Econometric Analysis of Financial Markets PDF
Preview Econometric Analysis of Financial Markets
Studies in Empirical Economics Aman Ullah (Ed.) Semiparametric and Nonpanmetric Econometrics 1989. VII, 172 pp. Hard cover DM 120, ISBN 3-7908-0418-5 Walter Kramer (Ed.) Econometrics of StructnnI Change 1989. X, 128 pp. Hard cover DM 85, ISBN 3-7908-0432-0 Wolfgang Franz (Ed.) Hysteresis Effects in Economic Models 1990. VIII, 121 pp. Hard cover DM 90, ISBN 3-7908-0482-7 John Piggott and John Whalley (Eds.) AppUed General Equilibrium 1991. VI, 153 pp. Hard cover DM 98, ISBN 3-7908-0530-0 Baldev Raj and Badi H. Baltagi (Eds.) Panel Data Analysis 1992. VIII, 220 pp. Hard cover DM 128, ISBN 3-7908-0593-9 Josef Christl The Unemployment I Vacancy Curve 1992. XVI, 152 pp. Hard cover DM 98, ISBN 3-7908-0625-0 Jiirgen Kaehler Peter Kugler (Eds.) Econometric Analysis of Financial Markets With 37 Figures Physica-Verlag A Springer-Verlag Company Editorial Board Wolfgang Franz, University of Konstanz, FRG Baldev Raj, Wilfrid Laurier University, Waterloo, Canada Andreas Worgotter, Institute for Advanced Studies, Vienna, Austria Editors Dipl.-Vw. Jiirgen Kaehler Z.E.W. Centre for European Economic Research Kaiserring 14-16 D-68161 Mannheim, Germany Professor Dr. Peter Kugler Institute of Economics University of Vienna Hohenstaufengasse 9 A-lOlO Vienna, Austria ISBN-13: 978-3-642-48668-5 e-ISBN-13: 978-3-642-48666-1 DOl: 10.1007/978-3-642-48666-1 CIP-Titelaufnahme der Deutschen Bibliothek Econometric analysis of financial markets / Jiirgen Kaehler; Peter Kugler (eds.). - Heidelberg: Physica-Verl., 1994 (Studies in empirical economics) ISBN-13: 978-3-642-48668-5 NE: Kaehler, Jiirgen [Hrsg.) This work is subject to copyright. All rights are reserved, whether the whole or part ofthe material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broad casting, reproduction on microfilms or in other ways, and storage in data banks. Duplication oft his publication or parts thereofis only permitted under the provisions ofthe German Copyright Law of September 9, 1965, in its version ofJune 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Physica-Verlag Heidelberg 1994 Softcover reprint of the hardcover 1s t edition 1994 The use ofr egistered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulati ons and therefore free for general use. 8817130-543210 -Printed on acid-free paper Preface This volume evolved from a conference on "Financial Markets Economet rics" held at the ZEW (Zentrum fiir Europaische Wirtschaftsforschung) in Mannheim, Germany in February, 1992. However, not all papers included in this volume were presented at the conference. In some cases the papers are follow-up papers to the ones presented. The purpose of the conference was to bring together researchers from several European countries to discuss their applications of recent economet ric methods to the analysis of financial markets. From a methodological point of view the main emphasis of the conference papers was on cointe gration analysis and ARCH modelling. In . cointegration analysis the links between long-run components of time series are studied and the methods can .be applied to the determination of equilibrium relationships between the vari ables, whereas ARCH models (ARCH is the acronym of autoregressive condi tional heteroskedasticity) are concerned with the measurement and analysis of changing variances in time series. These two models have been the most significant innovations' for the empirical analysis of financial time series in recent years. Six papers of this volume apply cointegration analysis (the papers by MacDonald/Marsh, Hansen, Ronning, Garbers, Kirchgassner/Wolters, and Kunst/Polasek) and seven papers deal with ARCH models (Kramer/Runde, Drost, Kunst/Polasek, Kugler, Eggington/Hall, Koedijk/Stork/deVries, and Demos/Sentana/Shah). Other econometric methods and models applied in the papers include factor analysis (Eggington/Hall and Demos/Sentana/ Shah), vector autoregressions (Kirchgassner/Wolters and Kunst/Polasek), Markov-switching models (Garbers and Kaehler /Marnet), spectral analysis (Kirchgassner/Wolters), stable Paretian distributions (Kramer/Runde and Drost) and ARFIMA models (Drost). The papers cover a wide range of issues and theories in financial and in ternational economics. Three papers are concerned with the term structure of interest rates (Kunst/Polasek, Kugler, and Eggington/Hall) and the papers by Kirchgiissner /Wolters and Garbers deal with international interest-rate linkages and interest rate parity. There are three papers on exchange-rate issues: McDonald/Marsh on purchasing power parity, Hansen on the mone tary approach to exchange-rate determination, and Koedijk/Stork/deVries on target-zone dynamics. The stock-market applications include issues of test ing for efficiency (Kramer/Runde), and of using the