THE PREDICTIVE POWER OF THE TERM STRUCTURE OF INTEREST RATES: THE CASE OF JORDAN Thesis submied for he degree of Docor of Philosophy a he Universiy of Leiceser by Sahar Sameeh Qaqeesh Deparmen of Economics Universiy of Leiceser April 2010
ABSTRACT This hesis invesigaes wheher he shor end of he erm srucure has he abiliy o predic he fuure movemens in shor erm raes and he inflaion rae using daa from a developing counry: he case of Jordan. A number of economeric echniques are employed o examine he predicabiliy of he erm srucure and o deal wih he low qualiy daa. In order o examine he abiliy of he erm srucure o predic he fuure movemens in shor erm raes, he validiy of he Expecaions Hypohesis (EH) is esed. The EH implies ha he erm spread is an opimal predicor of he fuure changes in shor erm raes. For he empirical esing, wo ses of daa are used; he erm srucure in he Jordanian inerbank marke and he erm srucure in he primary marke. The informaion conen of he erm srucure abou inflaion rae is examined by invesigaing wheher here is a long run equilibrium relaionship beween he shor erm raes and he inflaion rae; ha is, esing he Fisher Hypohesis, and beween he domesic erm spread and he inflaion rae. Moreover, given ha he exchange regime in Jordan is pegged o he US Dollar, he informaion conen of he US erm spread is also examined. The coinegraion analysis is he only echnique ha provides evidence ha he EH holds. In addiion, i provides evidence ha he domesic and he US erm spreads conain some informaion abou he inflaion rae. As a resul of dealing wih low qualiy daa, he Mone Carlo simulaion provides evidence ha he size disorion of he Dickey Fuller (DF) es becomes larger as he noise increases in he daa and faser as he sample size becomes bigger. This evidence suppors he lieraure ha discusses he size disorion of he DF es. 1
" I DEDICATE THIS THESIS TO THE MEMORY OF MY BELOVED PARENTS SAMEEH AND NABILAH TO MY ANGELS ON EARTH, MY SOUL MATES, MY FRIENDS, MY SISTERS HANADA, HANAN, HELEN WHOSE LOVE, SUPPORT, FAITH AND PRAYERS HAVE HELPED ME WRITE EACH WORD IN THIS THESIS. THANK YOU FOR LOVING ME THIS MUCH YOU MAKE MY LIFE WORTH LIVING. 2
ACKNOWLEDEGEMNET My graiude goes firs o my menor and supervisor Prof. Sephen G. Hall for his remarkable encouragemen, unforgeable paience and undersanding, and for his kindness. Thank you for all your effors and for he inspiraion. Thank you for being such an incredible eacher, Iam deeply indebed o you. I would like o hank Prof. Gianni De Fraja and Dr. Ali Al-Nowaihi for heir helpful commens and advices a he beginning of he docoral program and Dr. Eugenie Garganas for her help and kindness. Special hanks o he saff of he deparmen of Economics for heir suppor and help, Sebasian O'Halloran, Eve Kilbourne, Samanha Hill, Ladan Baker, Che Bhundia and Siân Maon. I would like o hank he senior managemen of he Cenral Bank of Jordan for being commied o achieving he excellence hrough encouraging he developmen of employees hrough learning and raining. Special hanks o all my brohers and sisers a he Cenral Bank of Jordan for heir help and suppor. Special graiude o Mr. Faris Sharaf, Mr. Saleh Al Tayeh, Mr. Bassam Toqan, Mr. Bassam Farmawi and Dr. Marwan Al Zoubi for believing in me and for heir remarkable encouragemen. I has been a privilege knowing and working wih you all. Special hanks and graiude o all my dear friends: Karen Kakish, Abeer Khoury, Ouriab Phakoury, Maha Al Bahoo, Reem Al Haddidi, Golda Emsis, Eklas Dobia, Nelly Bachoun, Rania Al Araj, Hala Kakish, Andrea Oerová, Kavia Sirichand, and Dalia El Edel for heir love and for always being here for me. You all have influenced my life in many ways. Special hanks o Hazar Badran for her unforgeable help in my firs year in Leiceser. Las bu no leas, special hanks o my dear brohers Marwan Kakish and Johnny Al Sabbagh, and o my wo nephews Omar and Zaid Kakish for heir love and caring. 3
TABLE OF CONTENTS TABLE OF CONTENTS Page Chaper One: Inroducion Thesis objecives, mehodology and srucure 16 Chaper Two: Lieraure Review 2.1 2.2 2.2.1 2.2.2 2.2.3 2.2.4 2.3 2.3.1 2.3.1.1 2.3.2 2.3.2.1 2.3.2.2 2.4 2.4.1 2.4.1.1 2.4.1.2 2.4.1.3 2.4.1.4 2.4.1.5 2.5 2.6 2.6.1 2.6.2 2.6.2.1 2.6.2.2 2.6.2.3 2.6.2.4 2.6.3 2.7 Inroducion The main heories of he erm srucure of ineres raes The expecaions heory (ET) The liquidiy preference heory The marke segmenaion heory The preferred habia heory The erm srucure and he predicabiliy of fuure movemens in shor erm ineres raes The heoreical framework of he expecaions hypohesis The spread The key elemens of he empirical esing of he expecaions hypohesis Tesing mehodologies The financial insrumens ha are used for esing The findings of he empirical esing of he expecaions hypohesis (EH) The rejecion of he expecaions hypohesis The esimaion problems The erm premia Moneary policy argeing The irraional expecaions The erm spread predics he wrong direcion in he subsequen changes in long erm ineres raes over shor erm horizon (Campbell and Shiller paradox CSP ) Oher implicaions of he expecaions heory (ET) The erm srucure and he predicabiliy of fuure inflaion rae The validiy of he Fisher hypohesis (FH) The main findings of he empirical esing of FH and he heoreical jusificaions for he deviaion of he esimaed parameer from is heoreical value one The ax effec The wealh effec The invered Fisher effec The nonsaionariy of he (ex ani) real ineres rae The abiliy of he slope of he erm srucure o predic inflaion rae Conclusion 26 26 27 29 29 30 31 31 35 40 40 43 48 49 50 52 56 59 59 66 70 70 76 76 79 79 80 81 89 4
TABLE OF CONTENTS Chaper Three: Tesing The Expecaions Hypohesis Of The Term Srucure In The Jordanian Money Marke: The Jordanian Dinar Inerbank Offered Rae (JODIBOR) 3.1 3.2 3.3 3.3.1 3.3.2 3.3.3 3.4 3.5 3.5.1 3.5.2 3.5.3 3.5.4 3.6 3.6.1 3.6.2 3.7 3.7.1 Inroducion The daa The mehodology The single equaion regression The VAR mehodology The coinegraion analysis Uni roo es The empirical resuls The uni roo es The single equaion mehod The VAR mehodology The coinegraion analysis Time varying parameers and he learning process Time varying parameer mehodology The empirical resuls of he ime varying parameer mehodology Conclusion and furher remarks Furher remarks 91 92 96 97 100 110 117 120 120 121 123 126 131 133 136 140 143 Chaper Four: The Term Srucure Of Ineres Raes In The Jordanian Primary Marke: Empirical Evidence For The Expecaions Hypohesis 4.1 4.2 4.3 4.3.1 4.3.2 4.3.3 4.4 4.4.1 4.4.2 4.4.3 4.5 4.5.1 4.5.1.1 4.5.1.1.1 4.5.1.1.2 Inroducion The daa The mehodology Uni roo es The coinegraion analysis Granger Causaliy es and he error correcion model (ECM) The empirical resuls The uni roo es The coinegraion analysis The error correcion model (ECM) and causaliy es Tesing he robusness of he causaliy resuls Forward recursive coinegraion analysis The empirical resuls for he forward recursive coinegraion analysis The coinegraion analysis The expecaions hypohesis (EH) 176 179 182 182 183 184 188 188 189 190 194 196 5
