AN INVESTIGATION INTO THE LINKAGES BETWEEN EURO AND STERLING SWAP SPREADS. Somnath Chatterjee* Department of Economics University of Glasgow

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1 AN INVESTIGATION INTO THE LINKAGES BETWEEN EURO AND STERLING SWAP SPREADS Somnah Chaerjee* Deparmen of Economics Universiy of Glasgow January, 2005 Absrac This paper examines he causal relaionship beween euro and serling swap spreads during he period January, 1999 o March, The absence of any correlaion beween changes in he wo swap spreads would indicae ha credi risk facors are counry-specific. Bu euro swap spreads showed some correlaion wih he ineres rae differenials beween he wo markes. Boh spreads follow a GARCH process bu serling swap spreads reaced more inensely o marke movemens and were more volaile han heir euro counerpars. There was evidence of mild volailiy ransmission from he serling swap spreads o he euro swap spreads bu he causaliy was one sided. Keywords: ineres rae swaps, swap spreads, bonds, volailiy. JEL classificaion: G15 * Address for correspondence: Universiy of Glasgow, Deparmen of Economics, Adam Smih Building, Glasgow G12 8RT. 1

2 I INTRODUCTION The observed difference beween he swap rae and he governmen bond yield of corresponding mauriy is known as he swap spread. Fixed income securiies, including corporae bonds and morgage-backed securiies use ineres rae swap spreads as a key benchmark for pricing and hedging. A convenional ineres swap is a conrac beween wo companies or counerparies in which one pary makes fixed ineres paymens, calculaed on a noional amoun, while he oher pary makes floaing-rae ineres paymens. If swap raes incorporae he risk of defaul hey would be sensiive o he credi raings of he counerparies. The fixed rae is se a he incepion of he conrac and he floaing-rae is linked o an exernal reference such as Libor 1 during he life of he swap. Ineres rae swaps, like mos bonds are raded over he couner (OTC), raher han, hrough an organised exchange. Similar o oher OTC securiies, swaps are characerised by he presence of credi and liquidiy risks. Each of he wo paries in an OTC ransacion is exposed o he defaul risk of he oher. Thus, o compensae for hese risks, marke swap raes are generally a a premium over he comparable governmen bond raes. This premium is ermed as he swap spread. Swap spreads, herefore, reflec he defaul risk of he inerbank marke quoing Libor/Euribor raes and he governmen reasury. However, he spread is no necessarily a pure measure of credi risk, as i can also be indicaive of liquidiy risk. 2

3 The imporance of ineres swap spreads derives from he dramaic recen growh in he noional amoun of ineres rae swaps ousanding relaive o he governmen bond markes. Afer he inroducion of he single currency, he euro swap marke has nearly doubled in size and grown much faser han he bond marke. 2 This can be aribued o he lack of homogeneiy in he euro-denominaed governmen securiies marke inducing a shif o ineres rae swaps for hedging and posiioning aciviy. Swap spreads can be volaile and his has been very much in evidence during recen years. The Russian deb crisis in he auumn of 1998 and he subsequen near collapse of Long-Term Capial Managemen (LTCM), resuled in a fligh o UK, US, and German governmen bonds which lowered yields and widened swap spreads. This "fligh-o-qualiy" caused by concerns abou a sysemaic meldown in he financial secor, had a profound effec on he imporance of he swap marke. A Treasury yield does no incorporae he risk premium ha characerises a swap spread. Tradiionally, i was he risk-free naure of he Treasury yield curve ha necessiaed is choice as a benchmark. During he 1998 financial crisis, he fligh-o-qualiy bid ha occurred in Treasury bonds, depressed heir yields below "rue" nominal risk-free raes and resuled in a seep increase in risk premiums. This impinged on he efficacy of Treasury bonds as benchmarks. As he marke for Treasury bonds decoupled from oher asse classes, marke paricipans who hedged heir porfolios wih Treasury securiies found hemselves being adversely affeced. 1 The reference rae is GBP 6monh Libor for serling swaps and EUR 6 monh Libor for euro swaps. 2 Remolona and Wooldridge (2003) 3

4 In he lieraure, swap spreads have been aribued mainly o wo facors: he credi risk of counerparies giving rise o a defaul premium and, he liquidiy of he swap marke relaive o he governmen securiies marke giving rise o a liquidiy premium. Sun, Sundaresan and Wang (1993), Sorensen and Bollier (1994), Brown, Harlow and Smih (1994) are among hose arguing in favour of defaul risk as a primary deerminan of swap spread changes. While Grinbla (1995) and Liu, Longsaff and Mandell (2002) suppor he view ha liquidiy risk is a more plausible deerminan of swap spreads han credi risk. Duffie and Singleon (1997) find ha boh credi and liquidiy risk affec he behaviour of swap spreads bu a differen ime horizons. Liquidiy facors are more imporan in shor horizons while credi shocks are more significan over long horizons. However, mos sudies show ha he expeced spread beween LIBOR raes and he corresponding Treasury bill raes (TED spread) is he mos basic deerminan of swap spreads. The purpose of his paper is no on analysing he deerminans of swap spreads, bu raher he dynamic behaviour of swap spreads. In paricular, we are focussing on he ransmission of informaion across he euro and serling fixed income markes and explore volailiy inerdependencies. Time series models of asse reurns have emphasised sylised facs in he form of volailiy clusering, whereby one period of high volailiy is followed by more of he same, and hen successive episodes of low volailiy. Generalised auoregressive condiional heeroskedasic (GARCH) processes which parameerise ime-varying condiional variances are able o capure his behaviour. 4

