MODEING THE US SWAP SPREAD Hon-un Chung, School of Accouning and Finance, The Hong Kong Polyechnic Universiy, Email: afalan@ine.polyu.edu.hk Wai-Sum Chan, Deparmen of Finance, The Chinese Universiy of Hong Kong, New Terriories, Hong Kong, Email: waisum@baf.msmail.cuhk.edu.hk Jonahan A. Baen, Graduae School of Managemen, Macquarie Universiy, Sydney, NSW Ausralia, Email: abaen@gmail.com ABSTRACT The dynamics beween 5-year US Treasury bonds and ineres rae swaps are examined using Bivariae Threshold Auoregressive (BTAR) models o deermine he drivers of spread changes and he naure of he lead-lag relaion beween he wo insrumens. This model idenifies he economic or hreshold - value ha marke paricipans consider significan before realigning heir porfolios. Three differen regimes are idenified: when he swap spread in he previous week is eiher high, or low, hen he Treasury bond marke leads he swap marke. However when he swap spread is low, hen none of he markes lead each oher. Key words: Swap spread, BTAR Models, regime swiching INTRODUCTION The obecive of his paper is o deermine he exac naure of he relaion beween swaps and risk-free bonds hrough he applicaion of nonlinear hreshold models, which previously have been widely used for invesigaing he dynamics wihin currency and sock markes (e.g. [3], [12]). These echniques are specifically applied o an invesigaion of he lead-lag dynamics beween he US Treasury bond and US$ denominaed swap markes where he change in he swap spread is he dependen variable. US Treasury bonds comprise he larges governmen bond marke in he world, while US denominaed ineres rae swaps comprise daily urnover in excess of US$81.3 rillion. We build upon earlier invesigaions in ineres rae and swap markes [4,5,6,7,9] by uilising a new class of bivariae hreshold auoregressive (BTAR) models [2] o capure he regime-swiching, lead-lag dynamics ha exis beween he wo US bond and swap markes. The BTAR model is chosen for a number of reasons. Firs, his model provides an exac measure of he economic incenive for a porfolio invesor o shif funds, in his case beween wo financial insrumens- he swap and a fixed rae bond of equivalen mauriy. This measure, ermed a hreshold or criical value in he BTAR model, may also be inerpreed as he hidden cos necessary for financial marke paricipans o shif beween asse classes. Second, if indeed hese hresholds values can be idenified, hen hey can be used o anicipae he change in he yield curve dynamics. This will allow raders o be more cauious in managing risk and help policymakers and cenral banks fine une moneary policies. Third, he hreshold value can be - 1 -
expressed in erms of ineres rae percenages or basis poins ; a number ha can be easily undersood and inerpreed by financial markes. This is quie differen from he informaion provided by oher models, such as Markov Swiching Models [8, 11]. DATA The weekly closing raes of US Treasury bond yields and US$ ineres rae swap raes from January 1995 o December 2004 are used in his sudy. In line wih he marke pracice for end of week porfolio realignmen, we use weekly daa. Doing so, also overcomes sickiness ha is oherwise eviden in daily daa. Thus, significan changes in he swap spread is clearer in weekly daa, whereas monhly observaions lose informaion, and he number of observaions is fewer. The daa were downloaded from he Bloomberg Fixed Income Daabase, on which he Treasury bond yields and swap raes are moniored closely by housands of raders worldwide. A sample sar dae in he mid 1990s is more appropriae due o he remendous growh in he ineres rae derivaive markes from is commencemen in he early 1980s and he more recen srucural change in he pricing and rading of swaps, such as he inroducion of maser agreemens from he Inernaional Swaps and Derivaives Associaion, Inc. and he neing agreemens for credi risk reducion ha were developed in he early 1990s. Depending on he expeced direcion of ineres rae movemen marke