<s> ADVANCED TRADING RULES
Butterworth-Heinemann Finance
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series titlesReturn Distributions in FinanceDerivative Instruments: theory, valuation, analysisManaging Downside Risk in Financial Markets: theory, practice and implementationEconomics for Financial MarketsGlobal Tactical Asset Allocation: theory and practicePerformance Measurement in Finance: ®rms, funds and managersReal R&D OptionsForecasting Volatility in the Financial MarketsAdvanced Trading Rules
Series editorDr Stephen SatchellDr Satchell is Reader in Financial Econometrics at Trinity College, Cambridge;Visiting Professor at Birkbeck College, City University Business School and University of Technology, Sydney. He also works in a consultative capacity to many ®rms,and edits the journal Derivatives: use, trading and regulations.
ADVANCED TRADING RULESSecond edition
Edited by
E. AcarBank of America
S. SatchellTrinity College, Cambridge, and Faculty of Economics,University of Cambridge, Cambridge
OXFORD AMSTERDAM BOSTON LONDON NEW YORKSAN FRANCISCO SINGAPORE SYDNEY TOKYO
PARIS
SAN DIEGO
Butterworth-HeinemannAn imprint of Elsevier ScienceLinacre House, Jordan Hill, Oxford OX2 8DP225 Wildwood Avenue, Woburn, MA 01801-2041First published 1998Reprinted 1998Second edition 2002Copyright # 1998, 2002, Elsevier Science Ltd. All rights reservedNo part of this publication may be reproduced in any material form (includingphotocopying or storing in any medium by electronic means and whetheror not transiently or incidentally to some other use of this publication) withoutthe written permission of the copyright holder except in accordance with theprovisions of the Copyright, Designs and Patents Act 1988 or under the terms ofa licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road,London, England W1T 4LP. Applications for the copyright holder's writtenpermission to reproduce any part of this publication should be addressedto the publishersBritish Library Cataloguing in Publication DataAdvanced trading rules. ± 2nd ed. ± (Quantitative ®nance series)1. International ®nance 2. Securities 3. Exchange 4. FuturesI. Acar, E. (Emmanuel) II. Satchell, Stephen E.332 0 .042Library of Congress Cataloguing in Publication DataA catalogue record for this book is available from the Library of CongressISBN 0 7506 5516X
For information on all Butterworth-Heinemann publications visitour website at www.bh.com
Data manipulation by David Gregson Associates, Beccles, SuolkPrinted and bound in Great Britain by Biddles Ltd., Guildford and King's Lynn
Contents
ForewordList of contributors
ixxi
Introduction
1
1. Technical trading rules and regime shifts in foreign exchangeBlake LeBaron1.1 Introduction1.2 Technical trading rules1.3 Null models for foreign exchange movements1.4 Empirical results1.5 Economic signi®cance of trading-rule pro®ts1.6 Conclusions
6
2. Foundations of technical analysis: computational algorithms,statistical inference and empirical implementationAndrew W. Lo, Harry Mamaysky and Jiang Wang2.1 Introduction2.2 Smoothing estimators and kernel regression2.3 Automating technical analysis2.4 Is technical analysis informative?2.5 Monte Carlo analysis2.6 Conclusions3. Mean-variance analysis, trading rules and emerging marketsDaan Matheussen and Stephen Satchell3.1 Introduction3.2 Data and portfolio construction
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Contents3.33.4
4.
5.
6.
7.
ResultsConclusions
Expected returns of directional forecastersEmmanuel Acar4.1 Introduction4.2 Trading rules4.3 Autoregressive models4.4 Technical indicators4.5 Conditional heteroskedasticity and linear rule returns4.6 Conclusions4.7 AppendixSome exact results for moving-average trading rules withapplications to UK indicesGeorge W. Kuo5.1 Introduction5.2 The moving-average trading rule5.3 The stochastic process for asset returns5.4 The moving-average 1; 1 rule5.5 Applications to UK stock and futures markets5.6 ConclusionsThe portfolio distribution of directional strategiesEmmanuel Acar and Stephen Satchell6.1 Introduction6.2 Portfolio returns of directional strategies6.3 Exact distribution under the normal random walkassumption6.4 Generalization6.5 ConclusionsThe pro®ts to technical analysis in foreign exchange markets havenot disappearedJohn Okunev and Derek White7.1 Introduction7.2 Data and methodology7.3 Trading strategies7.4 Results7.5 Conclusions
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Contents8. The economic value of leading edge techniques for exchange ratepredictionChristian L. Dunis8.1 Introduction8.2 Basic concepts, data processing and modelling procedure8.3 Empirical results and further developments8.4 Conclusions
9. Is more always better? Head-and-shoulders and ®lter rules in foreignexchange marketsP. H. Kevin Chang and Carol L. Osler9.1 Introduction9.2 De®ning ®lter rules and head-and-shoulders patterns9.3 Measuring pro®ts from technical signals9.4 Empirical pro®tability of the technical trading rules in FXdata9.5 The incremental pro®tability of the head-and-shoulderspattern9.6 Conclusions
10. Informative spillovers in the currency markets: a practical approachthrough exogenous trading rulesPierre Lequeux10.1 Introduction10.2 The series and their statistical properties10.3 The endogenous and exogenous trading rules10.4 Conclusions
11. Stop-loss rules as a monitoring device: theory and evidence from thebond futures marketBernard Bensaid and Olivier De Bandt11.1 Introduction11.2 The model11.3 A test of the existence of stop-loss strategies11.4 Empirical results11.5 Conclusions11.6 Statistical appendix11.7 Mathematical appendix
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Contents
12. Evolving technical trading rules for S&P 500 futuresRisto Karjalainen12.1 Introduction12.2 Genetic algorithms12.3 Evolving technical trading rules12.4 Testing the trading rules12.5 Analysing trading rule signals12.6 Conclusions13. Commodity trading advisors and their role in managed futuresDerek Edmonds13.1 Introduction13.2 Bene®ts of investing in managed futures13.3 Measures of investment and return13.4 Modern portfolio theory13.5 Overview of creating a managed futures program13.6 Commodity trading advisors13.7 Systematic versus discretionary traders13.8 Conclusions14. BAREP futures fundsDavid Obert and Edouard Petitdidier14.1 Introduction14.2 BAREP's organization14.3 Trading concepts14.4 Money management14.5 Epsilon futures fund14.6 Performance futures fund and BAREP commodities futuresfund14.7 Conclusions15. The need for performance evaluation in technical analysisFelix Gasser15.1 Introduction15.2 Tools and de®nitions15.3 Practical use of performance tools15.4 Robustness tests15.5 ConclusionsIndex
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Foreword
