of he DAX (30 December 1987). The corresponding base value should be se a a level of 100. This is why he old REXP* ime series was revised o sar as REXP in January 1967 wih 100/ * 100 = * REXP (13) REXP * * 100 REXP Formally, he REXP is compued as a chained index. This means ha he curren index level is deermined by muliplying he index value of he previous day wih a cerain facor. This facor represens he price change (REX * / REX -1) as well as he pro-raa coupon yield as performance componens:

16 Page 16 (14) REXP REXP 1 * * REX C j * D ACT REX 1 The accrued ineres (C j/act) per day is muliplied by he difference of value daes, and added accordingly. Each annual inerval (D -D -1 = ACT) feaures a REX coupon of percen. The lapse of ime iself already moves he various bond prices (so-called rolling-up-and-down-heyield-curve effec). Even if he marke remains oherwise unchanged, he prices of above-par issues are bound o fall, whereas heir below-par counerpars behave vice versa. A REX (REX * ) shorened in erms of mauriy is deermined wihin he framework of he corresponding adjusmen procedure: The mauriy period (l) indicaed in he regression formula is reduced by one day = 1/ACT wih he oher parameers involved o be lef unchanged. In he case of public holidays or weekends, he number of days is enhanced accordingly. The shorened mauriy period (l) for he sub-index (remaining erm = wo years; difference of value daes = one; normal year wih 365 days) is esablished as follows: 2 1/365 = years. The index componen issues are sold a he prices derived from he above equaion. The ensuing reinvesmen is execued a hose prices which resul from he original equaion, i.e. using he same parameers, however, using ineger erms. The resul of formula (10) is rounded o seven decimal places. The chosen ACT/ACT day-coun mehod corresponds o he pracice of accrued ineres selemen and is a he same ime in une wih he calculaion of yields. In is capaciy as a chained index, REXP is equal o he produc of all chaining facors which have accumulaed unil he day of calculaion, muliplied by he base value of 100. C * j REX * D ACT * (15) REXP * 100 i 1 REX 1

17 Page 17 whereby: REXP = REXP * = Performance index on day (base dae: 30 December 1987; base value = 100) Performance index wih a base dae of January 1967 and a base value of 100 (REXP * 0 = 100) REX = Price of he REX on day REX * = Price of he REX wih remaining erm reduced by D C j = Average coupon of he REX in year j (currenly a percen) D = Dae on day D = Number of days beween day and day -1 (according o he ACT/ACT day-coun mehod) D 0 = 31 January 1967

18 Page 18 3 Calculaion of REX Yields Apar from he various componen issues included in he REX and is sub-indices, Deusche Börse also compues and disribues he respecive yields once a day. Yields are compued on he basis of he weighing marix already presened in secion 1.4 above. Due o he noional bond concep and agains he backdrop of an unchanged weighing marix, yield calculaions are based on a fixed flow of paymens. Weigh Redempion Weighed Toal ineres Redempion + ineres Mauriy 6% 7.5 % 9% (1) coupon (2) (3)=(1)+(2) 1 year years years years years years years years years years Toal * *average weighed coupon Each of he yields for he REX and is sub-indices resuls from an inernal rae of reurn of he paymen series given below. For insance, he following yields are esablished for a given day: Paymen flows REX REX1 REX2 REX3 REX4 REX5 REX6 REX7 REX8 REX9 REX10 Price -111,34-104,08-107,48-109,89-111,38-112,31-113,20-113,70-113,55-112,91-111,85 1 year 14,83 107,39 7,39 7,37 7,35 7,39 7,53 7,63 7,60 7,46 7,20 2 years 15,70 107,39 7,37 7,35 7,39 7,53 7,63 7,60 7,46 7,20 3 years 16,50 107,37 7,35 7,39 7,53 7,63 7,60 7,46 7,20 4 years 17,44 107,35 7,39 7,53 7,63 7,60 7,46 7,20 5 years 16,65 107,39 7,53 7,63 7,60 7,46 7,20 6 years 14,97 107,53 7,63 7,60 7,46 7,20 7 years 14,51 107,63 7,60 7,46 7,20 8 years 12,57 107,60 7,46 7,20 9 years 10,83 107,46 7,20 10 years 6,92 107,20 Yield 4,98% 3,18% 3,46% 3,82% 4,20% 4,58% 4,94% 5,24% 5,46% 5,59% 5,61% The only variable wihin hese paymen series is represened by he respecive curren price of he REX or is sub-indices. Ineres paymen of he various sub-indices involved is based on he weighed coupons for he mauriies of one up o en years according o he above able, wih each of he corresponding redempion paymens o be effeced a a value of 100. The paymen series of he REX index comprises he aggregae of ineres and redempion paymens falling due wih regard o he individual coupon classes (cf. above able). REX yields are calculaed once a day and disribued as figures rounded o four decimal places.