TABLE OF CONTENTS 4.5.1.1.3 4.6 4.6.1 4.6.1.1 4.6.1.2 4.6.2 4.6.2.1 4.6.2.1.1 4.6.2.1.2 4.6.2.1.3 4.7 4.8 4.8.1 The Granger Causaliy Absence of coinegraion-furher research The learning process and ime varying parameers Time varying parameer mehodology The empirical resuls of he ime varying parameer mehodology The srucural breaks The empirical resuls-srucural breaks The coinegarion analysis The validiy of he expecaions hypohesis The error correcion mehod (ECM) wih dummy variables and he causaliy es Impulse response funcion (IRF) Conclusion and furher remarks Furher remarks Chaper Five: The Informaion Conen Of The Shor End Of The Term Srucure Of Ineres Raes And The Inflaion Rae: Empirical Evidence For Jordan 5.1 5.2 5.3 5.3.1 5.3.2 5.3.2.1 5.3.2.2 5.3.2.3 5.3.3 5.3.3.1 5.3.3.2 5.3.3.3 5.4 5.4.1 5.4.1.1 5.4.1.2 5.4.1.3 5.4.1.3.1 5.4.1.3.2 5.4.1.3.3 5.4.2 Inroducion The daa The mehodology Uni roo es The coinegraion analysis The validiy of he Fisher hypohesis (FH) The bivariae coinegraion analyses beween each of he wo erm spreads (The domesic and he US) and he monhly inflaion rae The mulivariae coinegraion analysis beween he domesic erm spread, he monhly inflaion and he Repo Granger Causaliy es and he error correcion model (ECM) The error correcion models (he wo shor erm ineres raes and he inflaion rae) The error correcion models (The wo erm spreads and he inflaion rae The error correcion model (The domesic erm spread, he inflaion rae and he Repo rae) The empirical resuls Uni roo res Cerificaes of deposis ineres raes, US Treasury Bills discoun yield and he Repo rae The domesic erm spread and he US erm spread The inflaion rae Mone Carlo analysis Mone Carlo analysis/experimen design Empirical resuls of Mone Carlo analysis The coinegraion analysis 6
TABLE OF CONTENTS 5.4.2.1 5.4.2.2 5.4.2.3 5.4.3 5.4.3.1 5.4.3.2 5.4.3.3 5.4.4 5.4.4.1 5.4.4.1.1 5.4.4.1.2 5.4.4.2 5.5 5.5.1 5.5.2 5.5.2.1 5.5.2.2 5.5.2.3 5.6 5.6.1 The validiy of he Fisher hypohesis (FH) The bivariae coinegraion analyses beween each of he wo erm spreads (The domesic and he US) and he monhly inflaion rae The mulivariae coinegraion analysis beween he domesic erm spread, he monhly inflaion, and he Repo Sabiliy ess The firs ECM conains wo equaions, he domesic erm spread and he inflaion rae The second ECM conains wo equaions, he US erm spread and he inflaion rae The hird ECM conains hree equaions, he domesic erm spread, he inflaion rae and he Repo rae The error correcion model (ECM) and causaliy es The bivariae sysems The error correcion model (The domesic spread and he inflaion rae) The error correcion model (The US spread and he inflaion rae) The mulivariae sysems Impulse response and variance decomposiion Impulse response Variance decomposiion The variance decomposiion of he domesic erm spread and he inflaion rae for differen ime horizons The variance decomposiion of he US erm spread and he inflaion rae for differen ime horizons The variance decomposiion of he domesic erm spread, he inflaion rae and he Repo rae for differen ime horizons Conclusion and furher remarks Furher remarks Chaper Six: Conclusions 6.1 6.2 6.2.1 6.2.2 6.2.3 6.3 General discussion Concluding remarks The daa The expecaions hypohesis (EH) The informaion conens of he erm srucure abou fuure inflaion rae Areas of furher research Appendices Appendix o chaper one Bibliography 358 362 7
LIST OF FIGURES Chaper Three: LIST OF FIGURES Figure 3.1 The JODIBOR Ineres Raes (levels) Figure 3.2 Overnigh rae (level and firs difference) Figure 3.3 One week rae (level and firs difference) Figure 3.4 One monh rae (level and firs difference) Figure 3.5 Three monh rae (level and firs difference) Figure 3.6 Six monh rae (level and firs difference) Figure 3.7 One year rae (level and firs difference) Figure 3.8 Acual spread and perfec foresigh spread (1W-1N) Figure 3.9 Acual spread and perfec foresigh spread (1M-1N) Figure 3.10 Acual spread and perfec foresigh spread (3M-1M) Figure 3.11 Acual spread and perfec foresigh spread (6M-1M) Figure 3.12 Acual spread and perfec foresigh spread (12M-1M) Figure 3.13 Acual spread and perfec foresigh spread (6M-3M) Figure 3.14 Acual spread and perfec foresigh spread (12M-3M) Figure 3.15 Acual spread and perfec foresigh spread (12M-6M) Figure 3.16 Acual spread and heoreical spread (1W-1N) Figure 3.17 Acual spread and heoreical spread (1M-1N) Figure 3.18 Acual spread and heoreical spread (3M-1M) Figure 3.19 Acual spread and heoreical spread (6M-1M) Figure 3.20 Acual spread and heoreical spread (12M-1M) Figure 3.21 Acual spread and heoreical spread (6M-3M) Figure 3.22 Acual spread and heoreical spread (12M-3M) Figure 3.23 Acual spread and heoreical spread (12M-6M) Figure 3.24 ( W, N ) Time varying parameer of he PFS, Kalman Filer Figure 3.25 ( M, N ) Time varying parameer of he PFS, Kalman Filer Figure 3.26 ( 3M,1M ) Time varying parameer of he PFS, Kalman Filer Figure 3.27 ( 6M,1M ) Time varying parameer of he PFS, Kalman Filer Figure 3.28 ( 12M,1M ) Time varying parameer of he PFS, Kalman Filer Figure 3.29 ( 6M,3M ) Time varying parameer of he PFS, Kalman Filer Figure 3.30 ( 12M,3M ) Time varying parameer of he PFS, Kalman Filer Figure 3.31 ( 12M,6M ) Time varying parameer of he PFS, Kalman Filer Chaper Four: Figure 4.1 Cerificaes of Deposis ineres raes - (All mauriies: one monh, hree monh, six monh and welve monh) Figure 4.2 Cerificaes of Deposis ineres raes (hree monh and six monh wih missing values) Figure 4.3 Cerificaes of Deposis ineres raes Spline esimaion (hree monh and six monh) Figure 4.4 Time varying parameer of he period (June 1997-Dec. 2007), Kalman Filer Figure 4.5 Time varying parameer of he period (June 1997-Dec. 1999), Kalman Filer 8
