(1 + Nominal Yield) = (1 + Real Yield) (1 + Expected Inflation Rate) (1 + Inflation Risk Premium)

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1 5. Inflaion-linked bonds Inflaion is an economic erm ha describes he general rise in prices of goods and services. As prices rise, a uni of money can buy less goods and services. Hence, inflaion is an imporan risk facor for invesors, because i can erode he purchasing power of heir invesmens. For example, suppose an invesor acquires a one-year nominal bond a par value wih an annual nominal rae of 5%. If annual inflaion urns ou o be 2%, hen he invesor s purchasing power increases by roughly 3%, bu if acual inflaion is insead 7%, hen he invesor s purchasing power would indeed decrease by 2%. Inflaion-linked bonds are securiies ha are designed o proec invesors from his inflaion risk. Like oher bonds, hey are issued wih a fixed coupon rae and a fixed mauriy dae, bu heir payoffs are linked o inflaion. So, if prices go up, paymens of hese bonds increase oo, mainaining he purchasing power of is holders. 5.1 Real and break-even raes Convenional bonds promise fixed nominal coupons and he redempion paymen of he principal, bu he real value, ha is how many producs and services can be bough wih hese paymens when hey are received, is unknown because i depends on he fuure inflaion rae. On he conrary, he paymens of inflaion-linked bonds are indexed o inflaion and herefore guaranee a fixed real reurn irrespecive of inflaion. The yield of a convenional bond consiss mainly of hree pars, a real yield which is a compensaion for delayed consumpion and an expeced inflaion over he life of he bond, which is a compensaion for he expeced loss in purchasing power due o inflaion. So, convenional bonds also compensae for inflaion, bu i is ex ane. If realized inflaion urns ou o be higher han expeced, hen he invesor suffers a loss in purchasing power. Due o his risk, he hird par of he yield of a convenional bond is an inflaion risk premium o compensae he invesor. So, 21 Nominal Yield = Real Yield + Expeced Inflaion Rae + Inflaion Risk Premium On he oher hand, he yield of an inflaion-linked bond consiss only of wo pars, a real yield and he realized inflaion over he life of he bond, bu as his inflaion compensaion is applied afer issuance, ex pos, he rae when he bond is issued consiss only of he real yield. Inflaion-linked Yield = Real Yield + Acual Inflaion Rae 21 This formula is an approximaion, he acual formula is (1 + Nominal Yield) = (1 + Real Yield) (1 + Expeced Inflaion Rae) (1 + Inflaion Risk Premium) This approximaion is appropriae when yields and inflaion are low and herefore is a general indusry pracice. page 36

2 From he nominal yields of a convenional bond and of a comparable inflaion-linked bond of he same mauriy, an esimaion of he inflaion expeced by he marke over he erm of he bonds can be obained. This is called he breakeven inflaion, and is calculaed, ignoring he inflaion risk premium 22, as: 23 Breakeven Inflaion = Nominal Yield Inflaion-linked Yield If acual inflaion exceeds breakeven inflaion over he lives of he bonds, hen inflaionlinked bonds would provide superior reurns o a similar convenional bond. Conversely, if acual inflaion is less han breakeven inflaion, convenional bonds would provide superior reurns o a similar inflaion-linked bond. If acual inflaion is equal o breakeven inflaion, hen an invesor would be indifferen beween boh of hem. 5.2 Invesmen characerisics Some of he characerisics of inflaion-linked bonds are equivalen o ha of convenional bonds, such as ime o mauriy, coupon paymen frequency, ec. This secion considers he key choices and consrains ha face he designers of inflaion-linked bonds and ha are specific for his asse class Reference price index The firs ask is o deermine how realized inflaion is measured. Cash flows are linked hroughou he life of he bond o changes in a specified price index. Inflaion-linked bonds are usually linked o he naional consumer price index. The proecion an invesor aains depends on he correlaion beween he baske used o form he index and he invesor s own consumpion. 24 The benefis of consumer price indices are ha hey are known o he general public, ha hey are published monhly and ha heir calculaions are reliable Indexaion Inflaion-linked bonds are designed o proec invesors agains he erosion of he bonds cash flows due o inflaion, bu his proecion can ake a variey of forms. 22 Inflaion-linked bonds are priced on he marke, and his marke is less liquid han he marke for convenional bonds, so a liquidiy risk premium is demanded for hese bonds. Thus, boh inflaion-linked and convenional bonds exhibi a risk premium. Assuming boh premiums are of similar value; i.e., ha hey compensae each oher, hen hey can be ignored for he calculaion of he breakeven inflaion. 23 This formula is also an approximaion, he acual formula is (1 + Nominal Yield ) Breakeven Inflaion = 1 (1+ Inflaion- linked Yield) 24 Counries from he European Union use he European Harmonised Index of Consumer Prices, formed wih household coss across differen European counries, insead of heir own consumer price index, o increase liquidiy. Bonds ha are linked o he same reference price index can be raded more easily beween hose counries, and he more radeable hey are, he lower he liquidiy premium ges, and herefore he less he counry needs o pay o issue hem. page 37

