Discovering the GDP-Linked Bonds

i Disco e ing he GDP-Linked Bonds Dó is Ma isa A onso Ca axo de Jesus Mendes Disse a ion p esen ed as pa ial equi emen o ob aining he Mas e ’s deg ee in S a is ics and In o ma ion Managemen i NOVA In o ma ion Managemen School Ins i u o Supe io de Es a ís ica e Ges ão de In o mação Uni e sidade No a de Lisboa DISCOVERING THE GDP-LINKED BONDS by Dó is Mendes Disse a ion p esen ed as pa ial equi emen o ob aining he Mas e ’s deg ee in In o ma ion Managemen , wi h a specializa ion in Risk Analysis and Managemen . Ad iso : P o esso Dou o Jo ge Miguel Ven u a B a o No embe 2021 ii ABSTRACT O e he yea s, economies ha e been hi by se e al inancial c isis which led o high deb a ios. One solu ion ha has been s udied by economis s o help go e nmen s o s abilize hei deb - o-GDP a io a e GDP-linked bonds, which a e so e eign bonds ha pay a e u n based on he pe o mance o he g oss domes ic p oduc o he issue coun y. In his con ex , his disse a ion will add ess he ad an ages and disad an ages o GDP-linked bonds ha ha e been discussed in li e a u e as well as he di e en ypes o hese ins umen s. Addi ionally, i will be simula ed he coupon indexa ion o GDP, acco ding o he me hodology applied by Bo ensz ein & Mau o (2004), o Po ugal, I aly and G eece, which we e h ee o he Eu opean coun ies wi h he highes le els o deb , in pe cen age o GDP, du ing he las mon hs o 2020. Mo eo e , hese esul s will be compa ed wi h 10Y go e nmen bonds o each coun y. As expec ed, he esul s show ha in imes o inancial c isis, GDP-linked bonds could be an a ac i e solu ion o inancing deb o go e nmen s when compa ed o plain anilla bonds. Thus, i is possible o conclude ha one o he main ad an ages o he issue coun y is he possibili y o educe he cos in case o so e eign de aul and also a mo e s able and o eseeable iscal policy (Ba , Bush, & Pienkowski, 2014b). On he o he side, in es o s ha e he possibili y o bene i om highe in e es a es when he economy o he coun y is imp o ing. Following he same me hodology, i was pe o med a sensi i e analysis on he pa ame e ela ed o he baseline GDP which was i s se on a 20-yea a e age wi h espec o each e e ence yea and inc eased and dec eased by 5 yea s. Finally, al hough his simula ion was only pe o med o he h ee Eu opean coun ies men ioned abo e, which makes i di icul o gene alize he esul s o he emaining Eu opean coun ies, i can con ibu e o he esul s o u u e s udies. Keywo ds: GDP Linked Bonds; paymen s uc u e; p emium; so e eign deb iii RESUMO Ao longo dos anos, as economias de odo o mundo êm sido a ingidas po á ias c ises inancei as que conduzi am a al os ní eis de endi idamen o. Assim, uma solução que em indo a se es udada pa a ajuda os países a es abiliza o seu ácio en e dí ida e P odu o In e no B u o (PIB) são as ob igações indexadas ao seu PIB, as quais dependem da pe o mance do p odu o in e no do país emi en e. Nes e con ex o, es a disse ação i á abo da as an agens e des an agens da implemen ação de ob igações indexadas ao PIB que êm indo a se es udadas po di e sos au o es, bem como os di e en es ipos des es ins umen os. Adicionalmen e, seguindo a me odologia de Bo ensz ein & Mau o (2004), é simulado o cupão indexado ao PIB pa a Po ugal, I ália e G écia, os quais e am ês dos países eu opeus com maio dí ida pública, em pe cen agem do PIB, no inal do ano de 2020. Adicionalmen e, es es esul ados são compa ados com os cupões das ob igações a 10 anos do espe i o país. Como espe ado, os esul ados demons am que em empos de c ise inancei a, quando compa ados às ob igações “plain anilla”, as ob igações indexadas ao PIB podem se um ins umen o a a i o pa a inancia a dí ida dos países. Uma das p incipais an agens des e ipo de ins umen os, pa a o país emi en e, é a possibilidade de eduzi cus os em caso de de aul e ainda a possibilidade de uma polí ica iscal mais es á el e p e isí el (Ba , Bush, & Pienkowski, 2014). Po ou o lado, os in es ido es êm a possibilidade de bene icia de axas de ju os mais ele adas quando a economia do país o alece. Assim, seguindo a me odologia aplicada an e io men e ealizou-se ainda uma análise de sensibilidade aplicada a um dos