Ground rules. Guide to the calculation methods of the FTSE Actuaries UK Gilts Index Series v1.9

Transcription

1 Ground rules Gude o he calculaon mehods of he FTSE Acuares UK Gls Index Seres v1.9 fserussell.com Ocober 2015

2 Conens 1.0 Inroducon Scope FTSE Russell Overvew of he calculaons Addonal deals for gls maury secor descrpons Range of calculaons Publcaon Managemen responsbles Gls ncluded n he ndexes Types of Gls Double-daed Gls Undaed Gls (Irredeemables) Elgble Convenonal Gls Elgble Index-lnked Gls Secor Indexes Replcaon Prce Index Addon of consuens Removal of consuens Aleraon o consuens Prce Index calculaons Formulae Applyng o boh Convenonal and Indexlnked Gls Accrued Ineres Gross or Dry prces XD Adjusmen Toal Reurn Index FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

3 5.5 Number of secures Secor wegh Formulae applyng o Convenonal Gls only Gross Redempon Yeld Macaulay duraon Modfed duraon Convexy Fed Yelds for Convenonal Gls Formulae Applyng o Index-lnked Gls only Coupon and redempon amoun calculaons Real redempon yeld calculaons Oher calculaons Calculaons for Index-lnked Gls wh a 3-monh lag Indexaon mehodology Calculang Coupon Paymens Calculang he Redempon Paymen Cashflows based on varous nflaon assumpons Accrued Ineres calculaons Appendx A: Accrued Ineres calculaons Appendx B: Redempon yeld compoundng frequency adjusmens Appendx C: Furher nformaon FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

4 Secon 1 Inroducon 1.0 Inroducon 1.1 Scope Ths gude descrbes he scope of he FTSE Acuares UK Gls Index Seres and he calculaon mehods used n her consrucon. I complemens he documen enled Ground Rules FTSE Acuares UK Gls Index Seres (Ground Rules). If a suaon arses where hs Gude and he Ground Rules can be nerpreed dfferenly, hen he Ground Rules ake prory. The FTSE Acuares UK Gls Index Seres cover separae calculaons for convenonal and ndexlnked gls. The ams of hs Gude are: A. To descrbe how he gl ndexes and her assocaed sascs are calculaed; B. To make easer for users o replcae he ndexes n order o suppor her radng and nvesmen sraeges; C. To asss users n undersandng he componen facors whch nfluence he performance of he ndexes. The gudng prncples behnd he calculaon mehods are: A. The calculaon mehods should reflec realy wherever praccal; B. The ndexes should be capable of beng replcaed by users; C. Only hsorc daa should be used n calculang he ndex sascs; D. Connuy wh he pas should be mananed wherever possble; E. The ndexes should be ransparen and predcable; F. The prmary purpose of he ndexes has always been o ndcae he curren level of yelds n he marke. A secondary purpose s o reflec accuraely movemens n he underlyng marke. In order o replcae he ndexes, s assumed ha he nvesor s able o deal a closng mddle marke prces, whou any expenses, and n any quany. In addon, for he oal reurn ndexes, s assumed ha he nvesor s able o renves he full neres amoun, on he ex-dvdend day, whou any ax or expense consderaons. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

5 1.2 FTSE Russell FTSE Russell s a radng name of Frank Russell Company (FRC), FTSE Inernaonal Lmed (FTSE) and FTSE TMX Global Deb Capal Markes, Inc. (FTSE TMX). FRC, FTSE and FTSE TMX are each benchmark admnsraors of ndexes. References o FTSE Russell should be nerpreed as a reference o he relevan benchmark admnsraor for he relevan ndex. 1.3 Overvew of he calculaons Due o her dfferen srucures, dfferen bu smlar calculaons are performed for he wo man caegores of gls: convenonal and ndex-lnked secures. Each caegory s sub-dvded no a number of secors. The secors are based on he ousandng erms o he assumed redempon daes of he gls. Convenonal Gls The calculaons for convenonal gls are dvded no he followng secors accordng o her assumed redempon (maury) daes: All socks Gls wh all ousandng erms Gls wh an assumed ousandng erm of up o 5 years Gls wh an assumed ousandng erm of over 5 years Gls wh an assumed ousandng erm of 5-10 years Gls wh an assumed ousandng erm of years Gls wh an assumed ousandng erm of 5-15 years Gls wh an assumed ousandng erm of up o 15 years Gls wh an assumed ousandng erm of over 15 years Gls wh an assumed ousandng erm of up o 20 years Gls wh an assumed ousandng erm of years Gls wh an assumed ousandng erm of over 25 years Irredeemable gls undaed gls In addon fed yelds are calculaed for he followng erms o maury: 5, 10, 15, 20, 25, 30, 35, 40, 45, 50 years and for rredeemables (undaed gls). Index-lnked Gls For ndex-lnked gls, all of whch have a sngle redempon dae, prce and coupon, ndexes are calculaed for he followng secors: All socks gls wh all ousandng erms Gls wh an ousandng erm of up o 5 years Gls wh an ousandng erm of 5-15 years Gls wh an ousandng erm of 5-25 years Gls wh an ousandng erm of over 5 years Gls wh an ousandng erm of over 15 years Gls wh an ousandng erm of years Gls wh an ousandng erm of over 25 years There are no undaed ndex-lnked gls. The yelds for he secors are calculaed assumng fuure nflaon raes of 0%, 3%, 5% and 10%. 1.4 Addonal deals for gls maury secor descrpons The followng deals apply o boh convenonal and ndex-lnked Gls. A maury secor descrbed n hs Gude o Calculaons as "up o XX years", s effecvely defned and reaed n he FTSE sysem as "up o, bu no ncludng, XX years". FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

6 A maury secor descrbed n hs Gude o Calculaons as "over XX years", s effecvely defned and reaed n he FTSE sysem as "XX years and over". A maury secor descrbed n hs Gude o Calculaons as a range of XX years o YY years, s effecvely defned and reaed n he FTSE sysem as "ncludng XX years and up o, bu no ncludng, YY years". These defnons wll become mporan when we consder shoreners (covered n Rule 3.4.2) n he conex of Gls wh exacly XX number of years o maury. Ths s also necessary when clarfyng FTSE s reamen of shoreners when hey occur on a non-busness day (.e. weekend or holday). Daes There are wo relevan daes on each day: he Calculaon dae, whch s he dae, afer he close of whch, he calculaons are done, and he Selemen dae, whch s he dae when he deals are seled. Normally he selemen dae s he nex followng workng day afer he calculaon dae, e.g. normally Tuesday afer a Monday, ec, and Monday afer a Frday, bu wh excepons a publc holdays. The calculaon dae s used o deermne he ousandng erm, and he selemen dae s used for he calculaon of accrued neres, redempon yelds ec. In hs Gude oday s used o mean he curren Calculaon dae, yeserday o mean he prevous Calculaon dae, and omorrow o mean he nex Calculaon dae. All calculaons of a Gl s erm o maury are deermned from Calculaon Dae raher han Selemen Dae. 1.5 Range of calculaons The man purpose of he ndexes s o calculae he level of yelds n he marke for Gls of dfferen ousandng erms 1. A secondary purpose s o calculae prce ndexes for he dfferen secors of he Gls marke. These prce ndexes are suppored by a range of oher assocaed sascs. Dfferen calculaons are performed for convenonal gls and for ndex-lnked gls. 1 See he paper nroducng he ndexes by G. M. Dobbe and A. D. Wlke (Journal of he Insue of Acuares Volume 105 Par ). FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

7 Convenonal Gls For each of he convenonal secor ndexes he followng nformaon s calculaed: Gross (or dry) prce ndex *2 ; Accrued neres; XD adjusmen for he year o dae; Toal reurn prce ndex *; Number of gls n he ndex*; Gross redempon yeld; Macaulay duraon; Modfed duraon; Convexy; Wegh of he secor as a percenage of he oal marke Day s Change* Monh s Change* Year s Change* In addon, yeld ndexes are calculaed whch gve he redempon yelds for convenonal gls wh ousandng erms of 5*, 10*, 15*, 20* years and for undaed secures *. Index-lnked Gls For each of he ndex-lnked secor ndexes he followng nformaon s calculaed: Gross (or dry) prce ndex *; Accrued neres; XD adjusmen for he year o dae; Toal reurn prce ndex *; Number of gls n he ndex; Wegh of he secor as a percenage of he oal marke * Day s Change* Monh s Change* Year s Change* In addon for each secor, based on assumed fuure annual nflaon raes of 0%*, 3%, 5%* and 10% of he UK Real Prce Index, he followng nformaon s calculaed: Real redempon yeld *; Macaulay duraon; Modfed duraon; Convexy; The real redempon yeld of an ndex-lnked gl s s calculaed gross redempon yeld, afer grossng up he scheduled fuure paymens a he assumed rae of nflaon, and hen dscounng he resulng value by he same assumed rae of nflaon. In oher words produces a reurn n excess of he assumed nflaon rae. I wll be seen n he calculaons, whch are descrbed n Secon 6, ha hs reurn s self dependen on he assumed nflaon rae. The duraons and convexy calculaons above are based on he real yeld calculaons and hence are also dependen on he assumed nflaon rae. 2 Values marked wh an asersk * are dsplayed on a daly bass n he Fnancal Tmes. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

8 1.6 Publcaon The ndexes are calculaed a he end of each busness day, and producs are produced by FTSE on a subscrpon bass. Some nformaon s also publshed n he Fnancal Tmes and s avalable on he FTSE web se FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

9 Secon 2 Managemen responsbles 2.0 Managemen responsbles The FTSE Acuares UK Gls Index Seres are calculaed daly n accordance wh he Ground Rules for he Managemen of he ndexes. The FTSE Bond Indces Commee has been esablshed jonly by FTSE Russell and he Faculy and Insue of Acuares. The Commee may approve changes o he Ground Rules. FTSE s responsble for he operaon of he FTSE Acuares UK Gls Index Seres, ncludng he daly calculaon of all he ndex values n accordance wh he Ground Rules. FTSE manans records of all he consuens and s responsble for he addon and deleon of gls and changes n nomnal amouns. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