paricipans will have a preference for using differen insrumens when hey expec he spread beween he wo markes (he swap spread) o narrow or widen. There are basically six differen scenarios. In he firs four of he scenarios, he ineres raes in he Treasury and swap markes are moving in he same direcion, which means changes in he wo markes are posiively correlaed. In he las wo scenarios, he ineres raes in he Treasury marke and he swaps marke are moving in differen direcions, which means changes in he wo markes are negaively correlaed. These differen scenarios are deailed below: Scenario I Bond and swap raes rise (posiive correlaion) wih a widened swap spread. Scenario II Bond and swap raes decline (posiive correlaion) wih a widened swap spread. Scenario III Bond and swap raes increasing (posiive correlaion) wih a reducing swap spread. Scenario IV Bond and swap raes declining (posiive correlaion) wih a reducing swap spread. In his scenario, marke paricipans prefer o receive fixed in a swap han purchase governmen bonds, all oher hings being equal. Scenario V Narrowing swap spread wih swap and bond raes converging (negaive correlaion). In his scenario, marke paricipans sell bonds and receive fixed in he swaps marke simulaneously, which causes a narrowing of he swap spread. Scenario VI Widening swap spread wih swap and bond raes converging (negaive correlaion). Noe ha over he sample period he average yield for he five-year Treasury bond is 5.01 percen, and he average five-year swap rae is 5.54 percen, which gives an average swap spread of 52 basis poins over he period. The volailiies are similar, a 1.31 percen and 1.32 percen, respecively. Boh he bond yield and he swap rae exhibi negaive skewness, which means ha yields end o say a he high end of he range. This is confirmed by he median bond yield and he median swap rae of 5.39 percen and 5.86 percen, respecively, which are higher han he - 2 -
average over he sample period. Boh he bond yield and he swap rae have a bimodal disribuion, which means ha hey end o remain a eiher he high end or a he low end of he range. This was in line wih he moneary policy of he Federal Reserve over he period, during which he Federal Fund arge rae was usually lifed or lowered in consecuive Federal Open Marke Commiee meeings so ha ineres raes would eiher be kep below 3.0 percen o avoid a liquidiy crunch, or mainained above 5.0 percen o curail inflaionary pressures in he broader economy. METHOD Based on Chan s [1] sudy of sock indices and index fuures, he lead-lag behaviour of he change (Δ) in he US Treasury bond (Gov ) and he ineres rae swap (IRS ) a ime () can be examined using he following regression, Equaion 1, where ε is a random variable: IRS a 4 k k4 b GOV k. (1) Given ha he change in he Treasury bond yield and he change in he swap rae are saionary ime series he Granger causaliy es (up o lag ) can be performed using he following ses of regressions (Equaions 2): IRS c GOV f i1 d IRS i i1 i i g GOV i 4 e GOV 1 h IRS BTAR modelling echniques are hen applied o he examinaion of he dynamic relaionship beween he change in he five-year US Treasury yield (GOV ) and he change in he five-year ineres rae swap rae (IRS ), where, Z = (z 1, z 2 ) and z 1 = GOV = GOV - GOV -1, and z 2 = IRS = IRS - IRS -1. The series under sudy is he weekly closing prices over he period January 1995 o December 2004, which gives 522 observaions. For he hreshold variable, defined as y = SS = SS - SS -1, he weekly change in he swap spread (SS ) is used. RESUTS In he lead-lag analysis he only coefficien ha is saisically significan is b 0. Neiher he lead variables (b 1 o b 4 ) nor he lag variable (b -1 o b -4 ) are saisically significan. The resuls indicae ha here is no lead-lag relaionship beween he change in he swap rae wih respec o he change in he Treasury bond yield for he lead variables, or he lag variable, over he enire sample period. The nex analysis involves pairwise esing for