advanced trading rules - acar 2002

Computer simulation of dynamicstrategies using real data from foreign exchange, emerging and futuresmarkets, will show that substantial risk-adjusted pro®ts can be achieved.However, as w

ADVANCED TRADING RULES

Butterworth-Heinemann Finance

aims andobjectives books based on the work of ®nancial market practitioners, and academics presenting cutting edge research to the professional/practitioner market

combining intellectual rigour and practical application

covering the interaction between mathematical theory and ®nancial practice to improve portfolio performance, risk management and trading book performance covering quantitative techniques

marketBrokers/Traders; Actuaries; Consultants; Asset Managers; Fund Managers; Regula-tors; Central Bankers; Treasury Ocials; Technical Analysts; and Academics forMasters in Finance and MBA market

series titlesReturn Distributions in Finance

Derivative Instruments: theory, valuation, analysis

Managing Downside Risk in Financial Markets: theory, practice and implementationEconomics for Financial Markets

Global Tactical Asset Allocation: theory and practice

Performance Measurement in Finance: ®rms, funds and managers

Real R&D Options

Forecasting Volatility in the Financial Markets

Advanced Trading Rules

Series editor

Dr Stephen Satchell

Dr Satchell is Reader in Financial Econometrics at Trinity College, Cambridge;Visiting Professor at Birkbeck College, City University Business School and Uni-versity of Technology, Sydney He also works in a consultative capacity to many ®rms,and edits the journal Derivatives: use, trading and regulations

ADVANCED TRADING RULES

Trinity College, Cambridge, and Faculty of Economics,

University of Cambridge, Cambridge

An imprint of Elsevier Science

Linacre House, Jordan Hill, Oxford OX2 8DP

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First published 1998

Reprinted 1998

Second edition 2002

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British Library Cataloguing in Publication Data

Advanced trading rules ± 2nd ed ± (Quantitative ®nance series)

1 International ®nance 2 Securities 3 Exchange 4 Futures

I Acar, E (Emmanuel) II Satchell, Stephen E

3320.042

Library of Congress Cataloguing in Publication Data

A catalogue record for this book is available from the Library of Congress

ISBN 0 7506 5516X

For information on all Butterworth-Heinemann publications visit

our website at www.bh.com

Data manipulation by David Gregson Associates, Beccles, Su€olk

Printed and bound in Great Britain by Biddles Ltd., Guildford and King's Lynn

2 Foundations of technical analysis: computational algorithms,

AndrewW Lo, Harry Mamaysky and Jiang Wang

6 The portfolio distribution of directional strategies 174Emmanuel Acar and Stephen Satchell

6.3 Exact distribution under the normal random walk

8 The economic value of leading edge techniques for exchange rate

Christian L Dunis

8.2 Basic concepts, data processing and modelling procedure 250

9.2 De®ning ®lter rules and head-and-shoulders patterns 265

9.4 Empirical pro®tability of the technical trading rules in FX

9.5 The incremental pro®tability of the head-and-shoulders

10 Informative spillovers in the currency markets: a practical approach

Pierre Lequeux

12 Evolving technical trading rules for S&P 500 futures 345Risto Karjalainen

13 Commodity trading advisors and their role in managed futures 367Derek Edmonds

David Obert and Edouard Petitdidier

14.6 Performance futures fund and BAREP commodities futures

viii Contents

It has been over 4500 years since the Egyptians coined the ®rst metal moneyand foreign exchange dealing can be traced down to ancient middle easterntowns It is not dicult to imagine ancient traders spending their dayexchanging coins from one caravan to another, and after a long day ofwork, traders sitting down on the dusty streets of their middle eastern townwondering about the mysterious forces that move markets

As exchanges grew over the centuries, so did the power of these forces,sometimes to the detriment of established ruling structures Inevitably, overthe centuries, many governments felt threatened by the freedom of markets.Their e€orts to control or even suppress them, from the extreme case ofcommunism to more subtle attempts such as price/salary or foreign exchangecontrols, all ended in costly failures and sometimes catastrophic changes ofpolitical systems

Some businessmen have tried to harness market forces and becomeimmensely rich in the process They tried to corner markets by poolinglarge resources and using them to manipulate prices They all failed and theirattempts always ended in pain and sorrow As markets continued to prosperthey attracted the attention of academics who made the ®rst serious e€orts tounderstand their working They ®rst recognized that the ¯ow of informationwas vital to any form of exchange Indeed it is not by chance that theinformation age has brought an explosion of trading volumes In their earlyattempts they ± very logically ± theorized that if and when information ¯owsfreely and is equally shared, markets develop into a `random walk'; a mostdiscouraging prospect to any trader

Although the random walk explanation dominated the theoretical ®eld,seasoned practitioners never believed this conclusion They always felt thatwhat the theory had failed to comprehend was that information did not movemarkets on its own They knew by experience that it was rather the humaninterpretation of facts that did As a result, they believed in mass and human

psychology As they were too busy trying, and succeeding to make money,despite the random walk threat, they never really tried to build theirexperience into a workable theory of markets.

In recent years however, more open minded academics and practitionershave joined forces and created the nascent ®eld of Computer Aided SystemTrading (I propose to call it CAST) Supported by advanced risk manage-ment techniques, new mathematical theories, and the power of moderncomputers, CAST is developing fast This is a time of invention and progress;

in other words, a remarkable time to get involved in a ®eld that couldrepresent the biggest advance in market studies since the Egyptians

Stochastic properties of trading rules such as neural networks, geneticalgorithms, Markowitz curves will become indispensable tools Very soon anyserious investor will have to be familiar with these concepts or be left out ofthe rapidly progressing ®eld of investment management

This remarkable book has been written by the new breed of traders, wellseasoned in some of the most active dealing rooms and with the best ®nancialdegrees It certainly ®lls a gap in the ®nancial literature by giving the reader acomplete overview of this burgeoning ®eld as well as acquainting him with theresults of the most recent cutting edge research In publishing this book, thecontributors have taken a worthwhile initiative that will accelerate theprogress of CAST

The unanswered questions remain of course: Where will CAST lead? Willhumans lose interest in trading? Will computers take over completely and, inthe end, control markets in a way that humans never managed to do?