10 Secon 3 Gls ncluded n he ndexes 3.0 Gls ncluded n he ndexes 3.1 Types of Gls Over he years he Brsh Governmen has ssued a varey of dfferen ypes of bonds, generally known as gls (for gl-edged secures ). These have ncluded convenonal gls wh fxed or varable fnal redempon daes, gls wh wo or four paymens per annum, annues, gls wh snkng funds, floang-rae noes and gls lnked o he real prce ndex. The ndexes and assocaed sascs conaned n he FTSE Acuares UK Gls Index Seres provde nformaon on boh convenonal gls and ndex-lnked gls. Whls he ndex-lnked marke s relavely new and all he exsng ssues work n a farly conssen way 3, hs s no so n he case of convenonal gls. Luckly many of he unusual feaures are only now found n gls ha are deemed o be oo small o be ncluded n he ndexes. However, he convenonal ndexes sll have o allow for double-daed and undaed gls. 3.2 Double-daed Gls A double-daed gl s one ha has been ssued wh a range of redempon daes, e.g. 7¾% Treasury 2012/15. Ths means ha he Brsh Governmen has he rgh o redeem hs gl a any me beween 2012 and 2015 provded hey gve approprae noce o he holders. The mnmum noce perod s 3 monhs. When ncludng such gls n he ndexes, s assumed ha he Brsh Governmen wll always ac n s own bes neres. In oher words, wll redeem he gl a he earles dae f feels ha can refnance he deb a a cheaper rae: oherwse, wll wa unl he las possble dae. Hence, s convenonal o assume ha f he redempon yeld of he gl o he earles dae s less han ha o he fnal dae, hen he gl wll be redeemed a he earles dae. Oherwse, s assumed ha wll be redeemed a he fnal dae. The prce of a gl a whch he gross redempon yelds o he possble frs and las redempon daes are he same s called he equlbrum prce. In pracce, he Governmen s unlkely o redeem a gl early f he prce goes margnally over he equlbrum prce because, oher hngs beng equal, of he coss nvolved n redeemng he ssue and of ssung new deb, and because longer daed deb ofen commands a hgher yeld. I s easy o show ha for a normal gl whou a specal frs or las coupon and whch s no beng raded ex-coupon ha he clean equlbrum prce CEP s gven by: 3 The number of decmal places used n he accrued neres and coupon calculaons does vary. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

11 CEP R (1 + C / R) 1 f (1 f ) C where: CEP clean equlbrum prce, (.e. he prce whou he accrued neres) R redempon value, (.e. 100 for convenonal gls) C normal coupon per cen payable a each fuure dae, whch equals he annual coupon rae dvded by he coupon frequency (.e. 2) f fracon of a sx-monhly perod from he selemen dae o he nex neres dae. Ths formula gves a clean equlbrum prce equal o he redempon amoun R on any normal coupon dae, (.e. when f equals 0 or 1). For a selemen dae of 1 March 2004 consder a gl whch can be redeemed a par (100) any me beween 1 March 2008 and 1 March 2011 a he dscreon of he ssuer. If he quoed clean prce of he gl s above 100, here wll be a capal loss a redempon, and so he yeld o 1 March 2008 wll be less han ha o 1 March 2011, wh he resul ha he ndex calculaons wll assume ha wll be redeemed a he earler dae,.e. n 4 years me. Smlarly f he clean prce of he gl had been below 100, would have been reaed as f had an ousandng erm of 7 years. On 1 June 2004 he clean equlbrum prce for a gl, wh a 6% annual coupon payable wce a year, whch can be redeemed a par any me beween 1 March 2008 and 1 March 2011 s gven by: f 92 /184 1/ 2 CEP 100 (1 + 3/100) (1 0.5) (1 0.5) When lookng a ndexes for specfc secors, such gls are always pu no he relevan secor for her assumed redempon dae. Ths means ha f he prce changes for such a gl, from below he equlbrum prce o above or vce versa, hen he gl can move from one secor o anoher. In recen years he Brsh Governmen has no ssued any double-daed gls, and s undersood ha hey do no have any plans o do so agan. 3.3 Undaed Gls (Irredeemables) Undaed gls are gls where he ssuer has no specfed a fnal redempon dae. The Brsh Governmen frs ssued undaed gls a very long me ago: for example, 2½% Consoldaed Sock (Consols) had been ssued n 1751, as a 3% gl consoldang a number of oher gls. I was convered o 2½% Consoldaed Sock n he early 20 h cenury. I s now repayable only wh an Ac of Parlamen. Undaed gls are also referred o as rredeemables, bu hs s no srcly correc as he governmen always has he opon o call he gl afer a specfc dae. The las new undaed gl, 2½% Treasury, was ssued n Ocober 1946 and he Brsh Governmen has no plans o ssue furher quanes of hese gls. The Brsh Governmen has had he rgh o redeem he 3½% War Loan a any me afer 1 December 1952 a par, wh 3 monhs noce. There s no fnal redempon dae. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

12 Undaed gls are ncluded n a separae secor of her own. Ths currenly only ncludes he 3½% War Loan. All oher undaed gls appear n he DMO s rump ls and hence are excluded from he FTSE ndexes. 3.4 Elgble Convenonal Gls All serlng convenonal gls are poenally ncluded n he convenonal prce ndexes provded ha: They are quoed on he Sock Exchange. They are of an ssue sze for here o be an effecve marke. Gls n he Deb Managemen Offce s rump sock ls are regarded as no beng suffcenly large for ncluson. They do no have a varable neres rae, such as floang rae noes and ndex-lnked gls. They are no sll n parly-pad form. Gls have no been ssued n parly-pad form for a number of years. (The las gl o be ssued n parly-pad form was 7% Treasury 2001 A, ssued n February 1994.) Such gls are no ncluded snce any change n neres raes has a dsproporonae effec on her prce. They are ncluded n he ndexes when hey become fully pad, f hey are oherwse elgble. Some, bu no all, convenonal gls are srppable. Tha s each gl may be broken down by a Gl-edged Marke Maker (GEMM) no s separae neres and capal cash flows, and each of hese cash flows may hen be raded separaely. In effec he gl s broken down no a number of zero coupon gls. In July 2003, 8% Treasury 2021, whch pays neres sem-annually on 7 June and 7 December, may be srpped no: 36 separae neres paymens (payable 7/12/2003, 7/06/2004,, 7/06/2021), and one capal paymen on 7/06/2021 Afer a gl has been srpped, s possble for a GEMM o re-combne he fuure cash flows agan o make an unsrpped gl. Ths process s referred o as reconsuon. The srpped componens of gls are no ncluded n he ndexes explcly snce he ssue szes of he unsrpped orgnal gls have no been adjused o allow for he fac ha par of he ssues have been srpped. Ths avods any double counng. In any case, he srpped componens are usually oo small for here o be a lqud marke n hem. In February 2003, 8% Treasury 2015 had he larges amoun of any gl n srpped form, wh 255m of nomnal srpped, compared wh s oal amoun n ssue of 7,377m. Gls ssued by he Deb Managemen Offce under her specal repo arrangemens are also no ncluded n he ndexes. Gls ssued wh unusual condons are no ncluded n he ndexes. Converble and converson gl are ncluded n he ndexes. However, here are currenly no such gls, and he las converble ssue maured n In addon o he above resrcons, he followng gls are excluded from he yeld ndex calculaons: Gls wh less han 1 year o her assumed redempon dae. Ths s because, a leas n par, a very small change n he prce of such gls can cause he shape of he consruced yeld curve o change consderably. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

13 Excluson of 6¾% Treasury 2004 from he fed yeld curve 6¾% Treasury 2004 had a redempon dae of 26 November FTSE announced ha he gl was removed from he calculaon of he fed yeld curve, bu no he prce ndexes, afer close of busness on Tuesday, 25 November 2003 (.e. wh effec from sar of radng on Wednesday, 26 November 2003). I was ncluded n he calculaon of he fed yeld curve on 25 November Converble ssues wh ousandng converson opons, gls wh subsanal snkng funds and gls wh specal ax saus (as defned by he FTSE Bond Indces Commee) are excluded snce her redempon yelds are dfferen o gls of smlar ousandng erm. Currenly only 5½% Treasury , whch has a specal ax saus, s excluded on hese grounds from he calculaon of he fed yeld curve. However n he pas, 3½% Converson was excluded, unl became a rump sock, because of s snkng fund. 3.5 Elgble Index-lnked Gls All ndex-lnked gls are poenally ncluded n he prce ndexes provded ha: They are quoed on he Sock Exchange. They are of an ssue sze for here o be an effecve marke. Gls n he Deb Managemen Offce s rump sock ls are regarded as no beng suffcenly large for ncluson. There are currenly no ndex-lnked gls n he rump sock ls. They are no converble ndex-lnked ssues wh ousandng converson opons. There are currenly no ndex-lnked converble gls only one has ever been ssued and hs maured n Any oher ndex-lnked gls would be excluded from he curren ndexes f hey were o be ssued wh condons whch were sgnfcanly dfferen from hose of he exsng ndex-lnked gls, (e.g. lnked o an ndex oher han he RPI). 3.6 Secor Indexes Gls are grouped ogeher n secors accordng o her assumed ousandng erms. The secors are lsed n Rule 1.3. Gls wll be ncluded n he relevan secors, provded hey are elgble for ncluson n he All-sock ndexes and her assumed redempon dae mees he creron for he secor. The ousandng erm of a gl s from he calculaon dae o he assumed redempon dae. Excep n he case of double-daed and undaed gls, here s a fxed redempon dae. Wh double-daed gls, he assumed redempon dae s dependen on wheher he prce of he gl s above or below s equlbrum prce (see Rule 3.2). A gl moves from he 5 o 10 year secor o he under 5 years secor a he end of he day on whch s exacly 5 years from he calculaon dae o s assumed redempon dae, or f hs urns ou no o be a busness day a he begnnng of he nex busness day. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