LIST OF FIGURES Figure 4.6 Time varying parameer of he period (June 1997-Dec. 2000), Kalman Filer Figure 4.7 Time varying parameer of he period (June 1997-Dec. 2001), Kalman Filer Figure 4.8 Impulse response funcions o shocks in ineres raes (VAR sysem wihou dummy variables) Figure 4.9 Impulse response funcions o shocks in ineres raes (VAR sysem wih dummy variables) Figure 4.10 Impulse response funcions o shocks in ineres raes (Unresriced VECM sysem wihou dummy variables) Figure 4.11 Impulse response funcions o shocks in ineres raes (Unresriced VECM sysem wih dummy variables) Figure 4.12 Impulse response funcions o shocks in ineres raes (Resriced VECM sysem wihou dummy variables) Figure 4.13 Impulse response funcions o shocks in ineres raes (Resriced VECM sysem wih dummy variables) Chaper Five: Figure 5.1 Specral Densiy for he domesic erm spread (JORSPD) Figure 5.2 Specral Densiy for he US erm spread (USTBSPD) Figure 5.3 The monhly inflaion rae (annualized) Figure 5.4 Specral Densiy for he monhly inflaion rae Figure 5. The yearly inflaion rae (annualized) Figure 5.6 The comparison beween he percenages of rejecion under Dickey Fuller es Figure 5.7 Three monh CDs ineres rae / inflaion rae (H=1 monh) Figure 5.8 Three monh CDs ineres rae / inflaion rae (H=12 monh) Figure 5.9 Six monh CDs ineres rae / inflaion rae (H=1 monh) Figure 5.10 Six monh CDs ineres rae / inflaion rae (H=12 monh) Figure 5.11 JORSPD / inflaion rae Figure 5.12 USTBSPD / inflaion rae Figure 5.13 JORSPD / inflaion rae CUSUM D(JORSPD) equaion Figure 5.14 JORSPD / inflaion rae CUSUM D(INFRATE) equaion Figure 5.15 JORSPD / inflaion rae CUSUM of square D(JORSPD) equaion Figure 5.16 JORSPD / inflaion rae CUSUM of square D(INFRATE) equaion Figure 5.17 USTBSPD / inflaion rae CUSUM D(USTBSPD) equaion Figure 5.18 USTBSPD / inflaion rae CUSUM D(INFRATE) equaion Figure 5.19 USTBSPD / inflaion rae CUSUM of square D(USTBSPD) equaion Figure 5.20 USTBSPD / inflaion rae CUSUM of square D(INFRATE) equaion Figure 5.21 JORSPD / inflaion rae / REPO rae CUSUM D(JORSPD) equaion Figure 5.22 JORSPD / inflaion rae / REPO rae CUSUM D(INFRATE) equaion Figure 5.23 JORSPD / inflaion rae / REPO rae CUSUM D(REPO) equaion 9
LIST OF FIGURES Figure 5.24 JORSPD / inflaion rae / REPO rae CUSUM of square D(JORSPD) equaion Figure 5.25 JORSPD / inflaion rae / REPO rae CUSUM of square D(INFRATE) equaion Figure 5.26 JORSPD / inflaion rae / REPO rae CUSUM of square D(REPO) equaion Figure 5.27 JORSPD / inflaion rae recursive coefficiens D(JORSPD) equaion Figure 5.28 JORSPD / inflaion rae recursive coefficiens D(INFRATE) equaion Figure 5.29 USTBSPD / inflaion rae recursive coefficiens D(USTBSPD) equaion Figure 5.30 USTBSPD / inflaion rae recursive coefficiens D(INFRATE) equaion Figure 5.31 JORSPD / inflaion rae / REPO rae recursive coefficiens D(JORSPD) equaion Figure 5.32 JORSPD / inflaion rae / REPO rae recursive coefficiens D(INFRATE) equaion Figure 5.33 JORSPD / inflaion rae / REPO rae recursive coefficiens D(REPO) equaion Figure 5.34 Impulse response under VAR sysem - (JORSPD and INFRATE) Figure 5.35 Impulse response under VAR sysem - (USTBSPD and INFRATE) Figure 5.36 Impulse response under VAR sysem - (JORSPD, INFRATE and REPO) 10
LIST OF TABLES Chaper Three: LIST OF TABLES Table 3..1 Uni roo es for he JODIBOR ineres raes ADF Table 3.1.2 Uni roo es for he JODIBOR ineres raes PP Table 3.1.3 Uni roo es for he perfec foresigh spread (PFS) and he acual spread (SPD) Table 3.2.1 Does he acual spread predic he fuure changes in shor erm ineres raes (OLS) Table 3.2.2 Does he acual spread predic he fuure changes in shor erm ineres raes (GMM) Table 3.3.1 VAR opimal lags selecion and diagnosics ess Table 3.3.2 The regression of he heoreical spread (S * ) on he acual spread (S ) using (OLS) Table 3.3.3 VAR ess - Theoreical Spread (S * ) and Acual spread (S ) Table 3.4 Bivariae coinegraion ess Table 3.4.1 Imposing resricions on he bivariae coinegraing vecors (Tesing he Expecaions Hypohesis) Table 3.5 Trivariae coinegraion ess (Two spreads es) Table 3.5.1 Imposing resricions on he rivariae coinegraing vecors (Tesing he Expecaions Hypohesis-The wo spreads) Table 3.6 Mulivariae coinegraion ess (Five spreads es) Table 3.6.1 Imposing resricions on he mulivariae coinegraing vecors (Tesing he Expecaions Hypohesis The five spreads) Table 3.6.2 Imposing resricions on he mulivariae coinegraing vecors (Tesing he Expecaions Hypohesis The five spreads) Table 3.7 The ime varying parameer Model Table 3.8 The inerbank volumes for differen mauriies in (JD MIO) during he period from January 2000 unil March 2008 Chaper Four: Table 4.1.1 Uni roo es (ADF AIC), (Levels and Firs Differences) Table 4.1.2 Uni roo es (ADF SIC), (Levels and Firs Differences) Table 4.2 Uni roo es (PP), (Levels and Firs Differences) Table 4.3 The coinegraion analysis, he Expecaions Hypohesis es and he error correcion model (ECM) whole sample period Table 4.4 The consruced error correcion model (ECM) whole sample period Table 4.5 Granger Causaliy resuls whole sample period Table 4.6.1 Bivariae coinegraion ess (Model 2) - Forward recursive esimaions Table 4.6.2 Imposing resricions on he bivariae coinegraing vecors (Tesing he EH). Table 4.6.3 Granger Causaliy es (Weak exogeneiy) Table 4.7 The ime varying parameer model (Forward recursive esimaion) Table 4.8.1 Bivariae coinegraion ess (Model 2) wih dummy variables (i.e. 11