I personally believe that although, in the future, markets will become huge,move considerably faster and be more vibrant, they will ®rmly remain theexpression of human freedom that they always have been

They will not, therefore, be taken over by arti®cial intelligence and will be,

as they have always been, controlled by humans The fact remains, however,that there is a limit to human intellect and speed of thought and one mightwonder how future traders will cope successfully with the explosion ofinformation and action surrounding them

It is clear that in order to survive, the descendants of ancient middle eastcaravan peddlers will have to harness the power of huge computers and useCAST with great expertise And after a long day of work, they might sit down

in a cyber cafe and talk about the early works on CAST and books such asthis one that paved the way to a better understanding of market forces

Robert AmzallagBanque Nationale de Paris

x Foreword

Emmanuel Acaris a Principal and Manager of Risk Management London, at Bank of America He previously worked at Citibank as a Vice-President in the FX Engineering Group He was a proprietary trader foralmost ten years at Dresdner Kleinwort Benson, BZW and Banque Nationale

Advisory-de Paris' London Branch He has experience in quantitative strategies, as anactuary and having done his PhD on the stochastic properties of tradingrules

Olivier De Bandt is a senior economist in the Research Department of theBank of France He graduated from the University of Paris and the Institutd'Etudes Politiques (Paris) He holds a PhD in Economics from theUniversity of Chicago

Professor BernardBensaidis a consultant of the Research Department of theBank of France He graduated from the Ecole Polytechnique and earned aPhD in Economics from the University of Paris He teaches at the University

of Paris and Lille

P H Kevin Changis currently Vice-President at Credit Suisse First Boston,London Since March 2001, he has been an Equity Derivatives Strategist,specializing in volatility strategies for indices and single stocks He waspreviously Vice-President and Senior Strategist in Global Foreign Exchange,focusing on portfolio and derivative strategies as well as technical tradingrules Before joining CSFB in 1998, he was on the ®nance faculty at the SternSchool of Business (New York University), Wharton School (University ofPennsylvania), and Marshall School of Business (University of SouthernCalifornia), teaching international ®nance His published academic researchfocused on the information content in foreign exchange options, macro-economic implications of FX option pricing, and technical trading rules in

foreign exchange He holds a PhD in Economics from MIT, and a Bachelor's

in Economics from Harvard

Christian L Dunisis Girobank Professor of Banking & Finance at LiverpoolBusiness School where he also heads the Centre for International Banking,Economics and Finance (CIBEF) He is also a consultant to asset manage-ment ®rms and a Senior Managing Consultant with Infacts Before this,Christian Dunis was Global Head of Markets Research at Banque Nationale

de Paris which he joined from Chase Manhattan Bank in 1996 At BNP, hemanaged the Markets Research Group, a 23-strong team covering ForeignExchange and Fixed Income strategies, developing its technical capabilitiesand determining the overall architecture of BNP's quantitative models AtChase Manhattan, where he stayed for 11 years, he headed the QuantitativeResearch & Trading group, a quantitative proprietary trading group usingstate of the art modelling techniques to trade a portfolio of spot currencies,stock indices and Government bond futures contracts

Derek Edmondsgraduated from Cornell University with a BA in Economicsand joined RefcoFund Holdings Corporation in 1990, where he was involved

in the development of the Refco Derivative Advisor Database Since 1994,Edmonds has been responsible for the management of all the derivativesproducts at RefcoFund Holdings Corporation His current functions includethe evaluation of trading advisors, the development of innovative statisticalanalyses in the advisor selection and allocation process, and the structuring ofunique products to meet the needs of clients

Felix Gasser is currently Assistant Vice-President at Credit Suisse PrivateBanking in Zurich, Switzerland Since October 1998, he co-writes the dailypublished newsletter on Forex and Commodities As Quantitative Analyst hespecializes in the development of systematic trading systems This includesperformance ratings of CTAs for the use of structured products He waspreviously Marketing Manager for Analytical Software at Dow Jones,supporting the Swiss client base in the development of computer-driventrading strategies Since the late 1980s he was involved in system-driventrading, having worked as a trader for some of the pioneers in the CTAbusiness, like E.D.&F Man's Fund Division, AHL or as a trader for some ofthe original Turtles He is a Chartered Market Analyst, has a Bachelor's inEconomics and studied Economics for 2 years at the University of Zurich.Risto Karjalainen is a ®xed income portfolio manager at Merrill LynchInvestment Managers in London He earned his PhD in Decision Sciencesfrom the Wharton School in the University of Pennsylvania in 1994 Prior tothat, he received an MSc in Systems and Operations Research in 1989 fromxii List of contributors

the Helsinki University of Technology, Finland Before joining MerrillLynch, he worked for a hedge fund, developing and trading quantitativemodels, and for JP Morgan Investment Management as an analyst Inaddition to evolutionary algorithms, his research interests include thevaluation of bond and currency markets.

George W Kuostudied and worked in Taiwan prior to coming to CambridgeUniversity to enrol in a Master of Philosophy in Finance He has completed aPhD in Finance, also at Cambridge George is now working as an academic

in Taiwan

Blake LeBaronhas a PhD in Economics from the University of Chicago He

is a Professor of Economics at the University of Wisconsin-Madison, aFaculty Research Fellow at the National Bureau of Economic Research, amember of the external faculty of the Santa Fe Institute, a Sloan fellow, and iscurrently visiting the Center for Biological and Computational Learning atMIT LeBaron served as a director of the Economics Program at the Santa FeInstitute in 1993 His research has concentrated on the issue of nonlinearbehaviour of ®nancial and macroeconomic time series He has been in¯uentialboth in the statistical detection of nonlinearities and in describing theirqualitative behaviour in many series LeBaron's current interests are inunderstanding the quantitative dynamics of interacting systems of adaptiveagents and how these systems replicate observed real-world phenomena.LeBaron is also interested in understanding some of the observed behaviouralcharacteristics of traders in ®nancial markets This behaviour includesstrategies such as technical analysis and portfolio optimization, along withpolicy questions such as foreign exchange intervention In general, he seeks to