14 On 7 December 2004 (a Tuesday), 5 ¾% Treasury 2009 wll be exacly 5 years from s redempon dae of 7 December The gl wll be ncluded n he 5-10 year and 5-15 year secor ndexes n he calculaons for 7 December Immedaely afer he nal calculaons for ha dae, wll be removed from he 5-10 year and 5-15 year secors, and wll be added o he up o 5 year secor, so ha on 8 December 2004 wll appear n he new secor. Thus he change n prce beween he 7 and 8 December of 5 ¾% Treasury 2009 s refleced n he new secor. On 7 December 2002 (a Saurday), 7 ¼% Treasury 2007 was exacly 5 years from s redempon dae of 7 December The gl was ncluded n he 5-10 year and 5-15 year secor ndexes on he 6 December 2002 (a Frday). On he 9 December 2002 (a Monday), was dropped from he 5-10 year and 5-15 year secors, bu added o he up o 5 years secor. No ndexes are calculaed for Saurdays and Sundays. 3.7 Replcaon One of he mos mporan facors wh any se of ndexes s a requremen o make possble for he ndexes o be replcaed. In he case of he FTSE Acuares UK Gls Index Seres hs s acheved by: Makng avalable dealed gudelnes of how he ndexes are consruced. Producng lss of he consuen gls ogeher wh rules for addng new ssues and deleng exsng ssues. Usng a publc source of relable prces for her calculaon. The prces used n he ndex calculaons are he GEMMA 4 prces compled and dsrbued by he UK Deb Managemen Offce each day on behalf of GEMMA. These are avalable on he DMO wre servce pages, as well as on s webse: 4 GEMMA s he Gl-edged Marke Makers Assocaon FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

15 Secon 4 Prce Index 4.0 Prce Index Fundamenal o he FTSE Acuares UK Gls Index Seres and oher assocaed nformaon, s he calculaon of he acual gross prce ndexes and how hey allow for changes n her consuen gls. Changes n he consuens of he secor ndexes can occur for a varey of reasons. The followng rules apply o boh convenonal and ndex-lnked ndexes, excep where noed. 4.1 Addon of consuens Gls may be added o a secor as a resul of: A new ssue. Such gls, unless hey are parly pad, are added on he busness day followng he aucon, syndcaon or placemen. Aucon of 4 ¾% Treasury 2015 On 16 Sepember 2003 he Uned Kngdom Deb Managemen Offce announced he aucon on a fully pad bass of 2,750 mllon nomnal of 4 ¾% Treasury 2015 on Thursday, 25 Sepember 2003 for selemen on Frday, 26 Sepember The aucon resuled n he accepance of bds beween and The gl was added o he FTSE Acuares UK Gls Index Seres afer close of busness on 25 Sepember 2003 (.e. wh effec from sar of radng on 26 Sepember 2003). The gl was ncluded n he ndexes wh an nal prce of (.e. Thursday s closng marke prce). Aucon of 2% Index-lnked Treasury 2035 On 10 July 2002 he Uned Kngdom Deb Managemen Offce announced he resuls of he aucon of 2% Index-lnked Treasury I had been allocaed a a unform srkng prce of The gl was ncluded n he FTSE Acuares Gl ndexes on Thursday, 11 July 2002 a an nal prce of FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

16 Syndcaed Offerng of 1 ¼ % Index-lnked Treasury Gl 2055 On 22 Sepember 2005 he Uned Kngdom Deb Managemen Offce announced he resuls of he syndcaed offerng of 1 ¼% Index-lnked Treasury I had been prced a and he closng marke prce for 22 Sepember was The announcemen saed ha he gl would be ssued and seled on 23 Sepember The gl was ncluded n he FTSE Acuares UK Gls Index Seres afer he close of busness on 22 Sepember (.e. wh effec from he sar of radng on 23 Sepember 2005) a an nal prce of (.e. he closng marke prce for 22 Sepember). Gls may also be added as a resul of converson from oher gls. Gls may also be added o secors as a resul of he shorenng ousandng erm of an exsng gl, whch was prevously n anoher secor. Shorenng of 5 ½% Treasury The earles dae a whch 5 ½% Treasury may be redeemed s 10 Sepember In 2003, hs s assumed o be he redempon dae as he clean prce of he gl s well over par. Afer he close of busness on he Wednesday, 10 Sepember 2003 (.e. wh effec from he sar of radng on 11 Sepember 2003), he gl was removed from he 5 10 years secor and added o he up o 5 years secor. The gl lef he 5 10 years secor wh a fnal clean prce of and was added o he up o 5 years secor a he same prce. Smlarly double-daed gls may slde from one secor o anoher and back agan. 4.2 Removal of consuens Gls may be removed from he ndexes or a secor as follows: Convenonal gls are removed from he ndexes on her redempon dae a he closng prce on he prevous day. They are removed from he calculaon of he fed yelds on he day hey reach one year o redempon. Deleon 10% Treasury % Treasury 2003 was redeemed on 8 Sepember The gl was removed from he FTSE Acuares UK Gls Index Seres afer close of busness on Frday 5 Sepember 2003 (.e. wh effec from he sar of radng on 8 Sepember 2003). The closng prce on 5 Sepember was Index-lnked gls are removed from he prce ndexes a her redempon dae a he closng prce of he prevous day. Deleon of 2 ½% Index-lnked Treasury ½% Index-lnked Treasury 2003 was redeemed on 20 May I was removed from he FTSE Acuares UK Gls Index Seres afer he close of busness on Monday, 19 May 2003 (.e. wh effec from sar of radng on 20 May 2003) a s closng prce of They are no longer deemed o be of a suffcen sze for here o be an effcen marke,.e. hey are now n he UK Deb Managemen Offce s rump sock ls. The FTSE Bond Indces Commee consders ha hey are no longer behavng n he same way as oher gls. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

17 A gl has been merged no anoher gl. Ths somemes occurs when a new ranche of a gl s ssued. Is erms are dencal o hose of an exsng gl, excep ha he frs neres paymen s dfferen. When he new gl goes ex-dvdend he frs coupon paymen, becomes dencal o he exsng gl. A hs sage he wo gls are merged ogeher,.e. become fungble. The las gl o be re-opened wh a ranche n hs way was 8% Treasury 2015 A, whch was ssued n Ocober A gl has convered wholly no anoher gl. I s removed from he ndexes on he converson dae a he closng prce on he prevous day. The gl now has a lfe ha s oo shor for he secor. Ths s referred o as a shorener. A gl s removed from he 5-10 year secor afer he close of busness on he day when s exacly 5 years o he assumed redempon dae,.e. f he redempon dae s 31 March 2009, wll be ncluded n he 5-10 year secor closng calculaons on 31 March 2004, bu wll be removed from hs secor mmedaely aferwards. The gl s a double-daed gl whch has moved o anoher secor as a resul of a change n s prce. 4.3 Aleraon o consuens The amoun n ssue of a gl can change from me o me. Ths can occur as a resul of: The governmen buyng back n he marke some of he gl, whch has hen cancelled. Converson or a swch aucon no anoher gl. Creaon of collaeral for cash managemen operaons Cancellaon of he UK Deb Managemen Offce s Holdngs On 10 March 2006 he Uned Kngdom Deb Managemen Offce (DMO) announced he cancellaon of s holdngs of mllon nomnal of 5½% Treasury Sock and mllon nomnal of 7½% Treasury Sock o ake effec from 13 March The DMO also announced an amendmen o he sze creron for rump gls o nclude gls wh nomnal amouns ha have been reduced o less han 850 mllon. Consequenly he above gls were declared rump socks. The effec on he FTSE Acuares UK Gls Index Seres was ha, afer he close of busness on Frday, 10 March 2006 (.e. wh effec from he sar of radng on Monday 13 March 2006) he above rump socks were deleed from he ndexes. Please noe, he above gls would have remaned n he ndexes wh a reduced nomnal f he new ousandng was a leas 850 mllon. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

18 Gl-edged Converson On 5 Augus 2002 he Uned Kngdom Deb Managemen Offce announced he resul of s converson offer from 9% Treasury 2008 no 5% Treasury % of holders acceped he offer. As a resul of he converson he nomnal value of 9% Treasury 2008 decreased from 5,495 mllon o mllon, and ha of 5% Treasury 2008 ncreased from 3,050 mllon o 8,971 mllon. The DMO mmedaely declared 9% Treasury 2008 o be a rump sock, and hence no elgble for he ndexes. The effec on he FTSE Acuares Gl Index Seres was ha afer he close of busness on Monday, 5 Augus 2002 (.e. wh effec from he sar of radng on 6 Augus 2002) he nomnal amoun 5% Treasury 2008 was ncreased o 8,971 mllon and 9% Treasury 2008 was deleed. Index-lnked Swch Aucon On 19 July 2001 he Uned Kngdom Deb Managemen Offce announced he resuls of a swch aucon from 2% Index-lnked Treasury 2006 no 2 ½% Index-lnked Treasury As a resul of hs aucon, he amoun of nomnal ousandng of 2% Index-lnked Treasury 2006 decreased by 500 mllon o 2,000 mllon and ha of 2 ½% Index-lnked Treasury 2016 ncreased by 561 mllon o 5,526 mllon. Boh gls remaned n he FTSE Acuares UK Gls Index Seres and her amouns n ssue were adjused afer he close of busness on Thursday, 19 July 2001 (.e. wh effec from he sar of radng on 20 July 2001). The ssuance of a new ranche of an exsng gl. New ranches are normally fungble from her ssue dae, alhough n he pas hey only became fungble afer he new ssue wen ex-dvdend for he frs me. Increase n nomnal of 2% Index-lnked Treasury 2035 The Uned Kngdom Deb Managemen Offce announced he ssue of a furher ranche of 650 mllon nomnal of 2% Index-lnked Treasury 2035 by aucon on a fully-pad unform prce bass on Tuesday, 23 Sepember 2003 and selemen on Wednesday, 24 Sepember I was sasfed a a srkng prce of The amoun n ssue of he gl was ncreased from 1,850 mllon o 2,500 mllon afer he close of busness on 23 Sepember 2003 (.e. wh effec from sar of radng on 24 Sepember). The closng prce of he gl on 23 Sepember 2003, a whch prce he exra ranche was added o he ndexes, was The ssue of a smaller amoun of an exsng gl ( mnaps ), or of very small amouns of all gls n ssue (whch s done from me o me for echncal reasons). Creaon of collaeral for cash managemen operaons On 6 June 2002 he DMO ssued relavely small amouns of a range of gls for use as collaeral n s cash managemen operaons. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

