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Intradaily Exchange Rate Movements PDF

172 Pages·2000·4.802 MB·English
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INTRADAILY EXCHANGE RATE MOVEMENTS Intradaily Exchange Rate Movements by Dominique M. Guillaume Catholic University ofL ouvain, Belgium and Oxford University, United Kingdom SPRINGER SCIENCE+BUSINESS MEDIA, B.V. A c.I.P. Catalogue record for this book is available from the Library of Congress. ISBN 978-1-4613-7089-5 ISBN 978-1-4615-4621-4 (eBook) DOI 10.1007/978-1-4615-4621-4 Printed on acid-free paper All Rights Reserved © 2000 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 2000 Softcover reprint of the hardcover 1s t edition 2000 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. Contents Preface ix Acknowledgements and Copyrights xv 1 A Typology of Foreign Exchange Rates Models 1 1.1 Models with fixed point .... 5 1.2 Models with multiple equilibria 8 1.3 Models with chaotic attractors 11 1.4 Models with multiple attractors . 12 1.5 Models with no attractor .. . . 12 1.6 Models with no attractor but some structure 13 2 From the Bird's Eye to the Microscope: A Survey of New Stylised Facts 15 2.1 Introduction .................. . 15 2.2 Description of the Foreign Exchange Market . 17 2.3 Definition of the Variables of Interest . 21 2.3.1 Definition 1: the price ..... 22 2.3.2 Definition 2: the change of price 24 2.3.3 Definition 3: the volatility . . . . 24 2.3.4 Definition 4: the relative spread. 25 2.3.5 Definition 5: the tick frequency . 26 2.3.6 Definition 6: the volatility ratio . 27 2.3.7 Definition 7: the directional change frequency . 28 2.4 Stylised facts . . . .. . ....... . . . ... . . 29 v VI CONTENTS 2.4.1 Distribution . . . . . . . 29 2.4.2 Price formation process 33 2.4.3 Heterogeneous Structure . 36 2.5 Conclusion 50 2.6 Appendix . 55 2.6.1 Appendix 1 55 2.6.2 Appendix 2 57 3 Chaos in the Foreign Exchange Markets 59 3.1 Methodology . . . . . . . . . . . . . . . . . . . .6 1 . . 3.1.1 Reconstruction of the embedding phase space 61 3.1.2 Computation of the fractal dimension . . . . 66 3.1.3 Detection of chaos: a summary of the steps . 67 3.2 Results... . 69 3.2.1 Data . 69 3.2.2 Results 70 3.3 Conclusion . . 76 4 Sources of Nonlinearities in the Foreign Exchange Markets 81 4.1 Introduction. 81 4.2 Methodology 82 4.2.1 Time scale transformations 82 4.2.2 Tests . 85 4.3 Results . . . . 86 4.3.1 The correlogram study . 87 4.3.2 The BDS-test results . 90 4.4 Conclusion ... . . . ... . 93 5 On the Intradaily Performance of G ARCH Processes 95 5.1 Introduction . ... . .. 95 5.2 Description of the data. 97 5.3 Alternative time scales 99 5.4 Results. . .. . .... . 103 CONTENTS vii 5.4.1 Impact of the seasonal heterogeneity . · 106 5.4.2 Impact of the temporal heterogeneity .107 5.4.3 Stability across the sample period .109 5.5 Conclusion · 110 5.6 Appendix . . 113 6 Do Technical Trading Rules Generate Profits? 117 6.1 Introduction.... .. . . 117 6.2 Data and methodology. . 119 6.2.1 Data..... . . . 119 6.2.2 The basic trading rule . 121 6.2.3 Accounting for transaction costs . 124 6.3 Results. . ........ . ...... . . . 125 6.3.1 Brief summary ofresults from sample (a) . 130 6.3.2 Results from sample (b) . 133 6.4 Conclusion · 138 Bibliography 141 Index 161 Preface In recent years, a broad consensus has emerged among economists that the different vintages of macro-economic models have largely failed to account for the foreign exchange rates movements in the short to medium run, that is, from daily up to quarterly or even yearly frequen cies (see e.g. Frankel and Rose (1995) for a recent survey). Only in the very long run do these models appear to have a predictive power superior to a random-walk, which is the simplest benchmark one could consider (Mark, 1995). Therefore, rather than to try linking foreign exchange rates with fundamentals, another route pursued by researchers was to question the rational expectation hypothesis assumed in these models. Using sur veys amongst traders, they brought to light the heterogeneity of their expectations (e.g., Takagi, 1991). More important even, it seems that traders have different expectations depending on the time horizon at which they are looking. In the short run, expectations tend to be desta bilising whereas in the long run they are regressive towards a long run fundamental equilibrium. This is quite understandable as it also ap peared that traders' preferred category of models in the short run is technical analysis, a broad class of techniques that extrapolate the in formation contained in past prices (Frankel and Froot, 1990; Allen and Taylor, 1992). The use of technical analysis as a systematic explana tion of the behaviour of exchange rates movements is, however, still a matter of debate because it would imply the existence of unexploited arbitrage opportunities. On the other hand, it has gained some acad emic acceptability since it was rationalised in theoretical models combin ing fundamentals and extrapolative expectations (De Long et al., 1990; De Grauwe and Dewachter, 1993). Some simulation studies have also demonstrated the potential profitability of technical analysis (Levich and Thomas, 1992). Another route followed by researchers was to investigate the statis tical process of foreign exchange rate returns. Indeed, foreign exchange IX x rate returns do not have to be identically and independently distrib uted as in a random walk to follow a martingale process. Dependencies could come through the second moment or even higher moments with out implying predictability of the mean. As a matter of fact, already in the 60s, Mandelbrot (1963) had shown that periods of quiescence tend to be followed by periods of quiescence rather than periods of turbu lence and vice-versa. This clustering of the volatility process was first made endogenous in the Auto-Regressive Conditional Heteroskedastic process (ARCH) by Engle (1982) and its generalised version by Boller slev (1986). The ARCH model has now expanded into a whole family of models (Bollerslev