Asset allocation and international investments (finance and capital markets series)

3.2 Theoretical framework of domestic and foreign biases 443.4 The determinants of domestic and foreign biases 56 4 The Critical Line Algorithm for UPM–LPM Parametric General Asset Alloc

Asset Allocation and International Investments

Greg N Gregoriou

Edited by

ASSET ALLOCATION AND INTERNATIONAL

INVESTMENTS

Also edited by Greg N Gregoriou

ADVANCES IN RISK MANAGEMENTDIVERSIFICATION AND PORTFOLIO MANAGEMENT OF MUTUAL FUNDS

PERFORMANCE OF MUTUAL FUNDS

Asset Allocation and

International

Investments

Edited by GREG N GREGORIOU

Selection and editorial matter © Greg N Gregoriou 2007

Individual chapters © contributors 2007

All rights reserved No reproduction, copy or transmission of this publication may be made without written permission.

No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued

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Asset allocation and international investments / edited by Gerg N Gregoriou p.cm — (Finance and capital markets)

Includes bibliographical references and index.

ISBN 0–230–01917–X

1 Asset allocation 2 Investments, Foreign 3 Globalization—Economic aspects.

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1 Time-Varying Downside Risk: An Application

Rachel Campbell and Roman Kräussl

2 International Stock Portfolios and Optimal

Currency Hedging with Regime Switching 16

Markus Leippold and Felix Morger

3.2 Theoretical framework of domestic and foreign biases 44

3.4 The determinants of domestic and foreign biases 56

4 The Critical Line Algorithm for UPM–LPM Parametric

General Asset Allocation Problem with Allocation

Denisa Cumova, David Moreno and David Nawrocki

4.2 The upside potential–downside risk portfolio model 82

5 Currency Crises, Contagion and Portfolio Selection 96

Arindam Bandopadhyaya and Sushmita Nagarajan

5.2 Stock market average rates of return and average volatility 97

6 Bond and Stock Market Linkages: The Case of

8.2 Higher moment performance analysis – the theory 138

9 Liquidity and Market Efficiency Before and

After the Introduction of Electronic Trading at

Mark Burgess and J Wickramanayake

10 How Does Systematic Risk Impact Stocks?

A Study of the French Financial Market 183

11 Matrix Elliptical Contoured Distributions versus a

Stable Model: Application to Daily Stock Returns of

Taras Bodnar and Wolfgang Schmid

I would like to thank Stephen Rutt, Publishing Director, and AlexandraDawe, Assistant Editor, at Palgrave Macmillan for their suggestions, effi-ciency and helpful comments throughout the production process, as well

as Keith Povey (with Elaine Towns) for copy-editing and editorial sion of the highest order In addition, I would like to thank the numerousanonymous referees in the US and Europe during the review and selectionprocess of the articles proposed for this volume

supervi-xi

Notes on the Contributors

The Editor

Greg N Gregoriou is Associate Professor of Finance and coordinator offaculty research in the School of Business and Economics at the State Uni-versity of New York (Plattsburgh) He obtained his PhD (Finance) fromthe University of Quebec at Montreal and is the hedge fund editor for the

peer-reviewed journal Derivatives Use, Trading and Regulation, published by

Palgrave Macmillan, based in the UK He has authored over fifty articles

on hedge funds, and managed futures in various US and UK peer-reviewed

publications, including Journal of Portfolio Management, Journal of Futures Markets, European Journal of Finance, Journal of Asset Management, European Journal of Operational Research and Annals of Operations Research He has

published four books with John Wiley and Sons Inc and four with Elsevier

The Contributors

Fathi Abidis a Professor of Finance He is Director of the research teamMODESFI specializing in financial modeling and financial strategy Helectures frequently on financial market theory and has taught investmentand portfolio management at Tunisian and European universities He haswritten and co-authored numerous articles in national and internationalscientific journals, books and proceedings

xii

N O T E S O N T H E C O N T R I B U T O R S xiii

Finance in the Accounting and Finance Department at UMass Boston, USA

He is also the Director of the College of Management’s Financial vices Forum A recipient of the Dean’s Award for Distinguished Research,

Ser-Dr Bandopadhyaya has published in journals such as the Journal of national Money and Finance, Journal of Empirical Finance, Journal of Banking and Finance and Review of Economics and Statistics He has presented his

Inter-work at national and international conferences such as those of the cial Management Association, European Finance Association and EuropeanEconomic Association He has presented research reports of the FinancialServices Form at the Boston Stock Exchange and the Federal Reserve Bank ofBoston Dr Bandopadhyaya teaches corporate finance, international financeand managerial economics He has received teaching awards from the Col-lege of Management, including the Professor of the Year Award and theBetty Diener Award for Teaching Excellence

Finan-Slah Bahloul is an Assistant Professor of Finance at Higher School ofBusiness Administration in Sfax, Tunisia He is a research assistant inthe MODESFI team and has taught international finance and financialdecision-making

Zsolt Berényiholds an MSc in Economics from the University of EconomicSciences in Budapest, and a PhD in Finance from the University of Munich.His main interests lie in the risk and performance evaluation of alternativeinvestments: hedge funds, CTAs and credit funds After working for manyyears for the Deutsche Bank, HypoVereinsbank and KPMG at various loca-tions throughout Europe, Zsolt now leads an independent consultancy inBudapest, Hungary

Taras Bodnarstudied Mathematics at the Lviv National University, Ukrainefrom 1996 to 2001 He received a PhD in Economics in 2004 from the Euro-pean University Viadrina, Frankfurt (Oder), Germany Currently, he is aresearch assistant at the Department of Statistics, European University Viad-rina His fields of interest are quantitative methods in finance, nonstationarytime series, elliptical distributions and econometric applications

Mark Burgesscurrently works in the financial services industry in Australia

He has a Bachelor of Business (Honors) degree from Monash University,Australia

Rachel Campbellcompleted her PhD on Risk Management in InternationalFinancial Markets at Erasmus University, Rotterdam, The Netherlands in

