for Trading and Investment

Applied Quantitative Methods for Trading and Investment. Edited by C.L. Dunis, J. Laws and P. Na¨m

±

™ 2003 John Wiley & Sons, Ltd ISBN: 0-470-84885-5

Wiley Finance Series

Applied Quantitative Methods for Trading and Investment

Christian L. Dunis, Jason Laws and Patrick Na¨m±

Country Risk Assessment: A Guide to Global Investment Strategy

Michel Henry Bouchet, Ephraim Clark and Bertrand Groslambert

Credit Derivatives Pricing Models: Models, Pricing and Implementation

Philipp J. Sch¨ nbucher

o

Hedge Funds: A resource for investors

Simone Borla

The Simple Rules: Revisiting the art of ¬nancial risk management

Erik Banks

Option Theory

Peter James

Risk-adjusted Lending Conditions

Werner Rosenberger

Measuring Market Risk

Kevin Dowd

An Introduction to Market Risk Management

Kevin Dowd

Behavioural Finance

James Montier

Asset Management: Equities Demysti¬ed

Shanta Acharya

An Introduction to Capital Markets: Products, Strategies, Participants

Andrew M. Chisholm

Hedge Funds: Myths and Limits

Francois-Serge Lhabitant

The Manager™s Concise Guide to Risk

Jihad S. Nader

Securities Operations: A guide to trade and position management

Michael Simmons

Modeling, Measuring and Hedging Operational Risk

Marcelo Cruz

Monte Carlo Methods in Finance

Peter J¨ ckel

a

Building and Using Dynamic Interest Rate Models

Ken Kortanek and Vladimir Medvedev

Structured Equity Derivatives: The De¬nitive Guide to Exotic Options and Structured Notes

Harry Kat

Advanced Modelling in Finance Using Excel and VBA

Mary Jackson and Mike Staunton

Operational Risk: Measurement and Modelling

Jack King

Interest Rate Modelling

Jessica James and Nick Webber

Applied Quantitative Methods

for Trading and Investment

Edited by

Christian L. Dunis

Jason Laws

and

Patrick Na¨m

±

Copyright ™ 2003 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester,

West Sussex PO19 8SQ, England

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Library of Congress Cataloging-in-Publication Data

Applied quantitative methods for trading and investment / edited by Christian Dunis, Jason

Laws, and Patrick Na¨m±

p. cm. ” (Wiley ¬nance series)

Includes bibliographical references and index.

ISBN 0-470-84885-5 (cased : alk. paper)

1. Finance”Mathematical models. 2. Investments”Mathematical models. 3.

Speculation”Mathematical models. I. Dunis, Christian. II. Laws, Jason. III. Na¨m,

±

Patrick. IV. Series

HG106.A67 2003

332.6 01 5195”dc21

2003049721

British Library Cataloguing in Publication Data

A catalogue record for this book is available from the British Library

ISBN 0-470-84885-5

Typeset in 10/12pt Times by Laserwords Private Limited, Chennai, India

Printed and bound in Great Britain by TJ International, Padstow, Cornwall

This book is printed on acid-free paper responsibly manufactured from sustainable forestry

in which at least two trees are planted for each one used for paper production.

