Handbook of the Fundamentals of Financial Decision Making - Part 1

916 Pages·2013·20.54 MB·English

by  Leonard C MacLean

HANDBOOK OF
THE FUNDAMENTALS OF
FINANCIAL
DECISION MAKING
Part I
World Scientific Handbook in Financial Economic Series
(ISSN: 2010-1732)
Series Editor: William T. Ziemba
University of British Columbia, Canada (Emeritus);
ICMA Centre, University of Reading, UK;
Visiting Professor at The Korean Advanced Institute for Science and Technology
and Sabanci University, Istanbul
Advisory Editors: Harry M. Markowitz
Kenneth J. Arrow University of California, USA
Stanford University, USA Robert C. Merton
George C. Constantinides Harvard University, USA
University of Chicago, USA Stewart C. Myers
Espen Eckbo Massachusetts Institute of Technology,
Dartmouth College, USA USA
The Handbooks in Financial Economics (HIFE) are intended to be a definitive source for comprehensive
and accessible information in the field of finance. Each individual volume in the series presents an
accurate self-contained survey of a sub-field of finance, suitable for use by finance, economics and
financial engineering professors and lecturers, professional researchers, investments, pension fund
and insurance portfolio mangers, risk managers, graduate students and as a teaching supplement.
The HIFE series will broadly cover various areas of finance in a multi-handbook series. The HIFE
series has its own web page that include detailed information such as the introductory chapter to each
volume, an abstract of each chapter and biographies of editors. The series will be promoted by the
publisher at major academic meetings and through other sources. There will be links with research
articles in major journals.
The goal is to have a broad group of outstanding volumes in various areas of financial economics. The
evidence is that acceptance of all the books is strengthened over time and by the presence of other
strong volumes. Sales, citations, royalties and recognition tend to grow over time faster than the
number of volumes published.
Published
Vol. 1 Stochastic Optimization Models in Finance (2006 Edition)
edited by William T. Ziemba & Raymond G. Vickson
Vol. 2 Efficiency of Racetrack Betting Markets (2008 Edition)
edited by Donald B. Hausch, Victor S. Y. Lo & William T. Ziemba
Vol. 3 The Kelly Capital Growth Investment Criterion: Theory and Practice
edited by Leonard C. MacLean, Edward O. Thorp & William T. Ziemba
Vol. 4 Handbook of the Fundamentals of Financial Decision Making (In 2 Parts)
edited by Leonard C. MacLean & William T. Ziemba
Forthcoming
The World Scientific Handbook of Insurance (To be announced)
The WSPC Handbook of Futures Markets
edited by A. G. Malliaris & William T. Ziemba
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World Scientific Handbook in Financial Economic Series — Vol. 4
HANDBOOK OF
THE FUNDAMENTALS OF
FINANCIAL
DECISION MAKING
Part I
Editors
Leonard C MacLean
Dalhousie University, Canada (Emeritus)
William T Ziemba
University of British Columbia, Canada (Emeritus); 
ICMA Centre; University of Reading, UK;
Visiting Professor at The Korean Advanced Institute for Science and Technology
and Sabanci University, Istanbul
World Scientific
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Library of Congress Cataloging-in-Publication Data
Handbook of the fundamentals of financial decision making (in 2 Parts) / edited by Leonard C. MacLean and
William T. Ziemba.
v. cm. -- (World scientific handbook in financial economic series, ISSN 2010-1732 ; v. 4)
Includes bibliographical references and index.
ISBN 978-9814417341 (Set)
ISBN 978-9814417372 (Part I)
ISBN 978-9814417389 (Part II)
1. Investments--Decision making. 2. Finance--Decision making. 3. Risk management.
4. Uncertainty I. MacLean, L. C. (Leonard C.) II. Ziemba, W. T.
HG4515.H364 2013
332--dc23
2012037307
British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
Copyright © 2013 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic
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This part is dedicated to the memory of Professor Paul Anthony Samuelson,
arguablythemostinfluentialeconomistofthe20th centuryandamajorcontributor
to the topics in this handbook.
Paul was born in Gary Indiana on May 15, 1915 and died in Belmont,
MassachusettsonDecember 13,2009.He wasInstitute ProfessorofEconomicsand
Gordon Y Billard Fellow at the Massachusetts Institute of Technology.
v
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Preface