pa âme os u ilizado na simulação do cupão, nomeadamen e ao “baseline GDP”, o qual se ez a ia 5 anos. Po im, apesa de a simulação e sido apenas ealizada pa a ês países eu opeus e consequen emen e o na di ícil a gene alização dos seus esul ados aos es an es países eu opeus, pode á con ibui pa a esul ados de es udos u u os Keywo ds: Ob igações indexadas ao PIB; Es u u a de pagamen o; p émio; dí ida sobe ana i ACKNOWLEDGEMENTS Fi s ly, I would like o hank my supe iso , P o esso Jo ge B a o o his guidance and suppo du ing he ime I was w i ing my hesis, as well as all he con ibu ions and ime dispended. Secondly, I would also like o hank my amily and iends o all he suppo and mo i a ion du ing his pe iod. CONTENTS 1. In oduc ion .................................................................................................................. 1 2. Li e a u e Re iew on GDP Linked bonds ...................................................................... 3 2.1. O e iew o S a e Con ingen Deb Ins umen s .................................................. 3 2.1.1. Equi y Componen .......................................................................................... 3 2.1.2. Indexing o in la ion ....................................................................................... 4 2.1.3. Indexing o GDP .............................................................................................. 4 2.2. Ad an ages o GDP-Linked Bonds ......................................................................... 4 2.3. Obs acles and Limi a ions o GDP Linked Bonds ................................................... 5 2.4. P e ious issues o GLBs ......................................................................................... 6 2.4.1. The case o A gen ina ..................................................................................... 6 2.4.2. The case o G eece ......................................................................................... 7 2.4.3. The case o Po ugal ....................................................................................... 8 2.5. P ocyclical Fiscal Policy .......................................................................................... 8 2.6. The design o GDP-Linked Bonds........................................................................... 8 2.6.1. P incipal-indexed Bonds ................................................................................. 9 2.6.2. Coupon-indexed bonds .................................................................................. 9 2.6.3. P emium ....................................................................................................... 10 2.7. Would GDP-linked Bonds be bene icial du ing he Co ona i us’ pandemic? ... 111 3. Da a & Me hodology .................................................................................................. 12 3.1. Me hodology ....................................................................................................... 12 3.2. Da a...................................................................................................................... 13 4. Resul s......................................................................................................................... 14 4.1. Coupon Simula ion .............................................................................................. 14 4.1.1. Po ugal ........................................................................................................ 14 4.1.2. G eece........................................................................................................... 15 4.1.3. I aly ............................................................................................................... 15 4.2. Coupon simula ion sensi i e analysis .................................................................. 16 4.2.1. Dec easing he a iable g* in 5 yea s ........................................................... 16 4.2.2. Inc easing he a iable g* in 5 yea s ............................................................ 