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 dicult 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 eorts 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 eorts 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
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Foreword
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 management 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 downin a cyber cafeÂ 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
Contributors
Emmanuel Acar is a Principal and Manager of Risk Management AdvisoryLondon, at Bank of America. He previously worked at Citibank as a VicePresident in the FX Engineering Group. He was a proprietary trader foralmost ten years at Dresdner Kleinwort Benson, BZW and Banque Nationalede 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 Bernard Bensaid is 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 Universityof Paris and Lille.P. H. Kevin Chang is 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, macroeconomic implications of FX option pricing, and technical trading rules in
xii
List of contributors
foreign exchange. He holds a PhD in Economics from MIT, and a Bachelor'sin Economics from Harvard.Christian L. Dunis is 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 management ®rms and a Senior Managing Consultant with Infacts. Before this,Christian Dunis was Global Head of Markets Research at Banque Nationalede 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 Edmonds graduated from Cornell University with a BA in Economicsand joined RefcoFund Holdings Corporation in 1990, where he was involvedin 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 from
List of contributors
xiii
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. Kuo studied 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 academicin Taiwan.Blake LeBaron has a PhD in Economics from the University of Chicago. Heis 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 Fundamental 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. Lo is 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
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List of contributors
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; nonlinear models of stock and bond returns; and, most recently, evolutionary andneurobiological models of individual risk preferences.Harry Mamaysky received his doctorate in Financial Economics from MIT in2000. Since then he has been an Assistant Professor of Finance at the YaleSchool of Management. His research ranges from trying to understand thefactors aecting 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 determinants 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 Matheussen is a Senior Consultant at ESR (CWA) where he specializesin risk, ®nance and insurance-related quantitative analysis. He has lived inBelgium and South Africa and studied Chemical Engineering at the University of Cape Town.David Obert is a co-founder of Systeia Capital Management. He has been inthe investment business for 15 years. As a Managing Director and ChiefInvestment Ocer, 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 specializing in alternative investment with Euro 6 Billion under management. DavidObert created the Epsilon Futures Program (managed Futures Program) in1994.Professor John Okunev joined 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 domestic
List of contributors
xv
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 eects of currency orders on high-frequency exchangerate dynamics.Edouard Petitdidier is 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 c75million) and a Statistical European Pair Trading Fund (launched in November 2001 with c75 million). Systeia is a subsidiary of Credit Lyonnais based inParis, created in early 2001 with an initial commitment of c250 million. Hehas 9 years' experience in the trading and investment business and was, from1994 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 Satchell has 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 econometrics 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 Wang is the Nanyang Technological University Professor of Finance atthe MIT Sloan School of Management. He received his PhD in Physics in1985 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 Review of Financial Studies. He was the recipient of theTretz 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.
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List of contributors
Derek White joined the University of New South Wales (UNSW) in August1998 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 developing programs to evaluate and hedge interest rate exposure. Derek's researchinterests include trading strategies for ®nancial assets, simulation work, andcompensation design for fund managers.
Introduction
In presenting the second edition of this book, we have added three newchapters, in particular focusing on the area of technical analysis (chartism).We feel that this material should be included in any broad contemporarystudy on trading rules and we hope this inclusion will encourage furtherresearch on this area.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 bya 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
2
Advanced Trading Rules
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 ecient market hypothesis. A market is said to beinformationally ecient if prices in that market re¯ect all relevant information as fully as possible. This demanding requirement for an ecient marketis 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 ecient according to this de®nition.This book hopes to combine intellectual challenge and practical application, 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 management 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 aspectsof the series studied. Finally, the economic signi®cance of the trading results
Introduction
3
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 from1962 to 1996 to evaluate the eectiveness of technical analysis. By comparingthe unconditional empirical distribution of daily stock returns to theconditional distribution ± conditioned on speci®c technical indicators suchas head-and-shoulders or double-bottoms ± they ®nd that over the 31-yearsample period, several technical indicators do provide incremental information and may have some practical value.3 Daan Matheussen and Stephen Satchell assess 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 outperform 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 sucient conditions to maximizepro®ts are speci®ed. This chapter shows that many technical forecasts can beformulated as linear predictors. The eect of conditional heteroskedasticity isinvestigated using Monte Carlo