Managing Downside Risk in Financial Markets. Theory, Practice and Implementation

271 Pages·2001·2.306 MB·English

by  Frank A. Sortino and Stephen E. Satchell (Eds.)

Contributors
Sally Atwater is the Vice President of the Financial Planning Business Unit
forCheckFreeInvestmentServices,NorthCarolina,USA.Sallyhasoverfifteen
years of experience in the financial arena. She began her career in accounting
andfinancialmanagement,andasaresultofaninterestinretirementandestate
planning, she accepted the position of Chief Operating Officer for Leonard
Financial Planning in 1993. Sally joined Mo¨bius Group in April of 1995 and
becameVicePresidentin1996.SoonaftertheacquisitionofMo¨biusbyCheck-
Free in 1998, Sally became Vice President of the Financial Planning Business
Unit. She is currently responsible for business, product, and market devel-
opment in the personal financial planning market for CheckFree Investment
Services. Sally holds an undergraduate degree in management sciences from
Duke University and an MBA from the Duke University Fuqua School of
Business.
LeslieA.Balzer,PhD(Cantab),BE(Hons),BSc(NSW),GradDipApplFin&
Inv (SIA), FSIA, FIMA, FIEAust, FAICD, AFAIM, Cmath, CPEng, is Senior
Portfolio Manager for State Street Global Advisors in Sydney, Australia. His
experiencecoversindustry,commerce,academiaandincludesperiodsasInvest-
mentManagerforLendLeaseInvestmentManagement,asPrincipalofconsult-
ing actuaries William M. Mercer Inc. and as Dean of Engineering at the Royal
Melbourne Institute of Technology. Dr Balzer holds a BE in Mechanical Engi-
neering with First Class Honours and a BSc in Mathematics & Physics from
the University of New South Wales, Australia. His PhD is from the Control
and Management Systems Division of the University of Cambridge, England.
HealsoholdsaGraduateDiploma inAppliedFinanceandInvestmentfromthe
SecuritiesInstituteofAustralia.Hehaspublishedwidelyinscientificandfinan-
cial literature and was awarded the prestigious Halmstad Memorial Prize from
the American Actuarial Education and Research Fund for the best research
contribution to the international actuarial literature in 1982. He was the first
non-AmericantowinthePaperoftheYearawardfromtheJournalofInvesting.
viii Contributors
Robert Clarkson – after reading mathematics at the University of Glasgow,
Scotland,UK,RobertClarksontrainedasanactuaryandthenfollowedacareer
in investment management at Scottish Mutual Assurance, latterly as General
Manager (Investment). Over the past twelve years he has carried out extensive
researchinto the theoretical foundations of finance and investment, particularly
in the areas of financial risk and stockmarket efficiency. He has presented
numerous papers on finance and investment to actuarial and other audiences
bothintheUKandabroad,andheiscurrentlyaVisitingProfessorofActuarial
Science at City University, London.
Gustavo M. de Athayde is a Senior Quantitative Manager with Banco Itau´
S.A. at Sa˜o Paulo, Brazil. He has consulting experience in econometrics and
finance models for the Brazilian Government and financial market. He holds
a PhD in Economics, and his present research interests are portfolio design,
in static and dynamic settings, econometrics of risk management models and
exotic derivatives.
Kathleen Ferguson is currently Principal of Investment Technologies. She
has experience of consulting to both plan sponsors and investment consultants
in matters relating to investment policy and asset management, with partic-
ular emphasis on asset allocation. Ms Ferguson has broad experience in areas
relatingtoinvestmentmanagementforemployeebenefitplansincludinginvest-
ment policy, strategies, and guidelines, selection and monitoring investment
managers, and performance measurement and ranking. She has contributed to
the Journal of Investing and Investment Consultant’s Review and is a member
oftheInvestmentManagementConsultantsAssociationandtheNationalAsso-
ciation of Female Executives. She holds an MBA in Finance from New York
University, New York, USA.
Hal Forsey is Professor of Mathematics emeritus from San Francisco State
University, USA. He has worked with Frank Sortino and the Pension Research
Institute for the last ten years. He has degrees in Business (A.A. San Fran-
cisco City College), Statistics (B.S. San Francisco State), Mathematics (PhD
University of Southern California) and Operations Research (MS University of
California, Berkeley), and presently lives on an island north of Seattle.
SebastiaandeGrootcurrentlyworksasanInvestmentAnalystforAcamAdvi-
sors LLC, a hedge funds manager in New York. Previously, he worked as an
AssistantProfessorandPhDstudentattheUniversityofGroningen,TheNether-
lands. His research includes work on behavioural finance and decision models,
primarily applied to asset management.