17 4.2.3. Compa ing p e ious scena ios ..................................................................... 18 i 5. Conclusion................................................................................................................... 20 6. Bibliog aphy ................................................................................................................ 21 7. Appendix ................................................................................................................... 233 ii LIST OF EQUATIONS Equa ion 1: A gen ina GDP-linked secu i y paymen ………………………………………………………….…..6 Equa ion 2: G eek GDP-linked secu i y paymen …………………………………………………………………...7 Equa ion 3: Fo mula o calcula e he amoun o p incipal on P incipal-indexed bonds……….….9 Equa ion 4: Coupon paymen s on P incipal-indexed bonds…………………………………………………...9 Equa ion 5: Coupon paymen s on coupon-indexed bonds…………………………………..…………..10,12 LIST OF FIGURES Figu e 1: A gen ina GDP G ow h (annual % change) (1980-2012). Sou ce: In e na ional Mone a y Fund (IMF) …………………………………………………………………………………………………………...7 Figu e 2: G oss Deb posi ion % GDP o Po ugal, G eece and I aly. Sou ce: Fiscal Moni o 2020, In e na ional Mone a y Fund websi e……………………………………………………………………….13 Figu e 3: Compa ison be ween Po uguese 10Y Go e nmen Bond and simula ed Po uguese GDP Linked Bond…………………………………………………………………………………………………………………14 Figu e 4: Compa ison be ween G eek 10Y Go e nmen Bond and simula ed G eek GDP Linked Bond…………………………………………………………………………………………………………………………15 Figu e 5: Compa ison be ween I alian 10Y Go e nmen Bond and simula ed I alian GDP Linked Bond…………………………………………………………………………………………………………………………16 Figu e 6: Compa ison be ween Po uguese 10Y Go e nmen Bond and simula ed I alian GDP Linked Bond o bo h g*=20y a e age and g*=15y a e age…………………………………………………17 Figu e 7: Compa ison be ween Po uguese 10Y Go e nmen Bond and simula ed I alian GDP Linked Bond o bo h g*=20y a e age and g*=25y a e age…………………………………………………18 Figu e 8: Compa ison be ween Po uguese 10Y Go e nmen Bond and simula ed I alian GDP Linked Bond o bo h g*=20y a e age, g*=15y a e age and g*=25y a e age………………………19 iii LIST OF TABLES Table 1: Di e ence be ween p emiums o g*=15y a e age and g*=20y a e age……………….17 Table 2: Di e ence be ween p emiums o g*=25y a e age and g*=20y a e age……………….18 6 ola ile GDP, such as G eece, would be eques ed o pay a highe p emium han coun ies wi h a lowe one, such Ge many (Milas, 2020). Las ly, i migh also ha e epu a ional impac since GLBs ha e been issued by coun ies coming ou o so e eign-deb c isis, which can lead o an ad e se ma ke pe cep ion and consequen ly o an inc ease in ola ili y and unding cos s (Ca doso, 2018). 2.4. PREVIOUS ISSUES OF GLBS Un il oday, he use o GLBs and o he S a e Con ingen Deb Ins umen s (SCDIs) ha e been limi ed, since i usually co esponds o a complemen o he exis ing po olio o con en ional deb ins umen s and i is o en discon inued a e some issuances (IMF, 2017). None heless, coun ies ha e issued secu i ies wi h simila i ies o GLBs as pa o deb es uc u ing p og ams, mainly as pa o he B ady es uc u ing p ocess ha ini ia ed in 1989. Some examples a e Bulga ia, Bosnia and Cos a Rica (in he mid-1990s), which issued bonds wi h a ached GDP gua an ee and included clauses o inc ease coupon paymen s a p ede e mined limi s o GDP a he han in sync wi h g oss domes ic p oduc (Kams a & Shille , 2009). Mo e ecen ly, he e is he case o A gen ina (2005), G eece (2012) and Uk aine (2015) whe e so e eigns issued GDP-linked secu i ies. 2.4.1. The case o A gen ina Looking a A gen ina’s example, in 2005, he go e nmen issued GDP-linked secu i ies as pa o i s deb es uc u ing p og am. This issuance allowed o exchange USD 82 billion in bonds on which he so e eign had de aul ed. In 2010, his ype o secu i ies was issued once again as pa o he es uc u ing o c edi o s ha ha e no accep ed he i s o e ing in 2005. Financial ma ke s as well as he coun y’s c edi o s did no see much alue on GDP-linked secu i ies, and consequen ly i ep esen ed a low gain o A gen ina. None heless, he e was an unexpec ed GDP g ow h o he coun y (see igu e 1) which led hese secu i ies o exceed expec a ions