19 The nomnal amouns are adjused a he close of busness on he day he UK Deb Managemen Offce ssues he gls. 4.4 Prce Index calculaons In order o ensure ha he prce ndex calculaons reflec changes o her consuens, hey are calculaed on a chan-lnked bass. The basc prncple used s: Marke _ Value( oday) Index ( oday) Index( yeserday) Equvalen _ Value( yeserday) where: Marke_Value(oday) s he oal marke value of all he relevan consuens oday (.e. on he calculaon dae); Equvalen_Value(yeserday) s he oal marke value of he same consuens yeserday (.e. on he prevous calculaon dae) adjused for changes n capal ec. The nal value of he ndex for each orgnal ndex was 100, bu where a secor has been dvded no smaller secors, he new secors have sared wh he ndex value of he larger secor (e.g. he nal ndex for he 5-10 year and year secors was derved from he 5-15 year secor). In he above formula, he marke value oday s he marke value, ncludng accrued neres, of all he gls ha were n he secor boh yeserday and oday. Thus f a new ssue s ssued oday, wll no be ncluded n he ndex unl omorrow (.e. he nex calculaon dae), as s no possble o compare s performance from he prevous day. The basc srucure of he ndex calculaons ensures ha he consuens of any ndex and her weghs reman consan durng he day, bu hey can change overngh. Throughou hs documen and n he Ground Rules, here are references o changes ha occur a or afer close of busness. These changes do no change oday s calculaons n any way, bu hey do change he comparson nformaon n he calculaon of omorrow s ndexes, (.e. hey change he composon of he denomnaor n he above formula). Mahemacally, he prce ndex value for secor s for day, can be defned as: I s, I s, 1 N N,, P P,, 1 where: I s, oday s ndex value I s,-1 N, P, P,-1 yeserday s ndex value adjused nomnal value of gl oday gross prce of gl oday gross prce of gl yeserday and where he summaons are over all gls n secor s oday, ncludng hose gls yeserday whch have been amalgamaed wh oher gls oday. The adjused nomnal value oday s normally he same as he acual ssued nomnal oday, bu here are a few excepons, e.g. when a new ssue comes o he marke, s no ncluded n he ndexes unl he day afer ssue, as was no possble o hold he gl yeserday. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

20 The calculaons make use of he gross prces of he gls,.e. her quoed clean mddle prces plus or mnus he calculaed accrued neres o he selemen dae. The accrued neres calculaons are descrbed n Appendx A Prce Index calculaon examples The followng examples show how he mehodology works and allows for changes n consuens. In all cases a selecon of he followng gl daa s used, and he prces nclude accrued neres: Nomnal Prce Nomnal Prce Nomnal Prce Gl day 1 day 1 day 2 day 2 day 3 day 3 A B C D E F G In he followng examples he prce ndex on day 1, I s, Normal case no change n consuens or amouns n ssue The ndex for days 1, 2 and 3 consss of jus wo gls A and B, as n he able above. Index( day1) Index( day2) Index( day3) New gl ssued on day 2 The ndex on day 1 conssed of wo gls A and B (see above). On day 2, a new ssue C s added o he elgble gls. The calculaons are now: Index( day1) Index( day2) Index( day3) Noe n hs case, he calculaons on day 2 are dencal o hose n he prevous example, as was no possble o hold he new gl on day 1. The new gl C s ncluded n he ndex calculaons on day 2. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

21 Gl s removed from he ndex On day 1, he ndex conssed of hree gls A, B and D. Gl D s removed from he ndex on day 2. The calculaons are now: Index( day1) Index( day2) Index( day3) Gl D does no nfluence day 2 s ndex calculaon, alhough dd hose on day 1. Hence s wegh n day 2 s calculaons mus be reduced o 0. Sze of gl s reduced On day 1, he ndex conssed of hree gls A, B and E (see above). On day 2, he sze of gl E was reduced o 50, possbly as he resul of a converson or he exercse of a snkng fund. The ndex calculaons are now: Index( day1) Index( day2) Index( day3) N.B. only he reduced sze of gl E has been ncluded n he ndexes. Two exsng gls become fungble On day 1, he ndex conssed of four gls A, B, F and G (see above). F was a new ranche of gl G, whch became fungble wh on day 2, afer hey boh wen ex-dvdend. On day 2 only he larger gl G s quoed. The ndex calculaons are now: Index( day1) Index( day2) Index( day3) N.B. on day 2, boh gls F and G are valued a her prces on day 1. They boh wen ex-dvdend by dfferen amouns on day 2, whch s allowed for n he XD adjusmen calculaon. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

22 4.4.2 Prce Index calculaons for a Shorener As has been already descrbed, ndexes are calculaed for gls wh specfc assumed ousandng erm ranges. As a resul, over me, wll be necessary o remove gls from one secor and o pu hem no a shorer secor. Such gls are called shoreners. The followng example descrbes he effec of a shorener on he calculaons of boh he longer secor (L) and he shorer secor (S) no whch he gl s placed. The example uses he followng gl daa: Nomnal Prce Nomnal Prce Nomnal Prce Gl day 1 day 1 day 2 day 2 day 3 day 3 A B C D E The shorer secor ndex on day 1, Index(S,day1) s 110, and he longer secor ndex Index(L,day1) s 120. Effec of a Shorener On day 1, Index (L,day1) consss of gls A, B and E, and Index(S,day1) consss of gls C and D. A he end of day 2, gl E moves from he longer ndex band o he shorer one. The effecs of hs are as follows: Index( S, day1) 110 Index( L, day1) Index( S, day2) Index( L, day2) Index( S, day3) Index( L, day3) FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

23 On Busness Days A gl sarng n an over XX years maury secor wll be moved from ha maury secor o he nexshores maury secor afer he close of busness on he day when s erm o maury s exacly equal o he number of years (XX) n ha secor (when s descrbed as a meous shorener ). I wll be moved a s closng prce on ha day. The nex-shores maury secor may be an "up o XX years" secor or an XX years o YY years secor. Anoher way of sayng hs s: If a gl s erm o maury (he exac number of years from he rade dae o he gl s maury dae) falls on a busness day (when radng s open), and s currenly a consuen n an over XX years maury secor, wll reman n ha secor unl afer he ndex s value s calculaed and dssemnaed for ha day. The followng day, when he gl s erm o maury s now one day shorer, wll become a consuen n he up o XX years secor. I may also hen become a consuen n an XX years o YY years secor, f one exss. A gl maurng on 23 Augus 2011 would be ncluded n he calculaon of he value of he "over 5 years" maury secor on 23 Augus 2006 (when had exacly 5 years remanng o maury). Afer he close of busness ha day, he gl would be moved o he "up o 5 years" maury secor. In oher words, would become a consuen n he shorer maury secor on he followng busness day. A gl sarng n an XX years o YY years maury secor wll be moved from ha maury secor o he nex-shores maury secor afer he close of busness on he day when s erm o maury s exacly equal o he mnmum erm (XX years) of ha secor (when s descrbed as a meous shorener ). I wll be moved a s closng prce on ha day. The shorer maury secor may be an "up o XX years" secor or anoher XX years o YY years secor. A gl maurng on 23 Augus 2023 would be ncluded n he calculaon of he value of he years maury secor on 23 Augus 2008 ( had exacly 15 years remanng o maury). Afer he close of busness on ha day, he gl would be moved o he up o 15 yeas maury secor. In oher words, would become a consuen n he shorer maury secor on he followng busness day. A gl maurng on 15 Ocober 2013 would reman a consuen n he over 5 years maury secor, he 5 10 years secor, he 5 15 years secor, he up o 15 years secor, he up o 20 years secor and he All-Socks secor up unl 15 Ocober Exacly on 15 Ocober 2008, he gl would reman a consuen n hose maury secors and s values would be ncluded n he closng values for hose secors ha were calculaed and dssemnaed o clens as of he close of busness on 15 Ocober On 16 Ocober 2008, when he gl now has less han 5 years o maury, would be ncluded n he up o 5 years secor, he up o 15 years secor, he up o 20 years secor and he All Socks secor. On Non-Busness Days If he gl s erm o maury (he exac number of years from he rade dae o he gl s maury dae) falls on a non-busness day (Saurday, Sunday or oher marke holday), and s a consuen n an over XX years maury secor or an XX years o YY years maury secor on he busness day precedng he non-busness day, wll reman n ha secor on ha precedng busness day (snce s erm o maury s over XX years as of ha busness day) unl afer he ndex s value s calculaed FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

24 and dssemnaed for ha day. The followng busness day wll become a consuen n he nexshores maury secor, snce s erm o maury wll now wll now be shorer (when s descrbed as a lae shorener ). A gl maurng on 15 Ocober 2013 would reman a consuen n he over 5 years maury secor, he 5 10 years secor, he 5 15 years secor, he up o 15 years secor, he up o 20 years secor and he All-Socks secor up unl 15 Ocober Exacly on 15 Ocober 2008, he gl would reman a consuen n hose maury secors and s values would be ncluded n he closng values for hose secors ha were calculaed and dssemnaed o clens as of he close of busness on 15 Ocober Assumng 16 Ocober was a Saurday, on ha day he gl now has less han 5 years o maury, would be ncluded n he up o 5 years secor, he up o 15 years secor, he up o 20 years secor and he All Socks secor begnnng Monday, 18 Ocober. Assumng 15 Ocober was a Saurday, and he gl was a consuen n an over XX years maury secor or an XX years o YY years maury secor on he busness day precedng ha Saurday, wll reman n ha secor on ha precedng busness day (snce s erm o maury s over XX years as of ha busness day) unl afer he ndex s value s calculaed and dssemnaed for ha day. The followng busness day (.e. Monday, 17 Ocober) wll become a consuen n he nex-shores maury secor, snce s erm o maury wll now be shorer han XX years Prce Index calculaons for Double-daed Gls The ndex calculaons for double-daed gls, when her prces are near her equlbrum prces, are more complcaed, especally as hey can slde from one secor o anoher and back agan. As a resul, hey are removed from, and added o, an ndex no a her prevous prces bu a her equlbrum prces. No double-daed gls have been ssued by he Brsh Governmen for some years, and here are now only wo such secures (5½% Treasury 2008/12 and 7¾% Treasury 2012/15) sll ncluded n he ndexes. The dealed mehod of allowng for double-daed gls ( slders ) s descrbed n he Ground Rules for he Managemen of he FTSE UK Gls Index Seres. When a double-daed gl moves from one secor o anoher a s equlbrum prce, necessaes he addonal calculaon of equvalen mean prces for all he oher gls n he secors. Ths s shown n he followng example. There are wo secors L and S. The longer secor L on day 1 consss of 3 gls: A, B and E (whch s double-daed), and he shorer secor S consss of 2 gls: C and D. Durng day 2 he prce of he double-daed gl rses above s equlbrum prce, wh he resul ha needs o move o he shorer secor. The gls n he secors have he followng daa: Nomnal Prce Nomnal Prce Nomnal Prce Gl day 1 day 1 day 2 day 2 day 3 day 3 A B C D E(doubledaed) The shorer secor s prce ndex on day 1, Index(S,day1) s 110, and he longer secor s ndex Index(L,day1) s 120. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