LIST OF TABLES Including wo srucural breaks) - Forward recursive esimaion Table 4.8.2 Imposing resricions on he bivariae coinegraing vecors (Tesing he EH) Table 4.8.3 Granger Causaliy es (Weak exogeneiy) - Forward recursive esimaion wih dummy variables Table 4.9 The coinegraion analysis, he Expecaions Hypohesis es and he error correcion model (ECM) - whole sample period wih dummy variables Table 4.10 The consruced error correcion model (ECM) whole sample period wih dummy variables Table 4.11 Granger Causaliy resuls whole sample period wih dummy variables Chaper Five: Table 5.1.1 Uni roo es (ADF AIC), (Levels and firs Differences) Table 5.1.2 Uni roo es (ADF SIC), (Levels and firs Differences) Table 5.2 Uni roo es (PP), (Levels and firs Differences) Table 5.3.1 Uni roo es (ADF AIC). (Term spreads and inflaion raes - Levels and Firs Differences) Table 5.3.2 Uni roo es (ADF SIC). (Term spreads and inflaion raes - Levels and Firs Differences) Table 5.4 Uni roo es (PP). (Term spreads and inflaion raes - Levels and Firs Differences) Table 5.5 ARFIMA model for US erm spread Table 5.6 The percenage of rejecion under Dickey Fuller (DF) es, (Mone Carlo analysis) Table 5.7 The criical values, (Mone Carlo analysis) Table 5.8 The bivariae coinegraion analysis, esing he validiy of Fisher hypohesis (FH) using monhly inflaion daa Table 5.9 The coinegraion analysis, esing he validiy of Fisher hypohesis (FH) beween he hree monh ineres rae and he monhly inflaion rae Table 5.10 The coinegraion analysis, esing he validiy of Fisher hypohesis (FH) beween he six monh ineres rae and he monhly inflaion rae Table 5.11 The bivariae coinegraion analysis, esing he validiy of Fisher hypohesis (FH) using he yearly inflaion rae Table 5.12 The bivariae coinegraion analysis beween each erm spread (he domesic and he US) and he monhly inflaion rae Table 5.13 The coinegraion analysis and he error correcion model (ECM) for JORSPD and INFRATE Table 5.14 The consruced error correcion model (ECM) for JORSPD and INFRATE. Table 5.15 Granger Causaliy resuls for JORSPD AND INFRATE Table 5.16 The coinegraion analysis and he error correcion model (ECM) for USTBSPD and INFRATE. Table 5.17 The consruced error correcion model (ECM) for USTBSPD and 12
LIST OF TABLES INFRATE. Table 5.18 Granger Causaliy resuls for USTBSPD and INFRATE Table 5.19 The mulivariae coinegraion es (he domesic spread, he monhly inflaion rae and he REPO rae) Table 5.20 The coinegraion analysis, and he error correcion model (ECM) for JORSPD, INFRATE and REPO Table 5.21 The consruced error correcion model (ECM) for JORSPD, INFRATE and REPO Table 5.22 Granger Causaliy resuls for JORSPD, INFRATE and REPO Table 5.23 The resuls of he sabiliy ess Table 5.24.1 Variance Decomposiion of he JORSPD Table 5.24.2 Variance Decomposiion of he INFRATE Table 5.25.1 Variance Decomposiion of he USTBSPD Table 5.25.2 Variance Decomposiion of he INFRATE Table 5.26.1 Variance Decomposiion of he JORSPD Table 5.26.2 Variance Decomposiion of he INFRATE Table 5.26.3 Variance Decomposiion of he REPO 13
ABBREVIATIONS ABBREVIATIONS ADF AIC AR CBJ CDs Corr CPI CUSUM CUSUMSQ d.f. DF ECM ECT EH FH GMM Augmened Dickey Fuller Akaike Informaion Crierion Auoregressive Cenral Bank of Jordan Cerificaes of Deposis Correlaion Coefficien Consumer Price Index Cumulaive Sum of Recursive Residuals Cumulaive Sum Squares Degrees of freedom Dickey Fuller Error Correcion Model Error Correcion Term Expecaions Hypohesis Fisher Hypohesis Generalised Mehod of Momens I(0) Inegraed Variable of Order 0 I(1) Inegraed Variable of Order 1 i.i.d. Idenically and Independenly Disribued JODIBOR The Jordanian Dinar Inerbank Offered Rae JORSPD The domesic erm spread LIBOR London Inerbank Offered Rae MA Moving Average OECD Organisaion for Economic Co-operaion and Developmen OLS Ordinary Leas Squares PEH Pure Expecaions Hypohesis PFS Perfec Foresigh Spread PP The Phillips-Perron m r Shor Term Ineres Rae wih Mauriy (m) n R Long Term Ineres Rae wih Mauriy (n) REHTS Raional Expecaions Hypohesis of he Term Srucure REPO Repurchase Agreemen S = SPD Acual spread (, m) S Spread Beween (n) Period Ineres Rae and (m) Period Ineres Rae a Time () * S Theoreical Spread s.d. Sandard Deviaion SDR Sandard Deviaion Raio SE Sandard Error 14
ABBREVIATIONS TVP USTBSPD VAR VECM Time Varying Parameer The US erm spread Vecor Auoregression Vecor Error Correcion Model 15
CHAPTER ONE INTRODUCTION The relaionship beween ineres raes of differen mauriies is, and will remain, one of he main concerns for all marke players in any financial marke. Moneary auhoriies, marke praciioners, invesors and economiss pay grea aenion o he characerisics of he erm srucure of ineres raes because i is he main ool ha relaes ineres raes of differen mauriies ogeher. One of he main characerisics ha have been he cenre of aenion for a long ime is he predicive power of he erm srucure, paricularly is abiliy o predic fuure economic aciviies such as he fuure movemens in ineres raes, he oupu growh and inflaion. Marke players, and in paricular policy makers, use he slope of he erm srucure o exrac imporan informaion abou he marke's expecaions of fuure economic aciviies. A subsanial body of he empirical lieraure concenraes on esing he predicive power of he erm srucure of ineres raes. A significan proporion of he empirical work examines he abiliy of he erm srucure o predic he fuure movemens in shor erm ineres raes while he remaining work examines wheher he erm srucure conains useful informaion abou macroeconomic variables such as he oupu growh and inflaion. The majoriy of he sudies focus on using daa from developed counries where he financial markes are well developed such as he US, OCED counries, and oher European counries, whereas few sudies focus on using daa from emerging and 16
CHAPTER ONE developing economies where he financial markes are eiher emerging markes or underdeveloped markes such as Malaysia, India, Mexico, Turkey and Sri Lanka. Tesing he predicive power of he erm srucure, paricularly is abiliy o predic he fuure changes in shor erm ineres raes, is normally done by esing he validiy of he Expecaions hypohesis (EH). One of he main purposes of esing he validiy of EH in mos of he empirical works ha use daa from developing and emerging economies is o invesigae he efficiency of he financial markes and he abiliy of hese markes o be used as an efficien vehicle for moneary policy implemenaion. Moreover, he commonaliy among all hese sudies is he ype of he ineres raes ha have been used for esing. Mos of hese sudies use he money marke ineres raes as he main daa se for esing mainly because he money marke is he only well developed marke in hese economies. There is a common belief ha he low qualiy of he economic daa in he emerging and developing economies could be one of he reasons for he lack of proper research in his area. The main characerisics of he low qualiy daa are: he daa are no available for long periods, hey may conain many missing values and or hey may conain noise wihin. This hesis focuses mainly on invesigaing wheher he shor end of he erm srucure has he abiliy o predic he fuure movemens in shor erm ineres raes and he inflaion rae using daa from a developing counry: he case of Jordan. The main challenge in his hesis is dealing wih low qualiy daa. The firs daa se, he Jordanian Dinar inerbank offered rae (JODIBOR), belongs o a newly esablished marke; ha is he Jordanian inerbank marke of differen mauriies, and he main limiaion of his daa se is ha i is only available for a very shor period. Moreover, due o he absence 17
