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Speculative Markets Dynamics Speculative Markets Dynamics An Econometric Analysis of Stock Market and Foreign Exchange Market Dynamics Speculative Markets Dynamics Ut;Ti An Econometric Analysis of Stock Market and Foreign Exchange Market Dynamics .-; • 'E"i»irf|i-8 PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Rijksuniversiteit Limburg te Maastricht, op gezag van de Rector Magnificus, Prof. Mr. M.J. Cohen, volgens het besluit van het College van Dekanen, in het openbaar te verdedigen op woensdag, 24 maart 1993 om 16.00 uur door Frederik Gertruda Maria Carolus Nieuwland geboren te Hoensbroek '•'-• '•-• -•- • - ••-'.. V; ••" •»/!*-.«•>.• ïlV*- '•.'••• "T" *' ï>' 'T' •• UPM • —-. UNIVERSITAIRE PERS MAASTRICHT Promotor: *• , -*. j Prof. dr. C.C.P. Wolff Beoordelingscommissie: ft;/l' '1 ^iï'-.-c.-. ' "i'.;;., Prof. dr. J.G. Backhaus (Voorzitter) Prof. dr. Th. E. Nijman Dr. P.C. Schotman •• .• . 1 *~': :' ' '-1-/1 .'- .-., (•- CIP-DATA KONINKLIJKE BIBLIOTHEEK, DEN HAAG Nieuwland, Frederik Gertruda Maria Carolus Speculative markets dynamics : an econometrie analysis of stock market and foreign exchange market dynamics / Frederik Gertruda Maria Carolus Nieuwland. - Maastricht: Universitaire Pers Maastricht. - 111., fig., tab. Thesis Maastricht. - With ref. ISBN 90-5278-069-2 NUGI 682/683 Subject headings: asset pricing model / GARCH models / risk premia. This dissertation is dedicated to the memory of : : Maria Nieuwland-Neff Gertruda Wiertz-Hollands Leonard Wiertz Without them I would not have been what I am today. Preface This dissertation is the result of four years of learning, reading, and doing research. I have enjoyed every minute of those four years and I have espe- cially learned to appreciate the freedom I had in setting my own goals and pursuing my own research interests. To me this dissertation is not the final result of a research project, which upon completion should end up in a filing cabinet. It is rather, an opening statement in a hopefully long-lasting dis- course. Four years ago I did not expect to be as fascinated by doing research as I am today, but in retrospect the preparation and writing of this disserta- tion has been one big thrill. Acknowledgements I could not have completed this dissertation without the general support I have received over the last four years. First of all I gratefully acknowledge research support by grant 450-227-009 from the Foundation for the Promo- tion of Research in Economic Sciences (Ecozoek), and financial assistance by the Staal Stichting 1966 to print this dissertation. I owe an unrepayable debt to many people that have never seized to encourage me. First in line is Christian Wolff, who has been much more than just a thesis advisor. Like a shepherd watching his flock, he always made sure that I did not wander off too much from the right track. Any good shepherd has a well-trained sheep- dog. This characterization fits the description of my room-mate Willem Verschoor. Whenever I strayed behind or had another crazy idea, like many sheep tend to have, he summoned me to hurry up, get my act together, and to get back in line. This sheep really needed that. Thanks to both of you! I would also like to thank my collegues at the Finance Department of the University of Limburg, who provided me with a first-class working environ- ment, and made me feel like a happy sheep in a happy flock. A special word of thanks goes out to Peter Schotman, Kees Koedijk, Art Selender, Franz Palm, Carina Wijnands and Nathalie Jansen, each of them knows why. The efforts of the members of my dissertation committee consisting of Jiirgen Backhaus, Theo Nijman, and Peter Schotman are also greatly appreciated. I welcome this opportunity to thank all my friends for the interest they have taken, in one form or another, in my research, and for providing me with a joyful social environment. Finally I would like to express my gratitude and love to my brother and parents, to whom I owe the largest of the unre- payable debts. Fred Nieuwland January 1993 Maastricht Table of Contents ••••."•;.