®nd out empirical implications of learning and adaptation as applied to

®nance and macroeconomics

Pierre Lequeux joined the Global Fixed Income division of ABN AMROAsset Management London in June 1999 Being currently Head of CurrencyManagement, he has the responsibility for both Quantitative and Funda-mental Currency management processes He previously was Head of theQuantitative Research and Trading desk at Banque Nationale de Paris,London branch, which he joined in 1987 Pierre is also an AssociateResearcher at the Center for International Banking and Finance of LiverpoolBusiness school and a member of the editorial board of Derivative, UseTrading & Regulation

Andrew W Lois the Harris & Harris Group Professor of Finance at the MITSloan School of Management and the director of MIT's Laboratory forFinancial Engineering He received his PhD in Economics from Harvard

List of contributors xiii

University in 1984, and taught at the University of Pennsylvania's WhartonSchool as the W P Carey Assistant Professor of Finance from 1984 to 1987,and as the W P Carey Associate Professor of Finance from 1987 to 1988 Hisresearch interests include the empirical validation and implementation of

®nancial asset pricing models; the pricing of options and other derivativesecurities; ®nancial engineering and risk management; trading technology andmarket microstructure; statistics, econometrics, and stochastic processes;computer algorithms and numerical methods; ®nancial visualization; non-linear models of stock and bond returns; and, most recently, evolutionary andneurobiological models of individual risk preferences

Harry Mamayskyreceived his doctorate in Financial Economics from MIT in

2000 Since then he has been an Assistant Professor of Finance at the YaleSchool of Management His research ranges from trying to understand thefactors a€ecting stock and bond prices to an analysis of why the mutual fundindustry has such a broad range of products His work on mutual funds shedslight on how the structure of the mutual fund industry re¯ects investorpreferences Another recent project investigates the fundamental determi-nants of movements in stock and bond prices ± he has developed a statisticalmethodology to extract `pure' factors from asset prices so that he can studytheir underlying economics

Daan Matheussenis a Senior Consultant at ESR (CWA) where he specializes

in risk, ®nance and insurance-related quantitative analysis He has lived inBelgium and South Africa and studied Chemical Engineering at the Uni-versity of Cape Town

DavidObertis a co-founder of Systeia Capital Management He has been inthe investment business for 15 years As a Managing Director and ChiefInvestment Ocer, he directs asset management activities and developsinvestment strategies including: Futures funds, Statistical Arbitrage, EventDriven and Fixed-income arbitrage Previously, he was Managing Director ofBarep Asset Management, a wholly owned subsidiary of SG Group specializ-ing in alternative investment with Euro 6 Billion under management DavidObert created the Epsilon Futures Program (managed Futures Program) in1994

Professor John Okunevjoined BT Funds Management as Head of InvestmentProcess and Control in March 2001 from the University of New South Waleswhere he was Professor of Finance Prior to joining the University of NewSouth Wales, John was Manager of Investment Technology at Lend Leasewhere he was responsible for reviewing and developing new ®nancialproducts These products included equity trading strategies, in both domesticxiv List of contributors

and international markets He was also responsible for the implementationand maintenance of risk management systems The major focus of John'sresearch is the development of equity trading strategies in domestic andinternational markets.

Carol L Osler is a Senior Economist at the Federal Reserve Bank of NewYork She specializes in exchange rate dynamics and the role of ®nancialmarkets in the real economy After receiving a BA from Swarthmore Collegeand a PhD from Princeton University she taught at the Amos Tuck School ofBusiness Administration at Dartmouth College, the Kellogg School atNorthwestern University, and at Columbia University Her most recentwork examines the e€ects of currency orders on high-frequency exchangerate dynamics

Edouard Petitdidieris co-head of the Systematic and Statistical Hedge FundDepartment of Systeia Capital Management and is co-responsible for therunning of a Managed Futures Program (started in August 2001 with cˆ75million) and a Statistical European Pair Trading Fund (launched in Novem-ber 2001 withcˆ75 million) Systeia is a subsidiary of Credit Lyonnais based inParis, created in early 2001 with an initial commitment ofˆc250 million Hehas 9 years' experience in the trading and investment business and was, from

1994 to March 2001, co-head of the systematic hedge fund department atBarep Asset Management, which included the running of the EpsilonProgram (Managed Futures, up to $950 million under management) and aRelative Value Equity Hedge Fund

Stephen Satchellhas PhDs from the Universities of Cambridge and London

He is a fellow of Trinity College, Cambridge, and a Reader in FinancialEconometrics at Cambridge University His research interests include econo-metrics and ®nance and he has strong links with the City as an academicadvisor and as a consultant His current particular interests involve assetmanagement, pension and risk

Jiang Wangis the Nanyang Technological University Professor of Finance atthe MIT Sloan School of Management He received his PhD in Physics in

1985 and his PhD in Finance in 1990, from the University of Pennsylvania.His research is in the area of asset pricing, investments and risk management.Jiang Wang has served on the editorial board of several academic journalsincluding the Journal of Financial Markets, Operations Research, QuantitativeFinance, and the Reviewof Financial Studies He was the recipient of theTre€tz Award in 1990, the Batterymarch Fellowship in 1995 and theLeoMelamed Prize in 1997 Jiang Wang is also a research associate of theNational Bureau of Economic Research and a trustee of Nanjing University

List of contributors xv

Derek Whitejoined the University of New South Wales (UNSW) in August

1998 where he is currently the Director of the Masters of Commerce StudiesProgram in Finance While at UNSW, Derek has served in various consultingpositions within the funds management industry Prior to joining theUniversity, Derek completed his PhD at the University of Texas at Austinand worked in International Treasury for Electronic Data Systems develop-ing programs to evaluate and hedge interest rate exposure Derek's researchinterests include trading strategies for ®nancial assets, simulation work, andcompensation design for fund managers

xvi List of contributors

The past few years have seen an extraordinary explosion in the use ofquantitative systems designed to trade in the foreign exchange and futuresmarkets This is witnessed by exponential growth of alternative investments,namely futures funds and hedge funds Curiously, research on this area hasbeen fragmented and sporadic The purpose of this book is to bring togetherleading academics and practitioners who are working on systematictrading rules It is well known that futures fund managers, among others,tend to rely on some sort of systematic trading rules Available statisticssuggest that systematic traders outnumber their discretionary counterparts by

a ratio of two to one As we will see in Chapter 13, the gap is even bigger forsectorized markets such as foreign exchange, interest rates and stock indexfutures