2001 She currently works at the University of Maastricht as an AssistantProfessor of Finance Her work has been published in a number of leading

xiv N O T E S O N T H E C O N T R I B U T O R S

journals, including the Journal of International Money and Finance, Journal of Banking and Finance, Financial Analysts Journal, Journal of Portfolio Manage- ment, Journal of Risk, and Derivatives Weekly She teaches with Euromoney

Financial Training on Art Investment, and works as an Independent nomic Adviser for the Fine Art Fund in London, and for Fine Art WealthManagement, UK

Eco-Adeline Chan currently works in the financial services industry in gapore She has a Bachelor of Business (Honors) degree from MonashUniversity, Australia

Sin-Denisa Cumovaworks in the fund management group at the BerenbergBank in Hamburg, Germany She received her PhD in Finance from theUniversity of Technology, Chemnitz, Germany

Hayette Gatfaoui gained a PhD in “Default Risk Valuation of FinancialAssets” University Paris 1 in 2000 He taught for five years at the Univer-sity Paris 1 (Pantheon-Sorbonne) France, and is now an Associate Professor

at Rouen Graduate School of Management, France He is a specialist inapplied mathematics (holding a Master’s degree in stochastic modeling forfinance and economics) He is currently advising financial firms about riskmeasurement and risk management topics for asset management, and for

credit risk management purposes Dr Gatfaoui is also a referee for the national Journal of Theoretical and Applied Finance (IJTAF) His current research

Inter-areas concern risk typology in financial markets, quantitative finance andrisk analysis

Roman Kräusslobtained a first-class honors Master’s degree in Economicswith a specialization in Financial Econometrics from the University of Biele-feld, Germany, in 1998 He completed his PhD on the Role of Credit RatingAgencies in International Financial Markets at Johann Wolfgang Goethe Uni-versity, Frankfurtam Main, Germany, in 2002 As the Head of QuantitativeResearch at Cognitrend GmbH, he was closely involved with the financialindustry Currently he is Assistant Professor of Finance at Vrije Univer-siteit Amsterdam, The Netherlands and research fellow with the Centrefor Financial Studies, Frankfurtam Main

Markus Leippoldis Assistant Professor of Finance at the Swiss BankingInstitute of the University of Zurich, Switzerland Prior to moving back toacademia he worked for Sungard, Trading and Risk Management Systems,and the Zurich Cantonal Bank His main research interests are term struc-ture modeling, asset pricing and risk management He obtained his PhD

in financial economics from the University of St Gallen, Switzerland, in

1999 During his PhD studies, he was a research fellow at the Stern School

of Business in New York He has published in several journals, such as the

N O T E S O N T H E C O N T R I B U T O R S xv

Journal of Financial and Quantitative Analysis, Journal of Economic Dynamics and Control, Journal of Banking and Finance, Review of Derivative Research, Jour- nal of Risk, and Review of Finance In 2003, he and his colleagues received an

award from the German Finance Association for their paper on the rium impacts of value-at-risk regulation, and an achievement award fromRISK for their paper on operational risk In 2004, their research paper oncredit contagion won the STOXX Gold Award at the annual conference ofthe European Financial Management Association

CarlosIII, Madrid, Spain, and a BSc degree in Mathematics from the sidad Complutense, Madrid He is currently Assistant Professor of FinancialEconomics and Accounting at Universidad Pompeu Fabra, Barcelona andCo-Director of the Master’s Program in Finance He has previously heldteaching and research positions at the Financial Option Research Centre(Warwick Business School, UK), Universidad CarlosIIIde Madrid, and atthe IESE Business School, Barcelona, Spain His research interests focus

Univer-on finance in cUniver-ontinuous time, with special emphasis Univer-on derivatives kets, financial engineering applications, pricing of derivatives, empiricalanalysis of different pricing models, portfolio management and term struc-ture models His research has been published in a number of academic

mar-journals including Review of Derivatives Research and Journal of Futures kets, as well as in professional volumes He has presented his work at a

Mar-number of international conferences and has given invited talks at many

academic and nonacademic institutions He is associate editor of Revista de Economía Financiera and a member of GARP (the Global Association of Risk

Professionals)

Felix Morgeris a fourth-year PhD student at the Swiss Banking Institute

of the University of Zurich, Switzerland The main part of his thesis isconcerned with the theoretical and empirical aspects of Bayesian learningmodels with Markov switching and their application to asset allocation.Prior to his PhD studies, he worked as a consultant in pension funds

Sushmita Nagarajanis a Senior Associate in the Structured Finance Group

at Moody’s Investor Service, New York Her areas of expertise are rating andmonitoring various types of structured derivative products using Moody’srating methodologies She also provides quantitative analysis and researchsurrounding complex derivative products such as asset-backed commer-cial paper structures Prior to joining Moody’s she was an intern at StateStreet Research and Management as a Fixed Income Research Analyst withemphasis on Collateralized Debt Obligations She graduated summa-cum-laude with a MSc degree in Finance from Boston College, and has an MBA

in Finance from Jawaharlal Nehru Technological University, India

xvi N O T E S O N T H E C O N T R I B U T O R S

David Nawrockiis the Katherine M and Richard J Salisbury Jr Professor

of Finance at Villanova University, Villanova, Pa., USA He is a tered investment adviser and is the director of the Institute for Research inAdvanced Financial Technology (IRAFT) at Villanova Nawrocki’s researchincludes work on financial market theory, downside-risk measures, systemstheory, portfolio theory, and business cycles He received his PhD in Financefrom the Pennsylvania State University, USA

regis-Wolfgang Schmidis a Full Professor at the European University in Frankfurt(Oder), Germany He received a PhD in Mathematics in 1984 at the Univer-sity of Ulm, Germany His fields of major statistical activities are quantitativemethods in finance, statistical process control and econometric applications

J Wickramanayakeobtained his PhD in 1994 from La Trobe University, tralia He completed his Master’s degree at Williams College, Williamstown,Ma., USA in 1982, and did postgraduate studies in the Netherlands in 1978