5 There have been several sudies ha have employed GARCH models for examining how news from one inernaional marke influences oher markes' volailiy process. For sock markes, Hamao, Masulis and Ng (1990) use he GARCH-M model o show ha volailiy spillovers exis from New York o Tokyo, London o Tokyo and New York o London. For currency markes, Engle, Io and Lin (1990) use a GARCH model o find ha Japanese news has he larges impac on he volailiy spillovers of he yen/dollar exchange raes. In he conex of fixed income markes, Tse and Booh (1996) use US Treasury bill and Eurodollar fuures o invesigae volailiy spillovers beween US and Eurodollar ineres raes. A bivariae EGARCH model ha allows for he asymmeric volailiy influence of he ineres differenial beween markes (Eurodollar minus Treasury rae or he TED spread) as well as ha of he domesic marke, is used o analyse he volailiy spillovers beween markes. The resuls show ha alhough he cross-marke volailiy effecs are insignifican, he lagged TED spread is he driving force of he volailiy process. Eom, Subrahmanyam and Uno (2002) analyse he ransmission of credi risk beween Japanese yen and U.S. dollar ineres rae swap markes beween 1990 and Alhough hey observed low correlaions beween yen and dollar ineres rae swap spreads, hey found ha dollar ineres rae swap spreads "Granger-cause" he changes in he yen swap spreads, for he 10-year mauriies. Using a GJR-GARCH model o capure he asymmeric effecs in he volailiy process, hey show ha here is a srong ransmission of volailiy from he dollar swap spread o he yen swap spread. 5

6 The mehodology used in his paper follows ha originally employed by Hamas, Masulis and Ng (1990) and also draws on he framework adoped by Eom, Subrahmanyam and Uno (2002). The moivaion for his paper is driven by he consideraion ha a comprehensive sudy on he linkages beween euro and serling swap markes has no been underaken so far. An invesigaion of he euro and serling swap markes would promoe a beer undersanding of he degree of inegraion, if any, beween he fixed income segmen of heir respecive financial markes. The flow of informaion beween financial markes is an issue ha has araced considerable aenion in he financial economics lieraure. Research in his area examines he exen o which a price shock in one marke affecs reurns and volailiies in oher markes. Bu mos of hese sudies focus on iner-linkages beween equiy markes raher han fixed income markes. Alhough a lo of research has been devoed o he deerminans of swap spreads, he issue of inernaional linkages beween hem has no been so well addressed. The paper is organised as follows. Secion II provides a descripion of he daa used and makes some inferences on he erm srucure of euro and serling swap spreads. Secion III aemps o race he variabiliy in hese swap spreads o imporan economic evens marking he euro and serling fixed income markes. Secion IV examines he conemporaneous and causal relaionship beween euro and serling ineres rae swap spreads. Secion V esimaes he volailiy in euro and 6

7 serling swap spreads and invesigaes he possibiliy of volailiy spillovers beween hese markes. Secion VI concludes he paper. II DATA AND SUMMARY STATISTICS The euro swap raes used in his sudy are quoed raes from he fixed ineres branch of a generic ineres rae swap of 2-, 3-, 5-, 7-, and 10-years. Daily quoed raes were obained from Daasream which are he average of bid and ask raes. These daa cover he period from January 29, 1999 o March 28, The euro swap spread is calculaed by subracing he swap rae from consan mauriy yields of German governmen bonds wih corresponding mauriies, which were also obained from Daasream. The daase consiss of 218 weekly observaions and 1086 daily observaions. 7

8 TABLE 1 Summary Saisics of he Euro Swap Spreads Euro swap spreads defined as he difference beween euro swap raes and consan mauriy yields of German sovereign bonds wih he corresponding mauriy. Panel A provides he mean, sandard deviaion, skewness, kurosis and ADF es for Non-Saionariy where he criical -raio a he 5% level of significance is The ess for inegraion of order zero or, or I(0), are carried ou on he levels of he variables and he ess for inegraion of order one, or I(1), are carried ou on heir firs differences. Daily daa are used from 29 January 1999 o 28 March 2003 (oal 1086 observaions). Panel B provides he same summary saisics for weekly Euro swap raes wih 218 observaions. Panel A: Daily Observaions Mauriy Mean Sd. Dev Skewness Kurosis ADF -sa ADF -sa for I(0) es for I(1) es 2 year year year year year Panel B: Weekly Observaions Mauriy Mean Sd. Dev Skewness Kurosis ADF -sa ADF -sa for I(0) es for I(1) es 2 year year year year year Table 1 Panel A repors he summary saisics for he daily euro swap spreads on yield basis. Panel B provides he same saisics for he weekly observaions in he euro swap spreads. As he able shows, he average spreads of he euro ineres rae swaps over he corresponding German governmen bonds is upward sloping wih mauriy. The sandard deviaions of swap spreads increase as he swap mauriy increases. Symmeric disribuions, such as he normal disribuion have a skewness of zero. Kurosis measures he hickness of he ails and is equal o 3 for a normal 8

9 disribuion. Euro swap spreads show posiive skewness across he erm srucure bu, relaively close o normal kurosis for he lower mauriies. The Augmened Dickey- Fuller (ADF) es is performed o deermine wheher he various ime series of swap raes are non-saionary. This is based on he null hypohesis of non-saionariy. The ADF saisics show ha we canno rejec he null-hypohesis a he 5% level of significance. This suggess ha euro swap spreads across all mauriies are nonsaionary. Table 2 Panel A provides he summary saisics for he serling swap spreads on a daily basis. Panel B provides he same saisics for he weekly serling swap raes. As he able shows, he average serling ineres rae swaps slopes upward iniially and hen flaens ou. I is ineresing o noe ha he average swap spreads of serling ineres rae swaps are much larger han hose of euro ineres rae swaps. This difference can be accouned for by several facors and is discussed in he following secion. The average sandard deviaions of he serling swap spreads are also larger han hose of he euro swap spreads for all mauriies. We rejec he saionariy of he serling swap spread and conclude ha hey follow a random walk. 9