This book does not present an exhaustive review of dynamic strategiesapplied by traders and fund managers, as this would be a hazardous taskgiven the speed at which forecasting techniques and markets evolve Thepurpose of this book is rather to introduce the reader to the theory of tradingrules and their application Numerous forecasting strategies are covered inthis book, including technical indicators, chartism, neural networks andgenetic algorithms

There are two common factors linking all the strategies investigated in thisbook First, all forecasting techniques attempt to predict the direction of pricemovements Second, the criterion used to assess forecasting accuracy is

economic signi®cance Trading rules are built out of forecasting strategies andtheir pro®tability subsequently measured.

Our primary concern is to specify trading rule-based tools which allowproper testing of the ecient market hypothesis A market is said to beinformationally ecient if prices in that market re¯ect all relevant informa-tion as fully as possible This demanding requirement for an ecient market

is often relaxed to a statement that trading systems cannot use information tooutperform passive investment strategies when transaction costs and risk areconsidered This book shows that many ®nancial markets, especially foreignexchange and futures, may not be ecient according to this de®nition.This book hopes to combine intellectual challenge and practical applica-tion, as re¯ected by the distinction and variety of the contributors: academics,traders, central bankers, tracking agencies and fund managers Some readerswill be interested in this book for what it says about the practical use oftechnical analysis and others for what it says about the distributionalproperties of dynamic strategies The interaction between mathematicaltheory and ®nancial practice has intensi®ed since the development of ModernPortfolio Theory in the 1950s and the Black±Scholes analysis of the early1970s, and this has reached a point where no ®rm can ignore it

Any virtue can become a vice if taken to extremes, and just so with theapplication of mathematical models in ®nance practice At times themathematics of the models become too interesting and we lose sight of themodels' ultimate purpose: improving portfolio performance, risk manage-ment and trading book performance Computer simulation of dynamicstrategies using real data from foreign exchange, emerging and futuresmarkets, will show that substantial risk-adjusted pro®ts can be achieved.However, as with any computer simulation in ®nancial markets, one cannotknow how accurate the analysis is until one tries in real time with real money.Consequently, a complementary study of the usefulness of quantitativetechniques must involve the review of fund managers' performance usingsystematic trading rules

This book includes three sections: the stochastic properties of tradingrules, applications to the foreign exchange market and trading the futuresmarkets We shall next discuss the contributions of each of the ®fteen papers.The ®rst section deals with the stochastic properties of trading rules (sixchapters)

1 Blake LeBaron uses moving-average based rules as speci®cation tests onthe process for foreign exchange rates Several models for regime shifts andpersistent trends are simulated and compared with results from the actualseries The results show that these simple models cannot capture some aspects

of the series studied Finally, the economic signi®cance of the trading results

2 Advanced Trading Rules

is tested Returns distributions from the trading rules are compared withreturns on risk-free assets and returns from the US stock market.

2 Andrew Lo, Harry Mamaysky and Jiang Wang propose a systematic andautomatic approach to technical pattern recognition using non-parametrickernel regression, and apply this method to a large number of US stocks from

1962 to 1996 to evaluate the e€ectiveness of technical analysis By comparingthe unconditional empirical distribution of daily stock returns to theconditional distribution ± conditioned on speci®c technical indicators such

as head-and-shoulders or double-bottoms ± they ®nd that over the 31-yearsample period, several technical indicators do provide incremental informa-tion and may have some practical value

3 Daan Matheussen andStephen Satchellassess the performance of varioustrading rules for TAA (tactical asset allocation) modelling across equityindices in the emerging markets The authors ®nd that rules based on meanand variance information and using a rolling window of information outper-form all others absolutely and in a risk-adjusted sense, even when they takeinto account transaction costs

4 Emmanuel Acar establishes the expected return and variance of linearforecasting strategies assuming that the underlying logarithmic returns followsome Gaussian process The necessary and sucient conditions to maximizepro®ts are speci®ed This chapter shows that many technical forecasts can beformulated as linear predictors The e€ect of conditional heteroskedasticity isinvestigated using Monte Carlo simulations

5 George Kuoderives some exact results about the probabilistic istics of realized returns from two simple moving-average trading rules The

character-®rst rule needs only the information contained in the asset return at thepresent time to issue trading signals while the second rule requires the wholepast history of the asset price to do so

6 Emmanuel Acar andStephen Satchellestablish the distribution of returnsgenerated by a portfolio including two active strategies assuming thatunderlying markets follow an elliptical distribution The timing is triggered

by linear forecasts for the sake of tractability The most important ®nding isthat conventional portfolio theory might not apply to active directionalstrategies even when the underlying assets follow a multivariate normaldistribution

The second section of this book demonstrates that the foreign exchangemarkets may be seen as inecient given the number of pro®table strategieswhich can be built out of varied forecasts (four chapters)

Introduction 3

7 John Okunev andDerek White evaluate the performance of multipleclasses of foreign exchange trading rules across eight base currencies.Speci®cally, they compare trading rules that focus on individual currencieswith those that follow a long±short strategy across multiple currencies Thetrading rules include pure momentum, buying/selling based upon relativeinterest rates, and moving-average rules They ®nd that a long±short strategyacross multiple currencies outperforms trading rules that focus on individualcurrencies In addition, they ®nd that signi®cant bene®ts may accrue bycombining long±short moving-average rules across multiple currencies withlong±short positions based upon relative interest rates.