and he e o e o an inc ease o hei p ices. These secu i ies ollowed h ee condi ions: i s eal GDP had o be highe han he base-case GDP; second eal annual GDP g ow h had o be highe han he GDP base-case GDP g ow h and he h eshold o eal GDP g ow h begins a 4.26% and i p og essi ely dec eases o 3% and onwa d; inally, o al paymen s a e no highe han he paymen cap, which was se a 0.48 pe uni o cu ency o he secu i y. Once hese condi ions a e me , he paymen will be as ollows (G i i h-Jones & He o a, 2013): 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 = 0.05 × 𝑒𝑥𝑐𝑒𝑠𝑠𝐺𝐷𝑃 × 𝑐𝑢𝑟𝑟𝑒𝑛𝑐𝑦𝐶𝑜𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑡 × 𝑛𝑜𝑡𝑖𝑜𝑛𝑎𝑙𝐺𝐿𝑆 (1) Whe e “excessGDP” de ines he amoun by which ac ual GDP exceeds he base case GDP, “cu encyCoe icien ” he uni o cu ency coe icien and “no ionalGLS” de ines he no ional alue o GDP-linked secu i ies. Due o he lag ha exis s in publishing GDP da a, he paymen based on he GDP pe o mance in a gi en yea is paid a he end o he ollowing one. Since A gen ina expe ienced a apidly g ow in he yea s ollowing he deb exchange, he base GDP le el was exceeded ea ly, esul ing in high paymen s on he secu i ies. The le el o GDP is mo e p obable o s ay abo e he base le el when he e is a high ea ly g ow h, and consequen ly his can 7 lead o an inc ease o u u e paymen s and i s alue which means ha he alue o he secu i y will also inc ease. Fo A gen ina, he paymen s on he secu i ies became e y cos ly, ising om USD 395 million in 2006 o USD 3.5 billion a he end o he yea o 2012, which ep esen ed mo e han 30 pe cen o he o al amoun o in e es on public sec o deb . None heless, A gen ina was able o pay a ound a hi d o i s o al GDP secu i ies paymen s in he i s se en yea s (G i i h-Jones & He o a, 2013). Figu e 2: A gen ina GDP G ow h (annual % change) (1980-2012). Sou ce: In e na ional Mone a y Fund (IMF) 2.4.2. The case o G eece In 2012, G eece issued GDP-linked secu i ies, which co esponded o EUR 172 billion p i a e deb , as pa o i s deb es uc u ing p og am. These secu i ies o e ed an annual paymen e e y yea be ween 2015 and 2042 o an amoun up o 1% o hei no ional i he condi ions a e me , mo e speci ically i nominal GDP exceeds he e e ence eal GDP and i GDP g ow h in eal e ms is posi i e and in excess o speci ied a ge s (Hellenic Minis y o Finance, 2012). In he case ha condi ions a e me , he go e nmen will make paymen s as ollows: 𝑃𝑎𝑦𝑚𝑒𝑛𝑡 = 1.5 × (𝑟𝑒𝑎𝑙𝐺𝐷𝑃 − 𝑟𝑒𝑓𝑒𝑟𝑒𝑛𝑐𝑒𝐺𝐷𝑃)× 𝑛𝑜𝑡𝑖𝑜𝑛𝑎𝑙𝐺𝐿𝑆 (2) Whe e “ ealGDP” de ines he eal GDP g ow h a e, “ e e enceGDP” he e e ence eal GDP g ow h a e, and “no ionalGLS” equals he no ional alue o GDP-linked secu i ies. Simila ly o A gen ina, he paymen based on g ow h o a ce ain yea , will be made on he ollowing yea . 8 2.4.3. The case o Po ugal Also, Po ugal issued easu y ce i ica es wi h p emium indexed o eal GDP g ow h (T easu y Ce i ica es Sa ing Plus (Ce i icados do Tesou o Poupança Mais) (CTPM)), in 2013, wi h ma u i y o 5 yea s and wi h p emium linked o he eal GDP g ow h in he inal 2 yea s. In Oc obe 2017, T easu y Ce i ica es Sa ings G ow h (Ce i icados do Tesou o Poupança C escimen o) (CTPC) we e also issued bu his ime wi h a inal ma u i y o 7 yea s and he p emium was indexed o 40% o eal GDP g ow h a e since he second yea . Bo h issuances we e edeemable a e 1 yea and had a coupon loo equal o ze o. Howe e , he CTPC also included a cap equal o 1.2%. 2.5. PROCYCLICAL FISCAL POLICY GDP indexa ion o bond epaymen s could c ea e a smoo he pa h o p ima y su plus, p ima y spending and axes o e he cycle and hus, could be possible o educe he necessi y o so e eigns o ca y ou p ocyclical iscal policies. So in he cases ha GDP g ow h is in e io o he end, he coun y will be able o ha e highe p ima y spending and lowe axes, (i.e., a lowe p ima y su plus) wi h indexa ion han wi hou i while in imes when GDP is highe han he end he opposi e o he desc ibed will happen (Bo einsz ein & Mau o, 2004). To demons a e wha is men ioned abo e, he au ho s Edua do Bo einszein and Paolo Mau o pe o med a small exe cise o 20 ad anced economies and 25 eme ging economies, whe e hey checked how much space would so e eigns ha e had o coun e cyclical iscal policy