Aus-He has been a member of the Financial Services Institute of Australasia forover ten years Dr Wickramanayake has more than twenty years’ experience

as a financial analyst at a central bank Currently, he teaches finance at bothundergraduate and postgraduate levels at Monash University, Australia

Dr Wickramanayake’s research interests involve banking, financial markets,mergers/acquisitions, bankruptcy and business failures, fund management,superannuation and pension finance

Chapter 1 deals with the economic downturn during 2000 which left manyinvestors with burnt fingers and weary of investing in equities There hasbeen a continued search for alternative asset classes to fulfill the need forpreserving returns while not taking on too high a risk One such innovativealternative is investing in art as an alternative to stocks, bonds and real estate.This chapter analyses in a detailed empirical study how the risk during theart market bubble increased dramatically before the collapse of the market inthe early 1990s Understanding how deviations from normality in the form

of extreme market returns link to the creation of a bubble in asset prices iscrucial to our understanding of risk-and-return relationships

Chapter 2 presents a model for strategic asset allocation and currencyhedging for an international investor, where the returns on stock indicesfollow a Gaussian regime-switching model The authors study a Bayesianinvestor, who has only partial information on the current regime switchingmodel being active, but updates the investor’s beliefs over time The resultsindicate that engaging in optimal currency hedging significantly improvesthe risk and return characteristics of the Bayesian investor

Chapter 3 describes an empirical study of the determinant factors ofdomestic and foreign home biases Using the equity holdings of thirtycountries, the authors find that a severe equity home bias exists for bothdeveloped and emerging markets Stock market development, informationcosts and familiarity factors are found to contribute the most to explainingforeign bias, whereas investor’s behavior has a significant effect on domesticbias

Chapter 4 discusses how human beings have always engaged in ent behavior above and below a target rate of return As a result, reverseS-shaped utility functions have been utilized to describe this human invest-ment behavior, ever since Friedman and Savage (1948) and Markowitz

differ-xvii

xviii I N T R O D U C T I O N

(1952) Fishburn (1977) made this approach operational with the lower

par-tial moment, LPM(a, t), model, which detailed risk-seeking and risk-averse

behavior below a minimum target return However, the Fishburn utilitymeasures have attracted criticism, since they assume a linear utility (riskneutral) above the target return Recently, the upper partial moment/lowerpartial moment (UPM/LPM) has been put forward as a solution to this prob-lem This chapter develops a UPM/LPM critical line algorithm that allowsthis model to be operational

Chapter 5 examines the characteristics of domestic and international folios from the perspective of a US investor in Asian emerging marketsduring a period where the economies have suffered a currency crisis Amongvarious portfolios constructed, a purely international portfolio posts supe-rior performance compared to a purely domestic one or a combination ofdomestic and international portfolios in the post-crisis period

port-Chapter 6 investigates the Brady bond markets of the two largest American economies – Mexico and Brazil Results indicate that, for the verynear future, the yield in each market is determined primarily by past yields

Latin-in the respective markets However, over a longer-term horizon, the Latin-relationships between the bond markets and the stock markets of the twocountries become increasingly important

inter-Chapter 7 provides an evaluation and comparison between the

explana-tory power of the macroeconomic model of Chen et al (1986) and the

three-factor model of Fama and French (1993) in explaining the variation

in returns in the Australian equity market for the decade of the 1990s Theempirical results show that firm attributes (Fama and French, 1993) aloneare insufficient to explain returns and macroeconomic variables (Chen et al.,1986) can be combined in a better multifactor model to explain the variation

in returns

Chapter 8 evaluates inter-market investment efficiency, which may be acomplicated task, especially across investment forms with widely differingreturn characteristics This chapter offers some new ideas on how to evaluatesuch investments, using the example of emerging markets The authorsshow that replicating the expected return distribution using options, theefficiency of any investment portfolio – for example, not just “emergingmarket” or “equity” – can be assessed and compared

Chapter 9 examines whether the Sydney Futures Exchange (SFE) in tralia has benefited from the introduction of electronic trading on November

Aus-15, 1999 Empirical results in this study show that during the early stage,

up to the beginning of August 2000 that the money SPI options were moreliquid at times of high volatility after the automation of the SFE However,the SPI futures were less liquid at times of medium to low market volatilityafter this event The authors also found a cointegrating relationship betweenthe Australian Stock Exchange (ASX) and the derivative market (SFE) before

is based on the assumption that any small stock market index is a distortedrepresentative of such a latent component Once this systematic risk factor

is exhibited, the authors attempt to assess its impact on a basket of Frenchstock returns

Chapter 11 explores the assumptions of independency and normalitywhich are not appropriate in many situations of practical interest, especiallyfor the data sets from emerging markets The authors propose to make use

of matrix elliptical distribution instead of the normal distribution cally, they show that the assumptions of the elliptical symmetry cannot berejected for daily returns

Empiri-Chapter 12 applies the modified Sharpe ratio to a small sample of dian hedge funds Many investors today use the traditional Sharpe ratio

Cana-to measure risk-adjusted performance, but the proposed modified VaRSharpe ratio is a superior and more precise method that can deal withthe skewed/non-normal returns that hedge fund possess The results showthat the modified Sharpe ratio is more precise when examining non-normalreturns

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C H A P T E R 1

Time-Varying Downside Risk: An Application to

Rachel Campbell and Roman Kräussl

1.1 INTRODUCTION

The economic downturn during 2000 left many investors with burnt fingersand weary of investing in equities Since then, there has been a search foralternative asset classes to fulfill the need to preserve returns, while notinvolving too high a risk Arising from the media’s continued concern about

a potential bubble in the housing market, many investors are showing anincreasing interest in alternative asset classes that are not so highly correlatedwith equities, and provide hedging potential as part of a diversified portfolio

of investments One such innovative alternative asset class to stocks, bondsand real estate is art, which is seen increasingly as not merely items withaesthetic value, but also as attractive investments with a potential capitalgain The planned launch of a Fund of Art Funds by ABN Amro in 2005,aiming to channel money into some existing (and some yet to be launched)independent art funds, serves to highlight this point