Contents

About the Contributors xi

Preface xv

1 Applications of Advanced Regression Analysis for Trading and

Investment 1

Christian L. Dunis and Mark Williams

Abstract 1

1.1 Introduction 1

1.2 Literature review 3

1.3 The exchange rate and related ¬nancial data 4

1.4 Benchmark models: theory and methodology 10

1.5 Neural network models: theory and methodology 20

1.6 Forecasting accuracy and trading simulation 31

1.7 Concluding remarks 36

References 39

2 Using Cointegration to Hedge and Trade International Equities 41

A. Neil Burgess

Abstract 41

2.1 Introduction 41

2.2 Time series modelling and cointegration 42

2.3 Implicit hedging of unknown common risk factors 45

2.4 Relative value and statistical arbitrage 47

2.5 Illustration of cointegration in a controlled simulation 50

2.6 Application to international equities 54

2.7 Discussion and conclusions 66

References 68

vi Contents

3 Modelling the Term Structure of Interest Rates: An Application

of Gaussian Af¬ne Models to the German Yield Curve 71

Nuno Cassola and Jorge Barros Lu´s

±

Abstract 71

3.1 Introduction 71

3.2 Background issues on asset pricing 77

3.3 Duf¬e“Kan af¬ne models of the term structure 78

3.4 A forward rate test of the expectations theory 83

3.5 Identi¬cation 84

3.6 Econometric methodology and applications 87

3.7 Estimation results 106

3.8 Conclusions 126

References 126

4 Forecasting and Trading Currency Volatility: An Application of

Recurrent Neural Regression and Model Combination 129

Christian L. Dunis and Xuehuan Huang

Abstract 129

4.1 Introduction 129

4.2 The exchange rate and volatility data 132

4.3 The GARCH (1,1) benchmark volatility forecasts 135

4.4 The neural network volatility forecasts 137

4.5 Model combinations and forecasting accuracy 142

4.6 Foreign exchange volatility trading models 145

4.7 Concluding remarks and further work 149

Acknowledgements 150

Appendix A 150

Appendix B 152

Appendix C 155

Appendix D 156

Appendix E 157

Appendix F 158

Appendix G 159

References 160

5 Implementing Neural Networks, Classi¬cation Trees, and Rule

Induction Classi¬cation Techniques: An Application to Credit

Risk 163

George T. Albanis

Abstract 163

5.1 Introduction 163

5.2 Data description 165

5.3 Neural networks for classi¬cation in Excel 166

5.4 Classi¬cation tree in Excel 172

Contents vii

5.5 See5 classi¬er 178

5.6 Conclusions 191

References 191

6 Switching Regime Volatility: An Empirical Evaluation 193

Bruno B. Roche and Michael Rockinger

Abstract 193

6.1 Introduction 193

6.2 The model 194

6.3 Maximum likelihood estimation 195

6.4 An application to foreign exchange rates 197

6.5 Conclusion 206

References 206

Appendix A: Gauss code for maximum likelihood for variance

switching models 208

7 Quantitative Equity Investment Management with Time-Varying

Factor Sensitivities 213

Yves Bentz

Abstract 213

7.1 Introduction 213

7.2 Factor sensitivities de¬ned 215

7.3 OLS to estimate factor sensitivities: a simple, popular but

inaccurate method 216

7.4 WLS to estimate factor sensitivities: a better but still

sub-optimal method 222

7.5 The stochastic parameter regression model and the Kalman

¬lter: the best way to estimate factor sensitivities 223

7.6 Conclusion 236

References 237

8 Stochastic Volatility Models: A Survey with Applications to

Option Pricing and Value at Risk 239

Monica Billio and Domenico Sartore

Abstract 239

8.1 Introduction 239

8.2 Models of changing volatility 244

8.3 Stochastic volatility models 246

8.4 Estimation 250

8.5 Extensions of SV models 261

8.6 Multivariate models 263

8.7 Empirical applications 265

8.8 Concluding remarks 284

Appendix A: Application of the pentanomial model 284

viii Contents

Appendix B: Application to Value at Risk 286

References 286

9 Portfolio Analysis Using Excel 293

Jason Laws

Abstract 293

9.1 Introduction 293

9.2 The simple Markovitz model 294

9.3 The matrix approach to portfolio risk 301

9.4 Matrix algebra in Excel when the number of assets increases 303

9.5 Alternative optimisation targets 308

9.6 Conclusion 310

Bibliography 311

10 Applied Volatility and Correlation Modelling Using Excel 313

Fr´ d´ rick Bourgoin

ee

Abstract 313

10.1 Introduction 313

10.2 The Basics 314

10.3 Univariate models 315

10.4 Multivariate models 324

10.5 Conclusion 331

References 332

11 Optimal Allocation of Trend-Following Rules: An Application

Case of Theoretical Results 333

Pierre Lequeux

Abstract 333

11.1 Introduction 333

11.2 Data 333

11.3 Moving averages and their statistical properties 335

11.4 Trading rule equivalence 336

11.5 Expected transactions cost under assumption of random walk 338

11.6 Theoretical correlation of linear forecasters 340

11.7 Expected volatility of MA 341

11.8 Expected return of linear forecasters 342

11.9 An applied example 344

11.10 Final remarks 346

References 347

12 Portfolio Management and Information from Over-the-Counter

Currency Options 349

Jorge Barros Lu´s

±

Abstract 349

12.1 Introduction 349

Contents ix

12.2 The valuation of currency options spreads 353

12.3 RND estimation using option spreads 355

12.4 Measures of correlation and option prices 359

12.5 Indicators of credibility of an exchange rate band 361

12.6 Empirical applications 365

12.7 Conclusions 378

References 379

13 Filling Analysis for Missing Data: An Application to Weather

Risk Management 381

Christian L. Dunis and Vassilios Karalis

Abstract 381

13.1 Introduction 381

13.2 Weather data and weather derivatives 383

13.3 Alternative ¬lling methods for missing data 385

13.4 Empirical results 393

13.5 Concluding remarks 395

Appendix A 396

Appendix B 397

References 398

Index 401

About the Contributors

George T. Albanis is currently working at Hypovereinsbank “ HVB Group. He obtained

his PhD from City University Business School, London and holds a BSc in Economics

from the University of Piraeus, Greece and Master™s degrees in Business Finance and

in Decision Modelling and Information Systems from Brunel University, London. An

experienced programmer, his interests are applications of advanced nonlinear techniques

for ¬nancial prediction in ¬xed income and credit derivatives markets, and quanti¬cation

of risk in ¬nancial modelling.

Yves Bentz is Vice President with Cr´ dit Suisse First Boston, specialising in high fre-

e

quency equity trading strategies and statistical arbitrage. He was previously a quantitative

trader with Morgan Stanley and with Beaghton Capital Management in London where he

developed automated equity and derivatives trading strategies. Yves holds a PhD from

the University of London (London Business School). He has published several research

papers on factor modelling and nonlinear modelling, in particular stochastic parameter

models and nonparametric statistics and their applications to investment management.

Monica Billio is Associate Professor of Econometrics at Universit` Ca™ Foscari of Venice.

a

She graduated in Economics at Universit` Ca™ Foscari di Venezia and holds a PhD degree

a

in Applied Mathematics from the Universit´ Paris IX Dauphine. Her ¬elds of interest are

e

simulation-based methods and the econometrics of ¬nance.

Fr´ d´ rick Bourgoin is an Associate Portfolio Manager in the Active Fixed Income Port-

ee

folio Management Team at Barclays Global Investors in London where he is involved

in the development of the active bond and currency strategies, as well as the risk man-

agement systems. Prior to joining BGI, he was a risk manager and quantitative analyst

at Portman Asset Management. Fr´ d´ rick holds a Post-Graduate Degree in Finance from

ee

ESSEC Business School and an MSc in Econometrics and Mathematical Economics from

Panth´ on-Sorbonne University in Paris.

e

Neil Burgess is a Vice President in the Institutional Equity Division at Morgan Stanley

where he works in the area of quantitative programme trading, leading and coordinating

new developments in trading systems and strategies for equities and equity derivatives

between Europe and the USA. He obtained his PhD from London University. He has

published widely in the ¬eld of emerging computational techniques and has acted as a

xii About the Contributors

programme committee member for international conferences: Forecasting Financial Mar-

kets, Computational Finance and Intelligent Data Engineering and Learning.

Nuno Cassola holds a PhD in Economics from the University of Kent at Canterbury. He

worked as an Associate Professor at the Technical University of Lisbon from 1992 until

1994. He then joined the Research Department of the Banco de Portugal in 1994 where

he became Head of the Monetary and Financial Division in 1996. In 1999 he joined the

European Central Bank in Frankfurt where he is currently Principal Economist in the

Monetary Policy Stance Division of the Monetary Policy Directorate.

Christian L. Dunis is Girobank Professor of Banking and Finance at Liverpool Business

School, and Director of its Centre for International Banking, Economics and Finance

(CIBEF). He is also a consultant to asset management ¬rms, a Visiting Professor of Inter-

national Finance at Venice International University and an Of¬cial Reviewer attached to

the European Commission for the Evaluation of Applications to Finance of Emerging

Software Technologies. He is an Editor of the European Journal of Finance and has pub-

lished widely in the ¬eld of ¬nancial markets analysis and forecasting. He has organised

the Forecasting Financial Markets Conference since 1994.

Xuehuan Huang graduated from Liverpool Business School with an MSc in International

Banking and Finance and from China™s Shenzen University with a BA in Business Man-

agement. After working as an auditor with Ernst & Young, she is currently a ¬nancial

analyst at Bayer DS European headquarters.

Vassilios Karalis is an Associate Researcher at the Centre for International Banking,

Economics and Finance of Liverpool Business School (CIBEF). Vassilios holds an MSc

in International Banking and Finance from Liverpool Business School and a BSc in

Mathematics with specialisation in probabilities, statistics and operational research from

the University of Ioannina, Hellas.

Jason Laws is a Lecturer in International Banking and Finance at Liverpool John

Moores University. He is also the Course Director for the MSc in International Banking,

Economics and Finance at Liverpool Business School. He has taught extensively in the

area of investment theory and derivative securities at all levels, both in the UK and in

Asia. Jason is also an active member of CIBEF and has published in a number of academic

journals. His research interests are focused on volatility modelling and the implementation

of trading strategies.

Pierre Lequeux joined the Global Fixed Income division of ABN AMRO Asset Man-

agement London in 1999. As Head of Currency Management, he has responsibility for

the quantitative and fundamental currency investment process. He was previously Head

of the Quantitative Research and Trading desk at Banque Nationale de Paris, London

branch, which he joined in 1987. Pierre is also an Associate Researcher at the Centre for

International Banking, Economics and Finance of Liverpool Business School (CIBEF)

and a member of the editorial board of Derivatives Use, Trading & Regulation.

Jorge Barros Lu´s is Head of Credit Risk Modelling with Banco Portuguˆ s de Investi-

± e

mento. Previous positions include Economist at the European Central Bank and Banco de

Portugal, Chief-Economist at Banif Investimento and Adviser to the Minister of Finance

and to the Secretary of State for the Treasury of the Portuguese Government. Jorge holds

About the Contributors xiii

a PhD in Economics from the University of York and has published several papers on

yield curve modelling and information extraction from option prices.

Patrick Na¨m is an engineer of the Ecole Centrale de Paris. He is the founder and

±

chairman of Elseware, a company specialised in the application of nonlinear methods to

¬nancial management problems. He is currently working for some of the largest French

institutions and coordinating research projects in the ¬eld at a European level.

Bruno B. Roche is Head of Research in the Global Management Research group of a

major multinational company where he leads a specialist team whose role is to provide

world class expertise, methodologies, technologies and knowledge management in mul-

tiple areas which have a global critical impact (e.g. ¬nancial markets, risk management

and advertising effectiveness). He is also a Researcher at the Solvay Business School at

the University of Brussels.

Michael Rockinger is Professor of Finance at the HEC School of Business of the Univer-

sity of Lausanne. He has been scienti¬c consultant at the French Central Bank for many

years. He is also af¬liated with CEPR and FAME. Previously, Michael taught Finance at

all levels at HEC-Paris. His research interests are various, one of them is the modelling

of asset prices. Michael earned his PhD in Economics at Harvard University. He is also

a graduate in Mathematics from the Swiss Federal Institute of Technology (EPFL) and

holder of a Master™s degree from the University of Lausanne.