i hei deb had been indexed o GDP since he beginning o he 1990s. Following his, p ima y su plus wi h indexa ion be ween 1992 and 2001 was calcula ed and las ly, co ela ion be ween GDP g ow h and p ima y balance was compu ed. The au ho s ound ha co ela ion (which is a measu e o he so e eigns’ abili y o conduc coun e cyclical iscal policy) be ween he wo a ian s would be signi ican ly highe wi h indexa ion, han wi hou i , and ha i is mo e e iden o eme ging coun ies han o ad anced coun ies. Thus, by equi ing a lowe paymen han usual in he yea s ha he economy has a weak g ow h and a highe paymen han usual when economy is s onge , GLBs would ac as an au oma ic s abilize and he e o e would help coun ies o educe hei need o p ocyclical iscal policies (Chamon & Mau o, 2006). 2.6. THE DESIGN OF GDP-LINKED BONDS O e he yea s, di e en ypes o models on how o p ice GLBs ha e been de eloped. K use e al. (2005), o example, de eloped a Black-Scholes ype p icing model, using a single- ac o s ochas ic model when GDP ollows a log-no mal dis ibu ion and in e es a es a e de e minis ic. The au ho s de eloped his me hod wi h he objec i e o es ima e e u ns on linked and plain bonds o Venezuela and Indonesia. Miyajima (2006) de eloped a p icing mechanism based on Mon e Ca lo me hods, which was calib a ed o di e en se s o pa ame e alues o ge p ojec ed low o deb paymen s and he p ice o secu i ies. 9 Kams a and Shille (2009) ollow a di idend-discoun ing me hod in o de o es ima e p ices and yields o GLBs. On he o he hand, Bowman and Naylo (2016), used he Capi al Asse P icing Model (CAPM) o ge a ange o p emia o coun ies ha belong o G20 (Consiglio and Zenios, 2018). Two main app oaches on how he paymen s o he GDP-linked bonds should be s uc u e ha e been p oposed o e ime: i only he coupon should be linked o he g ow h a e o GDP o i he p incipal should be included oo (Ben o d, Bes , Joy, & K uge , 2016). 2.6.1. P incipal-indexed Bonds Schille (1993) p oposed he idea o c ea ing long- e m bonds indexed o so e eign deb , o wha he named “ he ills”. The au ho a gues ha his idea would help educing he isk o he issue coun y and also, be a po en ial ehicle o e i emen sa ings. Based on his, Kams a and Schille (2009) de eloped he idea o P incipal-indexed bonds, whe e p incipal g ows wi h he nominal GDP o e ime while he coupon would be a ixed ac ion o he p incipal. P incipal would ollow: 0 0Y Y BB = (3) Whe e B0 ep esen s he amoun issued, Y0 and Y a e he nominal GDP alues a he issuing da e and da e (Consiglio and Zenios, 2018). In his case, coupon paymen s sa is y he ollowing exp ession: ( ) ( ) 0 000 11 Y Y BcBc +=+ (4) being c0 he baseline coupon. Once all he coupon paymen s a e made, a ma u i y , B will be paid o bondholde s as he p incipal eimbu semen . This ype o paymen s uc u e c ea ed by Schille (1993), which ocus on he p incipal, can be mo e amilia o in es o s and go e nmen s, none heless has also a disad an age o i which is he ac ha e en hough deb becomes mo e s able, deb paymen s will become less sensible o ecen economic pe o mance o e ime, since he mos ecen g ow h a e will no impac he p incipal signi ican ly (Bado, 2018). 2.6.2. Coupon-indexed bonds Bo ensz ein and Mau o (2004) p oposed o link he coupon paymen s o he eal g ow h o he GDP (Coupon-indexed bonds). In hei model, he p incipal would s ay ixed and he ac ual coupon a e would be: 10 ( )   0,*max gg Coupon i −+= (5) whe e co esponds o he coupon a e, gi o he ac ual g ow h a e o GDP and g* de ines he baseline g ow h a e o GDP. So, o he coupon a e o e lec he pe o mance o he GDP g ow h a e, i is necessa y o conside an indexa ion ac o , which will co espond o he di e ence be ween he ac ual g ow h a e and he baseline g ow h a e o he GDP, which will be added o he coupon a e. This baseline g ow h a e is ag eed be ween he con ac ing pa ies be o e he issue o he bond. So, when he economy g ows abo e his a e (g*), he coupon a e will be highe han , and simila ly, when he economy dec eases below g*, he coupon a e will be lowe han , bu ne e below ze o. This ype o indexa ion me hod is e e ed as “ loa e s” by he IMF (2017). On his indexa ion app oach, he annual