It is a well-known fact that investment in art is influenced strongly byincome and other fundamental economic factors The effect on the econ-omy from a collapse in the art market depends on the contagious impact ofthe art market on the rest of the financial system, predominately throughthe banking system Thus, what is the impact of a negative shock in theart market on the overall economy? We argue that the extent to whichreal effects are likely to occur from a bubble in the art market is likely to

1

2 T I M E -V A R Y I N G D O W N S I D E R I S K

be significantly less because of the type of investment that is made in theart market There are two main reasons for this First, as art is a luxurygood, investors tend to invest money into the art market that would notnecessarily be invested elsewhere in other asset classes beyond holding

it as surplus cash Second, the initial wealth levels of investors typicallyinvesting in art markets is higher, and therefore less at the mercy of thebanking system, as the banks are unlikely to let such investors becomeinsolvent

We argue that the likelihood of falling prices is only liable to affect thegeneral economy to the extent that the losses made might reduce liquid-ity in financial markets Even though booms in other markets, such as inreal estate, may lead to a collapse in the initial market followed by a col-lapse in the banking sector, this is much less likely to be the case in the artmarket

Although the real effects from a collapse in the art market may be icantly less than in other financial markets, the development of bubbles inthe art market is likely to be significantly greater The rate at which prices inthe art market are driven by taste and fashion, predominately via the media,

signif-is much greater than in other financial markets, where “value” signif-is a greaterfunction of market fundamentals The development of a large bubble in thegeneral price of all works of art was well documented in the early 1990s formost classes of art Indeed, it would appear that there was a severe devia-tion away from the fundamental valuation of art pieces during this period.This provides an extremely interesting and unique data series with which

to analyze the risk to the investor around the period of the bubble’s opment We focus on time-varying downside risk in relation to theory frombehavioral finance This, given our knowledge of the literature, is an area ofresearch that has not been undertaken before

devel-In this chapter we analyze the art market using a measure for time ance in the downside risk, which reflects “bubbliness” in the market Thisestimate measures the changing probability of large movements occurring

vari-in the return distribution of the historical time series of art price data Takvari-ingsuch an approach and using techniques developed in extreme value theory(EVT), we are able to provide some new insight into the creation and mea-surement of risk during times of the development of bubbles in financialmarkets We focus on a particularly interesting case: the art market Thismarket is highly media- and taste-driven, is illiquid and lacks transparency,and thus offers an ideal application in which to observe downside risk withprices that may deviate significantly from fundamental values

This chapter is organized as follows Section 1.2 briefly surveys theeconomic literature concerning art as an investment; we explore the finan-cial aspects of art investing by emphasizing similarities and differencesamong financial assets Section 1.3 discusses the data and the methodol-ogy, and presents the empirical results Section 1.4 presents some behavioral

R A C H E L C A M P B E L L A N D R O M A N K R Ä U S S L 3

explanations for our results Section 1.5 concludes and presents an outlookfor future research

1.2 ART AS AN INVESTMENT

1.2.1 The art market in general

Financial assets tend to be very liquid, allowing for diversification fits, and thus reduce risk Additionally, they are relatively transparent Mostfinancial assets can be selected on the basis of a fairly small set of objectivecriteria Fundamentals do exist and can be analyzed with standard financetools Such financial markets are characterized by a large number of indi-vidual buyers and sellers, transaction costs are low, and trades in perfectly(or nearly) identical assets are repeated millions of times daily in variousexchanges

bene-It goes without saying that, the first impression of the art markets isthat they differ significantly from other types of financial markets Mostart markets would appear to be characterized by product heterogeneity,illiquidity, behavioral anomalies, market segmentation, information asym-metries, and almost monopolistic price setting Moreover, there is no doubtthat a substantial amount of the return from art investment is derived notfrom classical financial returns but rather from intrinsic aesthetic qualitiesthrough art as a consumption good

Art works are not liquid assets, and transaction costs are high Shortselling is not possible, and supply is rather inelastic in the short term Thereare unavoidable delays between an owner’s decision to sell and the actualsale, since it takes about three to six months to “market a work” – that

is, to have it accepted by the auction house, take photographs and printand distribute the catalogue, publish advertisements for the coming auctionand so on Investing in art typically requires substantial knowledge of art andthe art market in general, and often a significant amount of capital to acquire

a work of a well-known artist Moreover, the art market is highly segmentedand dominated by a few large auction houses These auction houses, such asSotheby’s and Christie’s, are used by a restricted number of buyers, mostlywealthy collectors, public museums or private foundations Informationalasymmetries are essential features of these markets Furthermore, art sellsonly occasionally

Art objects are created by individuals Accordingly, there is only a single,unique piece of original work available This is an extreme case of a het-erogeneous commodity Therefore, financial risk in the art market is related

to specific material risk factors associated with the unique physical nature

of art works such as theft, fire, water damage, or the possible tion to another (less famous) artist Moreover, the value of an art object is

1.3 PREVIOUS EMPIRICAL STUDIES

In recent years, an extensive literature has arisen based on calculating thereturns on art investments Starting with Baumol (1986), these include,among others, empirical studies by Goetzmann (1993), Chanel (1995), Meiand Moses (2002) and Campbell (2005) Baumol (1986) and Goetzmann(1993) tend to concur that art is dominated as an investment product bystocks, bonds and real estate Goetzmann (1993) finds a positive relationshipbetween art investments and the stock market over shorter time periods Heargues that the high and significant positive correlation clearly makes artinvestment a poor instrument for the purposes of portfolio diversification.Goetzmann (1993) also finds evidence of a significant relationshipbetween aggregate financial wealth and the demand for art He concludesthat this empirical finding is sufficient evidence that the demand for artincreases with the wealth of art collectors since, in the twentieth century,art prices tended to follow stock market trends Chanel (1995) follows thisargumentation and concludes that financial markets react quickly to shocks

in the economy Profits generated on financial markets may be invested inart, so that developments in stock markets may be considered as leadingindicators for returns in the art markets