19 Page 19 4 Chaining in he Even of Changes in he Weighing Marix The weighing scheme on which he respecive bond indices are based (cf. secions above) is checked for is relevance once a year. If necessary, i is adjused accordingly. If such adjusmen akes place, chaining is carried ou in hree seps: a) Calculaion of he index value on he chaining dae according o he old weighing scheme The following applies accordingly: REX 10 3 K * P * Q j 1k 1 jk jk This value corresponds o he closing index published on he dae of chaining and is used wih four decimal places (as published) for all subsequen calculaions. b) Calculaion of an inerim value The inerim value is compued using he weighs valid on he chaining dae (Q * jk). The following applies accordingly: Inerim value 10 3 * P * Q j 1k 1 jk jk whereby: Q * jk = Updaed weigh of he bond wih remaining erm j and coupon k. c) Calculaion of he new chaining facor The following applies accordingly: K 1 REX Inerim value Afer chaining, he index is compued on he basis of he new chaining facor (K T+1 ). This procedure applies also o he various REX sub-indices.

20 Page 20 5 Changes in Composiion 5.1 Inclusion of new bonds The REX index is compued on he basis of sovereign bonds raded on he German bond marke. These are Federal governmen bonds, Federal deb obligaions and Treasury noes wih a remaining erm beween six monhs and 10.5 years, issued by he Federal Republic of Germany, he German Uniy Fund and he former Treuhandansal privaizaion agency. In addiion, only sraigh bonds feauring a fixed coupon are aken ino consideraion in order o avoid credi differenials beween he various bonds involved. When a bond is issued, i is incorporaed ino he index calculaion process wih is ask price a he end of he day of is iniial lising. 5.2 Eliminaion of bonds On he day on which a REX componen bond issue has less han six monhs o run, i is auomaically removed from he index calculaion process.

21 Page 21 6 Excepional rules 6.1 Handling of unforeseeable evens In he case of an excepional unforeseeable even ha is no considered in his rulebook, Deusche Börse AG will consider he respecive facs and may apply procedures ha differ from he aforemenioned rules in his rulebook. This holds rue especially in cases where i) here are no applicable rules, ii) he applicaion of presen rules does no lead o a clear resul, iii) he rules conradic each oher, and/or iv) he applicaion of hese rules lead o an inappropriae siuaion in he bond marke. An example of an inappropriae siuaion is if he sric applicaion of he rules heavily influences he liquidiy of a bond emission in he governmen bond marke. In he case ha Deusche Börse AG makes a decision ha is ouside he parameers of he rulebook, he decision will be published wihin an appropriae noice period. 6.2 Consideraion of exreme economic siuaions and marke disrupions In imes of exreme economic siuaions and marke disrupions, especially in cases where he price source is unavailable (e.g. marke suspension or resricion), Deusche Börse AG will generally use he las available price daa. Also in imes of exreme economic cases, addiional excepions from his rulebook can be made, e.g. posponemen of an ordinary review dae. All such changes will be published wihin an appropriae noice period.

22 Page 22 7 Your direc Line o Deusche Börse Deusche Börse AG STOXX Limied Cusomer Suppor Phone: Fax: cusomersuppor@soxx.com Inerne Mailing address Deusche Börse AG Frankfur/Main Germany