8 Christian Dunis considers Arti®cial Neural Networks (ANNs), anddiscusses their application to economic and ®nancial forecasting and theirincreasing success This chapter investigates the application of ANNs tointraday foreign exchange forecasting and stresses some of the problemsencountered with this modelling technique As forecasting accuracy does notnecessarily imply economic signi®cance, the results are also evaluated bymeans of a trading strategy

9 Kevin Chang andCarol Oslerassess the incremental value of the shoulders pattern (H&S), consistently cited by technical analysts as particu-larly frequent and reliable, relative to ®lter rules On an incremental basis,they show that the H&S trading rules add noise but no value Thus, a traderwould do no better, and possibly worse, by following both H&S and ®lterrules instead of ®lter rules only

head-and-10 Pierre Lequeuxinvestigates the assumption that the interest rates marketleads the currency markets as money ¯ows from one country to another For

a systematic trader the hypothesis is quite attractive; indeed if such a correlation exists it will enable him to devise pro®table trading strategies.Finally, the third section analyses the application of stop-loss rules andother technical strategies by futures traders (®ve chapters) The tradingmethodology and performance of futures funds managers is reviewed

cross-11 BernardBensaidandOlivier De Bandtexplain the existence of stop-lossrules in ®nancial institutions They develop a principal/agent model, where aninvestment ®rm (the principal) has to rely on the expertise of a trader (theagent) to invest in a risky asset (a future contract, say) Using daily data onindividual positions in the French Treasury bond future market, they ®ndevidence that positions are more likely to be sold o€ when realized pro®ts arevery negative More than 20 per cent of individual accounts seem to use stop-loss strategies in their database

4 Advanced Trading Rules

12 Risto Karjalainen uses genetic algorithm to ®nd technical trading rulesfor S&P 500 futures The rules are found to be pro®table in an out-of-sampletest period, with reduced volatility compared to the buy-and-hold strategy It

is also shown that there are characteristic patterns in option trading activitycoinciding with the trading rule signals The results are consistent with short-term overreaction that leads to a partial reversal of large returns on a fewdays' horizon

13 Derek Edmonds examines the merits of using managed futures as adiversifying vehicle for traditional investments The author carries out an in-depth examination of the performance characteristics of the two mostpopular schools of thought concerning trading: discretionary versus systema-tic The relative performance for each style of trading is studied in each of thevarious market sectors, yielding some surprising results

14 Edouard Petitdidier and David Obertexplain precisely BAREP's ment and techniques used to trade futures: choice of futures markets, creationand testing of strategies and money management This structure hasdeveloped a Futures Funds' asset management based on two leadingconcepts: Technical non-discretionary asset management, with investmentstrategies based on models of historical behaviour in futures markets The

manage-®nal section describes the funds' performance from 1994 to 1997

15 Felix Gasser investigates the need for performance evaluation intechnical analysis He studies not only the indicators and trading systemsthat are commonly applied by technical traders, but also the analytical dataused for evaluation

The range of forecasting strategies investigated in this book is large butnon-exhaustive The pace of innovation is so fast that new trading conceptswill appear which might be better suited to future market conditions.However, we hope that these contributions provide a host of ideas to helpimprove the risk±return pro®le of any trader or investor in the foreignexchange and futures markets We also feel that our book will act asbackground for academics and other researchers who would like to ®ndout more about this fascinating new area of ®nancial research

Introduction 5

For stock returns, many early studies generally showed technical analysis

to be useless, while for foreign exchange rates there is no early study showingthe techniques to be of no use Dooley and Shafer (1983) found interestingresults using a simple ®lter rule on several daily foreign exchange rate series

In later work, Sweeney (1986) documents the pro®tability of a similar rule onthe German mark In an extensive study, Schulmeister (1987) repeats theseresults for several di€erent types of rules Also, Taylor (1992) ®nds thattechnical trading rules do about as well as some of his more sophisticatedtrend-detecting methods

While these tests were proceeding, other researchers were trying to usemore traditional economic models to forecast exchange rates with much lesssuccess The most important of these was Meese and Rogo€ (1983) Theseresults showed the random walk to be the best out-of-sample exchange rateforecasting model Recently, results using nonlinear techniques have beenmixed Hsieh (1989) ®nds most of the evidence for nonlinearities in dailyexchange rates is coming from changing conditional variances Diebold andNason (1990) and Meese and Rose (1990) found no improvements using

nonparametric techniques in out-of-sample forecasting However, LeBaron(1992) and Kim (1989) show small out-of-sample forecast improvements.During some periods, LeBaron (1992) found forecast improvements of over 5per cent in mean squared error for the German mark Both of these papersrelied on some results connecting volatility with conditional serial correla-tions of the series.

This chapter breaks o€ from the traditional time series approaches and uses

a technical trading rule methodology With the bootstrap techniques of Efron(1979), some of the technical rules can be put to a more thorough test This isdone for stock returns in Brock, Lakonishok and LeBaron (1992).1 Thischapter will use similar methods to study exchange rates These allow notonly the testing of simple random walk models, but the testing of anyreasonable null model that can be simulated on the computer In this sense,the trading rule moves from being a pro®t-making tool to a new kind ofspeci®cation test The trading rules will also be used as moment conditions in

a simulated method of moments framework for estimating linear models.Finally, the economic signi®cance of these results will be explored Returnsfrom the trading rules applied to the actual series will be tested Distributions

of returns from the exchange rate series will be compared with those fromrisk-free assets and stock returns These tests are important in determining theactual economic magnitude of the deviations from random walk behaviourthat are observed

Section 1.2 introduces the simple rules used Section 1.3 describes the nullmodels used Section 1.4 presents results for the various speci®cation tests.Section 1.5 implements the trading rules and compares return distributionsand section 1.6 summarizes and concludes

This section outlines the technical rules used in this chapter The rules areclosely related to those used by actual traders All the rules used here are ofthe moving average or oscillator type Here, signals are generated based onthe relative levels of the price series and a moving average of past prices:

matˆ …1=L†X

pt i

For actual traders, this rule generates a buy signal when the current price level

is above the moving average and a sell signal when it is below the movingaverage.2 This chapter will use these signals to study various conditionalmoments of the series during buy and sell periods Estimates of theseconditional moments are obtained from foreign exchange time series, and

Technical trading rules and regime shifts in foreign exchange 7

these estimates are then compared with those from simulated stochasticprocesses Section 1.4 of this chapter di€ers from most trading rule studieswhich look at actual trading pro®ts from a rule Actual trading pro®ts will beexplored in section 1.5.