3 The majoriy of inflaion-linked bonds are srucured similar o nominal bonds excep ha he principal and he coupon paymens are no fixed, hey change following movemens of he reference inflaion index used, his srucure is known as capial indexed. In paricular, he principal is coninually indexed o realized inflaion and he coupons are se as a fixed percenage of his value. The principal indexed in each period is calculaed as: N = N + ( N π ) = N (1 + π ) where: π N inflaion accrued a ime principal inflaion indexed a ime Thus, cash flows a each coupon paymen are: where: CR CF real coupon rae of he bond = CR N And a mauriy T we simply add he indexed principal repaymen: CF = CR N + N T T T An inflaion-linked bond was issued by he German governmen a January 2009, wih a real coupon rae of 3%, face value of EUR 1000, mauring in five years. The inflaion during hese five years urned ou o be 0.8, 1.3, 2, 2 and 1.4, respecively. Which were he cash flows of he bond using he capial indexaion srucure? Inflaion Principal Coupon Cash Flow Anoher popular indexaion srucure is o only index he coupons, while he principal redempion value remains consan. This srucure is known as coupon indexed. The coupons are a variable percenage of he consan principal. Thus, he indexed coupon ineres raes (ICR) are calculaed simply by adding he inflaion rae of he period o he coupon rae of he bond. So, a each period are: ICR = CR + π Thus, cash flows a each coupon paymen are: CF = ICR N page 38

4 An inflaion-linked bond was issued by he German governmen he firs day of 2009, wih a real coupon rae of 3%, face value of EUR 1000, mauring in five years. The inflaion during hese five years urned ou o be 0.8, 1.3, 2, 2 and 1.4, respecively. Which were he cash flows of he bond using he coupon indexed srucure? Inflaion Principal Coupon Cash Flow Indexaion lag Ideally, bond cash flows would have o be in line wih realized inflaion. However, his is no possible in pracice because he lengh of ime i akes o compile daa and perform calculaions means ha price indexes are published wih a delay of a few monhs. So bond paymens are linked o a lagged value of he price index, his is called indexaion lag. For mos counries his indexaion lag is currenly hree monhs, 25 so a coupon paymen of an inflaion-linked bond in April is based on he inflaion accrued unil January. The indexaion lag causes ha here is a period a he end of a bond s life when here is no inflaion proecion a all, counerbalanced by a period of equal lengh before i is issued for which inflaion compensaion is paid. Unless boh periods have he same inflaion rae, he real reurn of he inflaion-linked bond would no be fully invarian o inflaion. This problem is more relevan he longer he indexaion lag and he shorer he bond s ime o mauriy. As in he previous examples, assume an inflaion-linked bond ha was issued in January 2009, mauring in 5 years. If he indexaion lag was hree monhs, he annual cash flows would be based on he inflaion accrued from Ocober o Sepember, boh included. So, for he hree monhs from Ocober o December 2013, here is no inflaion proecion, compensaed by he proecion for he period from Ocober o December Deflaion floor Mos inflaion-linked bonds include a deflaion floor, a guaranee ha an inflaion-linked bond s principal repaymen is never less han he original par amoun. So, if a mauriy, he indexed principal is below par he invesor will receive he original principal amoun. Thus, Principal repaymen a mauriy = Maximum ( Par Value, N T ) Generally, only he principal repaymen a mauriy is proeced agains deflaion. Tha is, if during he life of he bond he price index falls below is value a he bond issuance, coupons will be paid off on sub-par principal. Ausralia is he only imporan marke where coupons are also proeced agains deflaion. 25 In he U.K., prior o 2005, he indexaion lag was eigh monhs. page 39

5 A one-year capial indexed inflaion-linked bond wih an annual real coupon rae of 3% is issued wih a face value of EUR Wha would be is payoff a mauriy if inflaion urns ou o be - 1%? Principal indexed a mauriy: So, he payoff would be: N = 1000 (1 0.01) = EUR 990 T CF = 3% max(1000, 990) = EUR T A deflaion floor can be hough of as a pu opion embedded in he bond, which coss invesors a cerain amoun. A issuance his pu is a par, and he more inflaion accrued during he life of he bond, he furher ou-of-money i is. As long periods of deflaion are rare, being Japan he excepion in recen imes, he longer he mauriy of an inflaion-linked bond, he less likely he principal would be sub-par a mauriy, herefore he lower he embedded price of his opion. Currenly, mos of he counries include a deflaion floor on heir inflaion-linked bonds, excepions being for example he U.K. and Canada. Japan includes a deflaion floor in is issuances since Dual duraion 26 Duraion is a measure of he average ime for which capial is ied up in a bond and also reflecs how sensiive is value is o changes in ineres raes. The duraion for inflaion-linked bonds can be calculaed in he same way as for nominal bonds, bu needs o consider he indexaion of he coupons and he principal. Capial indexed inflaion-linked bonds end o have higher duraions han comparable bonds as principal repaymen a mauriy is usually larger due o is indexaion and as he early coupons of inflaion-linked bonds are smaller han hose of radiional bonds. A bond wih a 10-year mauriy pays a real annual coupon rae of 6%, and has a face value of EUR 100. The annual expeced inflaion equals 2%. Is yield o mauriy is k=10%. Wha is is Macaulay duraion using he coupon indexed srucure and he capial indexed srucure? 26 For a mahemaical approach of his concep, see Siegel and Waring (2004). page 40

