ABSTRACT. , and curvature parameter, β

Transcription

1 The Inernaional Journal of Business and Finance Research Volume 3 Number 9 THE USE OF TERM STRUCTURE INFORMATION IN THE HEDGING OF JAPANESE GOVERNMENT BONDS Jian-Hsin Chou, Naional Kaohsiung Firs Universiy of Science and Technology Chien-Yun Chang, Hsiuping Insiue of Technology Chen-Yu Chen, Naional Kaohsiung Firs Universiy of Science and Technology ABSTRACT This paper employs he Kalman filer o explore he impac of erm srucure variables in he hedging of Japanese Governmen Bonds (JGBs) wih reasury fuures. The erm srucure facors (level parameer β, slope parameerβ, and curvaure parameer, β ) are based on Nelson and Siegel (987) model. The ou-of-sample hedging performance is also provided by moving window echnology. The empirical resuls show he exisence of significan relaionships among he erm srucure facors, he earlier hedge raio, and he opimal hedge raio. However, he ime-varying hedge raio (which includes he erm srucure variables from he informaion se) did no provide good ou-of-sample hedging effeciveness. Neverheless, he ou-of-sample resuls did demonsrae ha he performance of he imevarying hedge raio wih erm srucure variables is beer han a hedge raio wih a naive hedge or OLS model in he 7 -year Japanese Governmen Bond index. JEL: G, G5, G3 INTRODUCTION T he so-called erm srucure of ineres raes (TSIR), which is also known as he yield curve, shows he expeced yield from zero-coupon governmen bonds under a given defaul risk. For many large financial insiuions, informaion derived from he TSIR has played an imporan role in he valuaion and hedging of ineres-rae-dependen insrumens. Moreover, he shape of he TSIR provides a good predicive indicaor of fuure economic aciviy, wih consequen implicaions for esimaions of GDP and inflaion raes (Esrella and Mishkin, 998; Esrella and Hardouvelis, 99) Invesors can, herefore, make udgmens on he fuure impac of financial and economic aciviies by observing changes in he TSIR, and can hus adus heir invesmen and hedging sraegies. Because he spo price of bonds is a funcion of ineres raes and he movemen of he yield curve is no parallel wihin differen mauriies, Lierman and Scheinkman (99) decomposed he curve of he TSIR ino hree phases: level, slope, and curvaure. Diebold and Li (6) used β, β and β in he Nelson and Siegel (987) model o designae hese hree phases, which hey inerpreed as he long-erm, shorerm, and middle-erm phases in he ineres rae. In addiion, apar from hese hree phases, he facor τ from he Nelson and Siegel (987) model governs he exponenial decay rae. When he value of τ is small, slow decay is produced and here is a beer fi wih he yield curve a long mauriies; conversely, when he value of τ is large, rapid decay is produced and here is a beer fi wih he yield curve a shor mauriies. Moreover, as Dolan (999) and Diebold e al. (6) have poined ou, he Nelson and Siegel (987) model is well suied o describing he dynamic process of he TSIR and providing good forecass. To promoe bond porfolio performance, bond invesmen managers obviously wish o manage ineres rae risks efficienly, and hey need o undersand he dynamic process of he TSIR. In his regard, Markowiz (99) decomposed porfolio risk ino: (i) sysem risk; and (ii) non-sysem risk. According o his view, bond invesmen managers can eliminae non-sysem risk by diversificaion of invesmen; 3