Mei and Moses (2002) take a somewhat different view They argue that adiversified portfolio of works of art play a more important role in portfoliodiversification They base their conclusions on their empirical finding thattheir art price index has lower volatility and a much lower correlation withother asset classes than was discovered in earlier research Campbell (2005)focuses on the extent of downside risk, which is less for the art market duringperiods in which the stock market performs badly This is highly likely to

be driven by issues relating to theories from behavioral finance, causednot only by the low liquidity on the art market, but also to investors being

R A C H E L C A M P B E L L A N D R O M A N K R Ä U S S L 5

anxious not to sell off art works representing a symbol of their reputation andstatus during falling financial markets Thus, maintaining art investmentremains strong during periods of economic downturn This helps to drivethe hedging connotation of art in the portfolio The cyclicality of the art andequity markets has been documented in a recent working paper by Bauer

et al (2005), who show that art investments perform well at times when

other asset classes are performing badly

Despite this strength during downturns, bubbles are also evident in theart market The famous bubble in the 1990s occurred because of the excessivedemand for works of art by the Japanese What happens to risk-and-returncharacteristics during these periods? Is risk time-varying during the expan-sion of the bubble? Could we have seen the extent to which a bubble wasdeveloping in the market? Before answering these questions, a number ofpreliminary queries need to be addressed on the definition and possibleestimation of a bubble

1.4 EMPIRICAL ANALYSIS

1.4.1 How to define a bubble in the art market?

What is a bubble in financial markets? How do we define bubbles ex ante or even ex post? A financial market bubble may be defined loosely as a sharp

increase in the price of an asset in a continuous process, with the initial risegenerating investors’ expectations of further future increases and therebyattracting new buyers These buyers are generally speculators, interested

in profits from trading in the asset rather than the asset’s earning capacity.Such a definition implies that a high and increasing price is not justified and

is fed by momentum investors who buy with the sole purpose of sellingquickly to other investors at a higher price

In recent years, economists have tried to give additional substance to thedefinition of a financial market bubble by linking asset price movements tofundamentals Fundamentals refer to those economic factors that togetherdetermine the price of any asset, such as cash flows and discount rates.For example, Stiglitz (1990, p 13) defines a bubble in financial markets in

the following way: “If the reason that the price is high today is only that

the selling price will be high tomorrow – when fundamental factors do notseem to justify such a price – then a bubble exists” In this context, Siegel(2003) argues that one cannot identify any asset price bubble immediately,because one has to wait a sufficient length of time to determine whether theprevious asset prices can be justified by the asset’s subsequent cash flows.Unfortunately, it is not that easy to find an operational definition of abubble in the art market If a bubble is defined only as excess changes inprices that are not captured by underlying economic fundamentals, then

wealth effects from real estate assets For example, Case et al (2001) show

that if the magnitude of the wealth effect from housing is around 5 percent,then a severe decline would lead to reduction in consumption of round-about US$150bn, which is about 2 percent of total personal consumptionexpenditures

Many analysts argue that the recent increase in home prices is tomatic of a real-estate bubble that will burst eventually, just as the stock mar-ket bubble did in 2000 This would imply the erasing of a significant amount

symp-of household wealth They add that such a decline symp-of disposable incomewould have sharp adverse macroeconomic effects, as already indebted con-sumers reduce spending even further to improve their weakened financialsituation

Despite the (technical and conceptual) difficulties of defining bubbles

in art markets, we believe that the likelihood of falling prices will affectthe general economy only to the extent that the losses made may reduceliquidity in financial markets

1.5 DATA

In order to look more specifically at both bull and bear markets, we usealmost thirty years’ of monthly data, from January 1976 to December 2004,from the Art Market Research (AMR) database AMR uses over 800 auctionhouses to collect sales data for hundreds of individual artists worldwide.This is the most comprehensive data set available for looking at performanceduring market extremes, since it is available as a monthly index Indicesare constructed for individual artists using the average prices of his or herpaintings obtained in the market A national index is constructed, comprised

of a number of chosen artists for each country Art indices for the USA andthe UK art markets are used, covering a large number of artists over severalmovements and periods in the art scene, as well as a general index whichcovers the markets that dominate the global market for art.2Log returns are

of art are rented out to museums or art collectors on loan, thus providing anadditional income stream The indices do not cover sales by private dealers,

or works of art that are bought in – that is, pieces put on the block but notselling; however, these represent a highly significant part of the global artmarket3 Figure 1.1 displays the development of the average price indices

Table 1.1 Summary statistics: monthly log return data, January 1976–December 2004

Annual average standard deviation 17.11% 15.86% 11.10%

Figure 1.1 Art indices: International art performance, January

1976–December 2004

Note: The average price indices from AMR for the General Art Market (ART

100): the top US artists (US 100) and the top British artists (UK 100)

to their fundamental values in the two years following the bubble in 1990.Figure 1.1 also indicates a Japanese phenomenon after the collapse of theJapanese economy, with money flowing directly out of the art market duringthis period Interestingly, the causality has been documented between thesetwo markets, as well as between other equity markets and the art market,

by Campbell (2005)

The restrictive supply of art, recently cited as the reason for increasingprices, and hence returns being made in art investment, is also a drivingfactor behind the occurrence of bubbles in the art market More recent devel-opments using art as collateral for credit loans only serve to lengthen theextent and duration of the resulting price rises and the size of the finan-cial bubble This optimism is exacerbated by the tendency of investors andbanks towards myopic disaster behavior The highly leveraged positions

of banks, holding collateral consisting of such opaque assets as real estateand artworks result in downside risk from the real estate and art marketsbeing shifted to the banking sector This effect is exaggerated by the feeling

of wealth created by increases in property prices and art prices feeding oneach other This can have severe implications for the banking sector and themacroeconomy, so this is one reason to evaluate carefully how much of theseassets act as collateral on the balance sheet