10 TABLE 2 Summary Saisics of he Serling Swap Spreads Serling spreads defined as he difference beween serling swap raes and consan mauriy yields of UK Treasury bonds wih he corresponding mauriy. Panel A provides he mean, sandard deviaion, skewness, kurosis and ADF es for Non-Saionariy where he criical -raio a he 5% level of significance is The ess for inegraion of order zero or, or I(0), are carried ou on he levels of he variables and he ess for inegraion of order one, or I(1), are carried ou on heir firs differences. Daily daa are used from 29 January 1999 o 28 March 2003 (oal 1086 observaions). Panel B provides he same summary saisics for weekly pound swap spreads wih 218 observaions. Panel A: Daily Observaions Mauriy Mean Sd. Dev Skewness Kurosis ADF -sa ADF -sa for I(0) es for I(1) es 2 year year year year year Panel B: Weekly Observaions Mauriy Mean Sd. Dev Skewness Kurosis ADF -sa ADF -sa for I(0) es for I(1) es 2 year year year year year III DEVELOPMENTS IN SWAP SPREADS This secion focuses on developmens in he serling and euro swap spreads. Figure 1 shows a ime series of 10-year euro and serling swap spreads using daily observaions from January 29, 1999 o March 28, The figure depics ha he serling swap spreads were percepibly wider han euro swap spreads since he launch of he single currency. During he period of observaion, he average serling swap 10

11 spread was basis poins as compared o basis poins for he euro swap spread. EUR and GBP swap spreads /01/99 29/03/99 29/05/99 29/07/99 29/09/99 29/11/99 29/01/00 29/03/00 29/05/00 29/07/00 29/09/00 29/11/00 29/01/01 29/03/01 29/05/01 29/07/01 29/09/01 29/11/01 29/01/02 29/03/02 29/05/02 29/07/02 29/09/02 29/11/02 29/01/03 Swap spreads (basis poins) Years Euro spreads Serling spreads Figure 1 Euro and Serling Euro Swap Spreads Alhough a number of facors may be cied o explain his divergence, he mos significan relaes o he issuance of bonds by Briish and oher European governmen bond markes as necessiaed by heir differing budgeary posiions. While in he UK budge surpluses caused he ne issuing volume of Treasury bonds o decline in 1999 and 2000, in Europe he issuing aciviy of governmens remained sable due o persisen budge deficis. In he UK, he scarciy of bonds led o a decline in bond yields, causing swap spreads o widen significanly. Cooper and Scholes (2001) examined he link beween swap spreads and ne supply of governmen bonds in he UK and US markes. The resuls were mixed. In boh markes, a very simple regression beween hese variables suggesed a srong negaive 11

12 relaionship. Bu when hey incorporaed oher variables, in paricular he slope of he yield curve, ne issuance ceased o be saisically significan. Brooke, Clare and Lekkos (2000) have cied a number of UK-specific supply and demand-side facors ha have influenced he shape of he gil yield curve over he few years prior o On he supply side, ne borrowing by he UK governmen had been negaive beween 1998 and 2000 and he ousanding sock of gils had, herefore, conraced. The heavy demand for gils from pension funds and insurance companies increased srongly during ha phase causing furher downward pressure on governmen bond yields. Pension funds were obliged o buy gils o comply wih he Minimum Funding Requiremen (MFR) of he Pensions Ac, 1995, designed o ensure ha pension fund managers do no ake excessive risks wih heir invesmens. Moreover, as yields coninued o decline markedly, he UK reasury yield curve invered. As an illusraion, Figure 2 shows he invered naure of he UK Treasury yield curve on April 28, 2000 where he spo and forward ineres raes have been esimaed using he Nelson and Siegel (1987) model. 3 3 The Nelson and Siegel (1987) model has been used o esimae he zero-coupon yield curve of spo ineres raes from observable coupon bonds. Marke daa on bond prices, coupon raes and yield o mauriy have been sourced from Daasream. 12

13 7.00% 6.00% Spo Rae (%) 5.00% 4.00% 3.00% 2.00% Time o Mauriy (years) Spo Raes Forward Raes Figure 2. UK Treasury yield curve on April 28, 2000 Anoher facor ha may have impaced on he yields on gils relaes o convergence plays associaed wih expecaions abou he Unied Kingdom joining EMU. Prior o he end of he year 2000 financial markes may have expeced ha he UK would adop he single European currency in he near fuure. Alhough governmen bond markes in he Eurozone have remained segmened, inegraion has been paricularly srong a he shor-erm end of he yield curve. As a resul, here is only one shor-erm ineres rae for all EMU member counries, se by he European Cenral Bank. Thus, a corollary of he UK joining EMU would be he evenual convergence of UK shor-erm ineres raes o he levels prevailing in he Eurozone. According o he expecaions heory of he erm srucure, here should be no expeced difference in he reurns from holding a long-erm bond or rolling over a sequence of shor-erm bonds. Based on he premise ha all bonds will generae a riskless reurn and ignoring liquidiy premia, convergence in fuure shor-erm ineres raes would enail convergence in long-erm bond yields. Therefore, he aciviies of 13