Domenico Sartore is Full Professor of Econometrics at Universit` Ca™ Foscari di Venezia.

a

Previously he taught at the University of Milan and the University of Padua. At present,

he is President of the economics and ¬nance consultancy GRETA (Gruppi di Ricerca

Economica Teorica ed Applicata) in Venice. His ¬eld of interest is the econometrics of

¬nance, where he has published many papers.

Mark Williams is an Associate Researcher at the Centre for International Banking,

Economics and Finance of Liverpool Business School (CIBEF). Mark holds an MSc

in International Banking and Finance from Liverpool Business School and a BSc in

Economics from Manchester Metropolitan University.

Preface

Applied Quantitative Methods for Trading and Investment is intended as a quantitative

¬nance textbook very much geared towards applied quantitative ¬nancial analysis, with

detailed empirical examples, software applications, screen dumps, etc. Examples on the

accompanying CD-Rom detail the data, software and techniques used, so that contrary to

what frequently happens with most textbook examples, they clarify the analysis by being

reasonably easily reproducible by the reader.

We expect this book to have a wide spectrum of uses and be adopted by ¬nancial

market practitioners and in universities. For the former readership, it will be of interest

to quantitative researchers involved in investment and/or risk management, to fund man-

agers and quantitative proprietary traders, and also to sophisticated private investors who

will learn how to use techniques generally employed by market professionals in large

institutions to manage their own money. For the latter, it will be relevant for students

on MSc, MBA and PhD programmes in Finance where a quantitative techniques unit is

part of the course, and to students in scienti¬c disciplines wishing to work in the ¬eld of

quantitative ¬nance.

Despite the large number of publications in the ¬eld of computational ¬nance in recent

years, most of these have been geared towards derivatives pricing and/or risk manage-

ment.1 In the ¬eld of ¬nancial econometrics, most books have been subject speci¬c,2 with

very few truly comprehensive publications.3 Even then, these books on ¬nancial econo-

metrics have been in reality mostly theoretical, with empirical applications essentially

focused on validating or invalidating economic and ¬nancial theories through econometric

and statistical methods.

What distinguishes this book from others is that it focuses on a wide spectrum of meth-

ods for modelling ¬nancial markets in the context of practical ¬nancial applications. On

top of “traditional” ¬nancial econometrics, the methods used also include technical analy-

sis systems and many nonparametric tools from the ¬elds of data mining and arti¬cial

intelligence. Although we do not pretend to have covered all possible methodologies,

1

See, for instance, Wilmott, P. (1998), Derivatives: The Theory and Practice of Financial Engineering, John

Wiley, Chichester and Alexander, C. (2001), Market Models, John Wiley, Chichester.

2

See, for instance, Dunis, C., A. Timmermann and J. Moody (2001), Developments in Forecast Combination

and Portfolio Choice, John Wiley, Chichester.

3

See Campbell, J. Y., A. W. Lo and A. C. MacKinlay (1997), The Econometrics of Financial Markets, Prince-

ton University Press, Princeton and Gouri´ roux, C. and J. Jasiak (2002), Financial Econometrics, Princeton

e

University Press, Princeton.

xvi Preface

we believe that the wide breadth of potential methods retained in this manual is highly

desirable and one of its strengths. At the same time, we have been careful to present even

the most advanced techniques in a way that is accessible to most potential readers, mak-

ing sure that those interested in the practical utilisation of such methods could skip the

more theoretical developments without hindering comprehension, and concentrate on the

relevant practical application: in this respect, the accompanying CD-Rom should prove

an invaluable asset.

An applied book of this nature, with its extensive range of methodologies and applica-

tions covered, could only bene¬t from being a collaborative effort of several people with

the appropriate experience in their ¬eld. In order to retain the practitioner™s perspective

while ensuring the methodological soundness and, should we say, academic respectability

of the selected applications at the same time, we have assembled a small team of quantita-

tive market professionals, fund managers and proprietary traders, and academics who have

taught applied quantitative methods in ¬nance at the postgraduate level in their respective

institutions and also worked as scienti¬c consultants to asset management ¬rms.

As mentioned above, the range of applications and techniques applied is quite large.

The different applications cover foreign exchange trading models with three chapters,

one using technical analysis, one advanced regression methods including nonparametric

Neural Network Regression (NNR) models and one a volatility ¬lter-based system relying

on Markov switching regimes; one chapter on equity statistical arbitrage and portfolio

immunisation based on cointegration; two chapters on stock portfolio optimisation, one

using Kalman ¬ltering techniques in the presence of time-varying betas and the other using

matrix algebra and Excel Solver to derive an optimal emerging stock market portfolio;

one chapter on yield curve modelling through the use of af¬ne models; one chapter on

credit classi¬cation with decision trees, rule induction and neural network classi¬cation

models; two chapters on volatility modelling and trading, one using Excel to compute both

univariate and multivariate GARCH volatility and correlation in the stock market, the other

using straddle strategies based on GARCH and Recurrent Network Regression (RNR) to

build a forex volatility trading model; one chapter on Value at Risk (VaR) and option

pricing in the presence of stochastic volatility; one chapter on the information contained

in derivatives prices through the use of risk-neutral density functions and, ¬nally, one

chapter on weather risk management when confronted with missing temperature data.

The ¬rst part of the book is concerned with applications relying upon advanced mod-

elling techniques. The applications include currencies, equities, volatility, the term struc-

ture of interest rates and credit classi¬cation. The second part of the book includes

three chapters where the applications on equities, VaR, option pricing and currency trad-

ing employ similar methodologies, namely Kalman ¬lter and regime switching. In the

¬nal part of the book there are ¬ve chapters where a variety of ¬nancial applications

ranging from technical trading to missing data analysis are predominantly implemented

using Excel.

In the following we provide further details on each chapter included in the book.

1. “Applications of Advanced Regression Analysis for Trading and Investment” by

C. L. Dunis and M. Williams: this chapter examines the use of regression models

in trading and investment with an application to EUR/USD exchange rate forecast-

ing and trading models. In particular, NNR models are benchmarked against some

other traditional regression-based and alternative forecasting techniques to ascertain

Preface xvii

their potential added value as a forecasting and quantitative trading tool. In addition

to evaluating the various models out-of-sample from May 2000 to July 2001 using

traditional forecasting accuracy measures, such as root-mean-squared errors, models

are also assessed using ¬nancial criteria, such as risk-adjusted measures of return.

Transaction costs are also taken into account. Overall, it is concluded that regression

models, and in particular NNR models, do have the ability to forecast EUR/USD

returns for the period investigated, and add value as a forecasting and quantitative

trading tool.

2. “Using Cointegration to Hedge and Trade International Equities” by A. N. Burgess:

this chapter analyses how to hedge and trade a portfolio of international equities,

applying the econometric concept of cointegration. The concepts are illustrated with

respect to a particular set of data, namely the 50 equities which constituted the

STOXX 50 index as of 4 July 2002. The daily closing prices of these equities are

investigated over a period from 14 September 1998 to 3 July 2002 “ the longest

period over which continuous data is available across the whole set of stocks in this

particular universe. Despite some spurious effects due to the non-synchronous closing

times of the markets on which these equities trade, the data are deemed suitable for

illustration purposes. Overall, depending on the particular task in hand, it is shown

that the techniques applied can be successfully used to identify potential hedges for

a given equity position and/or to identify potential trades which might be taken from

a statistical arbitrage perspective.

3. “Modelling the Term Structure of Interest Rates: An Application of Gaussian Af¬ne

Models to the German Yield Curve” by N. Cassola and J. B. Lu´s: this chapter shows

±

that a two-factor constant volatility model describes quite well the dynamics and the

shape of the German yield curve between 1986 and 1998. The analysis supports the

expectations theory with constant term premiums and thus the term premium structure

can be calculated and short-term interest rate expectations derived from the adjusted

forward rate curve. The analysis is carried out in Matlab and the authors include all

of the ¬les with which to reproduce the analysis. Their ¬ndings will be of interest

to risk managers analysing the shape of the yield curve under different scenarios and

also to policy makers in assessing the impact of ¬scal and monetary policy.