2 J. H. Chou e al The Inernaional Journal of Business and Finance Research Vol. 3 No. 9 however, he hedge funcion of fuures conracs or oher derivaives can diversify he sysem risk in he bond porfolio. Managemen of he ineres risk wih fuures conracs has become an imporan issue in bond porfolio managemen. The Tokyo Sock Exchange (TSE) has offered rading on -year Japanese Governmen Bond (JGB) Fuures conracs since Ocober 985. The rading volume of hese conracs has boomed, and he JGB Fuures marke is now regarded as one of he mos acive in he Asian financial sysem. These fuures bonds are popular because hey can be used o ransfer risk and hus provide bond invesors wih a hedge agains ineres rae risks. In hese circumsances, he deerminaion of he opimal hedge raio becomes a crucial issue in he hedge sraegy of invesors; however, heir abiliy o do his effecively has been inhibied by he fac ha mos empirical sudies of hese issues have focused only on he quesion of sock porfolio hedge. The presen paper addresses his gap in he lieraure by analysing he hedge funcion of ineres rae fuures in he JGB marke. Because he duraion of a bond porfolio is fundamenally a funcion of ineres raes, i is reasonable o assume ha he reurns of a bond porfolio will flucuae wih movemens in he yield curve. In accordance wih he approach adoped by Fink e al. (5), he presen sudy invesigaes he performance of an opimal hedge raio using moving window echnology based on he Kalman filer; however, he approach of Fink e al. (5) exended here hrough a more accurae esimaion of he yield curve facors. In his regard, Dolan (999) poined ou ha he parameers of he yield curve, esimaed using he Nelson and Siegel (987) model, could be prediced; indeed, Dolan (999) presened forecass of how he level, slope, and curve could have significan effecs on bond porfolio performance. The main conribuion of he presen work is o combine he yield curve facors of he JGB, using he Nelson and Siegel (987) model, wih he Kalman filer o generae he opimal hedge raio. The remainder of his paper is organised as follows. In he nex secion, we discuss he relevan lieraure. The nex secion inroduces he esimaion of yield curve facors, and he calculaion of he ime-varying opimal hedge raio, using he Kalman filer. The hird secion proceeds o an empirical analysis - describing: (i) he deailed daa; (ii) he esimaion of he model of yield curve and he Kalman filer; and (iii) he in-sample and ou-of-sample performance of a number of hedges. The final secion presens he conclusion. LITERATURE REVIEW Esimaing Term Srucure of Ineres Raes Many mehods exis o esimae he yield curves. Generally speaking, here are wo disinc approaches o esimae he erm srucure of ineres raes: he equilibrium models and he empirical models. The equilibrium models are formalized by defining sae variables characerizing he sae of he economy (relevan o he deerminaion of he erm srucure) which are driven by hese random processes and are relaed in some way o he prices of bonds. I hen uses no-arbirage argumens o infer he dynamics of he erm srucure. Examples of his include Vasicek (977), Dohan (978), Brennan and Schwarz (979), Cox Ingersoll and Ross (CIR, 985) and Duffie and Kan (996). Unforunaely, in erms of he expedien assumpions abou he naure of he sochasic process driving ineres raes, he erm srucure of ineres raes derived by hose models could only exis heoreically in an efficien marke and do no conform well o he observed daa on bond yields and prices. In conras o equilibrium models, he empirical models focusing on obaining a coninuing yield curve from cross-secional coupon bond daa based on curve fiing echniques are able o describe a richer 3

3 The Inernaional Journal of Business and Finance Research Volume 3 Number 9 variey of yield paerns in realiy. The resuling erm srucure esimaed from he saisical echniques can be direcly pu ino ineres rae models, such as he Ho and Lee (986), he Heah e al. (99) and Hull and Whie (99) models, for pricing ineres rae coningen claims. Since a coupon bond can be considered as a porfolio of discoun bonds wih mauriies daes consisen wih he coupon daes, he discoun bond prices hus can be exraced from acual coupon bond prices by saisical echniques. Examples of his approach include McCulloch (97, 975), Schaefer (98), Vasicek and Fong (98) and Seely (99). The maor advanage of he empirical models is able o characerize a pleny variey of reasonable yield curve paerns which are consisen wih real marke yield curves. Furhermore, among he empirical models, he Nelson and Siegel (987) model is mos suied o he ulimae purpose of deermining he opimal hedge raio. There are hree main superior feaures of he Nelson and Siegel (987) model. Firs, i has only hree maor parameers, and which can be well used o explain he meaning of he yield curve shape in real marke condiion; Second, i has been proved o be good a fiing yield curves (Willner, 996; Dolan, 999; Diebold and Li, 6; Diebold e al., 6); Finally, each parameer derived from he Nelson and Siegel (987) model can separaely presen he level, slope and curvaure changes, which are hree significan conribuions of varied yield curve shape. Revoluion of Hedge Raios Esimaion Tradiionally, hedge raios have been esimaed by regression analysis. However, Myers (99) has argued ha his mehod of esimaing hedge raios encouners wo problems: (I) he esimaed value of hedge raios using his mehodology does no involve all relevan informaion; and (ii) he hedge raio derived by his mehod is no ime-dependen because he covariance marix of spo and fuures prices will no change wih ime. As a resul, he assumpion of a fixed covariance marix could induce invesors o ake unaccepable risks wih fuures. To resolve hese difficulies in he radiional model, Engle (98) provided he auoregressive condiional heeroscedasiciy (ARCH) model, which predics he condiional variance by aking a weighed average of pas errors. In his model, recen informaion has more influence on he error erm han informaion from he disan pas. This ARCH model was exended in he Generalized ARCH model (known as he GARCH model), which was developed by Bollerslev (986). The GARCH model assumes ha variance is a weighed average beween previous variance and error erms. An even more generalized model has been proposed by Engle e al. (988), who ook ino consideraion he feedback relaionship beween spos and fuures. All of hese ARCH-ype models represen a significan advance on previously used mehods because hey all assume ha hedge raios are ime-varian, and many sudies have used hem o esimae ime-varying hedge raios (Baillie and Myers, 99; Kroner and Sulan, 993; Koumos, ; Rossi and Zucca, ). In order o avoid he difficuly of deciding he iniial value of he GARCH model, Fink e al. (5) uilised he Kalman filer o esimae a ime-varying opimal hedge raio. As noed above, he radiional assumpion ha hedge raios are ime-invarian is no susainable; raher, i is necessary o describe he dynamic relaionship beween yield-curve facors and hedge raios. To incorporae informaion on he level, slope, and curvaure of he yield curve ino he esimaion of a imevarying opimal hedge raio, he presen sudy uilises he Kalman filer, which avoids he difficuly of deciding he iniial value of he GARCH model. METHODOLOGY: CHOOSING A MODEL OF YIELD CURVE AND KALMAN FILTER The parsimonious model of he yield curve used in his paper is ha buil by Nelson and Siegel (987). Willner (996) conended ha his model is a useful mehod for approximaing he sensiiviy of a bond porfolio o yield-curve level, slope, and curvaure. In a similar vein, Diebold and Li (6) and Diebold e al. (6) argued ha he well-known Nelson-Siegel (987) model is well suied o approximaing 33