14 hedge funds and oher marke paricipans being on he convergence beween gil and bund yields would serve o reduce long-erm gil yields, furher invering he gil yield curve. By he year 2001, he UK budge posiion had moved away from surpluses o deficis wih increased spending on public services. The consequen increase in he supply of gils increased long-erm bond yields. Following he release of he Myners' Repor, 4 i was announced ha he MFR would be abolished. Removing his arificial demand shifed pension fund invesmen away from gils o UK corporae deb and wih he consequen narrowing of he spread beween 5-o 20-year gils he yield curve flaened. Wih a high balance of opinion agains EMU enry i became apparen ha he prospec of he UK joining he single currency in he near fuure was remoe. This may have also conribued o he sraighening ou of he long end of he yield curve. Euro swap spreads did no widen o he same degree as did serling swap spreads. However, a noable feaure was he surge in issuance of corporae bonds denominaed in euros since he inroducion of he single currency. Alhough, he budgeary siuaion was no so comforable in he main Euro-zone counries of France, Germany and Ialy hey all had upward sloping yield curves. Figure 3 shows he yield curve for German sovereign bonds on 28 April The Myners' Repor was commissioned o idenify he insiuionalised obsacles disoring he invesmen process. In paricular, Paul Myners was o deermine wha prevens he flow of long erm savings ino he growh poins of he economy - namely, new venures (privae equiy) and smaller companies. 14

15 7.0000% % Spo Rae (%) % % % % Time o Mauriy (years) Spo Raes Forward Raes Figure 3. German governmen Yield Curve on 28 h April 2000 From he year 2001 onwards serling swap spreads rended lower and fell more sharply han euro swap spreads. The UK budge posiion had also moved away from surpluses o deficis wih he increased spending on public services. The consequen increase in he supply of gils coupled wih he increased pension fund demand for UK corporae deb have aced as forces pulling serling swap spreads lower. In he years 2002 and 2003 public secor borrowing requiremens increased and he reurn o large-scale governmen deb issuance normalised he longer end of he serling yield curves, while also helping o narrow spreads beween governmen bonds and ineres rae swaps. The French, German, Ialian, Spanish and Duch governmens have all used swaps o reduce he average mauriy of heir deb. 5 When he swap spread widens, governmens find i aracive o receive fixed in he swap marke. However, he large 5 BIS Quarerly Review, March

16 budge deficis in he main euro-zone counries of France, Germany and Ialy have resuled in a narrowing of he spread beween euro swaps and heir respecive governmen bonds in 2001 and IV RELATIONSHIP BETWEEN SWAP SPREADS This secion examines he relaionship beween euro and serling swap spreads. Table 3 shows he correlaion coefficiens beween he changes in euro swap spreads, he changes in serling swap spreads, and he changes in ineres rae differenials beween he U.K. and Germany. As indicaed in preceding secion, boh he euro and serling swap spreads are non-saionary. Correlaions beween such ime series daa can be parly spurious if hey exhibi consisen rends. However, boh he variables are saionary if firs differences are considered. So in order o avoid spurious correlaions, he correlaions are analysed for he firs differences in hese variables and no heir levels. Given ha swap spreads are a measure of inerbank risk and he fac ha mos inernaional banks have global operaions i would be reasonable o expec swap spreads in euros and serling o be highly correlaed. Bu he coefficiens in Table 3 reveal ha his correlaion is negligible. The correlaion beween across 2-10 year verices ranges from o

17 TABLE 3 Correlaion beween Euro and Serling Swap Spreads The able indicaes he correlaion coefficiens among changes in he euro ineres swap spreads, EURsp, changes in Serling swap spreads, and he changes in ineres rae differenials beween UK and Germany (UK-GER).The ineres rae differenials are given by he consan mauriy yields of governmen bonds wih he same mauriy as he swaps. Mauriy Corr(EURsp, GBPsp) Corr(EURsp,UK-GER) Corr(GBPsp,UK-GER) 2 year year year year year However, he firs differences in euro swap spreads are more correlaed wih he firs differences in ineres rae differenials beween serling and eurodenominaed governmen bonds. The correlaion coefficien beween euro ineres rae swap spread and he ineres rae differenials given by he differences in yields of consan mauriy UK and German Treasury bonds has ranged form 0.38 o Bu he serling swap spread has displayed negligible correlaion wih hese ineres rae differenials as indicaed by he correlaion coefficiens ranging from o A possible explanaion for he high correlaion beween he changes in euro ineres rae swap spread and he ineres rae differenial is ha arbirageurs go long euro ineres rae swaps and go shor serling ineres rae swaps o consruc a spread posiion beween he governmen bonds in he wo counries. Such a spread posiion is consruced o ake advanage of he differenial beween he low long-erm yields of German sovereign bonds and he high long erm yields of UK gils. Eom, Subrahmanyam and Uno (2000) came o a similar conclusion on observing ha 17

18 changes in yen swap spreads were correlaed wih he ineres differenials beween US and Japanese reasury bond yields. Correlaion is inrinsically a shor-run measure of co-dependency and reflecs he conemporaneous relaionship beween ineres rae swap spreads. The analysis of correlaion is significan, in erms of depicing he degree of inegraion beween he swap markes. Addiionally, a lead-lag relaionship can also be expeced if here is some degree of co-dependency in ineres rae swap markes. Vecor auoregressive models can be used o invesigae any lead-lag behaviour beween ineres rae swap spreads. Granger causaliy ess are hen conduced o see if lagged changes in he spreads for serling ineres rae swaps cause changes in he spreads of euro ineres rae swaps. To illusrae his, le x be he firs differences in 10-year euro swap spreads and le y be he firs differences in 10-year serling swap spreads. Consider he bivariae VAR(2) model: x = c + a x + a x + b y + b y + e (1) y = c + a x + a x + b y + b y + e (2) of 21 The es for Granger causaliy from x o y is an F-es for he join significance a and a 22, in an OLS regression. Similarly, he es for Granger causaliy from y o x is an F-es for he join significance of b 11 and b