-*V ^ >r: page o/ CoH/entó 1 Lw/ o/ Mto 4 LIJ/ <ƒ Figures 5 1 Introduction, Motivation, and Setting 9 1.1 The History of Financial Economics 9 1.2 The Role of Financial Economics within Economics 12 1.3 Time-Varying Risk Premia in Financial Economics 16 1.4 GARCH as a Tool for Time-Varying Risk 17 1.5 Research Objectives 18 2 Conditional and Unconditional Distributions for Stock Returns 23 2.1 Introduction 23 2.2 Data and Summary Statistics 26 2.3 Conditional Heteroskedasticity Tests 30 2.4 GARCH Models and the Choice of a Conditional Distribution 37 2.5 Estimation Procedures and Results 42 2.6 Diagnostic Checks 51 2.7 The Effects of Temporal Aggregation 54 2.8 Conclusions 65 Appendix 2.A : Aggregation Results 66 An Intertemporal Three-Moment Capital Asset Pricing Model 69 3.1 Introduction 69 3.2 The Linearization of a Non-Linear Budget Constraint 72 3.3 The Utility and Optimal Behavior Framework 76 3.4 The Elimination of Consumption 85 3.5 Empirical Implementation 97 3.6 Conclusions 98 Appendix 3.A : The Derivation of the MRS 100 Appendix 3.B : The Linearization of the Euler Equations 103 Appendix 3.C : The Conditional Variance of Consumption Growth as a Linear Function of the Conditional Variance of the Market Return 104 Appendix 3.D : Revisions in the Expected Future Values of an ARMA Process 108 4 Asymmetry In Stock Returns : a New Approach ill 4.1 Introduction Ill 4.2 Data and GARCH-in-mean Results 117 4.3 The Model and its Assumptions 122 4.4 Calibration Results 125 4.5 Conditional Third Moment Specification 128 4.6 Estimation 130 4.7 Empirical Results 132 4.8 Conclusions 137 5 Stochastic Trends and Jumps In EMS ^ ^/ Exchange Rates 139 5.1 Introduction 139 3 5.2 Random Walks or Mean Reversion 142 5.3 Modelling EMS Exchange Rates 152 5.3.1 The Lognormal Diffusion Process 153 5.3.2 The Mixed Jump-Diffusion Process 153 5.3.3 The Diffusion-(G)ARCH Process 154 5.3.4 The Jump-Diffusion-(G)ARCH Process 155 5.3.5 The Jump-Diffusion-(G)ARCH-t Process 156 5.4 Empirical Results 157 5.5 Conclusions 168 Appendix 5.A : Unit Root Tests 170 i- 6 EMS Exchange Rate Expectations and Time- Varying Risk Premia 175 6.1 Introduction 175 6.2 A Brief Review of Theory 177 6.3 The Survey Data and their Summary Statistics 180 6.4 Time-Varying Exchange Risk Premia 186 6.5 Modelling Time-Varying Risk Premia 190 6.6 Empirical Results 193 6.7 Conclusions 204 . -i. ".'-.; i ,'. •/. • ". • .V-- •-.:•• • ' .)!.-• 7 Summary and Discussion 207 7.1 Summary and Discussion 207 213 (Sw/n/Tiary w Du/c/ij 227 231 • : <^ f/. • ' "! ) -i ÏH List of Tables Table " ,,. „ ,q ti-..:,... .- ., .>,, ;; : ,.;.. ,• -.• , ; Page •ft 2.1 Summary Statistics Weekly Returns 28 2.2 Summary Statistics Monthly Returns 29 2.3.a ARCH Tests for Weekly Returns 36 2.3.b ARCH Tests for Monthly Returns 36 2.4 GARCH(l.l) Normal Estimates, Weekly Returns 45 2.5 GARCH(l.l) Normal Estimates, Monthly Returns 46 2.6 GARCH(1,1) Student-t Estimates, Weekly Returns ...... 47 2.7 GARCH(1,1) Student-t Estimates, Monthly Returns . .': . 48 2.8 GARCH(1,1) GED Estimates, Weekly Returns 49 2.9 GARCH(1,1) GED Estimates, Monthly Returns 50 2.10 Modified Likelihood Ratio Tests 52 2.11.a Kurtosis Values for Standardized Weekly Residuals 53 2.11.b Kurtosis Values for Standardized Monthly Residuals 53 2.12 Direct Monthly Estimates Compared to Implied Estimates . 55 2.13 Optimal Choice of m, through Monte Carlo Simulations ... 59 2.14 Tail Index Estimates for Weekly Raw Stock Returns 61 2.15 Tail Index Estimates for Weekly Rescaled Innovations .... 62 2.16 Tail Index Estimates for Monthly Rescaled Innovations .... 62 2.17 Tests for Equality of Tail Index Estimates 64 4.1 GARCH(1,1)-M Normal Estimates, Weekly Returns .... 120 4.2 GARCH(1,1)-M Student-t Estimates Weekly Returns .... 121 4.3 Normal Implied Values for Three-Moment CAPM 127 4.4 Student-t Implied Values for Three-Moment CAPM 127 4.5 Parameter Estimates for GARCS Process 129 4.6 GMM Estimates for Three Moment CAPM 134 4.7 Correlations between Variance and Third Moment 135 4.8 Combined Parameters of Three Moment CAPM 136 5.1 Summary Statistics of Weekly Log Price Changes 144 5.2 Conditional Heteroskedasticity Tests 148 5.3.a Tests for Unit Roots in Log Exchange Rates 150 5.3.b Tests for Unit Roots in Parity Adjusted Rates 151 5.4 Diffusion Model Estimates 158 5.5 Diffusion-ARCH Model Estimates 159 5.6 Diffusion-GARCH Model Estimates 160 5.7 Jump-Diffusion Model Estimates 161 5.8 Jump-Diffusion-ARCH Model Estimates 162 5.9 Jump-Diffusion-GARCH Model Estimates 162 5.10 Generalized Likelihood Ratio Tests 164 5.11 Jump-Diffusion-GARCH-t Model Estimates 166 5.12 Diagnostics 167 6.1.a Summary Statistics of Expected Depreciation 183 6.1.b Summary Statistics of Forward Discount 184 6.1.c Summary Statistics of the Risk Premium 185 6.2 Test of Perfect Substitutability 188 6.3 Conditional Heteroskedasticity Tests 189 6.4 ARCH-in-mean Model Estimates 194 6.5 GARCH-in-mean Model Estimates 195 6.6 Generalized Likelihood Ratio Tests 201 6.7 Diagnostics for ARCH-in-mean Model 202 6.8 Diagnostics for GARCH-in-mean Model 203 List of Figures Figure 5.1 French Franc/Deutschmark Exchange Rate 146 5.2 Weekly Returns FF/DM Exchange Rate 146 5.3 Italian Lira/Deutschmark Exchange Rate 147 5.4 Weekly Returns IL/DM Exchange Rate 147 6.1.a Actual Premium and Estimated ARCH Premium DG/DM .
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