CHAPTER ONE of regular issues of Governmen securiies in he Jordanian financial marke and due o he fac ha he secondary marke for Governmen securiies is very hin during he period of he sudy, he second daa se, he Cenral Bank of Jordan Cerificaes of Deposis (CDs), is chosen from he Jordanian primary marke insead of he secondary marke. The main limiaions of he second daa se are ha i conains many missing values and here are jus wo mauriies available for esing; i.e. he hree and six monhs' ineres raes. The firs and he second daa ses are used for esing he validiy of he EH. The hird daa se is he monhly inflaion rae and he main limiaion of his se is ha i conains noise wihin. The second and he hird daa ses are used for examining he informaion conens of he erm srucure abou fuure inflaion rae. In his hesis, several advanced and mos up-o-dae economerics echniques are used o examine he predicive power of he shor end of he erm srucure and o deal wih he limiaions of he daa ses paricularly he missing values and he noisy daa. In he case of he missing values, he main goal was o reain he main properies of he daa se while esimaing he missing values. Moreover, he noise wihin he monhly inflaion rae series leads us o quesion wheher he sandard uni roo ess are qualified enough o idenify he rue order of inegraion of he monhly inflaion rae. This hesis provides robus evidence, hrough he Mone Carlo simulaion, ha in he case of noisy daa he resuls of he sandard uni roo es; i.e. he Dickey Fuller (DF) es, are misleading and implausible. 18
CHAPTER ONE The main objecives of his hesis are: - Conribuing o he lieraure by esing he abiliy of he shor end of he erm srucure o predic he fuure movemens in shor erm ineres raes and he inflaion rae for a developing counry where par of he financial marke is emerging and he oher par is sill underdeveloped. - Exploring he efficiency and he poenial of he newly esablished marke; ha is he Jordanian inerbank marke of differen mauriies, by sudying he evoluion of he marke players' behaviour which is considered as one of he main issues ha leads o he developmen of any marke. - Dealing wih he low qualiy of he economic daa in developing counries and his includes dealing wih daa ses ha conain many missing values or conain noise wihin. - Conribuing o he lieraure ha discusses he size disorion of he Dickey Fuller (DF) es by providing evidence ha he size disorion of he DF es increases when he daa se conains noise using Mone Carlo simulaion. 19
CHAPTER ONE The srucure of he hesis is as follows: Chaper wo discusses he lieraure review ha is relaed o he predicive power of he erm srucure of ineres raes. The firs par of his chaper concenraes on he empirical works ha examine he abiliy of he erm srucure o predic he fuure movemens in shor erm ineres raes hrough esing he validiy of he EH. The main focus is on he main heories ha explain he erm srucure of ineres raes and he empirical esing of he EH including he heoreical framework, he large variaion in he mehodologies and echniques, he counries involved, he daa ses, he sample periods ha have been used for esing and he findings of he empirical esing. In addiion his par discusses he oher implicaions of he Expecaions heory such as he relaionship beween he Expecaions heory and boh he concep of marke efficiency and he ransmission mechanism of moneary policy. The second par of his chaper concenraes on he empirical works ha examine he abiliy of he erm srucure o predic he macroeconomic variables, paricularly he inflaion rae. Therefore, his par includes he empirical works ha focus on examining wheher he shor erm nominal ineres raes conain useful informaion abou he inflaion rae hrough esing he validiy of he Fisher hypohesis (FH) and he empirical works ha focus on examining wheher he slope of he erm srucure; i.e. he erm spread, is an opimal predicor of he fuure inflaion rae. In chaper hree, he validiy of he EH is esed for he purpose of idenifying wheher he shor end of he erm srucure has he abiliy o predic he fuure movemens in shor erm ineres raes. The Jordanian Dinar inerbank offered rae (JODIBOR), which 20
CHAPTER ONE represens he erm srucure of ineres raes in he Jordanian inerbank marke of differen mauriies, is used for esing. Three well known economeric echniques are employed o es he validiy of he EH; he single equaion regression, he VAR mehodology (Campbell and Shiller 1987, 1991) and he coinegraion analysis using he Johansen approach. The firs conribuion of his chaper is o examine he predicive power of he shor end of he erm srucure for Jordan for he firs ime. Since he daa se ha is used in his chaper belongs o he Jordanian inerbank marke of differen mauriies which is a relaively new marke, he second conribuion is o explore he evoluion of he marke players' behaviour; ha is, sudying he marke players' abiliy o learn. The Time Varying Parameer es (TVP) is used as he main ool o examine he learning process. The empirical evidence of his chaper will shed ligh on he predicive power of he erm srucure in he Jordanian inerbank marke and accordingly on he efficiency of his marke including idenifying which par of he marke is more acive and has he highes poenial for furher developmen. In chaper four, anoher aemp is carried ou o examine he predicive power of he erm srucure; in paricular he erm srucure in he Jordanian primary marke. This chaper concenraes on esing he long run equilibrium relaionship beween ineres raes of differen mauriies, using he EH as he main ool, and he Granger Causaliy relaionship. A financial insrumen from he Jordanian primary marke is chosen for esing which is he Cenral Bank of Jordan Cerificaes of Deposis (CDs). The CDs are a moneary policy insrumen and hey are mainly used for liquidiy managemen by he Cenral Bank of Jordan (CBJ). Moreover, he CDs have exised in he marke for 21