25 On day 2, he equlbrum prce for he double-daed gl E s 100, hence needs o move from secor L o S. In order o do hs, mean prces have o be calculaed for all he gls n he secors usng lnear nerpolaon. As he equlbrum prce of he double-daed gl s mdway beween s closng prces on days 1 and 2, he mean prces of he oher gls wll also be mdway beween her wo prces. Gl Prce day 1 Prce day 2 Prce mean A B C D E(double-daed) The calculaons are as follows: Index( S, day1) 110 Index( L, day1) Index( S, day2) Index( L, day2) Index( S, day3) Index( L, day3) Prce Index mehodology usng a dvsor The Ground Rules for he Managemen of he FTSE Acuares UK Gls Index Seres, on he oher hand, descrbe he consrucon of he prce ndexes n erms of a dvsor. Wh he dvsor descrpon, he prce ndex I s, for secor s for oday s gven by: I s, where: I s, oday s ndex value N, P Dvsor N, adjused nomnal value of gl oday P, gross prce of gl oday Dvsor s, calculaed dvsor for secor s a me and where he summaon s over all gls n he secor s oday, ncludng hose gls yeserday whch have been amalgamaed wh oher gls oday. The dvsor n hs formula sared lfe as jus he marke value of he ndex a he base dae dvded by 100, (assumng ha he ndex sared wh a base value of 100). Ths formulaon of he ndex s easy s,, FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

26 o undersand as long as he consuens of he ndex do no change n any way, as he ndex value s jus he marke value of he consuens now dvded by her value a he base dae. Unforunaely, whenever here s a change o he consuens, he dvsor has o be changed o reflec hs. These changes have o allow for consuens beng removed from he ndex (hey may have performed dfferenly o ha of he ndex as a whole), he sze of consuens changng or new consuens beng added. Thus afer a whle he dvsor ceases o have any ndependen meanng. The way he dvsor changes are calculaed s descrbed fully n he Ground Rules. The wo mehods of descrbng he consrucon of he prce ndex, ha s n erms of he change over he prevous day and ha of usng a dvsor are equvalen. Consder an ndex I whch commenced on dae 0. Ths ndex has no had any changes o s consuens or changes o capal snce s base dae. The ndex s calculaed on daes 0, 1, 2, 3 n. Usng he chan-lnked mehod we ge: I I 100 N N,1,0 P,1 P,0 I n 100 N N,1,0 P,1 P,0 N N,2,1 P P,2,1... N N, n P, n 1, n P, n 1 I n 100 N N, n,0 P P, n,0 Wh he dvsor mehod, as he consuens, and her weghngs, have no changed snce he base dae, he dvsor self has no changed. I s gven by: Dvsor N P, 0,0 100 Hence he ndex a me n s: I n N, n P Dvsor, n 100 N N, n,0 P, n P whch s he same resul as wh he chan-lnked mehod.,0 FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

27 Secon 5 Formulae Applyng o boh Convenonal and Index-lnked Gls 5.0 Formulae Applyng o boh Convenonal and Index-lnked Gls 5.1 Accrued Ineres All gls n he ndexes accrue neres a a daly rae for he perod whch would ensure ha he oal coupon paymen would be accrued by he coupon paymen dae. Ths s no vsble as all gls go exdvdend (XD) 7 busness days (or n he case of 3½% War Loan 10 busness days) before he coupon paymen dae. If a gl s sold for selemen durng he XD perod, he seller reans he coupon. The accrued neres calculaons for secures are descrbed n Appendx A. The accrued neres for a secor s for day, A s, s calculaed as: N AI AI I,,, s, N, P, where: I s, gross prce ndex of secor s a me s N, AI, P, nomnal ousandng of gl a me accrued neres of gl a me gross prce of gl a me and where he summaon s over all gls n secor s a me. The prce ndex adjusmen s o make he calculaon comparable wh he prce ndex whch reflecs all he changes n consuens snce base dae. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

28 Consder a secor whch consss of wo gls A and B, whch have he followng curren nformaon: Gl Nomnal Gross prce Accrued neres A B The curren prce ndex s 150. The accrued neres for he secor s hen: Accrued _ Ineres( Secor) Gross or Dry prces Gls are quoed n he marke wh clean prces,.e. a a prce whch excludes any accrued neres. Ths means ha he prce quoaon does no have o be modfed every day o allow for he daly effec of accrued neres. When a gl s raded, he ransacon s execued a a gross or dry prce,.e. he clean prce of he gl plus/mnus any accrued neres o he approprae selemen dae. The selemen dae for a gl s usually he nex busness day. Thus normally on a Thursday, he accrued neres s calculaed o he followng day, he Frday, bu on a Frday s calculaed o he followng Monday (normally he nex busness day). In hs case, a ransacon execued on he Frday would nclude 3 days more accrued neres han one execued on he prevous Thursday (nsead of jus 1 day more), assumng he gl had no gone ex-dvdend. Gross prces are used n all he ndex calculaons. 5.3 XD Adjusmen The effec of a gl n an ndex gong ex-dvdend (XD) s o reduce he prce ndex of he secor, snce f he marke quoaon of he gl s unchanged, s gross prce wll have decreased. Somemes, as n he case of he Toal Reurn Index, s desrable o measure he effec of re-nvesng hese coupons. Ths s acheved by calculang he XD adjusmen facor. The XD adjusmen for secor s oday, XD s, s calculaed as: X XD, 1, s, I s, 1 N, 1 P, 1 N where: I s,-1 gross prce ndex of secor s a me -1 N,-1 nomnal ousandng of gl a me -1 XD, quanum neres for gl ha has gone ex-dvdend beween he las day on whch he ndexes were calculaed, and he openng of oday P,-1 gross prce of gl a me and where he summaon s over all gls n secor s a me -1. Noe ha he prevous day s values are now used o wegh he calculaons, as for he ex-dvdend o have an effec he gls mus have been held on he prevous day. XD, for gl s 0 f he gl has no gone ex-dvdend beween day -1 and day, oherwse s he percenage coupon paymen ha has gone XD. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

29 Consder a 5% gl ha goes XD on 4 Aprl of a sandard sem-annual coupon paymen of 2.5%. On 3rd Aprl, he XD adjusmen XD s 0 On 4h Aprl, he XD adjusmen XD s 2.5 On 5h Aprl, he XD adjusmen XD s 0. Consder a secor whch consss of wo gls A and B. On he prevous calculaon dae A and B had respecvely 100 and 200 of nomnal n ssue and gross prces of 95 and 90. Immedaely pror o oday gl A goes XD wh a paymen of 2.5%, and he prce ndex of he secor on he prevous day s 140. The calculaon of he XD adjusmen for he secor oday s: XD _ adjusmen( Secor) The publshed fgure for secor s for day s he XD adjusmen for he year o dae. Ths fgure s jus he sum of all he daly fgures for he curren year up o dae. 5.4 Toal Reurn Index The Toal Reurn Index for secor s for day, R s,, s calculaed from he secor Prce Index and XD adjusmen by: R s, R s, 1 where: I s, secor s prce ndex for day I s, 1 I s, XD X Ds, XD adjusmen facor for secor s for day. As he XD adjusmen facor for a secor s zero whenever here are no coupon paymens on he day n he secor. Hence he percenage movemen n he oal reurn ndex s dencal o ha of he gross prce ndex whenever here are no coupon paymens n he secor. If 3 weeks ago he prce ndex of a secor was 110 and s oal reurn ndex was 140, and s prce ndex s now 120, hen provded here have been no gls n he secor whch have gone ex dvdend n he nervenng perod, he curren oal reurn ndex s: 140 x 120 / Number of secures The number of secures s jus he number of dfferen secures oday n he ndex secor. s, FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

30 5.6 Secor wegh The wegh of a secor s s jus s marke value oday M s, dvded by he marke value of All-socks secor M A,. Tha s: M M s, A, s A N N,, P, P, where: N, nomnal ousandng of gl a me P, gross prce of gl a me and where he summaons are over all gls n secor s and he combned secor A respecvely a me. Then: W s, 100 M s, M A, where W s, s he percenage wegh of secor s oday. Assumng he All-socks secor consss of wo secors X and Y. Boh secors conss of wo gls A and B, and C and D respecvely. A he calculaon dae he gls have he followng daa: Gl Nomnal ousandng Clean prce Accrued neres A B C D The marke values M X, M Y of secors X and Y are: M M X Y Hence: W W X Y 100 (90 + 2) (95 + 1) (80 + 0) (85 + 4) % % where W X and W Y are he weghs of he wo secors. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

31 Secon 6 Formulae applyng o Convenonal Gls only 6.0 Formulae applyng o Convenonal Gls only 6.1 Gross Redempon Yeld As all he gls ncluded n boh he convenonal and he ndex-lnked ndexes pay coupons wce a year, s normal n he marke place o quoe redempon yelds whch are compounded on a sxmonhly bass. Ths convenon s adoped here. The redempon yeld of a convenonal gl wh 2 sem-annual coupon paymens, compounded annually can be deermned from he followng formula: P T 1 2 T 1 CF ( 1+ y / ) CF v where: P gross prce (.e. clean prce plus/mnus accrued neres) T number of fuure cash flows,.e. fuure coupon paymens and he fnal redempon amoun CF h cash flow,.e. neres and capal paymens me n perods (.e. sx-monhly coupon perods) o he h cash flow v dscounng facor,.e. v 1/(1 + y/2) y requred redempon yeld. Ths formula s used for gls wh more han one coupon paymens remanng. The redempon yeld for ndex-lnked gls s calculaed n a smlar way bu wh he followng dfferences: In deermnng he sandard equaon, fuure cash flows may be grossed up by he assumed nflaon rae; The resulng calculaed dscoun facor has o be need down by he assumed rae of nflaon. The dscounng perod used for each cash flow CF s he number of neres perods and fracon of perods o he relevan paymen dae. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