4 J. H. Chou e al The Inernaional Journal of Business and Finance Research Vol. 3 No. 9 yield-curve dynamics and providing good predicions. The model is used in he presen sudy o esimae he level, slope, and curvaure of he yield curve wih Japanese governmen coupon bonds. The heoreical price of a coupon bond is equal o he sum of he presen value of he fuure coupon and he principal paymens according o he following relaionship: M = i i = { R( } B ˆ C(, () i, )exp i, i, ) where: Bˆ i is he i h heoreical price of coupon bond; M i is he mauriy of he i h bond; C ( i, ) is he cash flow of he i h bond a ime ; and R ( i, ) is he spo rae a ime in he i h bond. Nelson and Siegel (987) chose a funcion for he forward rae curve ha can be ransferred by inegraing process o spo rae curve as follows: ( ) τ i, τ i, i, R + i, = β + β exp β exp + () i, τ i, τ τ Where β, β, β and τ are he parameers for a mauriy of years. The Nelson and Siegel (987) model implies an inuiive explanaion of he parameers: (i) he value of β, which is regarded as a long-erm ineres rae, is represened by he level of he curve; (ii) he value of β, which is regarded as a shor-erm ineres rae, is represened by he slope of he curve; (iii) he value of β, which is regarded as a medium-erm ineres rae, is represened by he curvaure of he curve; and (iv) he parameer τ, which governs he exponenial decay rae a which he shor-erm and medium-erm facors decay o zero. To generae hese parameers of he yield curve, we added he funcion of spo rae ino he heoreical price of he coupon bond funcion () as follows: Bˆ i = = z i = z i = ( ) exp ( ) R( ) C i, ( ( )) ( ) exp ( ) C i. i, τ i, β + β( ) exp( i, τ τ i, ) + β ( ) exp( i, τ i, )( + ) τ The parameers can hen be esimaed by minimising he difference beween he acual and heoreical bond price; ha is: (3) n [ ( B i Bˆ i )] Q = n i= where n is he number of bonds. (4) Because he obecive funcion is nonlinear, he Newon mehod can be used o approximae he parameers of he Nelson and Siegel (987) model. One advanage of his mehod is ha τ canno assume o be a consan; raher, i varies wih oher parameers. In his regard i should be noed ha Diebold and Li (6) esimaed he Nelson and Siegel (987) model wih a consan value of he τ, bu 34

5 The Inernaional Journal of Business and Finance Research Volume 3 Number 9 Hurn e al. (5) argued ha he curve from he Nelson and Siegel (987) model is sensiive o he scale parameer τ, which canno be fixed. Applying he Newon mehod o he Nelson and Siegel (987) model for each day generaes a ime series of esimaes of parameers, which can hen be placed as yieldcurve facors in he Kalman filer model o esimae he opimal hedge raio. The GARCH-based esimaion mehod for ime-varying hedge raios requires he imposiion of inequaliy resricions on model parameers and he use of a wide range of saring values (Fackler and McNew, 994; Harris and Shen, 3). To overcome hese negaive feaures of he GARCH mehod, he presen sudy uilised a Kalman filer o consruc a sae space specificaion o esimae he opimal hedge raio. A sae space represenaion of he relaionship beween spo and fuures reurn is given by he following sysem of equaions: S = f ν + µ ν = α + λν + γ β + γ β + γ β + ζ µ ~ N ζ ~ N - (, σ µ ) (, σ ) ζ 3 where S is he log reurn of he bond index a ime ; f is he log reurn of he -year JGB fuures conracs employed in he hedge porfolio a ime ; and ν, he opimal hedge raio a ime, deermines he value of fuures conracs purchased or sold o he underlying securiy. In he sae equaion, λ measures he persisence of he opimal hedge raio. Oher coefficiens ha inerpre he effec of he yield-curve shape are: γ, which represens he level effec of he yield curve; γ, which represens he slope effec of he yield curve; γ 3, which represens he curvaure effec of he yield curve. The boh error erms µ and ζ are assumed o follow a normal disribuion and are independen of each oher. The Kalman filer procedure akes ino accoun he serially correlaed and heeroscedasic disurbance in he relaionship beween changes in he spo reurn and changes in he fuures reurn. In addiion, he Kalman filer is a recursive algorihm for sequenially updaing he ime-varying hedge raios (given new informaion during he ime series). For insance, consider a daase ha includes T observaions wih he former sae vecor λ defined as he opimal hedge raio a ime one (which is esimaed a ime zero). In hese circumsances, he laer sae variable P represens he covariance marix of he condiional disribuion of he sae vecor λ (given informaion available a ime zero). Given ha he informaion parameers λ γ γ γ 3 σ µ, and σ ζ are assumed o be known, he one-sep ahead predicor of sae erms λ and P can be expressed as: ( P ) ( f ) F ( S λν ) ( P ) ( f ) F ˆ ˆ ˆ = ν + = P ν (6) P (7) (5) 35