This section describes some of the null models which will be used forcomparison with the actual exchange rate series These models will be runthrough the same trading rule systems as the actual data and then comparedwith those series Several of these models will be bootstrapped in the spirit ofEfron (1979) using resampled residuals from the estimated null model Thisclosely follows some of the methods used in Brock, Lakonishok and LeBaron(1992) for the Dow Jones stock price series

The ®rst comparison model used is the random walk:

log…pt† ˆ log…pt 1† ‡ "t

Log di€erences of the actual series are used as the distribution for "t andresampled or scrambled with replacement to generate a new random walkseries The new returns series will have all the same unconditional properties

as the original series, but any conditional dependence will be lost

The second model used is the GARCH model (Engle, 1982; Bollerslev,1986) This model attempts to capture some of the conditional heteroskedas-ticity in foreign exchange rates.3 The model estimated here is of the form:

Simulations of this model follow those for the random walk Standardizedresiduals of the GARCH model are estimated as:

8 Advanced Trading Rules

normality Bollerslev and Wooldridge (1990) have shown that the previousparameter estimates will be consistent under certain deviations from normal-ity Therefore, the estimated residuals will also be consistent.5

The third model has been proposed for foreign exchange markets in apaper by Engle and Hamilton (1990) It suggests that exchange rates followlong persistent swings following a two-state Markov chain It is given by:

1.4.1 Data summary

The data used in this chapter are all from the EHRA macro data tape fromthe Federal Reserve Bank Weekly exchange rates for the British pound (BP),the German mark (DM) and the Japanese yen (JY) are sampled everyWednesday from January 1974 to February 1991 at 12:00 pm EST

Returns are created using log ®rst di€erences of these weekly exchangerates quoted in dollars/fx Table 1.1 presents some summary statistics forthese return series All three series show little evidence of skewness and areslightly leptokurtic These properties are common for many high frequencyasset returns series The ®rst ten autocorrelations are given in the rowslabelled n The Bartlett asymptotic standard error for these series is 0.033.The BP shows little evidence of any autocorrelation except for lags four andeight, while the DM shows some weak evidence of correlation, and the JYshows strong evidence for some autocorrelation The Ljung±Box±Piercestatistics are shown on the last row These are calculated for ten lags andare distributed 2…10† under the null of independently identically distributed.The p-values are included for each in parentheses The BP and JY series rejectindependence, whereas the DM series does not

Technical trading rules and regime shifts in foreign exchange 9

The interest rate series used are also from the EHRA macro data tape Forthe dollar, the weekly eurodollar rate is used For the pound, the internationalmoney market call money rate is used For the mark, the Frankfurt interbankcall money rate is used, and for the yen, the Tokyo unconditional lender rate.Weekly rates are constructed ex post from the compounded rates fromWednesday to Tuesday These rates can only be viewed as proxies for thedesirable situation of having a set of interest rates from the same o€shoremarket at the same maturity At this time that is not available.

1.4.2 Random walk comparisons

In this section, simulations are performed comparing conditional momentsfrom the technical trading rules with a bootstrapped random walk generatedfrom the actual returns time series scrambled with replacement Threemoving-average rules will be used, the twenty-week, thirty-week and ®fty-week moving averages These are fairly common lengths used by traders Wewill see that the results are not very sensitive to the lengths used The moving-average rules force us to start the study after a certain number of weeks have

Table 1.1 Summary statistics

Summary statistics for BP (British pound), DM (German mark), JY

(Japanese yen) weekly exchange rates from January 1974 to February 1991.

10 Advanced Trading Rules

passed For this chapter, all tests for all the rules begin after week ®fty Thisgives the same number of weekly observations for all three rules.

Table 1.2 presents the results comparing the actual series for the BP with

500 simulated random walks Six comparison statistics are computed in thistable First, the column labelled `Buy' refers to the conditional mean duringbuy periods This is:

This gives a simple idea of how risky the buy or sell periods might be and tells

us something about what is happening to conditional variance The thirdcolumn, labelled `Fraction buy', is just the fraction of buy weeks Nb=N The

Table 1.2 BP random walk bootstrap

Technical trading rules and regime shifts in foreign exchange 11

next two columns, `Sell' and `s' repeat the previous descriptions for the sellperiods Let msbe the mean during the sell periods The ®nal column, `Buy±Sell', refers to the di€erence between the buy and sell means, mb ms.This table presents several results for each test The ®rst is the fraction ofsimulated random walks that generate a given statistic greater than that forthe original series This can be thought of as a simulated p-value For thetwenty-week moving-average rules, this result is given in the ®rst row of thetable For the BP series we see that 8 per cent of the simulations generated amean return greater than that from the actual series The next row,

`Simulation mean' shows the mean of mb for the 500 simulated randomwalks The third row, `Xrate mean' shows mbfor the exchange rate series Forthe BP series the table reports a mean one-week buy return of 0.091 per centwhich is greater than the simulated mean of 0.012 per cent The simulationsshow that this di€erence is weakly signi®cant with 8 per cent of thesimulations generating a mb greater than 0.091 per cent

The second column shows the results for the standard deviations of the buyreturns b The column shows that 56 per cent of the simulations hadstandard deviations greater than that in the original series This clearlyshows no signi®cant di€erence between the simulations and the originalseries In other words, although the buys generate a larger mean, they donot have a larger variance The next column reports that the fraction of buys

to sells for the actual series, third row, is 0.486 This does not appear to beunusually large or small relative to the simulated random walks

For the sells, ms, for the BP series is 0.134 per cent which compares with0.014 per cent for the simulation Table 1.1 shows that 98 per cent of thesimulated random walks generated msstatistics larger than 0.134, indicatingthat the sell period returns for the original series are unusually small whencompared with the random walk The next column, s, shows that thesereturns are not di€erent from the entire sample in terms of volatility.The ®nal column reports the di€erence mb ms For this rule, thedi€erence is about 0.2 per cent, but none of the simulated random walksgenerated such a large di€erence between buy and sell returns

The next six rows of the table repeat the same results for the other tworules, the thirty- and ®fty-week moving-average rules The results for theserules are similar to the ®rst two with the buy means unusually large and thesell means unusually small There still appears to be no e€ect in volatility.6The ®nal set of tests performs a joint test based on all three rules Anaverage is taken for the statistics generated from each of the three rules Forthe mean buys this would be:

mbˆ 1=3…mb…1; 20† ‡ mb…1; 30† ‡ mb…1; 50††

12 Advanced Trading Rules

Finding the distribution of this statistic would require knowledge of the jointdistribution across all the rules The results for each rule are clearly far fromindependent, so this would be a dicult job With the simulated randomwalks the rules can now be compared with results for the same averagestatistics over the 500 simulated random walks This section of the tableshows that the pattern for each of the individual rules is repeated in theaverage rules.