32 In he above equaon, all he cash flows CF, oher han he frs one n he case of new ssues and he las one, are normally equal o half he annual coupon of he secury, as he gls pay neres wce a year. The las cash flow s normally equal o he redempon amoun plus half he annual coupon. If s 7 Augus 2011 and a cash flow paymen of 8 s due on 7 Sepember 2012, hen s dscouned for wo and a b perods n he calculaons a fraconal perod from 7 Augus 2011 o 7 Sepember 2011, a whole perod from 7 Sepember 2011 o 7 March 2012 and anoher whole perod from 7 March 2012 o 7 Sepember The fraconal perod has a value 31/184 as here are 31 and 184 days from 7 Augus 2011 o 7 Sepember 2011 and 7 March 2011 o 7 Sepember 2011 respecvely. Ths cash flow wll hus have a conrbuon of 8 x v o he rgh hand sde of yeld equaon, (31/ ). Consder an 8% gl whch pays coupons sem-annually, whch s prced a on s coupon dae 18 monhs before s redempon. A holder of hs gl unl redempon wll receve he followng neres and capal paymens: 4 n 6 monhs me (1 perod ) 4 n 12 monhs me 104 n 18 monhs me (coupon plus he capal repaymen). To calculae he redempon yeld y for hs gl, s necessary o solve he equaon: v v + v where: y 2 x (1/v 1) Ths gves v and y % The gross redempon yeld for a secor s calculaed by dscounng all he cash flows from he gls n he secor a he same rae,.e. performs he redempon yeld calculaon as f he secor were jus a sngle gl. No dsncon s made beween cash flows emanang from dfferen gls. Consder a secor whch consss of jus wo gls. Gl A has a 6% coupon and pays neres on 7 March and 7 Sepember each year unl s redeemed on 7 Sepember Gl B has a 4% coupon and pays neres on 7 June and 7 December unl s redeemed on 7 December On 7 June 2003 gl A has ousandng 200m of nomnal value and a gross prce, ncludng accrued neres, of 105, whereas gl B 100m ousandng and a gross prce of 95. Exendng he formula gven above, he followng has o be solved o calculae he secor redempon yeld: 200 x x x v 0.5 x (3 + 3 x v +3 x v x v x v 13 ) x (2 x v + 2 x v x v x v 7 ) where v s he dscoun facor,.e. v 1 /(1 + y/2), and y s he requred secor redempon yeld. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

33 However, when reporng yeld, duraon and convexy fgures for ndvdual gls, FTSE follows marke convenon and uses dfferen formulae for bonds n her fnal coupon perod. A gl eners he fnal coupon paymen perod only afer he neres dae has passed, a whch pon he yeld, duraon and convexy calculaons swch o usng smple neres. The defnon of smple neres durng he las coupon paymen of a gl s as follows: SmpleIneresannualsed FnalPaymen 1 Dryprce YearsoMaury Equvalenly, he prce of a bond as a funcon of smple neres durng he las paymen perod s gven by: CF P 1 T ( + r f ) where: P gross prce (.e. clean prce plus/mnus accrued neres) 6.2 Macaulay duraon r annualsed smple neres rae CF T fnal cash flow (coupon and prncpal) f fracon of a year o maury The Macaulay duraon of a bond and hence by exenson ha of a secor, s jus he average lfe, expressed n years, of all he fuure cash flows afer hey have been dscouned by he gross redempon yeld. I hus measures how long, on average, he bond wll be ousandng. The Macaulay duraon s somemes jus referred o as he duraon. The duraon D Mac of a bond s derved by solvng an equaon of he form: D Mac 1 P 1 T CF T 1 2 T ( 1+ y / ) CF v 1 CF v where: D Mac Macaulay duraon n years frequency frequency T number of fuure cash flows,.e. fuure coupon paymens and he fnal redempon amoun CF h cash flow,.e. neres and capal paymens me n perods (.e. sx-monhly coupon perods) o he h cash flow frequency number of paymens per year,.e. 2 for gls. Ths s requred as he duraon s normally expressed n years. V dscounng facor,.e. v 1/(1 + y/2) y redempon yeld of he secury or secor. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

34 Consder a secor ha has a gross redempon yeld y, and an assocaed dscounng facor v, where v 1 / (1 + y / 2). I has ancpaed fuure cash flows of 100, 200 and 300 n 1, 2 and 3 sx-monhly perods respecvely, hen he duraon D Mac of he secor s: v v v D Mac / 2years Usng, as an example, he same gl as ha used n he redempon yeld calculaon,.e. an 8% gl yeldng 5% wh exacly 18 monhs o go o redempon. As y 0.05, and v , he duraon D Mac s gven by: D Mac / years When calculang he Macaulay duraon of an ndvdual bond n he fnal paymen perod, he followng formula s used: where f s he fracon of a year o maury. 6.3 Modfed duraon D Mac The modfed duraon of a bond or ndex measures how sensve he yeld s o a change n prce and vce versa. I s defned as he percenage change n prce for a un change n yeld. Hence, modfed duraon s a measure of volaly. The modfed duraon D Mod for a bond s gven by: where: P gross prce dp small change n prce D dp 1 Mod dy P dy correspondng small change n yeld. For a gl payng sem-annual coupons, modfed duraon s: D Mod f D ( 1 + y / 2) D v where: D Mac Macaulay duraon of he bond or secor v dscounng facor,.e. v 1 / (1 + y / 2) y gross redempon yeld of he bond or secor. Whenever an ndex has a posve yeld, he modfed duraon wll be less han he Macaulay duraon. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

35 If an ndex has a gross redempon yeld of 4.5% and a Macaulay duraon of 3 years, hen wll have a modfed duraon of: 3 v 3/( / 2) If a gl yeldng 5% p.a. compounded sem-annually has a Macaulay duraon of 1.44, hen s modfed duraon D Mod s gven by: D Mod 1.44 /( / 2) The modfed duraon D Mod for a bond n he fnal perod s: where: r annualsed sngle neres rae 6.4 Convexy f fracon of a year o maury f D Mod r 1 ( + f ) The relaonshp beween prce and redempon yeld s no lnear, bu curved. In a smlar way o modfed duraon, whch measures he slope of hs relaonshp, convexy measures he degree of 2 2 curvaure: s relaed o he second dervave d P dy. The formula below s for Macaulay Convexy wh 2 sem-annual coupon paymens: C Mac 1 P 1 T T 1 T 1 2 CF ( 1+ y / 2) CF v where: C Mac Macaulay Convexy CF v 2 frequency frequency T number of fuure cash flows,.e. fuure coupon paymens and he fnal redempon amoun CF h cash flow,.e. neres and capal paymens T me n perods (.e. sx-monhly coupon perods) o he h cash flow 2 2 Frequency number of paymens per year,.e. 2. Ths s requred f he convexy s o be expressed n years 2. v dscounng facor,.e. v 1/(1 + y/2) y redempon yeld of he secury or secor. Usng, as an example, he same gl as ha used n he redempon yeld calculaon,.e. an 8% gl yeldng 5% wh exacly 18 monhs o go o redempon. As y 0.05, and v , he convexy C Mac s gven by: FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

36 C Mac / The formula for Macaulay Convexy for a bond wh a sngle remanng coupon paymen s: C Mac f 2 Where f s he fracon of a year o maury or he Macaulay Duraon of he gl. 6.5 Fed Yelds for Convenonal Gls Fed yelds gve he heorecal yelds for convenonal gls wh ousandng erms of exacly 5, 10, 15, 20 and 25 years. A fed yeld s also calculaed for undaed secures. Ths s acheved by calculang for all he accepable daed convenonal gls, ncludng he undaed (rredeemable) ssues bu excludng all gls wh less han a year o maury, he bes f curve of her gross redempon yelds agans her ousandng erms. The form of he yeld curve, whch allows for wo changes of drecon, s: y( m) A + B e Cm + D e Em where A, B, C, D and E are parameers. The curve s found by mnmsng: S( A, B, C, D, E) N P ( y( m ) y ) where: y gross redempon yeld of he h gl m ousandng erm o redempon of he h gl y(m) yeld gven by he curve for ousandng erm m N amoun n ssue of he h gl P gross prce of he h gl 2 and where he summaon s over all he accepable daed gls. All he accepable daed gls n he prce ndexes whch have an ousandng erm of a leas one year are ncluded n he calculaon of he fed yelds. Fed yelds are publshed for erms of 5, 10, 15, and 20 years. For undaed gls (rredeemables) he yeld y( ), s also publshed and calculaed as: y ( ) N P y N P Tha s, s jus he average yeld of he undaed gls weghed by her ousandng marke values. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

37 Secon 7 Formulae Applyng o Index-lnked Gls only 7.0 Formulae Applyng o Index-lnked Gls only 7.1 Coupon and redempon amoun calculaons Boh coupon and redempon paymens for all ndex-lnked gls currenly n ssue are lnked o he UK real prces ndex (RPI). Indexaon for gls ssued pror o 22 Sepember 2005 s based on an 8- monh lag. New gls ssued on or afer ha dae are based on a 3-monh lag. s n he nex secon are based on 8-monh lag. s for gls wh 3-monh lag can be found n Secon 7. Consder an ndex-lnked gl whch s ssued on 26 January 2004 wh a 4% coupon, payable semannually, and whch wll be redeemed 10 years afer ssue on 26 January 2014 a par ndexed by he RPI. If he RPI for May 2003 (.e. 8 monhs pror o he ssue dae of January 2004) s 200, and he RPI values are as n he able below, he paymens wll be as shown. Paymen Dae RPI Dae RPI Value Paymen Ineres Nov x 200.5/ Ineres May x 201.0/ Ineres Nov x 202.0/ Ineres May x 280.0/ Capal May x 280/ As has been menoned before, he calculaons are based on assumpons ha n fuure he UK Real Prces Index wll rse by 0%, 3%, 5% and 10% per annum. However, f we are lookng a a cash flow whch s o be pad n one year s me, and we are assumng a fuure nflaon rae of 10% p.a., hs does no mean ha hs value wll be 10% more han s value oday because of he ndex laggng. In Augus 2003, for llusrave purposes assume ha he recen RPI values have been: Nov Dec Jan Feb Mar FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