6 J. H. Chou e al The Inernaional Journal of Business and Finance Research Vol. 3 No. 9 ( f ) P F = + σ µ (8) Therefore, he opimal hedge raio λ is prediced one sep ahead in he following way: ˆ ν λ K f ν + K S + α + γ β + γ β + γ β (9) ( ) ( ) ˆ + = = P f F + = λ { P ( P ) λ F } + σ ζ K λ () P () To complee he Kalman filer, he unknown elemens of he sysem marices mus be replaced by heir esimaes. Given he assumpion of he normaliy of µ and ζ, he parameers of he sysem equaions can be esimaed by formulaing he log likelihood funcion as follows: T T T θ log L = log(π ) log F, θ ˆ = S fν () F Daa = = The daa used in he empirical sudy referred o daily -year JGB nearby Fuures conracs raded on he Tokyo Securiy Exchange (TSE). The -year JGB nearby Fuures conracs selemen prices were obained from Daasream. The daily JGB price index was calculaed by JP Morgan and colleced from Daasream. The daa ransferred o he daily log reurn covered he period from 3 May o 8 April 7. The oal number of ime-series observaions in he daa se was 75. For esimaing he JGB yield curve, he daily JGB price was ploed. This consised of 79 observaions (on average) per day from 3 May o 8 April 7. A Newon mehod was used o exrac hese yield-curve facors embedded in he Nelson and Siegel (987) model. EMPIRICAL RESULTS From hese daa, i was possible o derive he parameers and variables as described in he previous secion. Table provides some descripive saisics of hese ime-series parameers and variables. The lef column of he able shows he means, mediums, maximums, minimums, and sandard deviaions. Among he yield-curve facors: () he mean of daily β was.37, which shows ha he long-erm ineres rae level ended o 3.7%; () he mean of daily β was -.336, which represens he posiive slope of he yield curve on average; (3) he mean of daily β was.36, which shows ha he slope of he yield curve was no only posiive, bu also had a hump in he JGB marke. In addiion, he maximum β and he minimum β were no all larger han zero, which shows ha he shapes of he yield curves in he JGB marke involved differen paerns. Therefore, he risk of yieldcurve changes should be aken ino accoun in ineres risk managemen. Table also shows he saisics of he JGB spo and fuures log reurn. The average log reurn of he JGB spo (.7%) was less han ha of he JGB fuures (.3%). Similarly, he sandard deviaion of spo log reurn (.453%) was also lower han ha of he fuures log reurn(.44%), which implies ha he volailiy of he fuures marke was greaer han ha of he spo marke. 3 36

7 The Inernaional Journal of Business and Finance Research Volume 3 Number 9 Table : Descripive Saisics for Yield Curve Facors, Spo and Fuures Reurns β β β JGB_Spo JGB_Fuures Mean.37 (.336) % -.3% Median.96 (.3).38.%.% Maximum.67 (.4).9.786%.55% Minimum.34 (.56) (.376) -.86% -.789% Sd. Dev %.44% The parameers β, β and β are he yield curve facors embedded in he Nelson and Siegel model. The daily reurns of JGB price index and fuures selemen price are ransferred o log reurns. Pearson correlaion analysis was employed o invesigae he yield-fiing abiliy of he Nelson and Siegel (987) model and he degree of relaionship beween he JGB spo and fuures reurns (as shown in Table ). The correlaion coefficien beween he -year JGB price index and -year JGB fuures selemen price was quie high (98.89%), which implies ha he -year JGB price index reurn was more srongly correlaed o he -year JGB fuures reurn. This relaionship is also clear from Figure. The srong correlaion beween hese facors indicaes ha he JGB -year fuures could provide a good hedge funcion for he JGB -year price index. Table : Correlaion of JGB Spo and Fuures Price wih JGB Yield and NS Yield yr JGB_Spo Index Price yr JGB_Fuures Selemen Price yr JGB_Yield yr JGB_NS_Yield yr JGB_Spo Index price yr JGB_Fuures Selemen Price yr JGB_Yield yr JGB_NS_Yield year JGB fuures selemen price was quie high (98.89%), which implies ha he -year JGB price index reurn was more srongly correlaed o he -year JGB fuures reurn. Figure : The Price of Year JGB versus he Selemen Price of Year JGB Fuures JGB_yr_Spo_Price JGB_yr_Fuures_Selemen_Price The srong correlaion beween hese facors indicaes ha he JGB -year fuures could provide a good hedge funcion for he JGB -year price index. 37