et al., 1992) as further properties of the volatil ity process, such as its long run memory, were unveiled. Though, an economic explanation for the clustering of volatility is yet to be given. Debate also arose on whether the statistical process underlying the distribution of foreign exchange rates returns was more akin to, for in stance, the ARCH process, a Student-Tor a Cauchy distribution. These developments are especially important if one considers foreign exchange rate returns from a portfolio optimisation perspective where the first two moments are the central parameters of interest, the mean representing the average return and the variance the risk involved. The next natural step to broaden the understanding of foreign ex change markets was to look at intradaily foreign exchange movements since more than 70% of the 1.4 billion USD average foreign exchange daily trading volume takes place between traders who close their posi tion at the end of the day (B.I.S., 1993). However, it was not before the very end of the eighties that research on the intradaily exchange rates was begun, mainly due to technical obstacles. These obstacles are quite formidable and range from the actual purchase of the data from data vendors such as Reuters and their massive storage on computers, to the transformation and filtering of the data into clean time series that can be used. Fortunately, very much at the same time as Goodhart (1989) published the first paper using a series of two weeks of intradaily foreign exchange rates, Olsen & Associates, a Swiss private research institute, Xl had made the necessary technological, human, and indeed capital invest ment required for a more systematic collection of this data. When the work contained in this book was started in 1993, it benefited from the enormous generosity of Olsen & Associates who shared their data which by then covered a period of seven years, that is, a couple of millions of data points. An extensive study of this data set has resulted in the dif ferent chapters of this book, some of which were written in collaboration with the Olsen & Associates research team. The research covered in this book has two main purposes: the sys tematic study of the characteristics of intradaily data and an empirical investigation using intradaily data of the three approaches to the mod elling of foreign exchange rates outlined above. In an introductory chapter, a more systematic attempt to classify the successive waves of foreign exchange rate models is proposed using a typology based on the type of asymptotic equilibria. The first objective of the book is then addressed to in the second chapter which surveys the main stylised facts on the intradaily foreign exchange rates . These facts provide a partial answer to some of the questions raised above. For example, thanks to the extremely large number of data available a study of the tails of the distribution could help categorise the distribution of exchange rates returns without falling into the non-negligible small sample bias usually associated with such studies. The nature of the volatility clustering captured by the Auto Regressive Conditional Heteroskedastic family of models could partly be understood in terms of the interaction between different markets. The relevance of macro-economic modelling could be tested in a nonlinear dynamic framework which does not imply predictability per se. And, the very short-lived impact of macro-economic news announcements could be verified. The analysis of this extremely large data set of intradaily foreign ex change rates has also uncovered new regularities of the foreign exchange rates. For example, parameters could not be disaggregated from daily frequency estimates into intradaily estimates as predicted theoretically Xli for a homogenous GARCH process, a hint at the presence of a different expectation process at the intradaily frequency than, say, at the daily or even monthly frequencies. On the other hand, intradaily data revealed the existence of a fractal law that links the average absolute foreign exchange price changes measured at different frequencies to these fre quencies in a very different way from the Gaussian, Student-T, Cauchy or GARCH distributions. The seemingly random large changes of the persistence parameters of the volatility in the Auto- Regressive Condi tional Heteroskedastic model over relatively long periods is consistent with important structural breaks which are yet to be explained in terms of changes of the underlying fundamentals, institutions, policy decision rules or contagion effects. Another important issue is the price formation process that takes place every other couple of seconds or minutes, also termed 'market microstructure' as first coined by Garman (1976). Whereas there is a huge theoretical and empirical literature on the topic for stock markets (see, for example, (O'Haara, 1995), progress in the understanding of the price formation process of the foreign exchange markets has been limited partly due to institutional differences from stock markets and partly due to data limitations. For instance, foreign exchange markets differ from most of stock exchange markets in that they are decentralised rather than centralised markets which prevents the easy transposition of stock markets models. Another difference from stock markets is that foreign exchange markets are virtually continuously open around the world. As a consequence, whereas stock market micro- structure explanations for the widening of the bid-ask spread at the end of the trading day may be valid for one particular market, say Europe, they cannot account at the same time for the absence of widening of this bid-ask spread in another simultaneously opened market, say New York (see, for example, Hsieh and Kleidon, 1996). In common with most other studies, our data set has important shortcomings for tests of microstructure hypotheses in that it is consti tuted of indicative quotes rather than transaction prices (which overes-

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