6 Firs, consider he coupon indexed bond: T (Years) Principal Coupon Cash flow CF PV (CF) CF weigh Time weighed by CF weigh [1] [2] [3]=[2]/(1+k) [4] = [3] / Price [5] = [1] [4] Price: Duraion: 7.04 The duraion of he bond is 7.04 years. I is easy o see, ha his srucure is equivalen o a nominal bond ha pays an 8% annual coupon. Second, consider he capial indexed bond: T (Years) Principal Coupon Cash flow CF PV (CF) CF weigh Time weighed by CF weigh [1] [2] [3]=[2]/(1+k) [4] = [3] / Price [5] = [1] [4] Price: Duraion: 7.63 The duraion of he bond is 7.63 years, which is higher han for he coupon-indexed bond and a comparable nominal bond. However, his does no mean ha he risk of price changes is higher for capial indexed inflaion-linked bonds han for nominal bonds, because he duraion of nominal bonds is calculaed wih nominal coupons, while duraion of inflaion-linked bonds is calculaed wih real coupons. Therefore, i is no possible o compare boh duraions. To do his comparison, i has o be aken ino accoun ha here are wo ypes of duraions, a concep known as dual duraion. Real rae duraion is he sensiiviy o changes in he real raes, while inflaion duraion is he sensiiviy o changes in inflaion. Nominal bonds are sensiive o boh changes, herefore for nominal bonds: nominal bond duraion = real duraion = inflaion duraion page 41

7 Bu, inflaion-linked bonds are proeced agains price movemens, so a change in inflaion will no affec he marke value of he bond, herefore: inflaion-linked bond duraion = real duraion inflaion duraion = 0 The bes way o compare he duraion of convenional and inflaion linked bonds is o make a clear separaion of he wo ypes of duraion calculaions. The bes ool for hese calculaions is o use key rae duraions Marke siuaion 28 Alhough he firs ever inflaion-link bond was issued back in 1780, 29 he marke has only been growing srongly over he las en years. In 1981, he Unied Kingdom was he firs indusrialized counry o supplemen is governmen bond issue wih inflaion-linked bonds. The Unied Saes wih is firs issuance in 1998 or Germany in 2006 are furher examples of how his asse class has expanded in recen years. As of 2014, all of he G7 counries are issuing inflaion-linked bonds and he number of counries issuing hese securiies is currenly expanding wih India in 2013 and Spain in 2014 being he mos recen counries o join. The oal marke value of inflaion-linked bonds issued worldwide currenly amouns o around USD 2.7 rillion (see Figure 5-1), being he U.S., he U.K. and Brazil he leading counries by marke value Japan Ausralia Canada Sweden Germany Spain Ialy France Brazil U.K. U.S. Source: Barclays Capial Figure 5-1: Evoluion of he marke of inflaion-linked bonds 27 See he module abou Ineres raes - erm srucure and applicaions. 28 Mos inflaion-linked bonds are issued by counries, only a very small number is issued by companies. Thus, we concenrae on governmen bonds in his secion. 29 By he sae of Massachuses due o inflaion caused during he American War of Independence. page 42

8 Prior o 1981, inflaion-linked bonds were only issued by counries ha were experiencing episodes of high inflaion, such as Brazil and Argenina in he 1950s and 1960s, because i was pracically he only way o finance heir deb over he long erm. The reason was ha invesors wished o proec heir purchasing power agains he erosion of he currency s value. Wha are he reasons for he recen growh of his marke, especially for counries where inflaion seems o be under conrol? 30 The mos cied explanaion is o reduce he borrowing coss. This can be achieved in wo ways. Firs, by issuing inflaion-linked bonds, counries can avoid paying he inflaion risk premium found on convenional bonds. Second, if he governmen believes ha fuure inflaion will be lower han ha implied by he marke, hen i will expec o reduce is deb refinancing coss hrough inflaion-linked bonds. 31 To reach new invesor groups who are araced o inflaion-linked bonds, because, for example, heir liabiliies are linked o he cos of living; i.e., such as pension funds. To help bol confidence in he governmen s figh agains inflaion, because he sae canno reduce he real cos of borrowing hrough inflaion. This reason is paricularly imporan for emerging counries. 30 For a more complee analysis see Deacon, Derry and Mirfenderesky (2004), chaper This laer reason was an imporan one for he issuance of he U.K. in page 43

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