4. “Forecasting and Trading Currency Volatility: An Application of Recurrent Neural

Regression and Model Combination” by C. L. Dunis and X. Huang: this chapter

examines the use of nonparametric Neural Network Regression (NNR) and Recurrent

Neural Network (RNN) regression models for forecasting and trading currency volatil-

ity, with an application to the GBP/USD and USD/JPY exchange rates. The results of

the NNR and RNN models are benchmarked against the simpler GARCH alternative

and implied volatility. Two simple model combinations are also analysed. Alterna-

tive FX volatility forecasting models are tested out-of-sample over the period April

1999“May 2000, not only in terms of forecasting accuracy, but also in terms of trad-

ing ef¬ciency: in order to do so, a realistic volatility trading strategy is implemented,

using FX option straddles once mispriced options have been identi¬ed. Allowing

for transaction costs, most trading strategies retained produce positive returns. RNN

models appear as the best single modelling approach, yet model combination which

has the best overall performance in terms of forecasting accuracy fails to improve

the RNN-based volatility trading results.

xviii Preface

5. “Implementing Neural Networks, Classi¬cation Trees, and Rule Induction Classi¬-

cation Techniques: An Application to Credit Risk” by G. T. Albanis: this chapter

shows how to implement several classi¬cation tools for data mining applications in

¬nance. Two freely available softwares on classi¬cation neural networks and deci-

sion trees, respectively, and one commercial software for constructing decision trees

and rule induction classi¬ers are demonstrated, using two datasets that are available

in the public domain. The ¬rst dataset is known as the Australian credit approval

dataset. The application consists of constructing a classi¬cation rule for assessing the

quality of credit card applicants. The second dataset is known as the German credit

dataset. The aim in this application is to construct a classi¬cation rule for assess-

ing the credit quality of German borrowers. Beyond these examples, the methods

demonstrated in this chapter can be applied to many other quantitative trading and

investment problems, such as the determination of outperforming/underperforming

stocks, bond rating, etc.

6. “Switching Regime Volatility: An Empirical Evaluation” by B. B. Roche and M.

Rockinger: this chapter describes in a pedagogical fashion, using daily observations

of the USD/DEM exchange rate from October 1995 to October 1998, how to estimate

a univariate switching model for daily foreign exchange returns which are assumed to

be drawn in a Markovian way from alternative Gaussian distributions with different

means and variances. The application shows that the USD/DEM exchange rate can

be modelled as a mixture of normal distributions with changes in volatility, but not

in mean, where regimes with high and low volatility alternate. The usefulness of

this methodology is demonstrated in a real life application, i.e. through the pro¬t

performance comparison of simple hedging strategies.

7. “Quantitative Equity Investment Management with Time-Varying Factor Sensitivities”

by Y. Bentz: this chapter describes three methods used in modern equity investment

management for estimating time-varying factor sensitivities. Factor models enable

investment managers, quantitative traders and risk managers to model co-movements

among assets in an ef¬cient way by concentrating the correlation structure into a small

number of factors. Unfortunately, the correlation structure is not constant but evolves

in time and so do the factor sensitivities. As a result, the sensitivity estimates have to

be constantly updated in order to keep up with the changes. The ¬rst method, based

on rolling regressions, is the most popular but also the least accurate. The second

method is based on a weighted regression approach which overcomes some of the

limitations of the ¬rst method by giving more importance to recent observations.

Finally, a Kalman ¬lter-based stochastic parameter regression model is shown to

optimally estimate nonstationary factor exposures.

8. “Stochastic Volatility Models: A Survey with Applications to Option Pricing and

Value at Risk” by M. Billio and D. Sartore: this chapter analyses the impact on Value

at Risk and option pricing of the presence of stochastic volatility, using data for the

FTSE100 stock index. Given the time-varying volatility exhibited by most ¬nancial

data, there has been a growing interest in time series models of changing variance in

recent years and the literature on stochastic volatility models has expanded greatly:

for these models, volatility depends on some unobserved components or a latent

structure. This chapter discusses some of the most important ideas, focusing on the

simplest forms of the techniques and models available. It considers some motivations

for stochastic volatility models: empirical stylised facts, pricing of contingent assets

Preface xix

and risk evaluation, and distinguishes between models with continuous and discrete

volatility, the latter depending on a hidden Markov chain. A stochastic volatility

estimation program is presented and several applications to option pricing and risk

evaluation are discussed.

9. “Portfolio Analysis Using Excel” by J. Laws analyses the familiar Markovitz model

using Excel. This topic is taught on Finance degrees and Master™s programmes all

over the world, increasingly through the use of Excel. The author takes time out to

explain how the spreadsheet is set up and how simple short-cuts can make analysis of

this type of problem quick and straightforward. In the ¬rst section of the chapter the

author uses a two-variable example to show how portfolio risk and return vary with

the input weights, then he goes on to show how to determine the optimal weights,

in a risk minimisation sense, using both linear expressions and matrix algebra. In

the second part of the chapter the author extends the number of assets to seven

and illustrates that using matrix algebra within Excel, the Markovitz analysis of an

n-asset portfolio is as straightforward as the analysis of a two-asset portfolio. The

author takes special care in showing how the correlation matrix can be generated

most ef¬ciently and how within the same framework the optimisation objective can

be modi¬ed without fuss.

10. “Applied Volatility and Correlation Modelling Using Excel” by F. Bourgoin. The

originality of this chapter lies in the fact that the author manages to implement

a range of univariate and multivariate models within the software package, Excel.

This is extremely useful as a large proportion of ¬nance practitioners, students and

researchers are familiar with this package. Using S&P500 return data the author

generates one-step-ahead forecasts of volatility using the J.P. Morgan RiskMetrics

model, the J.P. Morgan RiskMetrics model with optimal decay, a GARCH(1,1) model

with and without a variance reduction technique and ¬nally using the GJR model to

account for asymmetric reaction to news. A comparison of forecasts is made and

some useful insights into the ef¬cacy of the models highlighted. In the second part

of the chapter the author uses return data on the DAX30 and CAC40 to model the

correlation structure using a number of models. As with the univariate approach

this includes the J.P. Morgan RiskMetrics model with and without optimal decay, a

GARCH model with and without variance reduction and ¬nally the so-called “Fast

GARCH” model of which the author has previously made signi¬cant contributions

to the literature.

11. “Optimal Allocation of Trend-Following Rules: An Application Case of Theoretical

Results” by P. Lequeux uses sophisticated Excel modelling tools to determine what

should be the optimal weighting of trading rules to maximise the information ratio.

The trading rules utilised in the chapter are moving average trading rules ranging in

order from 2 to 117 days and they are applied to a sample of ¬ve currency pairs

(USD“JPY, EUR“USD, GBP“USD, USD“CAD and AUD“USD) over the period

15/02/1996 to 12/03/2002. The analysis could however be applied to any ¬nancial

asset and any linear trading rule. In the applied example the author attempts to

determine ex-ante what would be the optimal weighting between moving averages

of order 2, 3, 5, 9, 32, 61 and 117 to maximise the delivered information ratio.

To assist in understanding, the model has been programmed into a spreadsheet to

give the reader the possibility to experiment. The results show that in four currency

xx Preface

pairs out of ¬ve the optimal weighting procedure is superior, when measured by the

information ratio, to an equally weighted basket of trading rules.