The extent to which a bubble is able to develop depends on the upwardpressure on movements in prices, notably through such mechanisms asgreater media coverage, so that a large response to large price changesoccurs The development of a bubble through the occurrence of large pricemovements should be reflected by greater conditional volatility in financialmarkets Movements which occur with a greater probability than condi-tional volatility would suggest, can be accounted for by the use of a tailindex This is not a new methodology, but its application to the measure-ment of speculative asset-pricing bubbles, is, to our knowledge, new Before

we observe the relationship empirically between estimates for the bility of larger than conditionally normal movements in prices occurringduring the period of development of a speculative bubble, we shall firstoutline the methodology for estimating a tail index It is the conditional esti-mate of the tail index that we estimate using rolling observations, to see howthe probability of larger than “normal” movements in prices change overthe development and bursting of the bubble in the art market

proba-R A C H E L C A M P B E L L A N D proba-R O M A N K proba-R Ä U S S L 9

1.6 METHODOLOGY

In order to analyze the extent to which the market moves away from mental values through larger than “normal” probabilities occurring in largemovements of the return distribution, we shall apply below the Hill’s (1975)

funda-tail index estimator, which was further extended by Huisman et al (1997).

We use EVT to provide us with estimates of tail indices EVT looks ically at the distribution of the returns in the tails, and the tail fatness of thedistribution is reflected by the tail index This concept was first introduced

specif-by Hill (1975), and measures the speed with which the distribution’s tailapproaches zero The fatter the tail, the slower the speed and the lower thetail index given An important feature about the tail index is that it equalsthe number of existing moments for the distribution A tail index estimateequal to 2 therefore reveals that both the first and second moments exist,

in that case the mean and the variance; however, higher moments will beinfinite By definition, the tail index for normal distribution equals infinity,since in that case, all moments exist Since the number of degrees of free-dom reflects the number of existing moments, the tail index can thus be used

as a parameter for the number of degrees of freedom to parameterize the

student-t distribution.

To obtain tail index estimates, we use a modified version of the Hill

estimator, developed by Huisman et al (1997) Their estimator has been

modified to account for the bias in the Hill estimator, with the additionaladvantage of producing almost unbiased estimates in relatively small sam-

ples Specifying k as the number of tail observations, and ordering their

absolute values as an increasing function of size, we obtain the tail estimator

proposed by Hill This is denoted by γ, which is the inverse of α:

Following the methodology of Huisman et al., we can use a modified

version of the Hill estimator to correct for the bias in small samples Thebias in the Hill estimator stems from the fact that it is a function of thesample size A bias-corrected tail index is therefore obtained by observingthe bias of the Hill estimator as the number of tail observations increases up

to κ, whereby κ is equal to half of the sample size

The optimal estimate for the tail index is the intercept β0, while the α

estimate is the inverse of this estimate This is the estimate of the tail indexthat we use to estimate rolling estimations of the degree with which larger

Note: This table provides the alpha estimates using the Huisman et al (1997) estimator for the All Art

Index from Art Market Research, using monthly data.

than “conditionally normal” returns occur in the historical distribution ofreturns over time

1.7 RESULTS

Table 1.2 provides the alpha estimates using the Huisman et al.’s estimator

over the period January 1976 to December 2004 We first look at the alphaestimates for the whole sample We see that there is indeed deviation fromthe assumption of “normality”, since the alpha estimates are between 2and 3 This would imply that the tail index is able to capture some of theadditional movement occurring in returns beyond that of the assumption ofnormality, captured by volatility alone

There is a move away from fundamental distribution over time In Figure1.2, the inverse alpha estimates (gammas) using the previous eight years’sample of monthly data are plotted next to the actual monthly returns Wesee that, the more the returns fluctuate, the higher the inverse alpha estimateand the greater the movement away from fundamental values Indeed, thecorrelation between volatility and alpha is−0.42, which is highly significant

at the 95 percent confidence level

It has been shown that this measure increases during periods of lity.4Therefore, we would expect that the use of the gamma estimate is agood indicator for a movement away from fundamental values, and thedevelopment of an asset pricing bubble

4 3 2 1 0 1985/02

Figure 1.2 Art returns and time-varying downside risk, January

1976–December 2004

Notes: Art Index Returns and Gamma Estimates Monthly Data 96

Rolling Observation for Gamma Estimates for left tail of the Art Index

using 96 observations to estimate the downside risk

Based on the data for the art market, we use the eight years’ monthlydata available from 1976 to 1984 – a total of 96 observations – to calculatethe conditional gamma estimate for the distribution Obviously, the othermoments of the distribution, the mean and the standard deviation are able tochange conditionally over time, so that the gamma estimate is able to capturethe extent of larger than conditionally normal movements occurring in thereturn distribution The results are shown in Figure 1.2

There is an extremely high correlation between the bubble occurring in

1990 and the high values obtained from the tail index estimator over theperiod of the bubble The gamma estimates converge to their average valuesafter the bubble bursts in 1991, and maintain a value around the averagevalue over the rest of the sample until the current period

1.8 DISCUSSION

It would appear that the phenomenon of the bubble developing in the artmarket may be captured through the use of the tail index estimator, whichcaptures the probability of larger than conditionally normal movements inlarge returns occurring over the return distribution over time The analysis

so far has only been applied to the art market, but there is no reason why

12 T I M E -V A R Y I N G D O W N S I D E R I S K

the methodology may not be used for other financial markets in which it isthought that bubbles have occurred, or are thought to be present Indeed,the use of a relatively small sample of observations to analyze the tail indexestimator provides a robust estimator, which can be applied conditionallyover the historical time series of returns