8 J. H. Chou e al The Inernaional Journal of Business and Finance Research Vol. 3 No. 9 As shown in Table, he correlaion coefficien beween he -year JGB yield and he -year JGB price index was negaive ( 9.97%). Table also presens he correlaion beween he -year JGB yield and he -year JGB fuures selemen price ( %). The negaive relaionship beween he JGB yield and price is in accordance wih he inuiive percepion of bond pricing. Finally, boh Table and Figure show ha he -year JGB yield esimaed by Nelson and Siegel (987) had a correlaion of % wih he acual -year JGB yield, which suggess ha he Nelson and Siegel (987) model could fi he -year JGB yield well. For his reason, he parameers of he model should involve some informaion o explain he variey of he -year JGB yield. Figure : The Yield of Year JGB versus he NS Yield of Year JGB /5/ /8/ JGB_yr_Yield // 3// 3/5/ 3/8/ 3// 4// 4/5/ 4/8/ 4// 5// 5/5/ JGB_yr_NS_Yield 5/8/ 5// 6// 6/5/ 6/8/ 6// 7// Nelson and Siegel (987) model could fi he -year JGB yield. Thus, he parameers of he model should involve some informaion o explain he variey of he -year JGB yield. Effec of TSIR Facors on he Hedge Raio To compare he influence of differen parameers on he deerminaion of hedge raio, a number of consrained alernaives are specified. Table 3 shows resuls of a Kalman filer for unresriced and resriced models. The following observaions can be made. Firs, i is apparen ha he persisence parameer λ was significanly posiive in all models, which implies ha he movemen of he hedge raio displayed persisency. Secondly, he level coefficien γ (.34) in model was significanly posiive wih respec o he hedge raio. This phenomenon migh be due o invesors increasing heir hedge posiion as he level of ineres rae increases. Thirdly, he slope coefficien γ (.3873) in model was significanly posiive wih respec o he hedge raio, which implies ha he difference beween he shor-erm and long-erm ineres raes pushed invesors o increase heir hedge posiion. Finally, he curvaure coefficien γ 3 (.499) was no significan. These findings demonsrae ha he early hedge raio and he level and slope of he yield curve affec he nex opimal hedge raio. To gain a beer undersanding of he disribuion of each parameer from he empirical model, differen consrains of he parameers are shown as models o 8 in Table 3. The following observaions can be made. Model was esimaed wih a consrain of γ 3 =. The persisen coefficien λ (.36) of model remained significanly posiive. The yield-curve coefficiens γ (.956) and γ (.3896) also had a 38

9 The Inernaional Journal of Business and Finance Research Volume 3 Number 9 significan influence on he opimal hedge raio. Model 3 shows an alernaive resricion, in which γ =. The coefficiens λ and γ were significanly posiive. Model 4 imposed a consrain of γ =. The coefficien λ remained significanly posiive. Two consrains were imposed o compare he conribuion of each parameer in models 5 o 7. The coefficien λ was sill significanly posiive in hese hree models, bu only γ was significanly posiive in model 5. These models reurned similar resuls o hose of previous models. As shown in models o 7, i is apparen ha he coefficiens λ and γ were imporan parameers for explaining he hedge raio. Finally, model 8 had a consrain of λ = (which enabled consideraion of he effec of he yield-curve facor wihou he coefficien λ ). The coefficiens γ and γ were sill significanly posiive wih respec o he hedge raio, which implies ha he level and slope facors provide addiional informaion of imporance in explaining he deerminaion of he opimal hedge raio. Table 3: Resuls of Kalman Filer for Unresriced and Resriced Model λ γ γ γ 3 Model (no resriced).3 *** (.6).34 ** (.).3873 ** (.384).499 (.4338) Model ( γ 3 =).36 *** (.6).956 ** (.6).3896 ** (.379) Model 3 ( γ =).383 *** (.).54 * (.57).47 (.579) Model 4 ( γ =).38 *** (.).373 (.69).33 (.7745) Model 5 ( γ 3 =) ( γ =).34 *** (.).56 *** (.7) Model 6 ( γ 3 =) ( γ =).394 *** (.).34 (.667) Model 7 ( γ =) ( γ =).398 *** (.).45 (.764) Model 8 ( λ =).49 *** (.65).898 ** (.5).64 (.353) σ µ σ ζ Log likelihood This able provides parameer esimaes in he following model: S = fν + µ ν = α + λν - + γβ + γ β + γ 3β + ζ µ ~ N(, σ µ ) ζ ~ N(, σ ζ ) The S is log reurns of he JGB price index a ime. The variable f is he log reurns of he JGB fuures selemen price, ha i can srucure he hedge porfolio. The erm srucure facors β, β and β, form Nelson and Siegel model, show level movemen, slope change, and curvaure shif separaely. Theν presens he appropriae hedge raio a ime, and he coefficien λ is parameer of persisence o deermine he appropriae hedge raio. Finally, he coefficiens γ, γ, and γ 3 demonsrae he effec of erm srucure facor on hedge raio. The sample period is daily beween May 3, and April 8, 7 wih 75 empirical daa. Model hrough model 8 exhibi various resricions of parameers. The Wald es was used o examine he null hypohesis implied in Table 3. The resuls are shown in Table 4. Model demonsraed an insignifican coefficien ( γ 3 ), as expeced. The findings for models 3, 4, and 8 could no lead o a reecion of heir null hypoheses, which indicaes ha, he coefficiens, γ, γ and λ, all involve rich informaion in deciding he nex hedge raio. In conras, he resuls from models 5, 6, and 7 provide grounds for reecing heir null hypoheses. Model 8 also reecs he null hypohesis, which suppors he conenion ha coefficien λ has a significan relaionship wih he hedge raio. 39