A good question to ask at this point is how general these results are fordi€erent moving averages This chapter has used only three di€erent moving-average rules These are chosen to be close to those used by actual traders It

is quite possible that there may be some data-snooping problems here in thatthese rules have already been chosen because of their past performance in thedata This problem is partially accounted for in Figure 1.1, which displays thebuy±sell di€erences for several di€erent lengths of moving averages It is clearfrom this ®gure that the results are not overly sensitive to the length of themoving average chosen

Tables 1.3 and 1.4, repeat the results for the DM and JY series Turning tothe average rows, we see very similar results to Table 1.2 The buy±selldi€erences are large for both with p-values of 0

For the JY series, the standard deviations during the buy and sell periodsare not unusually small or large For the DM series, some weak di€erencesappear between the standard deviations during the buy and sell periods For

Moving-average length (weeks)

Figure 1.1 British pound buy±sell di€erences

Technical trading rules and regime shifts in foreign exchange 13

the average across the rules using the buy standard deviations, the simulatedp-value is 0.87, indicating that 87 per cent of the simulations were morevolatile than the actual exchange rate series For the sells, this value is 0.12,indicating that 12 per cent of the simulations were more volatile than theoriginal series This shows some weak evidence that the buy periods were less

Table 1.4 JY random walk bootstrap

volatile than average and the sells were more volatile than average Theresults are fairly weak for the average rule, but checking the individual rulesstronger rejections are found for the thirty- and ®fty-week moving averagesindividually This result moves counter to a simple mean variance connectionfor the exchange rate from a dollar perspective The higher conditionalreturns from the buy period should be compensating for more risk, butthese results show that for the DM the risk (in terms of own standarddeviation) is lower Although this is puzzling, measuring the riskiness of aforeign exchange series is more complicated than estimating the standarddeviation, so strong conclusions about risk premia require more adequatemodelling of the exact risk±return trade o€.

Another check for changes in the conditional distributions of returns isperformed in Table 1.5 In this table, skewness and kurtosis are estimated forthe returns during the buy and sell periods It is possible that these higher

Table 1.5 Skewness kurtosis

Table 1.6 Subsamples: random walk

moments might give a better indication of the riskiness of returns during each

of the periods This table combines the results for the three series into onetable The individual tests are summarized with a single row entry giving theirsimulated p-value and the averages are presented in three rows for eachexchange rate This table shows little di€erence in the higher momentsfrom the actual series buy and sell periods and their simulation counter-parts

Table 1.6 considers the stability of these results over various subsamples It

is quite possible that these rules may be picking up certain nonstationarities inthe data series The rules themselves are probably very good at checking forchanges in regime If these regime changes are relatively infrequent, thensplitting the sample into two and repeating the tests makes it less likely that therules will detect any di€erences between the buy and sell periods Table 1.6presents results from such an experiment, where each series is broken in halfand the previous random walk simulations are repeated for each subsample.For the BP, the results are basically unchanged across the subsamples.However, the trading rule results look slightly less signi®cant in the secondsubsample The simulated p-value for the average buy±sell di€erence movesfrom 0 to 0.052 Also, the average buy±sell di€erence falls from 0.37 per cent

to 0.195 per cent The DM series shows similar results for the buy and sellmeans in the two di€erent subsamples The p-value for the average buy±selldi€erence moves from 0.004 in the ®rst subsample to 0 in the secondsubsample The average buy±sell di€erence increases from 0.26 per cent to0.34 per cent For the standard deviations, the results look di€erent For thestandard deviations, the small volatility during buy periods is coming entirelyfrom the ®rst subperiod For the average standard deviations, the p-value for

b is 0.994 for the ®rst subsample and 0.330 for the second subsample Theresults on salso are much stronger during the ®rst subsample with a p-value

of 0.01 during the ®rst subsample and 0.566 during the second subsample

The results for the JY series change very little from the ®rst to the secondsubsample The mean buy±sell di€erence falls from 0.4 per cent to 0.3 percent The p-value for this number goes from 0 to 0.012.

1.4.3 GARCH comparisons

Table 1.7 shows the parameter estimates for GARCH(1,1)-AR(2) model foreach of the three exchange rate series The estimates show very similarestimates for the variance parameters, and 1, for the three exchange rateseries The AR(2) parameters show some signi®cant persistence in exchangerate movements for all three series, but the yen and the mark both show asomewhat larger amount of persistence with both the AR(1) and AR(2)parameters signi®cant

Standardized residuals from this model are run back through the samemodel to generate simulated time series for the three exchange rate series.Results of these simulations are presented in Table 1.8 This table shows thatthe GARCH model combined with the AR(2) causes some increase in themean buys and some decrease in the mean sells Most of this is probablycoming from the persistence in the AR(2) However, the magnitude of thesedi€erences is not as great as that for the actual series

For the BP, the average buy±sell di€erence for the three tests is 0.07 percent which compares with 0.29 per cent for the actual series The simulatedp-value here is 0.01 For the BP, the GARCH model leaves the previous

Table 1.7 GARCH(1, 1) parameter estimates

Estimation is by maximum likelihood Numbers in parentheses are asymptotic standard errors.

18 Advanced Trading Rules

results unchanged Also, there are no e€ects on volatility as previouslymentioned.