Contributors ix
Robert van der Meer holds a degree in Quantitative Business Economics, is
a Dutch CPA (registered accountant) and has a PhD in Economics from the
Erasmus University Rotterdam.
His business career started in 1972 with Pakhoed (international storage and
transport) in The Netherlands, andfrom1976 until 1989 he workedwith Royal
Dutch/Shell in several positions in The Netherlands and abroad. During this
time,hewasalsoManagingDirectorofInvestmentsoftheRoyalDutchPension
Fund. From 1989 until 1995 Robert van der Meer was with AEGON as a
member of the Executive Board, responsible for Investments and Treasury.
In March 1995 he joined Fortis as a member of the Executive Committee of
FortisandMemberoftheBoardofFortisAMEVN.V.InJanuary1999hewas
appointed member of the Management Committee of Fortis Insurance and of
the Board of Directors of Fortis Insurance, Fortis Investment Management and
Fortis Bank.
RobertvanderMeerisalsoapart-timeProfessorofFinanceattheUniversity
of Groningen, The Netherlands.
JosephMessinaisProfessorofFinanceandDirectoroftheExecutiveDevelop-
ment Center (EDC) at San Francisco State University, USA. Prior to assuming
his position as Director of EDC, Dr Messina was Chairman of the Finance
Department at San Francisco State University. Dr Messina received his PhD
in Financial Economics from the University of California at Berkeley and his
Masters Degree in Stochastic Control Theory from Purdue University.
Dr Messina has carried out research and consulting in the areas of the term
structure of interest rates, interest rate forecasting, risk analysis, asset allo-
cation, performance measurement, and behavioural finance. His behavioural
finance research has revolved around the theme of calibrating experts and how
informationisexchangedbetweenexperts(moneymanagers,staffanalysts)and
decision makers (pension plan sponsors, portfolio managers). His research and
consulting reports have been presented and published in many proceedings and
journals.
Auke Plantinga is an Associate Professor at the University of Groningen, The
Netherlands. He is currently conducting research in the field of performance
measurement and asset-liability management.
Neil Riddles serves as Chief Operating Officer with Hansberger Global
Investors, Inc., USA, where he oversees the performance measurement,
portfolio accounting, and other operational areas. He has a Master of Business
Administration degree from the Hagan School of Business at Iona College,
and he is a Chartered Financial Analyst (CFA) and a member of the Financial
Analysts Society of South Florida, Inc.
x Contributors
Mr Riddles is a member of the AIMR Performance Presentation Standards
ImplementationCommittee,After-TaxSubcommittee,GIPSInterpretationsSub-
committee and is an affiliate member of the Investment Performance Council.
He is on the advisory board of the Journal of Performance Measurement and
is a frequent speaker on performance measurement related topics.
Brian Rom is President and founder of Investment Technologies (1986) a
software development firm specializing in Internet-based investment advice,
asset allocation, performance measurement, and risk assessment software for
institutional investors. He developed the first commercial applications of post-
modem portfolio theory and downside risk in collaboration with Dr Frank
Sortino, Director, Pension Research Institute. Mr Rom is Adjunct Professor
of Finance, Columbia University Graduate School of Business. Over the
past 23 years he has published many articles and spoken at more than 50
investment conferences on investment advice, asset allocation, behavioural
finance,downside risk, performancemeasurementandinternational hedgefund
and derivatives investing. He holds an MBA from Columbia University, an
MBAfromCapeTownUniversity,SouthAfricaandaMSinComputerScience
and Mathematics from Cape Town University.
Editors:
Dr Stephen Satchell is a Fellow of Trinity College, a Reader in Financial
Econometrics at the University of Cambridge and a Visiting Professor at Birk-
beckCollege,CityUniversityBusinessSchool,LondonandattheUniversityof
Technology,Sydney.Heprovidesconsultancyforarangeof cityinstitutions in
thebroadareaofquantitativefinance.Hehaspublishedpapersinmanyjournals
and has a particular interest in risk.
Dr Frank Sortinofounded the Pension ResearchInstitute (PRI)in the USA in
1980andhasconductedmanyresearchprojectssince,theresultsofwhichhave
been published in leading journals of finance. For several years, he has written
a quarterly analysis of mutual fund performance for Pensions & Investments
Magazine. Dr Sortino recently retired from San Francisco State University as
Professor of Finance to devote himself full time to his position as Director of
Research at the PRI.