38 Apr May Jun Jul Aug Any paymen due n Sepember 2003, rrespecve of wheher s an neres or capal paymen, wll be based on he January 2003 RPI, hose due n Ocober 2003 on he February 2003 RPI ec. Irrespecve of wha assumpons are assumed abou fuure nflaon raes, hese paymens are unchanged. If an annual nflaon rae of 10% s assumed, hen he nflaon for each fuure monh s assumed o ncrease by he rao r, where r s gven by: r ( /100) 1/ Usng he above example, wh 10% nflaon he assumed fuure RPI fgures are: Sep x Oc x Nov x Dec x Jan x ec Agan usng he above example RPI, f a gl whch s ssued wh a 4% coupon, based on a base RPI of 198.0, pays sandard sx monhly neres paymens n January and July, hen he paymens wll be: Jul x Nov 02 RPI / x 199 / % Jan x May 03 RPI / x 203 / % July x Es. Nov 03 RPI / x 205 / % assumng no fuure nflaon July x Es. Nov 03 RPI / x / % assumng fuure nflaon of 10% FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

39 7.2 Real redempon yeld calculaons Real redempon yelds for ndex-lnked gls are calculaed n a smlar way o hose for convenonal gls, alhough here are wo dfferences: In solvng he sandard equaon, fuure cash flows may be grossed up by he assumed nflaon rae as descrbed n he prevous secon; The resulng calculaed dscoun facor has o be need down by he assumed rae of nflaon. The real redempon yeld for ndex-lnked gls s derved by solvng an equaon of he form: n P CF v where: P gross prce (.e. clean prce plus/mnus accrued neres) 1 n number of fuure cash flows,.e. fuure coupon paymens and he fnal redempon amoun L CF h cash flow,.e. neres and capal paymens, grossed up by he assumed fuure nflaon rae as descrbed n he prevous secon L me n perods (.e. sx-monhly coupon perods) o he h cash flow V dscounng facor wh he fuure cash flows grossed up by he assumed nflaon rae f necessary,.e. v 1/((1 + ry/2) x r 6 ) ry requred real redempon yeld r monhly nflaon rao,.e. r (1 + ) 1/12 I assumed annual nflaon rae, e.g for 5% nflaon Solvng hs equaon gves a real redempon yeld whch has been compounded sem-annually. In he above equaon, he frs cash flow amoun CF 1 s known as s based on an already known RPI. On 19 January 2004, consder an ndex-lnked gl wh a coupon of 4%, payable sem-annually, based on a base RPI of 180, whch wll be redeemed n 18 monhs me on 19 July The gl wll make neres paymens on 19 July 2004, 19 January 2005 and 19 July The nex neres paymen wll be based on he known RPI of for November 2003 (.e. 8 monhs before July 2004). The laes publshed monhly RPI of s for December The scheduled cash flows for he gl based on assumed fuure nflaon raes of 0%, 5% and 10% are: Assumed nflaon rae 0% 5% 10% Ineres n 6 monhs C C C Ineres n 12 monhs A A x r 5 A x s 5 Ineres n 18 monhs A A x r 11 A x s 11 Capal n 18 monhs B B x r 11 B x s 11 where: C 2 x 240 / % A 2 x 241 / % B 100 x 241 / % FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

40 r ( ) 1/12 s ( ) 1/12 The dscoun raes v 0, v 5 and v 10 for assumed nflaon raes of 0%, 5% and 10% respecvely are calculaed by solvng he followng equaons: P C v ( v A v0 + A + B) P C v A r v5 + ( A + B) r v5 P C v A s v10 + ( A + B) s v10 where: v j 1/((1 + ry j /2) x r 6 ) and ry j s he real redempon yeld a he relevan assumed nflaon rae. Real redempon yelds for ndex-lnked secors are calculaed, n a smlar way o ha for convenonal secors, from he projeced combned fuure cash flows of he gls n he secor n he same way as for a sngle secury. 7.3 Oher calculaons Macaulay Duraon, Modfed Duraon and Convexy for Index-lnked gls are calculaed n he same way as for convenonal gls, bu hese calculaons now use he dscounng facor v 1/((1 + ry/2) x r 6 ) from he calculaon of he real redempon yeld. I s mporan o realze ha he dscounng facor v s NOT 1/(1 + ry/2) where ry s he real yeld. The relaonshp beween Macaulay s duraon MD and modfed duraon D s sll: MD D v FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

41 Secon 8 Calculaons for Index-lnked Gls wh a 3-monh lag 8.0 Calculaons for Index-lnked Gls wh a 3-monh lag 8.1 Indexaon mehodology The ndexaon mehodology for he Index-lnked gls wh a 3-monh lag s as follows: Index Rao Dae Ref RPI Ref RPI Dae Frs Issue Dae (Rounded o 5 decmal places) Where Index Rao Dae refers o he Index Rao for a gven dae 1 Ref RPI Dae Ref RPI M + [Ref RPIM+1 - Ref RPI M ] D Where D Number of days n calendar monh n whch he gven dae falls. Calendar days correspondng o he gven dae. RPI M Reference RPI for he frs day of he calendar monh n whch he gven dae falls. Ref RPI M+1 Reference RPI for he frs day of he calendar monh mmedaely followng he gven dae. 1 Ref RPI Frs ssue Dae Ref RPI M + [Ref RPIM+1 - Ref RPI M ] D Ths s smlar o he Ref RPI Dae formula excep M denoes he calendar monh of he ssue dae. The worked examples below are based on a hypohecal 4% coupon gl ssued on he 26 January 2004 wh a maury dae of 26 January Ineres s payable sem-annually n January and July. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

42 8.2 Calculang Coupon Paymens Sem-annual Coupon Paymen 2 C x Index RaoDv paymen dae (Rounded o 6 decmal places) Where: C Annual Coupon Amoun Index Rao Dv paymen dae Ref RPI Ref RPI DvdendPaymenDae Frs Issue Dae Calculang he Reference RPI for he Coupon Paymen Dae 1 Ref RPI Dv paymen dae Ref RPI M + [Ref RPIM+1 - Ref RPI M ] D Where: D Number of days n calendar monh n whch he coupon paymen dae falls. Calendar days correspondng o he gven dae. RPI M Reference RPI for he frs day of he calendar monh n whch he gven dae falls. Ref RPI M+1 Reference RPI for he frs day of he calendar monh mmedaely followng he gven dae. For example, assumng he RPI values for Aprl 2004 and May 2004 are and respecvely, he reference RPI for 26 July 2004 s calculaed as follows: Ref RPI 26 July 2004 Ref RPI 1 July (26-1)/31 [Ref RPI 1 Augus 2004 Ref RPI 1 July 2004 ] RPI Aprl (25/31) [RPI May 2004 RPI Aprl 2004 ] (25/31)[ ] (Rounded o 5 decmal places) Calculang he Reference RPI for he Frs Issue Dae 1 Ref RPI Frs ssue Dae Ref RPI M + D Where: [Ref RPI M+1 - Ref RPI M ] D Number of days n calendar monh n whch he ssue dae falls. Calendar days correspondng o he gven dae. RPI M Reference RPI for he frs day of he calendar monh n whch he ssue dae falls. Ref RPI M+1 Reference RPI for he frs day of he calendar monh mmedaely followng he ssue dae. Assumng he RPI value of for Ocober 2003 and for November 2003, he reference RPI for 26 January 2004 (.e. frs ssue dae) s calculaed as follows: Ref RPI 26 January 2004 Ref RPI 1 January (26-1)/31 [Ref RPI 1 February 2004 Ref RPI 1 January 2004 ] RPI Ocober (25/31) + [RPI November 2003 Ref RPI Ocober2003 ] (25/31) + [ ] (Rounded o 5 decmal places) FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

43 8.2.3 Calculang he Index Rao Coupon Paymen Dae Recall The Index Rao dv paymen dae Ref RPI dv paymen dae/ref RPI Frs Issue dae / (Rounded o 5 decmal places) Calculang he Coupon Paymen Amoun Recall; Sem-annual Coupon Paymen Annual coupon/2 * Index Rao Dv paymen dae 4/2 x (Rounded o 6 decmal places) 8.3 Calculang he Redempon Paymen Redempon Paymen 100 x Rao Redempon dae Index Rao Redempon dae Ref RPI Redemon dae /Ref RPI Frs ssue dae Ref RPI Redemon dae Ref RPI M + [Ref RPI M+1 - Ref RPI M ] Where: D Number of days n calendar monh n whch he redempon dae falls. Calendar days correspondng o he gven dae. RPI M Reference RPI for he frs day of he calendar monh n whch he redempon dae falls. Ref RPI M+1 Reference RPI for he frs day of he calendar monh mmedaely followng he redempon dae. Assumng he RPI value of for Ocober 2013 and for November 2013, he reference RPI for 26h January 2014 (.e. redempon dae) s calculaed as follows: Ref RPI 26 January 2014 Ref RPI 1 January (26-1)/31 [Ref RPI 1 February 2014 Ref RPI 1 January 2014 ] RPI Ocober (25/31) x [RPI November 2013 RPI Ocober 2013 ] (25/31) x [ ] (Rounded o 5 decmal places) The Ref RPI Frs ssue dae calculaed as n prevous examples gvng a value of Index Rao Redempon dae / (Rounded o 5 decmal places) Redempon Paymen 100 x (Rounded o 6 decmal places) 8.4 Cashflows based on varous nflaon assumpons As has been menoned before, yeld, duraon, modfed duraon and convexy calculaons are based on assumpons ha n fuure he UK Real Prces Index wll rse by 0%, 3%, 5% and 10% per annum. However, f we are lookng a a cash flow whch s o be pad n one year s me, and we are assumng a fuure nflaon rae of 10% p.a., hs does no mean ha hs value wll be 10% more han s value oday because of he ndex laggng. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