19 Using 216 weekly observaions over he sample period from January 29, 1999 o March 28, 2003, each equaion has been esimaed separaely using OLS. Table 4 shows he resuls of he esimaion. TABLE 4 Bivariae VAR(2) Model using firs differences in 10-year swap spreads Sample period: January 29, March 28, 2003 Equaion (1) Equaion (2) F-saisic F-saisic 2.53 Coeff. -sa Coeff. -sa c c a a a a b b b b The -saisics (in parenheses) indicae ha he model coefficiens are more significan where he dependen variable is he change in 10-year euro swap spread. The F 4,211 saisic for goodness of fi is 20.1 for he euro swap spread equaion, and his is significan a he 5% level (F 4,211 = 2.37). The F-saisic for he euro swap spread o serling swap spread causaliy is only Alhough his is jus abou significan a he 5% level, i is much weaker han he causaliy from he serling o euro swap spreads. The resuls indicae ha las week's changes in he 10-year serling swap spread can have a predicive impac on his week's changes in 10-year euro swap spreads. 19

20 TABLE 5 Co-dependency beween Euro and Serling Swap Spreads The able represens he resuls of bivariae "Granger causaliy" ess among changes in euro swap spreads ( EURsp), changes in serling swap spreads (GBPsp) and he lagged changes in ineres rae differenials beween he euro and he serling (UK-GER). The numbers in he able are values of he F-saisic of he Granger causaliy es which have been performed for 2 lags. Weekly daa of changes in swap spreads are from 29 January 1999 o 28 March 2003 providing for a oal of 219 observaions. The quoaions of swap raes and he consan mauriy governmen bond yields were obained from Daasream. Mauriy EURsp o GBPsp GBPsp o EURsp 2 year year year year year Mauriy EURsp o UK-GER UK-GER o EURsp 2 year year year year year Mauriy GBPsp o UK-GER UK-GER o GBPsp 2 year year year year year Table 5 repors he Granger causaliy ess reflecing he lead-lag relaionship among changes in euro and serling swap spreads across he mauriies under consideraion. Granger causaliy ess are sensiive o he choice of he number of lags. These ess were performed using 2,3 and 4 lags which all produced qualiaively similar resuls. The resuls repored in Table 5 are for 2 lags. As revealed in he able, he naure of he causaliy depends on wheher one is considering he shor or long-end of he swap 20

21 curve. The F-value of he Granger causaliy es for changes in he 10-year serling swap spread o changes in he 10-year euro swap spread is 4.97, which is saisically significan a he 5% level. This indicaes ha lagged changes in he serling swap spreads Granger cause changes in he euro ineres swap spread a he 10-year mauriy. Bu his causaliy is one-sided and does no ransmi iself he oher way. Lagged changes in 10-year euro swap spreads do no have any significan impac on changes in serling swap spreads of he same mauriy. A similar resul emerges for he 7-year mauriy. Bu a he shor end of he swap curve he causaliy again reverses iself. A he 2-, 3- and 5-year mauriies, euro-swap spreads Granger cause serling swap spreads bu he causaliy does no run he oher way. 21

22 V VOLATILITY IN SWAP SPREADS In his secion we examine he dynamic behaviour of volailiy in he euro and serling swap spreads. We make use of a GARCH framework o capure he ime variaion and persisence in volailiy. The analysis is carried ou on he 10-year swap spreads in euro and serling markes using daily observaions over he period January 29, 1999 o March 28, GARCH Models The GARCH (p,q) model expresses he condiional variance of a given ime series ( σ ) as a linear funcion of p lagged squared errors and q lagged variances. 2 σ = ω + αε α ε + βσ β σ (3) p p 1 1 q q ω > 0, α,..., α, β,..., β 0 1 p 1 q Since esimaion is difficul for anyhing oher han low values of p and q, in pracice he mos frequen applicaion is he GARCH (1,1) model. In he conex of our analysis, he GARCH (1,1) model would consis of wo equaions: y = c+ xδ + ε ε / I 1 ~ N(0, σ ) (4) σ = ω + αε + βσ ω > 0, αβ, 0 (5) where in he condiional mean equaion (4), y represens he swap spread a ime, and ε heir unanicipaed componen disribued independenly over ime and 22

23 2 assumed o follow a normal disribuion wih zero mean and condiional variance σ, x as he swap spread of he oher currency. The condiional variance equaion (5) is a funcion of he consan erm, ω ; news abou volailiy from he previous period, 2 measured as he lag of he squared residual from he condiional mean equaion, ε ; 2 he previous period's forecas variance, σ. 1 1 Tesing for ARCH effecs Various mehods are available o es for he exisence of auoregressive condiional heeroskedasiciy (ARCH). A es based on he Lagrange muliplier (LM) principle formulaed by Engle (1982) is applied here. Le y denoe he swap spread of one counry a ime and x he swap spread of he oher counry a ime. The process begins by running an OLS regression of y on x of he following form: y = a+ bx (6) ˆ Now he residuals from his preliminary OLS esimaion can be esed for ARCH behaviour. The es proposed in Engle (1982) is o regress he squared residuals, residuals: 2 e (where e = y yˆ ) on a consan and p lagged values of he squared e = ˆ α + ˆ α e ˆ α + υ (7) p where υ is he error erm. 23

24 From he resuls of his auxillary regression in residuals, he LM es saisic is calculaed as (T-p)*R 2 where T is he number of observaions. As explained in Bollerslev (1986), he LM saisic has an asympoic chi-square χ 2 ( ) disribuion wih p degrees of freedom under he null hypohesis of no ARCH effecs. If he LM saisic, evaluaed under he null hypohesis exceeds he criical value from a chisquare disribuion wih q degrees of freedom, he null hypohesis is rejeced. The resuls of he auxillary regression, for one lag, are shown in Table 6. There is srong evidence o rejec he null hypohesis of no ARCH effecs as he LM es saisic of ha i reurns, far exceeds he criical value of χ 2 (1) = A regression residual series was generaed by increasing he number of lags o five. Bu he resuls for more lag lenghs were no qualiaively differen from ha obained for one lag and are no repored here. TABLE 6 ARCH LM Tess on 10-year swap spreads Sample period: January 29, March 28, 2003 Included observaions: 1085 afer adjusing end poins Euro Swap Spreads Serling Swap Spreads Coeff. -sa Coeff. -sa α α F-sa (0.0000) (0.0000) LM-sa (0.0000) (0.0000) Figures in parenhesis show probabiliies 24