12. “Portfolio Management and Information from Over-the-Counter Currency Options”

by J. B. Lu´s: this chapter looks at the informational content of risk-reversals and

±

strangles derived from OTC at-the-money forward volatilities. Three empirical appli-

cations of the literature are presented: one on the EUR/USD, followed by the analysis

of implied correlations and the credibility of the Portuguese exchange rate policy dur-

ing the transition to the EMU, and of the Danish exchange rate policy around the

euro referendum in September 2000. This chapter is supported by the necessary Excel

¬les to allow the reader to validate the author™s results and/or apply the analysis to a

different dataset.

13. “Filling Analysis for Missing Data: An Application to Weather Risk Management” by

C. L. Dunis and V. Karalis: this chapter analyses the use of alternative methods when

confronted with missing data, a common problem when not enough historical data or

clean historical data exist, which will typically be the case when trying to develop a

decision tool either for a new asset in a given asset class (say a recently issued stock

in a given company sector) or for a new asset class as such (for instance weather

derivatives). The application to weather data derives from the fact that most weather

derivatives pricing methodologies rely heavily on clean data. The statistical imputation

accuracy of different ¬lling methods for missing historical records of temperature data

is compared: the Expectation Maximisation (EM) algorithm, the Data Augmentation

(DA) algorithm, the Kalman Filter (KF), Neural Networks Regression (NNR) models

and, ¬nally, Principal Component Analysis (PCA). Overall, it is found that, for the

periods and the data series concerned, the results of PCA outperformed the other

methodologies in all cases of missing observations analysed.

Overall, the objective of Applied Quantitative Methods for Trading and Investment is not

to make new contributions to ¬nance theory and/or ¬nancial econometrics: more simply,

but also more practically, it is to enable its readers to make competent use of advanced

methods for modelling ¬nancial markets.

We hope that, with the numerous ¬les and software programs made available on the

accompanying CD-Rom, it will constitute a valuable reference textbook for quantitative

market professionals, academics and ¬nance graduate students.

Many of the authors of chapters contained in this book have an af¬liation to the Fore-

casting Financial Markets (FFM) conference which has been held each May since 1993.

The editors of the text and several of the authors are members or associates of the Centre

for International Banking, Economics and Finance (CIBEF) at Liverpool John Moores

University. Details of both the conference and CIBEF may be found at www.cibef.com.

February 2003

1

Applications of Advanced Regression

Analysis for Trading and Investment—

CHRISTIAN L. DUNIS AND MARK WILLIAMS

ABSTRACT

This chapter examines and analyses the use of regression models in trading and investment

with an application to foreign exchange (FX) forecasting and trading models. It is not

intended as a general survey of all potential applications of regression methods to the

¬eld of quantitative trading and investment, as this would be well beyond the scope of

a single chapter. For instance, time-varying parameter models are not covered here as

they are the focus of another chapter in this book and Neural Network Regression (NNR)

models are also covered in yet another chapter.

In this chapter, NNR models are benchmarked against some other traditional regression-

based and alternative forecasting techniques to ascertain their potential added value as a

forecasting and quantitative trading tool.

In addition to evaluating the various models using traditional forecasting accuracy

measures, such as root-mean-squared errors, they are also assessed using ¬nancial criteria,

such as risk-adjusted measures of return.

Having constructed a synthetic EUR/USD series for the period up to 4 January 1999, the

models were developed using the same in-sample data, leaving the remainder for out-of-

sample forecasting, October 1994 to May 2000, and May 2000 to July 2001, respectively.

The out-of-sample period results were tested in terms of forecasting accuracy, and in

terms of trading performance via a simulated trading strategy. Transaction costs are also

taken into account.

It is concluded that regression models, and in particular NNR models do have the ability

to forecast EUR/USD returns for the period investigated, and add value as a forecasting

and quantitative trading tool.

1.1 INTRODUCTION

Since the breakdown of the Bretton Woods system of ¬xed exchange rates in 1971“1973

and the implementation of the ¬‚oating exchange rate system, researchers have been moti-

vated to explain the movements of exchange rates. The global FX market is massive with

—

The views expressed herein are those of the authors, and not necessarily those of Girobank.

Applied Quantitative Methods for Trading and Investment. Edited by C.L. Dunis, J. Laws and P. Na¨m

±

™ 2003 John Wiley & Sons, Ltd ISBN: 0-470-84885-5

2 Applied Quantitative Methods for Trading and Investment

an estimated current daily trading volume of USD 1.5 trillion, the largest part concerning

spot deals, and is considered deep and very liquid. By currency pairs, the EUR/USD is

the most actively traded.

The primary factors affecting exchange rates include economic indicators, such as

growth, interest rates and in¬‚ation, and political factors. Psychological factors also play a

part given the large amount of speculative dealing in the market. In addition, the movement

of several large FX dealers in the same direction can move the market. The interaction

of these factors is complex, making FX prediction generally dif¬cult.

There is justi¬able scepticism in the ability to make money by predicting price changes

in any given market. This scepticism re¬‚ects the ef¬cient market hypothesis according

to which markets fully integrate all of the available information, and prices fully adjust

immediately once new information becomes available. In essence, the markets are fully

ef¬cient, making prediction useless. However, in actual markets the reaction to new infor-

mation is not necessarily so immediate. It is the existence of market inef¬ciencies that

allows forecasting. However, the FX spot market is generally considered the most ef¬cient,

again making prediction dif¬cult.

Forecasting exchange rates is vital for fund managers, borrowers, corporate treasurers,

and specialised traders. However, the dif¬culties involved are demonstrated by the fact

that only three out of every 10 spot foreign exchange dealers make a pro¬t in any given

year (Carney and Cunningham, 1996).

It is often dif¬cult to identify a forecasting model because the underlying laws may

not be clearly understood. In addition, FX time series may display signs of nonlinearity

which traditional linear forecasting techniques are ill equipped to handle, often producing

unsatisfactory results. Researchers confronted with problems of this nature increasingly

resort to techniques that are heuristic and nonlinear. Such techniques include the use of

NNR models.

The prediction of FX time series is one of the most challenging problems in forecasting.

Our main motivation in this chapter is to determine whether regression models and, among

these, NNR models can extract any more from the data than traditional techniques. Over

the past few years, NNR models have provided an attractive alternative tool for researchers

and analysts, claiming improved performance over traditional techniques. However, they

have received less attention within ¬nancial areas than in other ¬elds.

Typically, NNR models are optimised using a mathematical criterion, and subsequently

analysed using similar measures. However, statistical measures are often inappropriate

for ¬nancial applications. Evaluation using ¬nancial measures may be more appropriate,

such as risk-adjusted measures of return. In essence, trading driven by a model with a

small forecast error may not be as pro¬table as a model selected using ¬nancial criteria.

The motivation for this chapter is to determine the added value, or otherwise, of NNR

models by benchmarking their results against traditional regression-based and other fore-

casting techniques. Accordingly, ¬nancial trading models are developed for the EUR/USD

exchange rate, using daily data from 17 October 1994 to 18 May 2000 for in-sample

estimation, leaving the period from 19 May 2000 to 3 July 2001 for out-of-sample fore-

casting.1 The trading models are evaluated in terms of forecasting accuracy and in terms

of trading performance via a simulated trading strategy.

1

The EUR/USD exchange rate only exists from 4 January 1999: it was retropolated from 17 October 1994 to

31 December 1998 and a synthetic EUR/USD series was created for that period using the ¬xed EUR/DEM

conversion rate agreed in 1998, combined with the USD/DEM daily market rate.

Applications of Advanced Regression Analysis 3

Our results clearly show that NNR models do indeed add value to the forecast-

ing process.

The chapter is organised as follows. Section 1.2 presents a brief review of some of the

research in FX markets. Section 1.3 describes the data used, addressing issues such as

stationarity. Section 1.4 presents the benchmark models selected and our methodology.

Section 1.5 brie¬‚y discusses NNR model theory and methodology, raising some issues

surrounding the technique. Section 1.6 describes the out-of-sample forecasting accuracy

and trading simulation results. Finally, Section 1.7 provides some concluding remarks.