Preface
This book is dedicated to the many students we have taught over the years,
whose thought-provoking questions led us to rethink what we had learned as
graduate students. For all such questioning minds, we offer the researchefforts
of scholars around the world who have come to the conclusion that uncertainty
can be decomposed into a risk component and a reward component; that all
uncertainty is not bad.
Riskhastodowiththosereturnsthatcauseonetonotaccomplishtheirgoal,
which is the downside of any investment. How to conceptualize downside risk
hasastrongtheoreticalfoundationthathasbeenevolvingforthepast40 years.
However,abetterconceptisoflittlevaluetothepractitionerunlessitispossible
toobtainreasonableestimatesofdownsiderisk.Developingpowerfulestimation
procedures is the domain of applied statistics, which has also been undergoing
major improvements during this time frame.
Part 1 of this book deals with applications of downside risk, which is the
primary concern of the knowledgeable practitioner. Part 2 examines the theory
that supports the applications. You will notice some differences of opinion
among the authors with respect to both theory and its application.
Thedifferencesaregenerallyduetotheassumptionsoftheauthors.Theories
are a thing of beauty to their creators and their devotees. But the assumptions
underlying any theory cannot perfectly fit the complexity of the real world,
and applying any theory requires yet another set of assumptions to twist and
bend the theory into a working model. We believe that quantitative models
should not be the decision-maker, they should merely provide helpful insights
to decision-makers.
APPLICATIONS
The first chapter is an overview of the research conducted at the Pension
Research Institute (PRI) in San Francisco, California, USA. References are
xii Preface
made to chapters by other authors that either enlarge on the findings at PRI, or
offer opposing views.
Thesecondchapter,byRobertvanderMeer,dealswithdevelopinggoalsfor
largedefinedbenefitplansatFortisGroupinTheNetherlands.Thenextchapter,
by Sally Atwater, who developed the financial planning software at Checkfree
Inc., proposes a new paradigm for establishing goals for defined contribution
plans,suchastheburgeoning401(k)marketintheUS.Sallyoffersnewinsights
for financial planners and consultants to 401(k) plans.
Chapter 4 by Hal Forsey explains how to use the latest developments in
statistical methodology to obtain more reliable estimates of downside risk. Hal
also wrote the source code for the Forsey–Sortino model on the CD enclosed
with this book.
Chapter 5byBrianRomandKathleenFergusonillustratestheimportanceof
skewnessinthecalculationofdownsiderisk.Briandevelopedthefirstcommer-
cial version of an asset allocation model developed at PRI in the early 1980s.
Chapter 6 examines alternative risk measures that are gaining popularity.
Joseph Messina, chairman of the Finance Department at San Francisco State
University, evaluatesthe InformationRatioandValue atRiskmeasuresinlight
ofthe conceptof downside deviations. Josephpoints outboth thestrengths and
weaknesses of these alternative performance standards.
The final chapter in the applications part presents the case for measuring
downsideriskonarelativebasis.NeilRiddleswasresponsibleforperformance
measurement at the venerable Templeton funds. Neil is currently Chief Oper-
atingOfficeratHansbergerGlobalAdvisors.WhilePRItakesthecontraryview
expressed in Chapter 2 by van der Meer, we think Neil presents his arguments
well, and this perspective should be heard.
THEORY
The theory part begins with a chapter by Leslie Balzer, a Senior Portfolio
ManagerwithStateStreetGlobalAdvisorsinAustralia,andaformeracademic.
He develops a set of properties for an ideal risk measure and then uses them
to present a probing review of most of the commonly used or proposed risk
measures.Lesconfrontstheconfusionof‘uncertainty’with‘risk’bydeveloping
a unified theory, which separates upside and downside utility relative to the
benchmark. Benchmarkrelative downside risk measures emerge naturally from
the theory, complemented by novel concepts such as ‘upside utility leakage’.
In Chapter 9, Stephen Satchell expands the class of asset pricing models
based on lower-partial moments and presents a unifying structure for these
models. Stephenderivessome new resultsonthe equilibrium choiceofa target
return, and uncovers a representative agent in downside risk models.
Preface xiii
Next, Auke Plantinga and Sebastiaan de Groot relate prospect theory, value
functions, and risk adjusted returns to utility theory. They examine the Sharpe
ratio, Sortino ratio, Fouse index and upside-potential (U-P) ratio to point out
similarities and dissimilarities.
Our colleague in Brazil, Gustavo de Athayde, offers an algorithm in
Chapter 11 to calculate downside risk.
Finally, Robert Clarkson proposes what he believes to be a new theory for
portfolio management. This may be the most controversial chapter in the book.