25 The 10-year serling swap spreads demonsraed similar ARCH effecs where he squared residual series for one lag reurned an LM es saisic of Increasing he number of lags o five did no change he resuls in so far as he exisence of ARCH was concerned. Tesing for an asymmeric effec on volailiy Several sudies on he volailiy dynamics of asse markes have shown evidence of asymmery in he response of condiional variances o he ype of news revealed o he markes. This is also referred o as he leverage effec in volailiy and is ofen observed in equiy markes where downward movemens in he marke are followed by higher volailiies han upward movemens of he same magniude. In he conex of swap spreads he leverage effec would arise if, for insance, he volailiy of he swap spread increases more when here is a posiive shock, which increases he swap spread, han when here is a negaive shock. The GARCH model specified in equaion (5) canno capure any asymmeric effec, since he condiional variance is a funcion only of he magniudes of he lagged residuals and no heir signs. The residuals ε are specified as a square and so i makes no difference wheher hey are posiive or negaive. 2 In he exponenial GARCH (EGARCH) model of Nelson (1991), σ depends on boh he size and he sign of lagged residuals. The purpose of his EGARCH specificaion is o ry and build in some asymmery, so ha he sign of ε maers. The 25

26 condiional variance equaion in he EGARCH model is defined in erms of he sandard normal variae z : ln σ = ω+ gz ( ) + βlnσ (8) where g(.) is an asymmeric response funcion defined by gz ( ) = γ z+ α(/ z/ 2/ π) The lef-hand side of equaion (8) shows he log of he condiional variance. This implies ha he leverage effec is exponenial, raher han he quadraic, and ha he forecass of he condiional variance are guaraneed o be nonnegaive. The sandard normal variable z is he sandardized residual ε / σ. When α > 0, and γ < 0 negaive shocks o reurns ( z 1 < 0 ) induce larger condiional variance response han posiive shocks. Therefore, he presence of asymmeric effecs can be esed by he hypohesis ha γ < 0. The impac is asymmeric if γ 0. Formulas for higher order lags in ε can be found in Nelson (1991). To es for he possible exisence of his leverage effec in swap spread volailiy we applied he EGARCH model o sandardized residuals of he condiional mean model using one swap spread as he dependen variable and he swap spread of he oher currency as he exogenous variable. We applied he EGARCH model o he swap spreads of boh currencies over he sample period. The resuls are shown in Table 7. 26

27 Wih he 10-year euro swap spread as he dependen variable and he corresponding serling swap spread as he exogenous variable he asymmeric effec erm (γ), is posiive and equal o The z-saisic is equal o 0.98 which is no saisically differen from zero a he 5% level of significance given by We may, herefore, conclude ha he volailiy in 10-year euro swap spreads do no display asymmeric effecs. Performing an idenical operaion wih he serling swap spreads as he dependen variable and he euro swap spread as he exogenous variable revealed similar resuls. The asymmeric effec erm (γ) was again posiive a I was also no saisically significan from zero wih he z-saisic equal o Eom, Subrahmanyam and Uno (2002) employed a GJR-GARCH model and found ha here is an asymmeric volailiy effec of dollar swap spreads on yen swap spreads, while he asymmeric effec of he shock on he yen swap spread is insignifican. In heir analysis of he swap spreads in Ausralia, Brown, In and Fang (2002) used an EGARCH approach and found ha he asymmeric effecs are saisically significan for 3 and 5-year swaps bu no for 10-year swaps. Wih hese ess demonsraing he absence of any asymmeric volailiy effec of he shock on 10-year euro and serling swap spreads, i would be appropriae o confine ourselves o symmeric GARCH models for modelling volailiy. 27

28 TABLE 7 Tesing for he Asymmeric Effec on Volailiy EGARCH Model: 2 2 ln σ = ω+ gz ( 1) + βlnσ 1 where g(.) is an asymmeric response funcion defined by gz ( ) = γ z+ α(/ z/ 2/ π) Euro Swap Spread Serling Swap Spread Coeff. z-sa. Prob. Coeff. z-sa. Prob. EGARCH Model Asymmeric effec parameer (H 0 : γ < 0) Esimaing he GARCH (1,1) model To assess he appropriaeness of he GARCH specificaion for daily swap spreads, a GARCH (1,1) model based on equaions (4) and (5) is used. This specificaion was found o be he mos appropriae for modelling volailiy in boh euro and serling 10- year swap spreads. The model specificaion also includes a dummy variable for he rading day following a weekend, i.e. Monday, in he condiional variance equaion o capure poenial "day of he week" effecs. The model now has he following form: y = c+ ax + ε (9) σ = ω + αε + βσ + δd (10)

29 where D represens a dummy variable ha akes he value of 1 on Mondays and is 0 oherwise. Panel A of Table 8 shows he resuls of he esimaion of he GARCH(1,1) model for euro-swap spreads. There are no indicaions of any serious model misspecificaion. TABLE 8. Esimaion of GARCH(1,1) model using 10-year swap spreads Sample period: January 29, March 28, 2003 PANEL A PANEL B Euro Swap Spread Serling Swap Spread Number of obs Log-likelihood Coeff. z-sa Coeff. z-sa Condiional Mean c a Condiional Variance ω α β δ Residual Tess Saisic Prob. Saisic Prob. Skewness Kurosis Jarque-Bera 8.98 ( ) ( ) LM es saisic ( ) 2.49 ( ) 29