10 J. H. Chou e al The Inernaional Journal of Business and Finance Research Vol. 3 No. 9 Table 4: WALD Tes Model Model 3 Model 4 ( γ =) ( γ 3 =) ( γ =) ( γ 3 =) ( γ =) ( γ =) ( γ =).6 (.4348) 4.39** (.376) ** (.) * (.94) 7.37** (.96) 6.589** (.37) ( γ 3 =) Chi-square ( γ =) Model 5 Model 6 Model 7 Model 8 ( λ =).8578* ** (.6) The equaion in parenhesis exhibis hypohesis. *** indicaes significan a he %. ** indicaes significan a he 5%. * indicaes significan a he %. Resuls of Ou-of Sample Performance To examine he performance of one-sep-ahead hedge porfolios, he opimal hedge raios (based on models o 8) were esimaed, beginning from he firs period, proceeding o 5 days, and concluding wih he end period day (as shown in Figure 3). Figure 3: Ou of Sample Hedge for Moving Window Esimaion Window N... Window νˆ Window // T νˆ // Hedge Period The hedge porfolio consised of a long posiion on he JGB -year price index and a shor posiion on he JGB -year fuures, which muliplied by he one-sep-ahead opimal hedge raio (ν + ). Table 5 shows he sandard deviaion of reurns of he simulaed hedge porfolios when various resricions were imposed. A comparison of he various models shows ha model 9 (OLS mehod) had a greaer sandard deviaion (.84) han he oher models. This resul demonsraes ha he yield-curve facors and persisence facor can provide addiional explanaory power o decrease he sandard deviaion of he hedge porfolio. 4

11 The Inernaional Journal of Business and Finance Research Volume 3 Number 9 Table 5: Ou of Sample Resul for Sandard Deviaion of Hedge Posiion Model (no resriced) Model ( γ 3 =) Model 3 ( γ =) Model 4 ( γ =) Model 5 ( γ 3 =) Model 6 ( γ 3 =) Model 7 ( γ =) Model 8 ( λ =) Model 9 OLS ( γ =) ( γ =) ( γ =) Sandard Deviaion of Hedge Posiion The esimaion, used in model hrough model 9 wihin 5 daily daa, is se o forecas he hedge raio on nex day, so we can consruc a hedge porfolio. Wih his procedure of esimaion, we can ge 49 hedge porfolio reurns and sandard deviaion beween he 6 h day and 75 h day. Table 6 presens a mehodology suggesed by Ederingon (979) for esing hedge effeciveness, as follows: σ hedge h e = (3) σ unhedge where: σ is he variance of he hedged porfolio; and hedge σ unhedge is he variance of he unhedged porfolio. As he value of h e rends o higher levels, he hedged porfolio becomes more effecive. As shown in Table 6, i is apparen ha all models had impressive ou-ou-sample hedge effeciveness (up o 9%). This resul demonsraes ha he JGB fuures marke could provide an excellen environmen for hedge invesmens. This is likely o be due o he high dependence beween he spo and fuures prices and he high liquidiy of marke rading. Table 6: Ou of Sample Resul for Hedge Efficiency Resricion Hedge Efficiency Model No resriced % Model ( γ 3 =) 97.% Model 3 ( γ =) % Model 4 ( γ =) % Model 5 Model 6 ( γ 3 =) ( γ =) % ( γ 3 =) ( γ =) % Model 7 ( γ =) ( γ =) % Model 8 ( λ =) % Model 9 OLS 9.84% Model ν = % The esimaion, used in model hrough model 9 wihin 5 daily daa, is se o forecas he hedge raio on nex day, so we can consruc a hedge porfolio. Wih his procedure of esimaion, we can ge 49 hedge porfolio reurns and sandard deviaion o calculae he hedge efficiency beween he 6 h day and 75 h day. The model has aken he esimaion wih Perfec Hedge Mehod, or called Naive Hedge, which means he hedger can buy and sell he same amoun of fuures conrac in conras o his holding spo posiion. 4