CHAPTER ONE approximaely en years and hey are considered by all marke players o be a risk-free benchmark insrumen. The main shorcomings of he CDs are ha he CDs erm srucure only consiss of wo main mauriies; he hree and six monhs, and he six monh series conains many missing values. In his chaper, several economeric echniques are employed for he empirical esing: he Spline smoohing funcion o esimae he missing values in he six monh ineres rae series, he coinegraion analysis o es for he long run equilibrium relaionship, he Error Correcion Model (ECM) o es for he Granger Causaliy and he Impulse Response Funcion o es for he sabiliy of he coinegraed sysems. Moreover, in order o check he robusness of he findings ha concern he direcion of causaliy, a forward recursive coinegraion analysis is employed. Furhermore, in his chaper he effec of srucural breaks is addressed, paricularly heir effec on he resuls of he forward recursive coinegraion analysis. The main conribuion of his chaper is o deec wheher he EH holds for he erm srucure of ineres raes in he Jordanian primary marke. The subsidiary conribuion is dealing wih a daa se ha conains many missing values, and arguing ha he Spline funcion ha is used as a ool o esimae he missing values does no change he main properies of he daa. The empirical evidence may imply imporan informaion abou he predicive power of he CDs erm srucure and accordingly he efficiency of he primary marke. In summary, chapers hree and four have he same main objecive, which is examining he abiliy of he shor end of he erm srucure o predic he fuure movemens in shor 22
CHAPTER ONE erm ineres raes and idenifying he efficiency of he Jordanian money marke; ha is, he Jordanian inerbank marke of differen mauriies and he primary marke for he Cenral Bank of Jordan Cerificaes of Deposis. Chaper five focuses on anoher imporan issue of he predicabiliy of he erm srucure which is he abiliy of he erm srucure o predic he inflaion rae. In his chaper, he main objecive is o find ou wheher he shor end of he erm srucure of ineres raes conains useful informaion abou he inflaion rae in Jordan. Given he major oucome of chaper four which shows ha he CDs erm srucure has some predicive power, in his chaper he CDs erm srucure is used wih he monhly inflaion rae for esing. Two main ess are carried ou o idenify he informaion conens of he CDs erm srucure. Firs he informaion conen of he shor erm nominal ineres raes is idenified by esing he validiy of he Fisher Hypohesis (FH). Second he informaion conen of he slope of he erm srucure; i.e. he domesic erm spread, is idenified by esing wheher here is a long run relaionship beween he domesic erm spread and he inflaion rae; ha is, esing wheher he wo variables are bound ogeher by a common rend. Moreover, invesigaing he informaion conens of he erm srucure is exended o examine he influence of an addiional variable on he predicabiliy of he domesic erm spread, paricularly he variables ha reflec he moneary policy sances, and for his purpose he Repo rae which is one of he CBJ key ineres raes is used. Furhermore, given ha he exchange rae regime in Jordan has been pegged o US 23
CHAPTER ONE dollars for a long ime (since 1995), an invesigaion is carried ou o es wheher he US erm spread conains imporan informaion abou he Jordanian inflaion rae. The long run equilibrium relaionship and he causaliy relaionship beween he variables are used as he major ools o define he informaion conens of he erm srucure. Several economerics echniques are used for he empirical esing; he coinegraion analysis o idenify he long run equilibrium relaionship, he Error Correcion Model (ECM) o es for he Granger Causaliy and he Impulse Response and Variance Decomposiion analyses are employed o examine he sabiliy of he coinegraed sysems and o idenify he conribuion of each explanaory variable on he variance flucuaions of he inflaion rae. Moreover, idenifying he rue order of inegraion of he argeed variables becomes an issue in his chaper. Given he properies of he major variables, he sandard uni roo ess such as he Augmened Dickey Fuller (ADF) and Phillips-Perron (PP) provide conradicing resuls. Therefore, addiional ess are carried ou o verify he rue order of inegraion of some variables such as he Auoregressive Fracionally Inegraed Moving Average analysis (ARFIMA) and he Specrum analysis. In addiion, a Mone Carlo simulaion is employed o prove ha when he daa se conains significan noise wihin, he resuls of he sandard uni roo ess such as he DF es are misleading and implausible. The Mone Carlo simulaion provides robus evidence ha in he case of noisy daa he disribuion of he -saisic will be differen from he disribuion proposed by DF where he process is a pure random walk; hence using he sandard criical values of DF es leads o a severe size disorion of he es. 24
CHAPTER ONE Insead he Mone Carlo simulaion suggess new ses of criical values ha can be more reliable han he sandard ones. The evidence ha he size disorion of he DF es becomes larger as he noise increases in he daa and faser as he sample size becomes bigger provides suppor o he lieraure ha discusses he size disorion of he DF es. The main conribuion of his chaper is deecing wheher he shor end of he erm srucure conains useful informaion abou he inflaion rae in Jordan for he firs ime. The exisence of he long run equilibrium relaionship and he causaliy relaionship beween he main variables provides clear evidence abou he effeciveness of he informaion conens of he erm srucure. In addiion, he finding of Mone Carlo simulaion is anoher key conribuion. In chaper six, he main conclusion of he hesis is described in deail. Moreover, furher remarks and areas for poenial fuure research are addressed. 25
CHAPTER TWO LITERATURE REVIEW 2.1 INTRODUCTION The subsanial heoreical and empirical lieraure ha focuses on he predicabiliy of he erm srucure is an indicaion of he significance and uniqueness of he informaion conained in he erm srucure of ineres raes. In his chaper, we will address he lieraure review ha is relaed o he predicive power of he erm srucure of ineres raes; in paricular he empirical works ha examine he abiliy of he erm srucure o predic he fuure movemens in shor erm ineres raes and hen he empirical works ha examine he abiliy of he erm srucure o predic he macroeconomic variables paricularly he inflaion rae. This chaper is organised as follows: Secion wo describes he main heories ha explain he erm srucure of ineres raes; secions hree, four and five presen he lieraure review ha is relaed o he empirical esing of he Expecaions Hypohesis (EH); secion six discusses he lieraure review ha is relaed o he erm srucure and he predicabiliy of fuure inflaion rae and secion seven presens he conclusion. 2.2 THE MAIN THEORIES OF THE TERM STRUCTURE OF INTEREST RATES 26