Granger Causaliy. For he enire sample period (January 1995 o December 2004) he null hypohesis ha he change in he Treasury bond yield does no Granger-cause a change in he swap rae is reeced (F-saisic = 5.029) a leas a he 95% level. The null hypohesis is also reeced for periods from one lag up o five lags (F-saisic = 3.697 o 2.677) a leas a he 95% level. However, he null hypohesis ha a change in he swap rae does no Granger-cause a change in he Treasury bond yield canno be reeced, which shows ha he change in he Treasury bond yield has only a unilaeral causaliy on he change in he swap rae. (2) - 3 -
If he sample period is divided ino wo sub-periods, he firs from January 1995 o May 2000, hen he resul is similar o ha for he whole sample period: here is unilaeral causaliy wih he change in he Treasury bond yield Granger-causing he change in he swap rae. However, for he firs sub-period, he F-saisics (3.853 o 2.352) are only significan (a leas a he 95% level) from hree lags o five lags. These findings are also consisen wih he firs sub period and he overall sample. However he F-saisics (7.031 and 3.349 respecively) are only significan (a leas he 95% level) for he one lag period and wo lag period only. An ineresing resul is ha he change in he swap rae is marginally shown o Granger-cause a change in he Treasury bond yield for one lag period (a he 10% level wih F-saisic = 3.855). Using he BTAR modelling framework, hree regimes can now be consruced for he dynamics of he Treasury and he ineres rae swaps markes. The firs regime occurs when he weekly change in he swap spread is negaive and more han 3.3 basis poins {y -1 r 1 = -0.033}. The second regime occurs when {r 1 = -0.033 y -1 r 2 = 0.017}. The hird regime exiss when he weekly change in he swap spread is posiive and more han 1.7 basis poins {y -1 > r 2 = 0.017}. The weekly lead-lag relaionship beween he Treasury and ineres rae swaps markes in he k- h regime can be examined. If any of he upper off-diagonal elemens of he esimaed marices are significan, hen a change in he Treasury bond yield has a lead effec on he change in he swap rae. If any of he lower off-diagonal elemens of he esimaed marices are significan, hen a change in he swap rae has a lead effec on he change in he Treasury bond yield. CONCUSIONS This paper examines he dynamics beween US Treasury bond and swap markes using Bivariae hreshold auoregressive (BTAR) models. This approach, which may be applied o oher ineres rae producs in oher markes, ess wheher he lead-lag relaionship beween he bond marke and he swap marke is a nonlinear dynamic process, and second wheher his relaionship is governed by he change in he ineres rae differenial, or spread, beween hese wo markes. The findings from he BTAR models may be summarised in Figure 1 where hree regimes are idenified. In he firs regime, he Treasury marke leads he swaps marke when he change in he swap spread is negaive and more han 3.3 basis poins on a weekly basis. In he second regime, here is no significan lead-lag relaionship beween he wo markes when he change in he swap spread falls wihin a narrow range of negaive 3.3 basis poins and posiive 1.7 basis poins. In he hird regime, he Treasury bond marke leads he swaps marke when he change in he swap spread is posiive and more han 1.7 basis poins. Simple lead-lag sudies do no reveal any paricular informaion abou he dynamics beween he wo markes. However, Granger causaliy ess are useful for revealing he overall movemen of he wo markes, because i shows ha he change in he Treasury bond yield can Granger-cause a change in he swap rae. Subecive udgmen can enhance he performance of he Granger causaliy es. - 4 -