30 The parameer esimaes for he condiional variance equaion (10) correspond o α = , β = , ω = and δ = The z-saisics reveal ha all coefficiens are saisically significan. The coefficien of he dummy variable is negaive indicaing he influence of more subdued rading in governmen securiies on a Monday. 2 2 If we pu σ = σ for all in equaion (10) above, we ge an expression for he long-erm seady sae variance in a GARCH (1,1) model: = (11) 2 σ ω/(1 α β) Equaion (11) can hen be rewrien as: V = ω / γ (12) where V is he long-erm variance which can be calculaed as ω/γ. A sable GARCH (1,1) process requires ha he sum α + β be less han 1. Only hen will he GARCH volailiy erm srucures converge o a long-erm average level of volailiy ha is deermined by (12). In his esimaion he sum of he α and β is equal o which is less han one indicaing ha volailiies of he 10-year euro swap spread converge o some long-erm average level of volailiy. Since γ = 1 α β, i follows ha γ = And since ω = γv, i follows ha V = In oher words, he long-run average variance per day implied 30

31 by he model is This corresponds o a volailiy of = or % per day. The residual ess display descripive saisics of he sandardised residuals, ε / σ. Under he null hypohesis of a normal disribuion, he observed value of he Jarque-Bera es saisic of exceeds he criical value of χ (2) = So he sandardised residuals are no normally disribued. However, we canno rejec he null hypohesis of no ARCH effecs in he sandardised residuals as he observed LM es saisic of is well shor of he criical value of 2 χ 0.95(1) = This clearly indicaes ha here are no ARCH effecs lef in he sandardised residuals. The same GARCH (1,1) was hen employed o esimae volailiy in he 10- year serling swap spreads. Panel B of Table 3. shows he resuls of he esimaion. In he condiional variance equaion, α = , β = , ω = and δ = As revealed by he z-saisics, all coefficiens are saisically significan. The sum of he GARCH coefficiens is given by α + β = , which being very close o one indicaes ha volailiy shocks are quie persisen. The value of he coefficien α in he case of serling swap spreads is much higher han wha i is for euro swap spreads. Large GARCH error coefficiens α mean ha volailiy reacs quie inensely o marke movemens, and so if α is relaively high and β is relaively low hen volailiies end o be more spiky. Using equaions (11) and (12) above, he long-erm variance V works ou o This means a volailiy of = or 13.57% per day. So we find he volailiy of he serling swap spread o be somewha higher han ha of he euro swap spread. 31

32 In he case of boh he euro and serling swap spreads, he disribuion of he sandardised residuals does no follow a normal disribuion. However, he disribuion of euro swap spread residuals are relaively closer o a normal disribuion, whereas he serling swap spreads exhibi a much more asymmeric and considerably broader disribuion. Accordingly, he serling swap spreads are more volaile han heir euro counerpars. Volailiy Spillovers Having esimaed he volailiies of boh he euro and serling swap spreads over he sample period he paper examines he possibiliy of a ransmission of volailiy beween hem. Alhough he GARCH (1,1) specificaion used above was descripively accurae for esimaing volailiy in individual markes i did no incorporae he spillover effecs from oher markes. So i is necessary o inroduce an exogenous variable ino he condiional variance equaion ha capures he poenial spillover effec from one marke ino he oher. The squared residual from one marke is inerpreed as a "volailiy surprise" and is included in he oher marke's condiional variance specificaion: σ = ω+ αε + α ξ + βσ + δd (13) where ε is he lagged squared residual of he domesic swap spread and ξ is he 1 lagged squared shock arising from he foreign marke's swap spread. 1 32

33 The resuls of esimaing his model for boh he euro and serling swap spreads are shown in Table 9 TABLE 9 Volailiy spillovers beween swap spreads Sample period: January 29, March 28, 2003 PANEL A PANEL B Euro Swap Spread Serling Swap Spread Number of obs Log-likelihood Coeff. z-sa Coeff. z-sa Condiional Mean c a Condiional Variance ω α α β δ Residual Tess Saisic Prob. Saisic Prob. Skewness Kurosis Jarque-Bera 9.27 ( ) ( ) LM es saisic 0.67 ( ) 2.58 ( ) Panel A of Table 9 shows here is evidence of an elemen of volailiy spillover from he serling swap spreads o he euro swap spreads. The parameer esimae on he serling swap spread volailiy surprise ξ 1 is posiive and saisically significan a he 5% level. Therefore, he null hypohesis of no foreign volailiy surprise is rejeced 33

34 a he 5% significance level, indicaing ha here are mild volailiy ransmissions from he serling swap spreads o euro swap spreads. However, Panel B of Table 3.9 shows ha here is no such volailiy spillover from euro swap spreads o serling swap spreads as he parameer esimae is no saisically significan. These volailiy spillover effecs are consisen wih he findings on Granger causaliy ess for 10-year swap spreads in Table 6. VI CONCLUSIONS This paper empirically examines he case of marke inegraion beween euro and serling swap spreads during he period January, 1999 o March, The swap spreads are deermined by he difference beween he swap raes and he consan mauriy yields of governmen bonds wih corresponding mauriy. Euro swap spreads have been proxied using German sovereign bonds. To begin wih, he main characerisics of he erm srucure of swap spreads in boh he euro and serling markes were examined. Boh swap spreads are nonsaionary across he erm srucure and follow a random walk. However, serling swap spreads have been percepibly wider han euro swap spreads since he launch of he single currency. This largely relaes o he ne supply of governmen bonds in Briish and European markes as driven by heir respecive budgeary posiions. While in he UK, budge surpluses caused he ne issuing volume of Treasury bonds o decline in 1999 and 2000, in he main European markes of France, Germany and Ialy he issuing aciviy of governmens remained sable due o persisen budge 34