While we may not share all of Robert’s views, we welcome new ideas that
make us think anew about the problem of assessing the risk-return trade off in
portfolio management.
AtutorialforinstallingandrunningtheForsey–Sortinomodelisprovidedin
theAppendix.Thistutorialwalksthereaderthrougheachstepoftheinstallation
anddemonstrateshowtousethemodel.TheCDprovidedwiththisbookoffers
two differentviewsof how to measuredownside risk in practice.The program,
written by Hal Forsey in Visual Basic, presents the view of PRI. The Excel
spreadsheet by Neil Riddles presents the view of the money manager.
It is our sincere hope that this book will provide you with information that
will allow you to make better decisions. It will not eliminate uncertainty, but it
should allow you to manage uncertainty with greater skill and professionalism.
Frank A. Sortino
StephenE. Satchell
P.S.: The woman petting the rhino is Karen Sortino, and the unaltered picture
on the following page was taken on safari in Kenya.
xiv Preface
Justbecauseyougotawaywithitdoesn’tmeanyoudidn’ttakeanyrisk
Chapter 1
From alpha to omega
FRANK A. SORTINO
SUMMARY
This chapter is intended to provide a brief history of the research
carriedoutatthePensionResearchInstitute(PRI)andsomeimport-
ant developments surrounding it. According to Karl Borch (1969),
the first person to propose a mean-risk efficient ranking procedure
was a British actuary named Tetens in 1789. However, it was Harry
Markowitz(1952)whofirstformalizedthisrelationshipinhisarticleson
portfoliotheory.Thiswasthebeginningofthetheoreticalfoundation,
commonlyreferredtoasModernPortfolioTheory(MPT).MPTcaused
aschismamongstacademicsintheUnitedStatesthatexiststothis
day. As a result, Finance Departments in the School of Business in
most US universities stress the mean-variance (M-V) framework of
Markowitz,whileeconomists, statisticians and mathematicians offer
competing theories. Ihave singled out afew ofthe conflicting views
Ithinkareparticularlyrelevantforthepractitioner.
1.1 MODERNPORTFOLIOTHEORY(MPT)
MPT has come to be viewed as a combination of the work for which Harry
Markowitz and Bill Sharpe received the Nobel Prize in 1990. It is a theory
that explains how all assets should be priced in equilibrium, so that, on a risk-
adjusted basis, all returns are equal. The implicit goal is to beat the market
portfolio, and of course, in equilibrium, one cannot beat the market. It would
behardtooverestimatetheimportanceofthisbodyofwork.BeforeMarkowitz,
there was no attempt to quantify risk. The M-V framework was an excellent
beginning, but that was almost 40 years ago. This book identifies some of the
4 Managing Downside Risk in Financial Markets
68.26%
95.44%
99.74%
−3s −2s −1s 0 +1s +2s +3s
Figure1.1 Thenormaldistribution
advancements that have been made and how to implement them in portfolio
management.
Jensen (1968) was the first to calculate the return the manager earned in
excessofthemarket.Heregressedthereturnsofthemanageragainstthereturns
of the market to calculate the intercept, which he called alpha. Sharpe (1981)
proposed measuring the performance of managers in terms of both the excess
returntheyearnedrelative to abenchmark,and the standarderrorof the excess
return. This has come to be called the ‘information ratio’. The excess return
in the numerator of the information ratio is also called alpha by most consult-
ants (see Messina’s contribution in Chapter 6 for a detailed critique of the
information ratio).
MPT assumes investors make their decisions based solely on the first and
second moments of a probability distribution, i.e. the mean and the variance,
and that uncertainty always has the same shape, a bell-shaped curve. Whether
markets are at a peak or a trough, low returns are just as likely as high returns,
i.e. the distribution is symmetric (see Figure 1.1). Of course, there isn’t any
knowingwhatthetrueshapeofuncertaintyis,butweknowwhatitisn’t,andit
isn’tsymmetric.Sinceallyoucanloseisallyourmoney,thedistributioncannot
go to minus infinity. In the long run, it has to be truncated on the downside,
and therefore, positively skewed.
1.2 STOCHASTICDOMINANCERULES
This was an important development in the evolution of risk measurement that
mostpractitionersfindtediousandboring.So,Iamgoingtoreplacemathemat-
icalrigourwithpicturesthatcapturetheessenceoftheserules.Iurgethosewho
want a complete and rigorous development of risk measures to read Chapter 8
by Leslie Balzer.
Hadar and Russell (1969) were the first to offer a competing theory to M-V.
They claimed that expected utility theory is a function of all the moments