44 In Augus 2004, for llusrave purposes assume ha he recen RPI values have been: Oc Nov Dec Jan Feb Mar Apr May Jun July Aug Any paymen due n January 2005, rrespecve of wheher s an neres or capal paymen, wll be based on he RPI values for Ocober 2004 and November 2004 snce he Ref RPI for January s based on he RPIs for hose monhs. Irrespecve of wha assumpons are assumed abou fuure nflaon raes, hese paymens are unchanged. If an annual nflaon rae of 10% s assumed, hen he nflaon for each fuure monh s assumed o ncrease by he rao r, where r s gven by: r ( /100) 1/ Usng he above example, wh 10% nflaon he assumed fuure RPI fgures are: Sep x Oc x Nov x ec. Agan usng he above example RPI, f a gl whch s ssued wh a 4% real coupon, hen he paymen on 26 January 2005 be: Sem-annual Coupon Paymen 2 C x Index RaoDv paymen dae (Rounded o 6 decmal places) The Index Rao dv paymen dae Ref RPI Dv paymen dae /Ref RPI Frs ssue dae Ref RPI Dv paymen dae RPI Ocober (25/31) [RPI November 2004 RPI Ocober2004 ] (25/31)[ ) (Rounded o 5 decmal places) The Ref RPI was calculaed n prevous example as The ndex rao s / (Rounded o 5 decmal places) Sem-annual coupon paymen 4/2 x (Rounded o 6 decmal places). Assumng no fuure nflaon, an RPI value of wll be used for boh Ocober 2004 and November The calculaon s shown below. Ref RPI Dv paymen dae (25/31)[ ] FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

45 The ndex Rao / (Rounded o 5 decmal places) Sem-annual coupon paymen 4/2 x (Rounded o 6 decmal places). 8.5 Accrued Ineres calculaons Ineres accrues on an acual/acual bass and s calculaed o he selemen dae. c C x x Index Rao Selemen dae s 2 Where: c s he number of calendar days from he prevous quas-coupon dae o he selemen dae s s he number of calendar days n he quas-coupon perod C s he annual coupon. The Index Rao Selemen dae Ref RPI Selemen dae /Ref RPI Frs ssue dae 1 Ref RPI Selemen dae Ref RPI M + D Where: [Ref RPI M+1 - Ref RPI M ] D Number of days n calendar monh n whch he selemen dae falls. Calendar days correspondng o he gven dae. RPI M Reference RPI for he frs day of he calendar monh n whch he selemen dae falls. Ref RPI M+1 Reference RPI for he frs day of he calendar monh mmedaely followng he selemen dae. Assumng selemen dae of 24 h June 2004 and RPI of for March 2004 and for Aprl Issue dae of 26 h January 2004 Ref RPI Selemen dae RPI March (23/30) [RPI Aprl 2004 RPI March 2004 ] (23/30) [ ] (Rounded o 5 decmal places) The Ref RPI was calculaed n prevous example as Index Rao Selemen dae / (Rounded o 5 decmal places) Accrued neres 150/182 x 4/2 x (Rounded o 6 decmal places) FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

46 Appendx A: Accrued Ineres calculaons Boh convenonal and ndex-lnked gls accrue neres daly on an acual/acual bass. The accrued neres, when purchasng a gl, s calculaed o he selemen dae. The basc prncple used n he accrued neres calculaon s ha from one normal neres paymen dae o he nex, he gl accrues neres a he same amoun for each calendar day a such a rae ha wll have accrued exacly he paymen amoun by he coupon dae. Consder a gl wh a 6% coupon, whch pays 3% on 7 March and on 7 Sepember. The daly accrued neres per 100 nomnal of he gl beween he 7 March and 7 Sepember s 3/184% as here are 184 days beween 7 March and 7 Sepember. However, he daly accrued neres beween 7 Sepember and 7 March s eher 3/181% % (181 days n a non-leap year), or 3/182% % (182 days n a leap year). 2½% Treasury Index-Lnked Sock 2013 The 2½% Treasury Index-lnked Sock 2013 was ssued on 21 February I pays sem-annual coupons on 16 February and 16 Augus, and he adjused Real Prce Index (RPI) a he ssue base dae s The calculaon of accrued neres for hs gl for selemen on 2 June 2004 s as follows. The gl las pad a coupon on 16 February 2004 and he nex coupon s expeced on 16 Augus Ths coupon wll be based on a RPI of (.e. he RPI 8 monhs before he paymen). The coupon paymen s adjused by he rao of he wo RPIs. Hence he expeced paymen s: 1.25 x / As here are 107 days from 16 February 2004 o 2 June 2004 and 182 days from 16 February 2004 o 16 Augus 2004, he accrued neres on 2 June s: x 107 / % Somemes gls have eher long or shor coupon paymen perods. When hs occurs, pseudo or quascoupon paymen daes are creaed so ha he gl accrues neres a he same daly rae as a gl wh he same coupon wh he same normal neres paymen daes. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

47 Consder a gl wh a 6% coupon, whch wll normally pay 3% neres on 7 March and on 7 Sepember, whch has been ssued hs year on 7 June. Pror o he frs coupon paymen on 7 Sepember, he gl wll accrue neres a he same daly rae as a gl wh a 6% coupon whch las pad neres on 7 March,.e. a a daly rae of 3/184% (here beng 184 days from 7 March o 7 Sepember). The frs coupon paymen for such a gl wll be 3 x 92 / 184% 1.5%, as here are 92 days from 7 June o 7 Sepember. The poson n a gl ha has a long frs coupon perod s slghly more complcaed. Consder a 6% convenonal gl, whch wll normally pay 3% neres on 7 March and on 7 Sepember, whch has been ssued hs year (no a leap year) on 7 February. I has been specfed ha he frs coupon paymen wll be on 7 Sepember,.e. a perod of 7 monhs. From he 7 February o 7 March he gl wll accrue neres a daly rae of 3/181%, as here are 181 days from he prevous 7 Sepember o he 7 March. From 7 March o 7 Sepember wll hen accrue a a daly rae of 3/184%. The frs neres paymen on 7 Sepember wll be (3 x 28 / )% %. Gls (oher han he 3½% War Loan) go ex-dvdend (XD) 7 busness days before he coupon paymen dae. Ths means ha he seller as opposed o he buyer s enled o he accrued neres assocaed wh he gl, when he selemen dae s n he XD perod. The accrued neres for such a ransacon s now negave. 3½% War Loan goes XD 10 busness days before s coupon daes on 1 June and 1 December. Consder a 6% convenonal gl, whch pays 3% on 7 March and on 7 Sepember. I has been sold for selemen on 1 Sepember,.e. whn he XD perod, wh a negave accrued neres. The accrued neres per 100 nomnal assocaed wh he ransacon s now -3 x 6 / 184% %, as he selemen dae s 6 days before he coupon dae n a 184 day perod. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

48 Appendx B: Redempon yeld compoundng frequency adjusmens In some markes s cusomary o calculae redempon yelds wh he neres beng compounded annually, whereas n ohers s compounded sem-annually. Ths appendx shows how s possble o conver yelds from one compoundng bass o anoher. Redempon yelds for boh convenonal and ndex-lnked gls and secors are calculaed wh neres beng compounded on a sem-annual bass. Ths s hsorcal because nearly all he gls pay neres wce a year. I s normal o compound neres on a sem-annual bass n markes, such as USA and Canada, where coupons are normally pad sem-annually. However, n markes where coupons are normally pad annually, such as n connenal Europe, yelds are normally compounded annually. Redempon yelds compounded sem-annually appear o be less han hose compounded annually. Ths s because he holder has use of half he annual coupon for an exra sx monhs. Consder a 10% convenonal gl, whch pays annually. If s prced a par (100) and has exacly 10 years o redempon, hen has a redempon yeld compounded annually of 10%. However, f on he oher hand were o pay 5% neres every 6 monhs, n 6 monhs me one would ge 5 for every 100 of nomnal held whch one could nves for he nex exra 6 monhs a 10% p.a., assumng yelds do no change. Thus on an annual compoundng bass he redempon yeld would now be: 100 x 10 / x 10 / (2 x 100) 10.25% Generally he formula for converng sem-annually compounded yelds o annually compounded ones and vce versa s: (1 + y ) (1 + a ys 2 2 ) where: y a yeld compounded annually y s yeld compounded sem-annually. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49

49 Appendx C: Furher nformaon A Glossary of Terms used n FTSE Russell s Ground Rule documens can be found usng he followng lnk: hp:// Furher nformaon on FTSE Acuares UK Gls Index Seres Gude o Calculaon s avalable from FTSE. For conac deals please vs he FTSE webse or conac FTSE clen servces a [email protected]. Webse: London Sock Exchange Group companes. All rghs reserved. London Sock Exchange Group companes ncludes FTSE Inernaonal Lmed ( FTSE ), Frank Russell Company ( Russell ), MTS Nex Lmed ( MTS ), and FTSE TMX Global Deb Capal Markes Inc. ( FTSE TMX ). All rghs reserved. FTSE, Russell, MTS, FTSE TMX and FTSE Russell and oher servce marks and rademarks relaed o he FTSE or Russell ndexes are rade marks of he London Sock Exchange Group companes and are used by FTSE, MTS, FTSE TMX and Russell under lcence. All nformaon s provded for nformaon purposes only. Every effor s made o ensure ha all nformaon gven n hs publcaon s accurae, bu no responsbly or lably can be acceped by he London Sock Exchange Group companes nor s lcensors for any errors or for any loss from use of hs publcaon. The London Sock Exchange Group companes do no provde nvesmen advce and nohng n hs documen should be aken as consung fnancal or nvesmen advce. The London Sock Exchange Group companes make no represenaon regardng he advsably of nvesng n any asse. A decson o nves n any such asse should no be made n relance on any nformaon heren. Indexes canno be nvesed n drecly. Incluson of an asse n an ndex s no a recommendaon o buy, sell or hold ha asse. The general nformaon conaned n hs publcaon should no be aced upon whou obanng specfc legal, ax, and nvesmen advce from a lcensed professonal. No par of hs nformaon may be reproduced, sored n a rereval sysem or ransmed n any form or by any means, elecronc, mechancal, phoocopyng, recordng or oherwse, whou pror wren permsson of he London Sock Exchange Group companes. Dsrbuon of he London Sock Exchange Group companes ndex values and he use of her ndexes o creae fnancal producs requre a lcence wh FTSE, FTSE TMX, MTS and/or Russell and/or s lcensors. The Indusry Classfcaon Benchmark ( ICB ) s owned by FTSE. FTSE does no accep any lably o any person for any loss or damage arsng ou of any error or omsson n he ICB. FTSE Russell Gude o he Calculaon Mehods of he FTSE Acuares UK Gls Index Seres, v1.9, Ocober of 49