1.2 LITERATURE REVIEW

It is outside the scope of this chapter to provide an exhaustive survey of all FX applica-

tions. However, we present a brief review of some of the material concerning ¬nancial

applications of NNR models that began to emerge in the late 1980s.

Bellgard and Goldschmidt (1999) examined the forecasting accuracy and trading per-

formance of several traditional techniques, including random walk, exponential smoothing,

and ARMA models with Recurrent Neural Network (RNN) models.2 The research was

based on the Australian dollar to US dollar (AUD/USD) exchange rate using half hourly

data during 1996. They conclude that statistical forecasting accuracy measures do not

have a direct bearing on pro¬tability, and FX time series exhibit nonlinear patterns that

are better exploited by neural network models.

Tyree and Long (1995) disagree, ¬nding the random walk model more effective than the

NNR models examined. They argue that although price changes are not strictly random,

in their case the US dollar to Deutsche Mark (USD/DEM) daily price changes from 1990

to 1994, from a forecasting perspective what little structure is actually present may well

be too negligible to be of any use. They acknowledge that the random walk is unlikely

to be the optimal forecasting technique. However, they do not assess the performance of

the models ¬nancially.

The USD/DEM daily price changes were also the focus for Refenes and Zaidi (1993).

However they use the period 1984 to 1992, and take a different approach. They developed

a hybrid system for managing exchange rate strategies. The idea was to use a neural

network model to predict which of a portfolio of strategies is likely to perform best

in the current context. The evaluation was based upon returns, and concludes that the

hybrid system is superior to the traditional techniques of moving averages and mean-

reverting processes.

El-Shazly and El-Shazly (1997) examined the one-month forecasting performance of

an NNR model compared with the forward rate of the British pound (GBP), German

Mark (DEM), and Japanese yen (JPY) against a common currency, although they do not

state which, using weekly data from 1988 to 1994. Evaluation was based on forecasting

accuracy and in terms of correctly forecasting the direction of the exchange rate. Essen-

tially, they conclude that neural networks outperformed the forward rate both in terms of

accuracy and correctness.

Similar FX rates are the focus for Gen¸ ay (1999). He examined the predictability of

c

daily spot exchange rates using four models applied to ¬ve currencies, namely the French

franc (FRF), DEM, JPY, Swiss franc (CHF), and GBP against a common currency from

2

A brief discussion of RNN models is presented in Section 1.5.

4 Applied Quantitative Methods for Trading and Investment

1973 to 1992. The models include random walk, GARCH(1,1), NNR models and nearest

neighbours. The models are evaluated in terms of forecasting accuracy and correctness of

sign. Essentially, he concludes that non-parametric models dominate parametric ones. Of

the non-parametric models, nearest neighbours dominate NNR models.

Yao et al. (1996) also analysed the predictability of the GBP, DEM, JPY, CHF, and

AUD against the USD, from 1984 to 1995, but using weekly data. However, they take an

ARMA model as a benchmark. Correctness of sign and trading performance were used

to evaluate the models. They conclude that NNR models produce a higher correctness

of sign, and consequently produce higher returns, than ARMA models. In addition, they

state that without the use of extensive market data or knowledge, useful predictions can

be made and signi¬cant paper pro¬t can be achieved.

Yao et al. (1997) examine the ability to forecast the daily USD/CHF exchange rate

using data from 1983 to 1995. To evaluate the performance of the NNR model, “buy and

hold” and “trend following” strategies were used as benchmarks. Again, the performance

was evaluated through correctness of sign and via a trading simulation. Essentially, com-

pared with the two benchmarks, the NNR model performed better and produced greater

paper pro¬t.

Carney and Cunningham (1996) used four data sets over the period 1979 to 1995

to examine the single-step and multi-step prediction of the weekly GBP/USD, daily

GBP/USD, weekly DEM/SEK (Swedish krona) and daily GBP/DEM exchange rates.

The neural network models were benchmarked by a na¨ve forecast and the evaluation

±

was based on forecasting accuracy. The results were mixed, but concluded that neural

network models are useful techniques that can make sense of complex data that de¬es

traditional analysis.

A number of the successful forecasting claims using NNR models have been pub-

lished. Unfortunately, some of the work suffers from inadequate documentation regarding

methodology, for example El-Shazly and El-Shazly (1997), and Gen¸ ay (1999). This

c

makes it dif¬cult to both replicate previous work and obtain an accurate assessment of

just how well NNR modelling techniques perform in comparison to other forecasting

techniques, whether regression-based or not.

Notwithstanding, it seems pertinent to evaluate the use of NNR models as an alternative

to traditional forecasting techniques, with the intention to ascertain their potential added

value to this speci¬c application, namely forecasting the EUR/USD exchange rate.

1.3 THE EXCHANGE RATE AND RELATED FINANCIAL DATA

The FX market is perhaps the only market that is open 24 hours a day, seven days a

week. The market opens in Australasia, followed by the Far East, the Middle East and

Europe, and ¬nally America. Upon the close of America, Australasia returns to the market

and begins the next 24-hour cycle. The implication for forecasting applications is that in

certain circumstances, because of time-zone differences, researchers should be mindful

when considering which data and which subsequent time lags to include.

In any time series analysis it is critical that the data used is clean and error free since

the learning of patterns is totally data-dependent. Also signi¬cant in the study of FX time

series forecasting is the rate at which data from the market is sampled. The sampling

frequency depends on the objectives of the researcher and the availability of data. For

example, intraday time series can be extremely noisy and “a typical off-¬‚oor trader. . .

Applications of Advanced Regression Analysis 5

would most likely use daily data if designing a neural network as a component of an

overall trading system” (Kaastra and Boyd, 1996: 220). For these reasons the time series

used in this chapter are all daily closing data obtained from a historical database provided

by Datastream.

The investigation is based on the London daily closing prices for the EUR/USD

exchange rate.3 In the absence of an indisputable theory of exchange rate determina-

tion, we assumed that the EUR/USD exchange rate could be explained by that rate™s

recent evolution, volatility spillovers from other ¬nancial markets, and macro-economic

and monetary policy expectations. With this in mind it seemed reasonable to include,

as potential inputs, other leading traded exchange rates, the evolution of important stock

and commodity prices, and, as a measure of macro-economic and monetary policy expec-

tations, the evolution of the yield curve. The data retained is presented in Table 1.1

along with the relevant Datastream mnemonics, and can be reviewed in Sheet 1 of the

DataAppendix.xls Excel spreadsheet.