GLBs paymen s luc ua e mo e when compa ed o he Schille e sion, since i allows a s onge linkage be ween ecen economic pe o mance and deb expense. Cecche i and Schoenhol z (2017) men ioned in hei pape ha he di e ence be ween GDP-p incipal- indexed bonds and GDP-coupon-paymen s is he iming o paymen s. In he i s , he la ges pa o he compensa ion o nominal g ow h happens a ma u i y, while on he second i will come wi h he pe iodic paymen s. Consiglio and Zenios (2018) compu ed p emium o bo h p incipal-indexed and coupon-indexed bonds wi h ze o based coupon and compa ed he isk p emia in which hey obse ed ha o he i s ones he e is a highe p emium which di e ence can each 200bp o high expec ed economic g ow h. None heless, he esul s can be signi ican ly impac ed by he design pa ame e s. 2.6.3. P emium Al hough GLBs p esen bene i s, hese can be weakened by a high isk p emium, when compa ed o con en ional bonds. As men ioned by he Eu opean Commission (2017), as he e is no his o ical p eceden , alue o isk p emium is empi ically unknown and consequen ly, he no el y and liquidi y p emium can be high ini ially howe e , i is likely o dec ease o e ime as has al eady happen wi h in la ion-linked bonds. Acco ding o he In e na ional Mone a y Fund (2017), po en ial in es o s o his ype o ins umen s belie e ha he c ea ion o a well-de ined and s anda dized ins umen could help con aining such p emium. Addi ionally, is e e ed he a emp s on he li e a u e ela ed o es ima e he g ow h isk p emium, which is conside ed c i ical. Fo ins ance, Kams a and Schille (2009) ha e es ima ed a isk p emium o 150 bps on a GLB o he US, in 2009, based on he capi al asse p icing model. Also, al hough based on di e en model, Pienkowski (2017) eaches simila es ima es o ad anced economies. Las ly, i is men ioned he de aul isk p emium. Wi h a signi ican issuance o GLBs, public deb would be mo e sus ainable and a educ ion in he de aul p emium could be obse ed. 11 2.7. WOULD GDP-LINKED BONDS BE BENEFICIAL DURING THE CORONAVIRUS’ PANDEMIC? In Ma ch 2020, a pandemic was decla ed by he Wo ld Heal h O ganiza ion due o he sp ead o co ona i us, which has led economies in o a se e e con ac ion all o e he wo ld. In esponse o his pandemic, mos so e eigns ha e implemen ed iscal s imulus p og ams which ha e conduc ed public deb o one o he highes le els in his o y (Roch and Roldán, 2021). Fo Gallo and o he s (in Financial Times, 2020), his is he ime o implemen GDP-linked bonds, as a esponse ha would p o ide a long- e m elie o coun ies. Go e nmen s should swap he cu en deb ins umen s in o GLBs since would allow enough cash low elie in he ea ly s age. Addi ionally, he au ho s men ion ha hese ypes o ins umen s should be ma ke able as soon as possible, by de eloping p icing models and allowing o hei inco po a ion in exis ing indices. 12 3. DATA & METHODOLOGY In his chap e , i will be p esen ed he me hodology and da a used o simula e he coupons o GDP- linked bonds o Po ugal, G eece and I aly which esul s a e p esen ed on chap e 4. 3.1. METHODOLOGY Following he designs p esen ea lie , he coupon-indexed app oach is going o be implemen ed o s udy he possible impac on h ee selec ed coun ies which belong o ad anced economies. Remembe ing wha was illus a ed be o e, Bo ensz ein & Mau o’s (2004) p opose an app oach o es ima e he coupon a e o coupon-indexed GDP bonds (which he au ho s applied o he example o Mexico and A gen ina in hei a icle). Acco ding o he au ho s, conside ing a loa ing a e bond wi h a coupon ha changes acco ding o he pe o mance o he coun y, he o mula o calcula e a coupon a e will equal o: ( )   0,*max gg Coupon i −+= (5) whe e co esponds o he 10-yea go e nmen bond yield o he coun y; gi equals he ac ual g ow h a e o GDP; g* is he baseline g ow h a e o GDP, which is ag eed be ween he con ac ing pa ies be o e he issue o he bond, none heless o simplici y he au ho s assumed o be he a e age GDP g ow h a e o e he p e ious 20 yea s wi h espec o each e e ence yea . Thus, he coupon paymen s will luc ua e acco ding o he economy e olu ion: in imes o economic down u n, he coupon a e o e ed o in es o s will be lowe han he 10-yea go e nmen