A further issue is that it is not possible to test strictly for efficiency in the artmarket We have discussed so far possible reasons for inefficiencies of the artmarket – for example, information asymmetries But there are good reasonswhy particular behavioral anomalies are even larger and more widespread

in the art market compared to the financial markets Many private collectorsare not profit-oriented and are particularly prone to the behavioral anomaliesthat arise from leaving endowments, opportunity costs and sunk cost effects.Circumstantial evidence suggests that private collectors are strongly sub-ject to the endowment effect, which implies that they value an art objectowned to a greater extent than one not owned The result is that peopleoften demand much more to give up an object than they would be willing topay to acquire it (see Thaler, 1980) This is what Samuelson and Zeckhauser(1988) call a status quo bias; that is, the preference for the current state thatbiases someone against both buying or selling an object These anomaliesare manifestations of an asymmetry of value that Tversky and Kahneman(1991) call “loss aversion” Loss aversion means that the disutility of selling

an object is greater than the utility associated with buying it

Loss aversion also explains why there is no market for renting art objects.Frey and Eichenberger (1995) argue that the consumption benefits of viewingart should be revealed in the rental fees for art objects The consumer wouldpay a fee for enjoying art while being unaffected by price changes in theart market The reason why such market-revealing pure psychic benefitsfrom art do not exist must be sought in property rights and a correspondingownership effect

While the decision to buy art might be based on financial calculations,the desire to possess a beautiful and internationally famous work that willimpress friends and clients unquestionably adds to the attraction The owner

of a work of art has a monopoly over that specific object, while other assetsmay be held by many individuals The major difference between investing

in art and in common financial assets is that art is tangible and is associatedwith a given lifestyle This implies that an art object yields additional ben-efits if it is owned and not just rented, because the art object’s aura is alsoappropriated (Benjamin, 1963)

Apart from the endowment effect and its corresponding ownership effect,there is also the opportunity cost effect This implies that many collectorsisolate themselves from considering the returns of alternative uses for theirinvestments A third behavioral anomaly that plays a large part in the artmarket is the sunk cost effect This describes the tendency to be excessivelyattached to activities (things) for which one has expended resources resulting

R A C H E L C A M P B E L L A N D R O M A N K R Ä U S S L 13

from past efforts at building up a (specific) art collection Additionally, theself-deception theory suggests that the tendency to adjust attitudes to matchpast actions is a mechanism designed to persuade the individual that he orshe is a skillful decision-maker

Are art investors reluctant to realize their losses? Or are investorsextremely reluctant to realize their losses in art? Mental accounting is a kind

of narrow framing that involves keeping track of gains and losses related

to decisions in separate mental accounts Thaler (1985) argues that uals reexamine each account only intermittently when it is action-relevant.Mental accounting may explain the disposition effect (Shefrin and Statman,1985) – that is, the excessive propensity to hold on to assets that have declined

individ-in value and to sell the windivid-inners Such a mechanism may even be side-trackedwhen the individual avoids recognizing losses Self-deception theory rein-forces this argument, since a loss is an indicator of poor decision-making,and a self-deceiver maintains self-esteem by avoiding the recognition of this.Regret avoidance may also reflect a self-deception mechanism designed to

protect self-esteem about poor decision ability Kahneman et al (1991) show

that regret is stronger for individual decisions that involve action rather thanpassivity This effect is also known as the “omission bias”

A bequest aspect is also highly relevant Gifts from parents to their dren, or inheritances of family members in the form of art objects are valuedmore highly by the owner than they would be purely for their monetaryvalue Frey and Eichenberger (1995) argue that, by selling the object, theowners are transferring with it part of their own “nature”

chil-1.9 CONCLUSION

Using a unique set of data with which to observe and quantify the extent

of a bubble in the art market, we have been able to gain a greater insightinto the nature of bubbles with respect to the larger than “normal” move-ments that appear to occur during the build-up and breakdown of financialbubbles More detailed analysis with regard to return distribution will nodoubt enable a richer analysis of the make-up of the asset bubbles, and will

be extremely interesting avenues for further research

By defining the degree of “bubbliness” in a market as the degree to whichlarge movements are more likely to occur, the gamma of the distribution ofhistorical returns can be estimated conditionally over time We see that there

is an extremely high correlation between the size of the gamma estimatesand prices during the period of the bubble The larger the gamma estimate,the greater the probability of more extreme movements in the return distri-bution This should indeed be constant over time However, we see that thecorrelation of the gamma estimates increases during the period of the bub-ble, and is thereafter fairly constant We therefore premise that the bubble

14 T I M E -V A R Y I N G D O W N S I D E R I S K

can be defined ex post from a larger probability occurring in the tails of the

distribution, observed conditionally over time – from rolling observationsused to estimate the degree of “bubbliness” in the market

Although the results presented here are preliminary in nature, they vide an extremely innovative and interesting avenue for further researchinto the notion of bubbles in financial markets The use of the art market,which represents a market in which deviations from fundamental valuesare much more likely, provides a particularly interesting market with which

pro-to observe such measures There are many further areas that may need pro-to

be addressed before any definite conclusions can be drawn For example,the use of this measure on alternative asset classes in which bubbles havebeen observed The “dot.com” mania and real estate markets in particular.Although the results are in a preliminary form, they should help to generatefurther discussion and insight into the determination and measurement ofbubbles in financial markets

NOTES

1 All errors are the responsibility of the authors Many thanks to participants at the ference on “Art: An Alternative Asset Class” at Sotheby’s, London, for their valuable comments.

con-2 Figures on the exact numbers of artists per index are available from the authors on request, or from AMR.

3 In a similar manner, the S&P 500 only represents a segment of the whole market for

Baumol, W (1986) “Unnatural Value: or Art Investment as a Floating Crap Game”,

American Economic Review, 76(2): 10–14.

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Market versus the Housing Market”, Advances in Macroeconomics, 5(1): 1–32.

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and Evaluation”, European Economic Review, 39(3–4): 528–37.

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Centuries”, American Economic Review, 83(5): 1370–6.

R A C H E L C A M P B E L L A N D R O M A N K R Ä U S S L 15 Hill, B (1975) “A Simple General Approach to Inference about the Tail of a Distribution”,

Annals of Mathematical Statistics, 3(5): 1163–74.

Huisman, R., Koedijk, K G., Kool, C and Palm, F (1997) “Fat Tails in Small Samples”, Working Paper, Erasmus University, Rotterdam.