Table 1.1 Data and Datastream mnemonics

Number Variable Mnemonics

1 FTSE 100 “ PRICE INDEX FTSE100

2 DAX 30 PERFORMANCE “ PRICE INDEX DAXINDX

3 S&P 500 COMPOSITE “ PRICE INDEX S&PCOMP

4 NIKKEI 225 STOCK AVERAGE “ PRICE INDEX JAPDOWA

5 FRANCE CAC 40 “ PRICE INDEX FRCAC40

6 MILAN MIB 30 “ PRICE INDEX ITMIB30

7 DJ EURO STOXX 50 “ PRICE INDEX DJES50I

8 US EURO-$ 3 MONTH (LDN:FT) “ MIDDLE RATE ECUS$3M

9 JAPAN EURO-$ 3 MONTH (LDN:FT) “ MIDDLE RATE ECJAP3M

10 EURO EURO-CURRENCY 3 MTH (LDN:FT) “ MIDDLE RATE ECEUR3M

11 GERMANY EURO-MARK 3 MTH (LDN:FT) “ MIDDLE RATE ECWGM3M

12 FRANCE EURO-FRANC 3 MTH (LDN:FT) “ MIDDLE RATE ECFFR3M

13 UK EURO-£ 3 MONTH (LDN:FT) “ MIDDLE RATE ECUK£3M

14 ITALY EURO-LIRE 3 MTH (LDN:FT) “ MIDDLE RATE ECITL3M

15 JAPAN BENCHMARK BOND-RYLD.10 YR (DS) “ RED. YIELD JPBRYLD

16 ECU BENCHMARK BOND 10 YR (DS) ˜DEAD™ “ RED. YIELD ECBRYLD

17 GERMANY BENCHMARK BOND 10 YR (DS) “ RED. YIELD BDBRYLD

18 FRANCE BENCHMARK BOND 10 YR (DS) “ RED. YIELD FRBRYLD

19 UK BENCHMARK BOND 10 YR (DS) “ RED. YIELD UKMBRYD

20 US TREAS. BENCHMARK BOND 10 YR (DS) “ RED. YIELD USBD10Y

21 ITALY BENCHMARK BOND 10 YR (DS) “ RED. YIELD ITBRYLD

22 JAPANESE YEN TO US $ (WMR) “ EXCHANGE RATE JAPAYE$

23 US $ TO UK £ (WMR) “ EXCHANGE RATE USDOLLR

24 US $ TO EURO (WMR) “ EXCHANGE RATE USEURSP

25 Brent Crude-Current Month, fob US $/BBL OILBREN

26 GOLD BULLION $/TROY OUNCE GOLDBLN

27 Bridge/CRB Commodity Futures Index “ PRICE INDEX NYFECRB

3

EUR/USD is quoted as the number of USD per euro: for example, a value of 1.2657 is USD1.2657 per euro.

The EUR/USD series for the period 1994“1998 was constructed as indicated in footnote 1.

6 Applied Quantitative Methods for Trading and Investment

All the series span the period from 17 October 1994 to 3 July 2001, totalling 1749

trading days. The data is divided into two periods: the ¬rst period runs from 17 October

1994 to 18 May 2000 (1459 observations) used for model estimation and is classi¬ed

in-sample, while the second period from 19 May 2000 to 3 July 2001 (290 observa-

tions) is reserved for out-of-sample forecasting and evaluation. The division amounts to

approximately 17% being retained for out-of-sample purposes.

Over the review period there has been an overall appreciation of the USD against

the euro, as presented in Figure 1.1. The summary statistics of the EUR/USD for the

examined period are presented in Figure 1.2, highlighting a slight skewness and low

kurtosis. The Jarque“Bera statistic con¬rms that the EUR/USD series is non-normal at the

99% con¬dence interval. Therefore, the indication is that the series requires some type of

transformation. The use of data in levels in the FX market has many problems, “FX price

movements are generally non-stationary and quite random in nature, and therefore not very

suitable for learning purposes. . . Therefore for most neural network studies and analysis

concerned with the FX market, price inputs are not a desirable set” (Mehta, 1995: 191).

To overcome these problems, the EUR/USD series is transformed into rates of return.

Given the price level P1 , P2 , . . . , Pt , the rate of return at time t is formed by:

Pt

Rt = ’1 (1.1)

Pt’1

An example of this transformation can be reviewed in Sheet 1 column C of the

oos Na¨ve.xls Excel spreadsheet, and is also presented in Figure 1.5. See also the comment

±

in cell C4 for an explanation of the calculations within this column.

An advantage of using a returns series is that it helps in making the time series sta-

tionary, a useful statistical property.

Formal con¬rmation that the EUR/USD returns series is stationary is con¬rmed at the

1% signi¬cance level by both the Augmented Dickey“Fuller (ADF) and Phillips“Perron

(PP) test statistics, the results of which are presented in Tables 1.2 and 1.3.

The EUR/USD returns series is presented in Figure 1.3. Transformation into returns

often creates a noisy time series. Formal con¬rmation through testing the signi¬cance of

1.60

1.50

1.40

1.30

EUR/USD

1.20

1.10

1.00

0.90

0.80

0.70

0.60

95 96 97 98 99 00 01

17 October 1994 to 3 July 2001

EUR/USD London daily closing prices (17 October 1994 to 3 July 2001)4

Figure 1.1

4

Retropolated series for 17 October 1994 to 31 December 1998.

Applications of Advanced Regression Analysis 7

200

Series:USEURSP

Sample 1 1749

Observations 1749

150

Mean 1.117697

Median 1.117400

Maximum 1.347000

100

Minimum 0.828700

Std. Dev. 0.136898

’0.329711

Skewness

Kurtosis 2.080124

50

Jarque“Bera 93.35350

Probability 0.000000

0

0.9 1.0 1.1 1.2 1.3

Figure 1.2 EUR/USD summary statistics (17 October 1994 to 3 July 2001)

Table 1.2 EUR/USD returns ADF test

’18.37959 ’3.4371

critical valuea

ADF test statistic 1%

’2.8637

5% critical value

’2.5679

10% critical value

a

MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey“Fuller Test Equation

Dependent Variable: D(DR’ USEURSP)

Method: Least Squares

Sample(adjusted): 7 1749

Included observations: 1743 after adjusting endpoints

t-Statistic

Variable Coef¬cient Std. error Prob.

’0.979008 ’18.37959

DR’ USEURSP(’1) 0.053266 0.0000

’0.002841 ’0.059636

D(DR’ USEURSP(’1)) 0.047641 0.9525

’0.015731 ’0.381009

D(DR’ USEURSP(’2)) 0.041288 0.7032

’0.011964 ’0.355179

D(DR’ USEURSP(’3)) 0.033684 0.7225

’0.014248 ’0.593095

D(DR’ USEURSP(’4)) 0.024022 0.5532

’0.000212 ’1.536692

C 0.000138 0.1246

R-squared 0.491277 Mean dependent var. 1.04E-06

Adjusted R-squared 0.489812 S.D. dependent var. 0.008048

’7.476417

S.E. of regression 0.005748 Akaike info. criterion

’7.457610

Sum squared resid. 0.057394 Schwarz criterion

F -statistic

Log likelihood 6521.697 335.4858

Durbin“Watson stat. 1.999488 Prob(F -statistic) 0.000000

8 Applied Quantitative Methods for Trading and Investment

Table 1.3 EUR/USD returns PP test

’41.04039 ’3.4370

critical valuea

PP test statistic 1%

’2.8637

5% critical value

’2.5679

10% critical value

a

MacKinnon critical values for rejection of hypothesis of a unit root.

Lag truncation for Bartlett kernel: 7 (Newey“West suggests: 7)

Residual variance with no correction 3.29E-05

Residual variance with correction 3.26E-05

Phillips“Perron Test Equation

Dependent Variable: D(DR’ USEURSP)

Method: Least Squares

Sample(adjusted): 3 1749

Included observations: 1747 after adjusting endpoints

t-Statistic

Variable Coef¬cient Std. error Prob.

’0.982298 ’41.04333

DR’ USEURSP(’1) 0.023933 0.0000

’0.000212 ’1.539927

C 0.000137 0.1238

’1.36E-06

R-squared 0.491188 Mean dependent var.

Adjusted R-squared 0.490896 S.D. dependent var. 0.008041

’7.482575

S.E. of regression 0.005737 Akaike info. criterion

’7.476318

Sum squared resid. 0.057436 Schwarz criterion

F -statistic

Log likelihood 6538.030 1684.555

Durbin“Watson stat. 1.999532 Prob(F -statistic) 0.000000

0.04

0.03

EUR/USD returns

0.02

0.01

0

’0.01

’0.02

’0.03

18 October 1994 to 3 July 2001

Figure 1.3 The EUR/USD returns series (18 October 1994 to 3 July 2001)

Applications of Advanced Regression Analysis 9

the autocorrelation coef¬cients reveals that the EUR/USD returns series is white noise

at the 99% con¬dence interval, the results of which are presented in Table 1.4. For such

series the best predictor of a future value is zero. In addition, very noisy data often makes

forecasting dif¬cult.