bond yield, while in imes o economic g ow h, his a e will be highe . Fo example, i we conside o be equal o 7%, and economy is g owing a he baseline g ow h a e, he coupon a e will be 7%. The e o e, i economy is g owing abo e g*, he coupon a e will be highe han 7% and i i is below g* he coupon paymen will be lowe bu ne e below ze o. In hei explana ion, he au ho s also poin ou ha con inui y, whe e small changes in ealized g ow h esul s in small changes in coupon paymen s, seems o be desi able so incen i es o mis epo s a e minimized. Fu he mo e, i is explained why a minimum o ze o is imposed o he coupon a e in hei exe cise: many ins i u ional bond in es o s a e only allowed o hold asse s in hei po olio ha pay a posi i e in e es a e. The esul s o his simula ion in he au ho ’s pape show ha GLBs could be bene icial o bo h coun ies. In Mexico’s example, when he ou pu con ac ed mo e han 6% du ing he Tequila c isis o 1995, he coupon a e would ha e allen o ze o, allowing Mexico o ob ain a educ ion in in e es bill and consequen ly, lea ing mo e oom o a oid p ocyclical iscal measu es. Simila ly, A gen ina would ha e managed o dec ease i s coupon paymen s in 1995 (Tequila C isis) and 1999 (B azil c isis). None heless, when economies g ew o e hei 20-yea a e age, hey would ha e paid highe - han- a e age coupon a es. 13 Finally, a e ollowing Bo ensz ein & Mau o’s (2004) app oach, he paymen obliga ions o simula ed GDP-linked bonds will be compa ed o he 10-yea go e nmen bond o each coun y wi h he objec i e o unde s and which one p o ides a cheape inancing op ion o he na ions. In o de o apply his me hod and each he esul s, Mic oso Excel was used. 3.2. DATA Po ugal, G eece and I aly we e he coun ies selec ed o simula e he coupon indexa ion o GDP in his disse a ion. This selec ion had as c i e ia he highes deb as pe cen age o GDP wi hin Eu opean Union, apa om Po ugal, in o ma ion ha was accessed on FMI’s websi e. In Oc obe 2020, se e al na ions had 100% o mo e g oss deb posi ion when compa ed o he espec i ely GDP (See appendices 2.). The e olu ion o g oss deb in pe cen age o GDP o each o he h ee chosen coun ies, can be seen on he igu e below. As expec ed, due o Co ona i us’ pandemic, he deb le els in 2020 a e he highes e e egis e ed. Figu e 2: G oss Deb posi ion % GDP o Po ugal, G eece and I aly. Sou ce: Fiscal Moni o 2020, In e na ional Mone a y Fund websi e: h ps://www.im .o g/ex e nal/da amappe /G_XWDG_G01_GDP_PT@FM/JPN/PRT/GRC (accessed on 8 h Decembe 2020) Annual da a o 10Y go e nmen bond yields o each o he coun ies analyzed we e collec ed om he Fede al Rese e Bank o S . Louis o he pe iod be ween 2000-2020 and in o ma ion ega ding he eal GDP g ow h, conside ing he annual pe cen age change, was accessed on he Wo ld Economic ou look (Oc obe 2020) published by he In e na ional Mone a y Fund, o he pe iod o 1980-2020. The pe iod analyzed is be ween 2000 and 2020, whe e is possible o obse e how he coupon indexa ion o GDP oscilla es du ing yea s o bo h economic down u n and g ow h. The da a ega ding 1980-1999 is used o compu e g* o he i s yea o he pe iod analyzed. 14 4. RESULTS 4.1. COUPON SIMULATION In his chap e , he esul s o he coupon simula ion, ollowing Bo ensz ein & Mau o’s me hodology, o each o he h ee coun ies selec ed (Po ugal, G eece and I aly) a e p esen ed. 4.1.1. Po ugal Figu e 3 below, displays he compa ison o he Po uguese 10-yea go e nmen bond wi h he Po uguese GDP-linked Bond ha was simula ed. On he same igu e, is also possible o see he annual pe cen age change o GDP and he 20-yea a e age GDP g ow h. When analyzing he igu e, we see ha o mos o he ime, mo e speci ically be ween 2001 and 2014, GLBs a e o e ing a lowe paymen obliga ion han he Po uguese 10-yea go e nmen bond. Mo eo e , i we look o 2008, he yea o he inancial c isis, and he yea a e , we see a signi ican di e ence be ween bo h paymen obliga ions, in which he paymen o GDP-linked bond eaches ze o. Du ing hese yea s and he ollowing ones when a coun y is ying o eco e , would be in e es ing o he go e nmen o be able o inance i s public deb wi h hese ins umen s, ins ead o plain anilla bonds. In 2020, due o he impac o co