12 J. H. Chou e al The Inernaional Journal of Business and Finance Research Vol. 3 No. 9 I should be noed ha he models ha involved he yield-curve facors produced greaer hedge effeciveness. This was especially apparen in models and, which exhibied he greaes hedge effeciveness. This resul shows ha he models ha include informaion abou he level and slope facors provide significanly greaer benefis. In addiion, our empirical resuls are quie differen wih Fink e al. (5), which indicae ha boh he level of ineres raes and he slope of he yield curve are unimporan variables in deermining he empirically opimal hedge raio beween morgage-backed securiies and Treasury fuures conracs. To summarise he resuls of ou-of-sample esing, i has been demonsraed ha he yield-curve informaion (such as level and slope facors) can improve he deerminaion of he opimal hedge raio and hus improve he effeciveness of he hedge. The persisence facor, λ, is also an imporan facor in deermining he opimal hedge raio. CONCLUSION The presen sudy has incorporaed facors from Nelson and Siegel (987) wih a Kalman filer approach o invesigae hedge effeciveness beween Japanese Governmen Bond (JGB) spo and fuures. The sudy has demonsraed saisically significan effecs from he persisen, level, and slope facors from an insample es. An analysis of ou-of-sample prediced performance has demonsraed ha he use of yieldcurve informaion (such as persisence, level and slope facors) in deermining he opimal hedge raio can improve he effeciveness of he hedge. The findings also conribue o he lieraure by revealing ha he erm srucure informaion need o be accouned for direcly in he hedging of he governmen bonds wih ineres raes fuures conracs. Fink, e al. (6) find ha boh he level of ineres raes and he slope of he yield curve are unimporan variables in deermining he empirically opimal hedge raio beween MBS and Treasury fuures conrac. On he conrary, his aricle concludes he yield-curve informaion, inuiion suggess hem o be relevan deerminans, should play a significan role in he deerminaion of he ime-varying hedge raio beween Treasury bonds and Treasury fuures. Since he chief source of basis risk comes from he prepaymen of morgages underlying he MBS, he basis risk in Treasury fuures and is underlying asse is much lower han ha of Treasury fuures and MBS. Thus, i seems reasonable ha our empirical findings could be generalised o oher governmen bond markes. Furhermore, his paper compares he hedging effeciveness in hedging -year bonds wih a Kalman filer approach. Also, our JGB fuures conracs are based on Japanese governmen bonds wih a erm o mauriy of years. Thus, he improvemen in hedge effeciveness based on yield-curve informaion will be limied when we choose he 7-year or he 5-year cash bonds as hedging obecs. More research should be done o assess he bond feaures: Is he ype of issuer imporan when comparing he hedging effeciveness wih a Kalman filer approach? Wha is he difference beween he developed and developing bond marke? How should he liquidiy risk affec he hedging effeciveness? How should he opimal hedge raio be measured. Answers o hese quesions will conribue he lieraure in helping he compuaion of a more reliable hedge raio beween Treasury bonds and Treasury fuures. REFERENCES Baillie, R., & Myers, R. (99) Bivariae GARCH Esimaion of he Opimal Commodiy Fuures Hedge, The Journal of Applied Economerics, vol. 6, p

13 The Inernaional Journal of Business and Finance Research Volume 3 Number 9 Bollerslev, T. (986) Generalized Auoregressive Condiional Heeroscedasiciy, The Journal of Economerics, vol. 3, p Bollerslev, T., Engle, R. F., & Wooldridge, J. M. (988) A Capial Asse Pricing Model wih Time- Varying Covariances, The Journal of Poliical Economy, vol. 96(), p. 6-3 Brennan, M.J. & Schwarz, E. S. (979) A Coninuous-Time Approach o he Pricing of Bonds, Journal of Banking and Finance, vol. 3(), p Cox, J.C., Ingersoll, J.E., & Ross, S.A. (985) A Theory of he Term Srucure of Ineres Rae, Economerica, vol. 53(), p Diebold, F. X., Rudebusch, G. D., & Aruoba, S.B. (6) The Macroeconomy and he Yield Curve: A Dynamic Laen Facor Approach, The Journal of Economerics, vol. 3, p Diebold, F. X., & Li, C. (6) Forecasing he Term Srucure of Governmen Bond Yields, The Journal of Economerics, vol. 3, p Dolan, C. (999) Forecasing he Yield Curve Shape: Evidence from Global Markes, The Journal of Fixed Income, vol. (), p Dohan, L.U. (978) On he Term Srucure of Ineres Raes, Journal of Financial Economics, vol. 6(), p Duffie, D., & Kan, R. (996) A Yield-Facor Model of Ineres Raes, Mahemaical Finance, vol. 6, p Ederingon, L. (979) The Hedging Performance of he New Hedging Markes, The Journal of Finance, vol. 34(), p Engle, R. F. (98) Auoregressive Condiional Heeroscedasiciy wih Esimaes of he Variance of Unied Kingdom Inflaion, The Economerica, vol. 55(), p Esrella, A., & Hardouvelis, G. (99) The Term Srucure as A Predicor of Real Economic Aciviy, The Journal of Finance, vol. 46(), p Esrella, A., & Mishkin, F. S. (998) Predicing U.S. Recessions: Financial Variables as Leading Indicaors, The Review of Economics and Saisics, vol. 8(), p Fackler, P. L., & McNew, P. K. (994) Nonconsan Opimal Hedge Raio Esimaion and Nesed Hypoheses Tess, The Journal of Fuures Markes, vol. 4(5), p Fink, J., Fink, K. E., & Lange, S. (5), The Use of Term Srucure Informaion in he Hedging of Morgage-Backed Securiies, The Journal of Fuures Markes, vol. 5(7), p Harris, R., & Shen, J. (3) Robus Esimaion of he Opimal Hedge Raion, The Journal of Fuures Markes, vol. 3, p