The EUR/USD returns summary statistics for the examined period are presented in

Figure 1.4. They reveal a slight skewness and high kurtosis and, again, the Jarque“Bera

statistic con¬rms that the EUR/USD series is non-normal at the 99% con¬dence

interval. However, such features are “common in high frequency ¬nancial time series

data” (Gen¸ ay, 1999: 94).

c

Table 1.4 EUR/USD returns correlogram

Sample: 1 1749

Included observations: 1748

Q-Stat.

Autocorrelation Partial correlation Prob.

1 0.018 0.018 0.5487 0.459

’0.012 ’0.013

2 0.8200 0.664

3 0.003 0.004 0.8394 0.840

’0.002 ’0.002

4 0.8451 0.932

5 0.014 0.014 1.1911 0.946

’0.009 ’0.010

6 1.3364 0.970

7 0.007 0.008 1.4197 0.985

’0.019 ’0.019

8 2.0371 0.980

9 0.001 0.002 2.0405 0.991

10 0.012 0.012 2.3133 0.993

11 0.012 0.012 2.5787 0.995

’0.028 ’0.029

12 3.9879 0.984

400

Series:DR_USEURSP

Sample 2 1749

Observations 1748

300

’0.000214

Mean

’0.000377

Median

Maximum 0.033767

200

’0.024898

Minimum

Std. Dev. 0.005735

Skewness 0.434503

Kurtosis 5.009624

100

Jarque“Bera 349.1455

Probability 0.000000

0

’0.0250 ’0.0125 0.0000 0.0125 0.0250

Figure 1.4 EUR/USD returns summary statistics (17 October 1994 to 3 July 2001)

10 Applied Quantitative Methods for Trading and Investment

A further transformation includes the creation of interest rate yield curve series, gen-

erated by:

yc = 10 year benchmark bond yields“3 month interest rates (1.2)

In addition, all of the time series are transformed into returns series in the manner

described above to account for their non-stationarity.

1.4 BENCHMARK MODELS: THEORY AND METHODOLOGY

The premise of this chapter is to examine the use of regression models in EUR/USD

forecasting and trading models. In particular, the performance of NNR models is compared

with other traditional forecasting techniques to ascertain their potential added value as

a forecasting tool. Such methods include ARMA modelling, logit estimation, Moving

Average Convergence/Divergence (MACD) technical models, and a na¨ve strategy. Except

±

for the straightforward na¨ve strategy, all benchmark models were estimated on our in-

±

sample period. As all of these methods are well documented in the literature, they are

simply outlined below.

1.4.1 Na¨ve strategy

±

The na¨ve strategy simply assumes that the most recent period change is the best predictor

±

of the future. The simplest model is de¬ned by:

ˆ

Yt+1 = Yt (1.3)

ˆ

where Yt is the actual rate of return at period t and Yt+1 is the forecast rate of return for

the next period.

The na¨ve forecast can be reviewed in Sheet 1 column E of the oos Na¨ve.xls Excel

± ±

spreadsheet, and is also presented in Figure 1.5. Also, please note the comments within

the spreadsheet that document the calculations used within the na¨ve, ARMA, logit, and

±

NNR strategies.

The performance of the strategy is evaluated in terms of forecasting accuracy and in

terms of trading performance via a simulated trading strategy.

1.4.2 MACD strategy

Moving average methods are considered quick and inexpensive and as a result are rou-

tinely used in ¬nancial markets. The techniques use an average of past observations to

smooth short-term ¬‚uctuations. In essence, “a moving average is obtained by ¬nding the

mean for a speci¬ed set of values and then using it to forecast the next period” (Hanke

and Reitsch, 1998: 143).

The moving average is de¬ned as:

(Yt + Yt’1 + Yt’2 + · · · + Yt’n+1 )

ˆ

Mt = Yt+1 = (1.4)

n

Applications of Advanced Regression Analysis 11

Figure 1.5 Na¨ve forecast Excel spreadsheet (out-of-sample)

±

where Mt is the moving average at time t, n is the number of terms in the moving average,

ˆ

Yt is the actual level at period t 5 and Yt+1 is the level forecast for the next period.

The MACD strategy used is quite simple. Two moving average series M1,t and M2,t

are created with different moving average lengths n and m. The decision rule for tak-

ing positions in the market is straightforward. If the short-term moving average (SMA)

intersects the long-term moving average (LMA) from below a “long” position is taken.

Conversely, if the LMA is intersected from above a “short” position is taken.6 This strat-

egy can be reviewed in Sheet 1 column E of the is 35&1MA.xls Excel spreadsheet, and

is also presented in Figure 1.6. Again, please note the comments within the spreadsheet

that document the calculations used within the MACD strategy.

The forecaster must use judgement when determining the number of periods n and m

on which to base the moving averages. The combination that performed best over the

in-sample period was retained for out-of-sample evaluation. The model selected was a

combination of the EUR/USD series and its 35-day moving average, namely n = 1 and

m = 35 respectively, or a (1,35) combination. A graphical representation of the combina-

tion is presented in Figure 1.7. The performance of this strategy is evaluated in terms of

forecasting accuracy via the correct directional change measure, and in terms of trading

performance.

Several other “adequate” models were produced and their performance evaluated. The

trading performance of some of these combinations, such as the (1,40) combination, and

5

In this strategy the EUR/USD levels series is used as opposed to the returns series.

6

A “long” EUR/USD position means buying euros at the current price, while a “short” position means selling

euros at the current price.

12 Applied Quantitative Methods for Trading and Investment

Figure 1.6 EUR/USD and 35-day moving average combination Excel spreadsheet

1.40

1.30

1.20

EUR/USD

1.10

1.00

0.90

0.80

95 96 97 98 99 00 01

17 October 1994 to 3 July 2001

Figure 1.7 EUR/USD and 35-day moving average combination

the (1,35) combination results were only marginally different. For example, the Sharpe

ratio differs only by 0.01, and the average gain/loss ratio by 0.02. However, the (1,35)

combination has the lowest maximum drawdown at ’12.43% and lowest probability of

a 10% loss at 0.02%.7 The evaluation can be reviewed in Sheet 2 of the is 35&1MA.xls

and is 40&1MA.xls Excel spreadsheets, and is also presented in Figures 1.8 and 1.9,

7

A discussion of the statistical and trading performance measures used to evaluate the strategies is presented

below in Section 1.6.

Applications of Advanced Regression Analysis 13

Figure 1.8 (1,35) combination moving average Excel spreadsheet (in-sample)

respectively. On balance, the (1,35) combination was considered “best” and therefore

retained for further analysis.

1.4.3 ARMA methodology

ARMA models are particularly useful when information is limited to a single stationary

series,8 or when economic theory is not useful. They are a “highly re¬ned curve-¬tting

device that uses current and past values of the dependent variable to produce accurate

short-term forecasts” (Hanke and Reitsch, 1998: 407).

The ARMA methodology does not assume any particular pattern in a time series, but

uses an iterative approach to identify a possible model from a general class of models.

Once a tentative model has been selected, it is subjected to tests of adequacy. If the

speci¬ed model is not satisfactory, the process is repeated using other models until a

satisfactory model is found. Sometimes, it is possible that two or more models may

approximate the series equally well, in this case the most parsimonious model should

prevail. For a full discussion on the procedure refer to Box et al. (1994), Gouri´ roux

e

and Monfort (1995), or Pindyck and Rubinfeld (1998).

The ARMA model takes the form:

Yt = φ0 + φ1 Yt’1 + φ2 Yt’2 + · · · + φp Yt’p + µt ’ w1 µt’1 ’ w2 µt’2 ’ · · · ’ wq µt’q

(1.5)

8

The general class of ARMA models is for stationary time series. If the series is not stationary an appropriate

transformation is required.

14 Applied Quantitative Methods for Trading and Investment