For the DM and JY series, the GARCH model has a slightly strongere€ect The simulations generate average buy±sell di€erences of 0.10 and 0.13per cent respectively The p-values for these di€erences are now 0.054 and0.028 respectively The added persistence of the AR(2) has caused a largebuy±sell di€erence for these series Although this does have a small impact onthe results from the simulations, the di€erences remain small relative to thebuy±sell di€erence for the actual series

1.4.4 Regime shift bootstrap

Some of the results for the GARCH model suggest that although this model

is moving in the right direction, the persistence generated is not strong enough

to generate the trading rule results that are seen in the data The rules usedcontinue to generate buy or sell signals after the price has cut through themoving average, not just in the neighbourhood of the moving average.Long-range persistence could be generated using the regime shifting modelused by Engle and Hamilton (1990) In this model, conditional means andvariances follow a two-state Markov process The parameter estimates forthis model are given in Table 1.9 For only one of the three series, the JY, areboth the conditional mean parameters signi®cantly di€erent from zero Forthe BP series, they are both insigni®cantly di€erent from zero There is also asign pattern reversal on the JY series For this series, high variance periodsare high mean periods For the other two series, this result is reversed

It seems doubtful that the magnitudes of the regime shift parameters will belarge enough to generate the conditional mean di€erences For example, forthe BP series, the conditional mean for Stˆ 0 is 0.05 per cent and for the

Stˆ 1 period it is 0.02 per cent It is dicult to see how this will generate abuy±sell spread of 0.29 per cent This is con®rmed in Table 1.10 which showsthe results for simulations of this model using a normal random numbergenerator to generate errors There is little evidence of this model capturing

Table 1.9 Regime shift parameter estimates

Estimation is by maximum likelihood Numbers in parentheses are asymptotic standard errors.

20 Advanced Trading Rules

what the trading rules are picking up for any of the series For the DM and

BP series, the buy±sell di€erences are actually negative For all the series, thep-values for the buy±sell di€erences are all close to zero

This should not rule out this model in general, but at these relatively highfrequencies (weekly) it does not seem to capture what is going on There may

be some numerical problems in estimation as the probabilities, p and q, areclose to one at this time horizon In Engle and Hamilton (1990), theconditional mean estimates are signi®cant and larger than those foundhere This may be due to the use of quarterly data It remains to be seenwhether other estimation techniques can help repair these results for theregime shift model

Table 1.10 Regime shift bootstrap

1.4.5 Interest rate differentials

The use of the previous simple processes for foreign exchange movementsignores much of the information available in world ®nancial markets Thissection incorporates some of this information into further simulations.The relation that will be used here is uncovered interest parity This relationcan be written as:

Et…st‡1† stˆ it it

where i and i are the domestic and foreign interest rates and st is the log ofthe exchange rate In a risk-neutral world, the interest rate di€erential overthe appropriate horizon should be equal to the expected drift of the exchangerate

Although uncovered parity, and theories closely related to it, have beenrejected by several studies, it is important to see if this long-range persistentdrift could be causing what the trading rules are picking up For this test amodel of the form:

st‡1ˆ st‡ it it ‡ "t

where "tis independently identically distributed noise will be used One majorproblem is getting the interest rates and their timing correct This is extremelydicult For the weekly exchange rates used here, weekly eurorates would bethe most useful series to have This study is constrained by what is available

on the EHRA tapes For the dollar, weekly eurorates are available at dailyfrequency and will be used as the risk-free dollar rate for each week beginning

at the close on Wednesday Unfortunately, the other currencies do not havesuch rates available The weekly rates are constructed from daily ex postovernight rates from Wednesday to the following Tuesday Assuming theexpectations hypothesis holds at the very short end of the term structure:

in October 1977 The lengths of the BP, DM and JY series are 832, 832 and

690 weeks respectively

Rather than immediately adjusting these series for the interest di€erential,

a slightly di€erent approach is taken at ®rst Representative series of theform:

st‡1ˆ st‡ t‡ "t

will be simulated The drift, t, is obtained from the appropriate interestdi€erential An estimate of the residual series ^"t is obtained by removing thedrift from the actual exchange rate changes This is then scrambled withreplacement, and a new series is generated using the original drift series andthe scrambled residuals This gives us representative exchange rate seriesre¯ecting the appropriate information from the interest rates

These simulations are then run through the same trading rule tests run inprevious sections Results of these tests are presented in Table 1.11 Theresults are comparable to those found for the random walk simulations inTables 1.2, 1.3 and 1.4 For all three series, none of the rules generate buy±selldi€erences as large as those generated from the original series The adjust-ment for the interest di€erential appears to have had little e€ect on thetrading-rule results

Table 1.12 repeats some of the earlier GARCH simulations accounting forinterest di€erentials In this case, the more traditional approach of subtract-ing the expected drift from the exchange rate returns is done A GARCHmodel is then ®tted to these `zero drift' terms and simulated back usingscrambled, standardized residuals as in section 1.4.3 Comparing Table 1.12with Table 1.8 shows very few di€erences Adjusting the exchange rate seriesusing the expected drift has very little impact on the GARCH simulations.The large (small) returns during buy (sell) are still not replicated well by thesimulated null model

1.4.6 Simulated method of moments estimates

The previous tests have not incorporated the trading-rule diagnostic tests intothe estimation procedure This section presents a method where the two can

be brought together in one combined procedure

One problem with the trading-rule measures is that it is dicult to deriveanalytic results for these measures One technique for estimating parametersusing conditions which can only be simulated is simulated method ofmoments This technique was developed for cross-section data by McFadden(1989) and Pakes and Pollard (1989) It is extended to time series cases inDue and Singleton (1993) and Ingram and Lee (1991)

Technical trading rules and regime shifts in foreign exchange 23

20 Advanced Trading Rules

what the trading rules are picking up for... asymptotic standard errors.

18 Advanced Trading Rules

results unchanged Also, there... of the rules generate buy±selldi€erences as large as those generated from the original series The adjust-ment for the interest di€erential appears to have had little e€ect on thetrading-rule results