CAPM (Ronning) and the APT (Demos/Sentana/Shah). Analysis of derivative instruments is con tained in the paper of Kaehler/Marnet who study option price effects under stochastic volatility. Finally, the more technical paper by Drost examines the question for several time-series models of whether models which are applied VI Preface to high-frequency (e.g.) daily data can also consistently be extended to low frequency (e.g. monthly) data. It is, therefore, of fundamental importance for many applications in empirical finance. Participants of the ZEW conference were not only academics but also quantitative researchers from financial institutions. Financial economics is probably that area in economics where the flow of methods and models from the academic world to the business world is strongest and quickest. The wide spread adoption of the CAPM, the APT, and the Black-Scholes option-pricing approach is evidence of this. There is always a great interest of bankers, in vestment managers and financial analysts in new developments in theoretical and empirical finance. Therefore, this volume should not only appeal to academics and students working in the fields of finance and international eco nomics but also to professionals from financial institutions who are involved in quantitative research or quantitative orientated investment management. All papers of this volume went through an anonymous referee process prior to publication. We would like to thank all referees for the time and effort they spent on reviewing the papers. We are also grateful to Julie Kaehler, who read all papers, for her editorial assistance as a native speaker. The word processing in T£X was done at the ZEW and was competently performed by Volker Jankowski, Ingo Fink, Karin Oppolzer and Angelika Neufert. Finally, we wish to thank Wolfgang Franz for his support of this project and Werner A. Miiller and Gabriele Keidel of Physica-Verlag for their pleasant coopera tion. J. Kaehler, ZEW and Universitiit Mannheim P. Kugler, Universitiit Bern Contents Some Pitfalls in Using Empirical Autocorrelations to Test for Zero Correlation among Common Stock Returns W. Kramer and R. Runde ............................................... 1 Temporal Aggregation of Time-Series F.C. Drost .............................................................. 11 On Long- and Short-Run Purchasing Power Parity R. MacDonald and I. W. Marsh .......................................... 23 Cointegration and the Monetary Model of the Exchange Rate G. Hansen.............................................................. 47 Does Cointegration Matter in the Empirical Analysis of the CAPM? G. Ronning ............................................................. 65 Constructing an Empirical Model for Swiss Franc Exchange Rates and Interest Rate Differentials H. Garbers ............................................................. 79 Frequency Domain Analysis of Euromarket Interest Rates G. Kirchgassner and J. Wolters ......................................... 89 Structuring Volatile Swiss Interest Rates: Some Evidence on the Present Value Model and a VAR-VARCH Approach R. M. Kunst and W. Polasek............................................ 105 The Expectation Hypothesis and Interest Rate Volatility on the Euromarket: Some Empirical Results P. Kugler ............................................................... 129 An Investigation of the Effect of Funding on the Slope of the Yield Curve D.M. Egginton and S.G. Hall ........................................... 139 Stylized Facts, Realignments and Investment Strategies in the EMS K.G. Koedijk, P.A. Stork and C.G. de Vries............................. 163 Risk and Return in January: Some UK Evidence A. Demos, E. Sent ana and M. Shah ..................................... 185 Markov-Switching Models for Exchange-Rate Dynamics and the Pricing of Foreign-Currency Options J. Kaehler and V. Marnet ............................................... 203 Some Pitfalls in Using Empirical Autocorrelations to Test for Zero Correlation among Common Stock Returnsl By Walter Kramer and Ralf Runde2 Abstract: We consider the null distribution of empirical autocorrelation coefficients of sta tionary time series under nonstandard circumstances. We show that this null distribution is not robust to ARCH-effects and to non-existing variances, both of which are typical for common stock returns. These results are then applied to several stocks traded on the Frankfurt stock exchange, with the result that the "significance" of empirical autocorrela tions is in general reduced. 