35 deficis. The serling swap spreads subsequenly rended lower due o he UK budge posiion moving away from surpluses o deficis and he shif in demand of UK pension funds from gils o corporae deb. The correlaion coefficien beween changes in euro swap spreads and changes in serling swap spreads is negligible indicaing ha credi risk can be aribued counry specific facors as opposed o global influences. However, he changes in euro swap spreads are correlaed, o some degree, wih changes in ineres differenials beween serling and euro-denominaed governmen bonds. Bu no evidence is found of serling swap spreads being correlaed wih he ineres rae differenials. A plausible inerpreaion for he correlaion beween he euro swap spread and he ineres differenial is ha arbirageurs go long euro ineres raes swaps and go shor serling ineres raes swaps o consruc a spread posiion beween he governmen bonds in he wo counries. Such a spread is consruced o ake advanage of he low long-erm yields of German bunds and he high long erm yields of UK gils. Granger causaliy ess, reflecing he lead-lag relaionship among changes in euro and serling swap spreads reveal ha he causaliy depends on wheher one is considering he shor or long-end of he swap curve. Lagged changes in serling swap spreads Granger cause changes in euro ineres swap spreads a he 10-year mauriy. Bu here is no evidence o sugges ha euro swap spreads Granger cause serling swap spreads a he 10-year mauriy. Bu a he shor end of he swap curve he causaliy again reverses iself. A he 2-, 3- and 5-year mauriies, euro swap spreads Granger cause serling swap spreads bu here is no causaliy in he reverse direcion. 35

36 The noion of marke efficiency dicaes ha i should no be possible o predic swap spreads in one marke using lagged informaion generaed in anoher marke. To he exen ha lagged changes in he spreads for serling ineres raes swaps cause changes in he spreads of euro ineres swaps, he laer could be characerised as being informaionally inefficien. However, ineres rae differenials beween hese wo markes do no Granger cause swap spreads in eiher of he markes. The analysis of he causal relaionship beween swap spreads was hen exended o he dynamic behaviour of volailiy in 10-year euro and serling swap markes. The ime series of boh he euro and serling swap spreads show volailiy clusering and reveal srong ARCH effecs. An EGARCH model was employed o es for he exisence of any asymmeric response in he volailiy of 10-year swap spreads. Bu he volailiies did no display asymmeric effecs for eiher of he swap spread markes. The GARCH (1,1) specificaion was found o be he mos appropriae for modelling volailiy in 10-year swap spreads for boh he markes. Volailiy shocks were found o be quie persisen in boh he markes. Bu volailiy in he serling swap spreads reaced more inensely o marke movemens and were more volaile han heir euro counerpars. However, boh volailiy erm srucures converged o a long-run average level of volailiy. The possibiliy of volailiy spillover effecs beween 10-year euro and serling swap spreads were also examined. There was evidence of mild volailiy ransmission from he serling swap spreads o euro swap spreads bu no spillover 36

37 effecs he oher way round. This observaion was consisen wih he findings on Granger causaliy. This invesigaion ino he causal relaionship beween euro and serling swap spreads could conribue o an undersanding of he degree of financial marke inegraion beween he UK and he Eurozone. An awareness of he naure of volailiy spillover across he markes could be of imporance o economic policy makers from a financial sabiliy perspecive. Given our findings ha here is no volailiy ransmission from he euro swap spreads o serling swap spreads, i seems unlikely ha a credi risk shock in he euro fixed income marke would have a desabilising effec on he serling fixed income marke. However, he more general conclusions ha can be drawn from his paper are somewha enaive because of he limied period of observaion. 37

38 REFERENCES Bollerslev, T. (1986). Generalised auoregressive condiional heeroskedasiciy. Journal of Economerics, 31: Bollerslev, T. (1987). A condiional heeroskedasic ime series model for speculaive prices and raes of reurn. Review of Economics and Saisics, 69: Brooke M., A. Clare and I. Lekkos (2000), "A comparison of long bond yields in he Unied Kingdom, he Unied Saes and Germany", Bank of England Quarerly Bullein. May Brown, K., W.V. Harlow and D.J.Smih, (1994). An empirical analysis of ineres swap spreads. Journal of Fixed Income, 3, Brown, R., In, F., Fang, V, (2002). Modelling he Deerminans of Swap Spreads. Journal of Fixed Income, 12, Cooper, N., and Scholes, N., (2001). Governmen bond marke valuaions in an era of dwindling supply. BIS Papers, No.5: The changing shape of fixed income markes. Duffie, D., and K. Singleon, (1997). An economeric model of he erm srucure of ineres-rae swap yields, Journal of Finance, 52, Edwards, F.R., (1999). Hedge funds and he collapse of Long-Term Capial Managemen. Journal of Economic Perspecives, 13, Engle, R.F., (1982). Auoregressive Condiional Heeroskedasiciy wih Esimaes of he Variance of Unied Kingdom Inflaion. Economerica, 50, Eom, Y.H., Subrahmanyam, M.G., and Uno, J. (2000). Credi risk and he yen ineres rae swap marke. Unpublished manuscrip, Sern Business School, New York. Eom, Y.H., Subrahmanyam, M.G., & Uno. J. (2002). Transmission of Swap Spreads and Volailiies in he Japanese Swap Marke. Journal of Fixed Income, 12, Grinbla, M., (1995). An analyic soluion for ineres-rae swap spreads. Working Paper, UCLA, Anderson Graduae School of Managemen. Hamao, Y., Masulis, R., and Ng, V., (1990). Correlaions in price change and volailiy across inernaional sock markes. Review of Financial Sudies, 3, Hull, J.C. (2000). Opions, fuures and oher derivaives. Pearson Educaion Inc. Liu, J., Longsaff, F.A., and Mandell, R.E. (2002). The Marke Price of Credi Risk: An Empirical Analysis of Ineres Rae Swap Spreads. Working Paper, UCLA. Nelson, R., and Siegle, F, (1987). Measuring he erm srucure of ineres raes. Journal of Business 44,

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