Figure 1 Three Regimes Regime I Change in Swap Spread (SS -1 ) is more han 3.3 basis poin per week GOV leads IRS (he coefficien is posiive) Number of observaions = 83 (15.99% of he oal sample) Only 1 lag is significan SS -1 Regime II Change in Swap Spread (SS -1 ) is beween 3.3 basis poin and + 1.7 basis poin per week < -3.3 b.p. No lead-lag Number of observaion = 294 (56.65% of he oal sample) -3.3 b.p. < SS -1 < 1.7b.p. Regime III Change in Swap Spread (SS -1 ) is more han 1.7 basis poin per week Mixed lead-lag relaion (wo condiions) Number of observaions = 142 (27.36% of he oal sample) Firs condiion GOV leads IRS (he coefficien is posiive) onger lags (1, 2, 3) are significan Second condiion IRS lead GOV (he coefficien is negaive) ags 2 marginally significan SS -1 > 1.7 b.p. By dividing he daa ino wo sub-periods, we also find ha for he second sub-period, he change in he swap rae can marginally Granger-cause a change in he Treasury bond yield for one lag period. However, his informaion canno be revealed if a subecive decision is no made. The BTAR model, however, can reveal more informaion wihou he use of subecive decision making. The regime swich process can occur in individual observaions because he swiching is deermined by he sae of he hreshold variable, namely, he magniude and direcion of he change in he swap spread. The dominance of Treasury bonds in leading he swaps marke occurs when eiher a widening or a narrowing of he swap spread occurs. This seems o fall in line wih he Fligh o Qualiy and Fligh o iquidiy phenomena and is probably due o he naure of Treasury securiies. Usually, no credi limi is required for ransacions o be carried ou for financial insiuions, and Treasury securiies have a minimal impac on he balance shees of various insiuions. Overall, he BTAR model provides a deeper insigh han simple lead-lag sudies and Granger causaliy ess ino he dynamics beween he US Treasury bonds and ineres rae swaps markes. Imporanly, his approach can be applied o oher ineres rae producs in oher markes. By idenifying he regimes and he condiions for change in he regimes, marke paricipans and regulaors can become more informed abou he probable changes ha will occur in he Treasury bond and ineres rae swaps markes. Similar o he findings of Chappell e al. [3], who idenify he bounds wihin which he French Franc/Deuschmark exchange rae kep o before he launch of he Euro, he movemens of he Treasury bond marke and he ineres rae swaps marke are governed by he direcion and magniude of he change in he swap spread. The BTAR model is able o idenify he hreshold value of he change in he swap spread ha bond and swap marke - 5 -
paricipans considered o be significan. Furher research can be conduced o explain he exisence of he hreshold values. REFERENCES [1] Chan, K. (1992). A furher analysis of he 1eadlag relaionship beween he cash marke and sock index marke. Review of Financial Sudies 5, 123-152. [2] Chan, W. S. and Cheung, S. H. (2005). A bivariae hreshold ime series model for analyzing Ausralian ineres raes. Mahemaics and Compuers in Simulaion 68, 429 437. [3] Chappell, Padmore, J., Misry, P. and Ellis, C. (1996). A hreshold model for he French Franc/Deuschmark exchange rae. Journal of Forecasing, 15, 155-164. [4] Duffie, D. and M. Huang (1996). Swap Raes and Credi Qualiy. Journal of Finance 51, 921 949. [5] Cores, Fabio. (2006). "Undersanding he Term Srucure of Swap Spreads." Bank of England Quarerly Bullein 46, no. 1: 45-56. [6] Feldhuer, P. and D. ando (2008). Decomposing Swap Spreads. Journal of Financial Economics 88, 375 405. [7] Grinbla, M. (2001). An Analyical Soluion for Ineres Rae Swap Spreads. Inernaional Review of Finance 2 (3), 113 149. [8] Hamilon, James D. (1996). Specificaion Tesing in Markov-Swiching Time-Series Models, Journal of Economerics 70, 127-157. [9] Io, Takayasu. (2007). "The Analysis of Ineres Rae Swap Spreads in Japan." Applied Financial Economics eers 3, no. 1-3: 1-4. [11] Tsay, R. S. (1989). Tesing and modelling hreshold auoregressive processes. Journal of he American Saisical Associaion, 84, 231-240. [12] Tsay, R. S. (1998). Tesing and modelling mulivariae hreshold models. Journal of he American Saisical Associaion, 93, 1188-1202. - 6 -