1 Introduction We consider empirical autocorrelation coefficients of stationary univariate time-series {Xdt=l, ... ,n' In our empirical applications, Xt is the continuously compounded daily return of a common stock, i.e. X In ' (S~~J (1) t := where St denotes the daily closing price, and stocks are taken from the Frank furt stock exchange. A fundamental assumption respectively requirement in various branches of modern capital market theory is that successive asset returns are indepen dent or at least uncorrelated, as motivated and discussed in e.g. Taylor (1986, p. 9) or Akgiray (1989, pp. 61 ff). A wide-spread rough and ready method to check for this is to compute the empirical first order autocorrelation coefficient r = -E~-=~2(~X-t- --X-~)(~X~t--1- ---X~) (2) E~=l(Xt - X)2 lWe are grateful to "Deutsche Finanzdatenbank" (DFDB), in particular to Torsten Liideke, for the data used in this report, to an unknown referee for helpful insights and comments, to Victor Ng for providing us with his EZARCH software for the estimation of ARCH-models, and to "Deutsche Forschungsgemeinschaft" (DFG) for additional support. 2Walter Kramer and Ralf Runde, Department of Statistics, University of Dortmund, Vogelpothsweg 87, 44227 Dortmund, Germany. 2 W. Kramer and R. Runde 11'1 and to reject the null hypothesis of zero autocorrelation when becomes too large. The problem with this rule is to correctly determine what is meant by "too large". For instance, for VW stocks we found a first order empirical autocorrelation coefficient, based on n = 3014 daily returns, of l' = 0.057. Is this or is this not sufficient to reject the null hypothesis of zero population correlation? The standard argument assumes independence and finite higher mo ments of returns, so that we have vn1' ~ N(O, 1), (3) and we reject Ho (say at a 1% significance level) whenever Ivn1'l > 2.57. In the VW example, this yields 54.9 r = 3.10, so VW returns are judged serially correlated at 1% significance. The present paper challenges this view, using two quite unrelated argu ments. The first is the obvious one that zero autocorrelation is less restrictive than serial independence, so rejection of the latter does not imply rejection of the former. This is particularly important in the context of stock returns, where large values tend to cluster, in contradiction of the independence as sumption, but where returns can still be uncorrelated. We elaborate this point in the context of an ARCH-structure in the returns, where the limiting relationship (3) no longer holds. Our'second objection is based on infinite variance returns, which likewise lead to a violation of the limiting relation ship in equation (3), and which lead to a decidedly non-normal limit law 1'. for Again, this point is particularly important for stock returns, which in the wake of Mandelbrot (1963) and Fama (1965) are often assumed to follow stable distributions with infinite variance. More formally, our problem can be phrased like this: How robust is the limit law in (~) to deviations from the standard assumptions of i.i.d. returns with finite higher moments, under which it is usually derived? Can it also be used to test a less restrictive null hypothesis, or do we then need a different decision rule? For simplicity, we confine our explicit treatment of this question to the 1'. first order empirical autocorrelation coefficient Extensions to higher order empirical autocorrelation coefficients are obvious. Less obvious are extensions to various summary statistics like the Box-Pierce Q, which we reserve for future work. Our discussion of the consequences of ARCH-type serial dependence draws heavily on Heyde (1981) and Milhoj (1985). The mathematics behind the infinite-variance case are taken from Davis and Resnick (1986), and a preliminary discussion of the present problem is also available in Kramer and Runde (1990, 1991). Some Pitfalls in Using Empirical Autocorrelations 3 2 Empirical Autocorrelation in the Context of ARCH Effects To better understand the behaviour of the autocorrelation coefficient T' in nonstandard situations, it helps to first consider its limiting distribution in the standard case of i.i.d.(/1, (7"2) returns with finite higher moments. To that purpose, define Xt := Xt - /1 and Zt = XtXt-I and note that (4) In In so the limits in distribution of ~ (Xt - X)(Xt_I - X) and ~ Zt are identical. However, since {Zd is a martingale difference sequence with (5) we deduce from well-known Martingale Central Limit theorems (see e.g. Brown, 1971) that ..1;n ~~ Zt ---d- -t N ( 0, (7" 4) . (6) On the other hand, we have from the law of large numbers that (7) which in conjunction with (4) and (6) produces the well known result c = -Tn L:;=2(Xt - X)(Xt- I - X) ~ ~N(O (7"4) = N(O 1). (8) V n T' ~ ",n (X _ X)2 (7"2' , n L....t=l t Now assume that Xt follows at stationary ARCH(p)-process, i.e. that Xt can be written as (9) where the Ct are i.i.d.(O, 1), 'Pi ~ 0 (i = 1, ... ,p) and ~'Pi < 1. From E(ZtIXt-I, Ct-I, Xt-2, Ct-2, ... ) + + ... + /(7"2 'PI (XL - (7"2) 'Pp(Xt-p - (7"2) .Xt-IE(ctIXt-I,Ct-I" .) 0, (10)
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