14 J. H. Chou e al The Inernaional Journal of Business and Finance Research Vol. 3 No. 9 Heah, D., Jarrow, R., & Moron, A. (99) Bond Pricing and he Term Srucure of Ineres Rae: A New Mehodology for Coningen Claims Valuaion, Economerica, vol. 6, p Ho, T.S. & Lee, S. (986) Term Srucure Movemens and Pricing Ineres Rae Coningen Claim, Journal of Finance, vol. 4(5), p.-8 Hull, J., & Whie, A. (99) Pricing Ineres-Rae-derivaive Securiies, Review of Financial Sudies, vol. 3, p Hurn, A.S., K.A. Lindsay, & Pavlov, V. (5) Smooh Esimaion of Yield Curves by Laguerre Funcions, Proceedings of Advances and Applicaions for Managemen and Decision Making on Inernaional Congress on Modelling and Simulaion (MODSIM5), Ausralia. Koumos, G., () Common Volailiy in MBS Reurn: A Facor GARCH Approach, The Journal of Fixed Income, vol. 3(3), Sepember, p Kroner, K., and Sulan, J. (993) Time-Varying Disribuions and Dynamic Hedging wih Foreign Currency Fuures, The Journal of Financial and Quaniaive Analysis, vol. 8, p Lierman, R., & Scheinkman, J. (99) Common Facors Affecing Bond Reurns, The Journal of Fixed Income, vol. (), Sepember, p Markowiz, H. (99) Foundaion of Porfolio Theory, The Journal of Finance, vol. 46, p McCulloch, J. H. (97) Measure he Term Srucure of Ineres Raes, Journal of Business, vol. 44(), p. 9-3 McCulloch, J. H. (975) The Tax-Adused Yield Curve, Journal of Finance, vol. 3(3), p Myers R. J. (99) Esimaing Time-Varying Opimal Hedge Raios on Fuures Markes, The Journal of Fuures Markes, vol., p Nelson, C. R., & Siegel, A. F. (987) Parsimonious Modeling of Yield Curves, The Journal of Business, vol. 6(4), p Rossi, E., & Zucca, C. () Hedging Ineres Rae Risk wih Mulivariae GARCH, The Applied Financial Economics, vol., p. 4-5 Schaefer, S. M. (98) Measuring a Tax-Specific Term Srucure of Ineres Raes in he Marke of Briish Governmen Securiies, The Economic Journal, vol. 9, p Seeley, J. M. (99) Esimaing he Gil-Edged Term Srucure Basis Splines and Confidence, Journal of Business Finance and Accouning, vol. 8(4), p Vasicek, O. A. (977) An Equilibrium Characerizaion of he Term Srucure, Journal of Financial Economics, vol. 5, p Vasicek, O. A., & Fong H. G. (98) Term Srucure Modeling Using Exponenial Splines, Journal of Finance, vol. 37(), p

15 The Inernaional Journal of Business and Finance Research Volume 3 Number 9 Willner, R. (996) A New Tool for Porfolio Managers: Level, Slope, and Curvaure Duraions, The Journal of Fixed Income, vol. 7(), June, p ACKNOWLEDGEMENT Jian-Hsin Chou, Naional Kaohsiung Firs Universiy of Science and Technology, hanks Naional Science Council, gran no. NSC H - 37, for funding his research. BIOGRAPHY Jian-Hsin Chou received his Ph.D. degree in Business Adminisraion from Naional Taiwan Universiy of Science and Technology in Taiwan. He is a professor a he Deparmen of Risk Managemen and Insurance, Taiwan, R.O.C. His research ineress include bond marke and risk managemen of financial markes. His papers have been published a Journal of Business Finance and Accouning, Managerial Finance, Applied Financial Economics, Journal of Saisics and Managemen Sysems, and Journal of Chinese Insiue of Indusrial Engineers. Chien-Yun Chang received his Ph.D. degree a Graduae Insiue of Managemen, Naional Kaohsiung Firs Universiy of Science and Technology in Taiwan. He is an assisan professor of Deparmen of Financial Managemen, Hsiuping Insiuion of Technology in Taiwan. His researches include he esimaion of erm srucure of ineres raes, exploraion of fixed income securiies marke, and he assessmen of fuures and opions. His papers have been published a Naional Taiwan Universiy Managemen Review, Sun Ya-Sen Managemen Review, and Journal of Saisics & Managemen Sysems. Chen-Yu Chen is currenly a Ph.D. candidae a Insiue of Managemen, Naional Kaohsiung Firs Universiy of Science and Technology in Taiwan. His maor research areas include financial marke, bond marke and fuures marke. His papers have been published a Invesmen Managemen and Financial Innovaions, Sun Ya-Sen Managemen Review, Journal of Chinese Insiue of Indusrial Engineers, Commerce & Managemen Quarerly, and Fu Jen Managemen Review. 45