CHAPTER TWO 2.2.1 THE EXPECTATIONS THEORY (ET) The ET is considered he main heory of he erm srucure of ineres raes because of is imporan implicaions in he predicion of he fuure movemens in ineres raes. The ET which is inroduced by Irving Fisher (1930) saes ha long erm ineres raes are an average of curren and expeced fuure shor erm ineres raes. The ET is based on he following main assumpions: 1- Marke paricipans are risk neural 1 and heir behaviour is raional. Campbell and Shiller (1991) sae ha he raional expecaions of fuure shor erm ineres raes are he dominan facor ha deermines he curren level of long erm ineres raes. This assumpion is very imporan because he ET saes ha in equilibrium he curren long erm raes should equal he marke's expecaions of he average of curren and fuure shor erm raes. Accordingly he financial insrumens ha have he same characerisics, excep he erm of mauriy, can be considered a perfec subsiuion for each oher; i.e. he reurn from holding a bond wih (n) period o mauriy where (n>1) should equal he reurn from holding a bond wih one period o mauriy and hen roll i over (n) periods ahead, assuming ha he ransacion coss are minimal. 2- Marke is efficien; informaion is available o all marke players. The curren ineres raes and he expecaions of fuure shor erm ineres raes in he efficien markes are influenced by he changes in he informaion ha affec he expecaions of marke players. 1 Risk neural indicaes ha marke paricipans are indifferen o he level of risk. 27
CHAPTER TWO The wo main versions of he Expecaions Hypohesis which have been used exensively by he researchers are he Pure Expecaions Hypohesis (PEH) and he Expecaions Hypohesis (EH). The main assumpion under he PEH which is proposed by Luz (1940) is ha he erm premia is assumed o be equal o zero while under he EH he erm premia is assumed o be consan. The slope coefficien beween he acual spread 2 and he perfec foresigh spread or he heoreical spread 3 under boh he PEH and he EH is considered o be equal one. Furhermore, he ET is one of he key heories ha explain he shapes (slopes) of he erm srucure which mainly ake he following shapes: - The erm srucure akes he normal shape which is upward sloping when shor erm rae is currenly low bu i is expeced o rise in he fuure. - The erm srucure is downward sloping (also called invered erm srucure) when shor erm rae is currenly high bu i is expeced o fall in he fuure. - The erm srucure is fla, when shor erm rae is expeced o remain consan; herefore boh he shor erm and long erm raes are equal. - The erm srucure is humped, when shor and long erm raes are almos equal while he medium erm rae is higher han boh raes. 2 The acual spread is he simple difference beween long and shor erm ineres raes. 3 The heoreical spread is calculaed as he weighed sum of he expeced changes of shor erm ineres raes; he full deails are described in secion 2.3 28
CHAPTER TWO 2.2.2 THE LIQUIDITY PREFERENCE THEORY This heory was inroduced by Hicks in 1939 and i akes ino consideraion he risk preferences of he marke paricipans. The main assumpion under he liquidiy preference hypohesis is ha invesors are risk averse so hey prefer o hold shor erm bonds because hey are more liquid and less risky, whereas in order o hold long erm bonds hey require higher liquidiy premium as a compensaion; he longer he mauriy of he bond, he larger he liquidiy premium hey require, so he premium is no consan across differen mauriies. Accordingly curren long erm ineres raes reflec he invesors' expecaions abou fuure shor erm ineres raes plus he liquidiy premium. Because of he liquidiy premium, he long erm ineres rae ends o be higher han he shor erm ineres rae. In his case he slope of he erm srucure will be posiive and he erm srucure will be upward sloping. 2.2.3 THE MARKET SEGMENTATION THEORY This heory was inroduced by Culberson in 1957 and i akes ino consideraion invesors' preferences in respec of financial asses mauriies. The main assumpion of he marke segmenaion hypohesis is ha marke paricipans are also risk averse as in he liquidiy preference hypohesis. According o Culberson his heory explains he role ha he insiuions play in shaping he erm srucure of ineres raes. The insiuions normally like o inves heir funds in mauriies ha mach he mauriies of heir liabiliies; for example if heir liabiliies have long erm mauriies hen hey prefer o place heir funds in long erm invesmens, so in order o inves in shor erm invesmens hey need o be compensaed wih a premium. 29
CHAPTER TWO This also rue for he insiuions ha have shor erm liabiliies, in ha hey prefer o inves heir money in shor erm invesmens, and in order o change o longer erm invesmens hey need also o be compensaed wih a premium. In view of ha, separae markes will be found and he yields in hese markes will be deermined solely by he demand and supply for he financial asses. Furhermore, he large demand for specific mauriy may affec he shape of he erm srucure; for example when he demand for shor erm bonds increases significanly, he prices will increase and he yields will decrease. On he oher hand, he demand for long erm bonds will decrease, and his will cause he prices o decrease and yields o increase. As a resul, he erm srucure will ake he normal shape which is upward sloping. 2.2.4 THE PREFERRED HABITAT THEORY This heory was inroduced by Modigliani and Such (1966) and he main assumpion wihin his heory is ha invesors are risk averse and have differen invesmen horizons; i.e. inves only in long erm deb or only in shor erm deb, and in order o inves in financial insrumens ou of heir habia hey have o be compensaed wih premium. This heory is a combinaion of he marke segmenaion heory and he ET. The main aspec of he las hree heories is ha hey explain why he erm premium is no consan in some cases. 30