ona i us pandemic, Po uguese’s GDP had a signi ican dec ease, which akes he paymen o GDP-linked bonds o ze o once again. None heless, o he i s ime, he 10-yea go e nmen bond yield ell below ze o on 26 h No embe 2020, since he e we e expec a ions ega ding new asse pu chases by he Eu opean Cen al Bank which had allowed a eco e y in Eu ozone deb (FT, 2020). As men ioned ea lie , he coupon paid by he GLBs ne e alls below ze o. Figu e 3: Compa ison be ween Po uguese 10Y Go e nmen Bond and simula ed Po uguese GDP Linked Bond 15 4.1.2. G eece Unlike Po ugal, he G eek GLBs’ p emium is highe han he anilla bonds paymen mos ly un il 2007 (excep o 2005), since he g ow h a e is highe han he p e ious wen y-yea g ow h a e age. F om his momen on, i becomes lowe han he 10Y Go e nmen bond p emium un il 2016. Fo so e eigns his las scena io would be he ideal since hey would be able o inance i sel a a lowe cos . On he o he hand, o bondholde s, hey ha e a highe incen i e o in es in pe iods simila o he i s desc ibed. Figu e 4: Compa ison be ween G eek 10Y Go e nmen Bond and simula ed G eek GDP Linked Bond 4.1.3. I aly Finally, he igu e below, displays he compa ison be ween each bond o I aly. Simila ly, o wha occu ed in Po ugal’s case, GLBs’ paymen s a e lowe a he beginning o he pe iod in analysis, while be ween 2015 and 2018 a e highe . Du ing he inancial c isis, is also no iceable he di e ence be ween paymen obliga ions o I aly o GLBs and he 10-yea go e nmen bond, as i was also in bo h coun ies p e iously men ioned. So, in his case, I aly could ha e lowe ed i s paymen s obliga ions d as ically in 2008 and on mos o he ollowing ones. 22 Ins i u - Leibniz-Ins i u ü Wi scha s o schung an de Uni e si ä München, München, Vol. 11. Hellenic Republic, Minis y o Finance. (2012). P ess Release, 24 Feb ua y 2012. A hens: Hellenic Republic. IGCP Agência de Ges ão de Tesou a ia e da Dí ida Pública. Os No os Ce i icados do Tesou o Poupança C escimen o (CTPC). A ailable a : h ps://www.igcp.p / o os/edi o 2/2018/Rela o io_Anual/PT/CTPC.pd [ Accessed Oc obe , 29, 2020] In e na ional Mone a y Fund (2017). S a e-Con ingen Deb Ins umen s o So e eigns, MF Policy Pape , May. Kams a, M. & Shille , R. (2009). The Case o T ills: Gi ing he People and Thei Pension Funds a S ake in he Weal h o he Na ion. In Cowles Founda ion Discussion Pape s 1717, Cowles Founda ion o Resea ch in Economics, Yale Uni e si y. Kim, J., & Os y, J. (2019). Boos ing Fiscal Space : The Roles o GDP-Linked Deb and Longe Ma u i ies. In 69 h Economic Policy Panel Mee ing. K use, S., Mei ne , M., Sch öde M. (2005), On he p icing o GDP-linked inancial p oduc s. In Applied Financial Economics Vol. 15, No. 16. Milas, C. (2020), How o a oid a co ona i us deb c isis? Issue a new ype o go e nmen bonds linked o GDP. In The Con e sa ion UK. A ailable a : h ps:// hecon e sa ion.com/how- o-a oid-a- co ona i us-deb -c isis-issue-a-new- ype-o -go e nmen -bonds-linked- o-gdp-136623 [Accessed June 26,2021]. Miyajima, K., 2006. How o E alua e GDP-Linked Wa an s –P ice and Repaymen Capaci y. In: Wo king Pape WP/06/85. In In e na ional Mone a y Fund. No iko a, N. e al. (2017). “S a e-con ingen deb ins umen s o so e eigns”, In e na ional Mone a y Fund. A ailable a : h ps://www.im .o g/en/Publica ions/Policy- Pape s/Issues/2017/05/19/pp032317s a e-con ingen deb -ins umen s- o -so e eigns [Accessed: Oc obe 23, 2021]. OECD Da a Websi e. A ailable a : h ps://da a.oecd.o g/gdp/qua e ly-gdp.h m#indica o -cha Pienkowski, A. (2017). Deb limi s and he s uc u e o public deb . In IMF Wo king Pape , no. 17 / 117, May. Shille , R. (1993), Agg ega e Income Risks and Hedging Mechanisms. In NBER Wo king Pape s 4396, Na ional Bu eau o Economic Resea ch, Inc. 23 7. APPENDIX 7.1 In oduc ion o In la ion-Indexed Secu i ies by So e eigns Sou ce: Bo ensz ein, E., & Mau o, P., Chamon, M., Jeanne O. & Ze elmeye J. (2005). So e eign Deb S uc u e o C isis P e en ion. In IMF Occasional Pape 237. 24 7.2 G oss deb posi ion % GDP, Fiscal Moni o (Oc obe 2020) Sou ce: In e na ional Mone a y Fund websi e: h ps://www.im .o g/ex e nal/da amappe /G_XWDG_G01_GDP_PT@FM/ADVEC/FM_EMG/FM_LID C/JPN Page | i