Kahneman, D., Knetsch, J and Thaler, R (1991) “The Endowment Effect, Loss Aversion,

and Status Quo Bias”, Journal of Economic Perspectives, 5(1): 193–206.

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Masterpieces”, American Economic Review, 92(5): 1656–68.

Pownall, R A and Koedijk, K G (1999) “Capturing Downside Risk in Financial Markets:

the Case of the Asian Crisis”, Journal of International Money and Finance, 18(6): 853–70 Samuelson, W and Zeckhauser, R (1988) “Status Quo Bias in Decision Making”, Journal

of Risk and Uncertainty, 1(1): 7–59.

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Losers Too Long: Theory and Evidence”, Journal of Finance, 40(3): 777–90.

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consid-to their means according consid-to the theory of purchasing power parity, andinvestors should maintain an unhedged foreign currency position There-fore, for an investor with a long investment horizon, it becomes optimal not

to hedge at all Froot argues that real-exchange rates may deviate from theirtheoretical fair value over shorter horizons, and currency hedging in thiscontext may become beneficial

As a compromise between these two extreme viewpoints, Black (1989)argues that, using Siegel’s paradox, there is a constant universal hedge

16

M A R K U S L E I P P O L D A N D F E L I X M O R G E R 17

ratio between zero and one However, Black has to impose some strongassumptions and because of the time-period sensitivity and significantvariability and volatility of input parameters in the optimal hedge ratio,there is a significant dispersion in what constitutes the optimal constanthedge ratio In contrast, the evidence of Glen and Jorion (1993), who ana-lyze the performance of mean-variance efficient stock and bond portfoliosfrom the G5 countries when hedging the associated currency risk with cur-rency forwards, shows that there is a substantial improvement when usingconditional time-varying hedging strategies

It is beyond the scope of this chapter to provide a full account of theexisting literature on currency hedging, but we refer, for example, to therecent contribution by Dales and Meese (2001) for an overview We note thatmost of the literature builds on simplifying assumptions on the dynamics

of the underlying returns Indeed, there is now ample empirical evidenceagainst the normal distribution for return dynamics and a lot of statisti-cal justification for so-called regime-switching models For example, Turner

et al (1989), Garcia and Perron (1996), Gray (1996), Perez-Quiros and

Tim-mermann (2000), Whitelaw (2000), Ang and Bekaert (2002a, 2002b), Angand Chen (2002), Connolly, Stivers and Sun (2005) and Guidolin and Tim-mermann (2005a, 2006) report evidence of regimes in stock or bond returns.Therefore, in our study, we analyze the impact of such regime-switchingmodels on optimal currency hedging

Closely related to our study are the works by Ang and Bekaert (2002a)and Guidolin and Timmermann (2005a) Both papers make use of regime-switching models Ang and Bekaert (2002) analyze the optimal investmentstrategy within a mean-variance framework Concerning the modeling ofregime switches, they do not consider a Bayesian updating rule to infer onstate probabilities Guidolin and Timmermann (2005b) assume preferencesover the moments of wealth distribution In addition, they explore the opti-mal asset allocation of an international portfolio with unhedged returns.They do not address the issue of optimal currency hedging We use a moregeneral CRRA (Constant Relative Risk Aversion) utility setting and we com-pare the non-Bayesian investor with the Bayesian one We show that it reallypays to go Bayes! Furthermore, we explicitly allow the investor to hedgehis or her currency exposure Whereas Guidolin and Timmermann (2005b)find that their model offers a rational explanation of the strong home biasobserved in US investors’ asset allocation, our results contrast with theirconclusion While we find a slight decrease in foreign asset holdings for astrategy with unhedged returns, the strategy with optimal currency hedg-ing substantially increases the exposure to foreign markets Therefore, thehome bias becomes even more puzzling

The plan of this chapter is as follows In Section 2.2, we present the switching model and the optimization problem Section 2.3 provides theestimation results for several model specifications In Section 2.4, we provide

regime-18 I N T E R N A T I O N A L S T O C K P O R T F O L I O S A N D O P T I M A L C U R R E N C Y H E D G I N G

a discussion of several aspects of our results; in particular, we discuss theeconomic benefits of using regime-switching models and we analyze theoptimal portfolio allocation Section 2.5 concludes

2.2 THE MODEL

Regime-switching models consist of two generic processes, the state process

s t and the return process r t The unobservable state process s tdetermines

which state is active at time t For the state s t, we assume a discrete

first-order Markov chain with S possible states or regimes The constant transition probability for moving from state i to state j is denoted as

p ij = P{s t+1= j|s t = i, s t−1= k, }

= P{s t+1 = j|s t = i}, for i, j = 1, , S

and we collect all the p ij ’s in the transition matrix P For the N-dimensional

return vector r t, we assume the state dependent dynamics

dr t = µ(s t )dt +
(s t )dB t

where B t is a N × 1 dimensional Wiener process Both the drift vector µ(s t)

and the N × Ndimensional covariance matrix
(s t) depend on the active

regime Therefore, the distribution of r t+1 conditional on the state s t is a

mixture of S normal distributions with probability density function

We note that the regime-switching model defined above can account for

skewed and fat-tailed returns Furthermore, with p ij > 1/S as a sufficient

condition, we can also generate correlation breakdowns and volatility ters Both are often observed in the joint dynamics of international stockmarkets

clus-2.2.1 Portfolio selection with perfect knowledge of the

active state

We assume that the investor can invest in N assets, where the Nth asset

is the risk-free asset The investment horizon T is fixed The investor has

the possibility of rebalancing the asset allocation at the beginning of every

period; for example, at times t = 0, , T − 1 There are no transaction costs.

where we assume γ > 1 for the relative risk aversion coefficient.

We start with the situation in which the investor has perfect knowledge of

the active state We denote by α t the vector of portfolio weights at time t To

maximize the investor’s terminal wealth, he/she has the following objectivefunction:

recur-Given state s t = i, we obtain the FOC of the investor’s allocation problem as

i,t+1)

⎞

⎟

⎠