CHAPTER TWO 2.3 THE TERM STRUTURE AND THE PREDICTABILITY OF FUTURE MOVEMENTS IN SHORT TERM INTEREST RATES The abiliy of he erm srucure o predic fuure movemens in shor erm ineres raes is normally idenified by examining he validiy of he Expecaions Hypohesis (EH). The EH saes ha he erm spread; i.e. he slope of he erm srucure, is an opimal predicor of he expeced changes in fuure shor erm ineres raes. The researchers who use he PEH or he EH believe ha if he erm premia is zero or consan hen all he changes in he curren long erm ineres raes should be explained only by he expeced changes in fuure shor erm ineres raes. The heoreical framework of he EH is described in deail in he following secion. A furher secion covers he key elemens of he empirical esing of he EH. 2.3.1 THE THEORETICAL FRAMEWORK OF THE EXPECTATIONS HYPOTHESIS The ET of he erm srucure of ineres raes is abou he relaionship beween he long erm ineres raes, (n) period ineres rae n R, and he shor erm ineres raes, (m) period ineres rae m r. The following general form of he expecaions model is borrowed from Paerson (2000). I represens he simple version of he expecaions model which has been used in mos of he empirical sudies of he erm srucure. 31
CHAPTER TWO n R = 1 k k i 1 E r m ( i 1) m + m Tp Eq2.3.1.1 Where k = m n Equaion (2.3.1.1) says ha a long erm ineres rae is a weighed average of he curren and expeced fuure shor erm ineres raes plus a erm premium ( Tp ). According o he PEH he erm premium ( Tp ) is assumed o be equal o zero while under he EH, m he erm premium ( Tp ) is assumed o be consan. Equaion (2.3.1.1) has been derived as follows: m m The long erm ineres rae a curren ime () is equal o he weighed average of he acual shor erm ineres rae a curren ime () and subsequen sequence of shor erm forward raes. n R = 1 k k i 1 m F i 1) m ( Eq 2.3.1.2 Example: if n=3 and m=1 hen k= m n = 3 1 R = [ 1 r + 3 3 F + 1 1 F ] 1 2 So he acual long erm ineres rae 3 R is equal o he weighed average of he acual one period yield o mauriy ( r 1 ) and wo subsequen sequences of one period forward 32
CHAPTER TWO 1 raes ( F 1and F 1 2 ). The idea here simply means ha in an efficien marke he reurn from holding (n) periods bond a ime () or from holding a sequence of shorer periods (m) bonds should be equal and if i does no, any arbirage opporuniy will disappear quickly as he marke is efficien. The forward raes can be rewrien in he form of acual raes as follows: = E r ) + F m j ( m j m j Eq 2.3.1.3 The explanaion of his form is ha (m) period forward rae ( j) is equal o he expeced (m) period rae for he period ( j) plus an addiional facor ( m j ) which represens he erm premia. According o he previous example where n=3 and m=1, he forward raes can be wrien as follows: 1 F 1= E ( r 1 1) + 1 1 F = E r ) + 1 2 ( 1 2 1 2 Subsiue Eq (2.3.1.3) in Eq (2.3.1.2), he resul will be Eq (2.3.1.1): n R = 1 k k i 1 E r m ( i 1) m + m Tp Where m Tp = k 1 [ k i 1 m i 1) m ( ], represens he erm premia. 33
CHAPTER TWO To clarify he idea of he expecaions model, he following example is abou he relaionship beween he hree monh ineres rae and he one monh ineres rae of a pure discoun rae bond. This relaionship had been esed exensively in he lieraure, especially in erms of he validiy of he EH a he shor end of he erm srucure. n = 3 monh, m = 1 monh, so k = 1 3 = 3. According o equaion (2.3.1.1), n R = 1 k k i 1 E r m ( i 1) m + m Tp 3 1 R = [ 3 E ( 1 r ) + E ( r 1 1) + E ( r )] + 1 2 1 Tp According o he raional expecaions hypohesis: E ( 1 r ) = 1 r a ime (), so 3 1 R = [ 1 r + E ( r 1 1) + E ( 3 r )] + 1 2 1 Tp The above equaion means ha he hree monh ineres rae is a simple weighed average of a one period acual ineres rae a curren ime () and he one period expeced ineres raes a ime (+1 and +2) plus a erm premium. The weighs are sum o one. Under he main assumpion ha he erm premia is consan or zero, he changes in he long erm ineres raes will occur as a resul of he expeced changes in fuure 34
CHAPTER TWO shor erm ineres raes. Therefore, he curren hree monh ineres rae should increase if he fuure one monh ineres raes a ime (+1 and +2) are expeced o increase. Regarding he financial insrumens ha are coupon carrying, he relaionship beween he long erm ineres rae and he shor erm ineres rae for a coupon carrying bond is described in he following model: n R = k 1 1 1 k i 1 i E r + m ( i 1) m m Tp The long rae in his case is no a simple average of curren and expeced fuure shor erm ineres raes. The weighs are exponenially declining so he expeced raes in he near fuure receive he larges weigh while he raes in he disan fuure receive smaller weigh, and he scale (1- k ) is se o ensure ha he oal of he weighs sums o one. According o Shiller (1979) he parameer =1/(1+ R ) relaes he long erm ineres raes ( R ) o he presen value of fuure shor erm ineres raes discouned by (R ). n This model is appropriae for coupon carrying bonds which are selling near par or for consols (perpeuiies bonds) wih n. 2.3.1.1 THE SPREAD According o he ET, he spread is as an opimal forecas of he expeced changes in fuure shor erm ineres raes plus a erm premia (Campbell and Shiller (1991). The spread beween he (n) period rae and (m) period rae is represened as S = ( n, m) 35
CHAPTER TWO R - r. The slope of he erm srucure is affeced by he sign of he spread; if he n m spread is posiive hen he slope of he erm srucure will be upward and his means ha long erm ineres rae is higher han shor erm ineres rae which indicaes ha he expeced fuure shor erm raes are going o rise. The spread model Eq (2.3.1.1.1) is derived by subracing m r from boh sides of Eq (2.3.1.1) and rearranging erms, ( R - n m r ) = k 1 i 1 i 1 E ( k m r ) + m im m Tp Eq 2.3.1.1.1 ( n, m) The lef hand side describes he acual spread (i.e. S ), and he righ hand side represens he erm premia ( Tp ) plus he perfec foresigh spread (PFS) which was mainly developed by Campbell and Shiller (1991). m According o Campbell and Shiller (1991), he perfec foresigh spread is obained if here is perfec foresigh abou fuure ineres raes. Wih perfec foresigh, if (m) period raes are going o rise over he life of he (n) period, hen he curren (n) period yield needs o be higher han he curren (m) period yield, so he reurn on he (n) period bond which is held o mauriy equals he reurn on a sequence of (m) period bonds. So PFS = ( n, m) k 1 i 1 i 1 E ( k m r ) m im Where he m indicaes ha he change is measured over (m) periods, 36