Thetheoryandpracticeofdecisionmakinginfinancehasalongandstoriedhistory.
Many of the fundamental concepts in economics as wellas the models in stochastic
optimization have their origins in finance. In this handbook, a selection of the key
papersinfinancialdecisionmakingarebroughttogethertoprovideacomprehensive
picture of the components and methods. The handbook is composed of two parts.
Part I consists of a collection of reprints of seminal papers on the foundations of
decision making in finance. Part II contains mostly original papers which explore
aspects of decision models. A special emphasis is placed on models which optimize
capital growth.
In Section A of Part I, the concept of arbitrage is presented in a set of papers.
Arbitrage is an opportunity for risk free gains, and an absence of arbitrage is a
condition for a stable financial market. The seminal paper is from Ross (1976),
where the Arbitrage Pricing Theory (APT) is introduced. He defines the prices
on assets by a linear relation to common factors (latent random variables) each
with expectation zero. After accounting for risk there is no price premium, that is,
arbitragedoesnotexist.Anotherwayofstatingthisconditionisthatafteradjusting
for risk, the price process is a martingale.
TheFundamentalTheoremofAssetPricingstatesthat“noarbitrage”isequivalent
totheexistenceofanequivalent“martingalemeasure.”ThepapersbySchachermayer
(2010a,2010b)putthefundamentaltheoreminageneralsetting.Thereexistsamar-
tingalemeasureifandonlyifthepriceprocesssatisfiesanofreelunchwithvanishing
riskcondition.Themartingalemeasureisarisk-neutralmeasureandallassetshavethe
sameexpectedvalue(therisk-freerate)undertherisk-neutralmeasure.
Kallio and Ziemba (2007) use Tucker’s theorems of the alternative from math-
ematical programming to establish the existence of risk neutral probabilities for
the discrete time and discrete space price process. The equivalence between no
arbitrage and the existence of a martingale measure is extended to markets with
various imperfections.
The concept of utility as an expression of preference is developed in Section B.
Fishburn’s paper (1969) gives a succinct presentation of expected utility theory.
With a set of assumptions over decision maker preferences, Fishburn establishes
the existence of a utility function and subjective probability distribution such that
rationalindividuals actas thoughthey weremaximizingexpected utility.Expected
utility allows for the fact that many individuals are risk averse, meaning that the
individual wouldrefuse a fair gamble(a fair gamblehas anexpected value of zero).
vii
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viii Preface
In expected utility theory, the utilities of outcomes are weighted by their prob-
abilities. Machina (2004) in his paper describes non expected utility. It has been
shownthat people overweightoutcomes that are consideredcertain relativeto out-
comes which are merely probable. There have been a variety of proposals for deal-
ing with the violation of the independence axiom and the linearity in probabilities.
One approach is Prospect Theory proposed by Kahneman and Tversky (1979).
The value function is S-shaped, being convex for losses (x < 0) and concave for
gains (x>0).
ProspectTheoryhasitscritics.ThepapersbyLevyandLevy(2004)castdoubt
on the S-shaped value function, based on experimental results. The basis of their
analysis is stochastic dominance which orders random variables. The paper by
Wakker (2003) reinforces the importance of probability weighting as well as the
S-shaped value in prospect theory. He re-examines the experiments, showing that
the S-shape is compatible with the data when probability weighting is used cor-
rectly. Baltussen et al. (2006) provide experimental results supporting the usual
risk averse (concave) function over either the S-shape or reverse S-shape.
Infinancialdecisionmaking,the(investment,consumption)processisdynamic,
with the alternatives consisting of investment and consumption decisions at points
intime.KrepsandPorteus(1979)considertheinter-temporalconsistencyofutility
for making dynamic decisions. Preferences at different times are linked by a tem-
poral consistency axiom, so that decisions are consistent in the sense that revealed
outcomes at a later time would not invalidate the optimality of earlier decisions.
ThepaperbyEpsteinandZin(1989)buildsonthetemporalutilityformtodefine
a recursive utility which incorporates inter-temporal substitution and risk aversion
separately.The Epstein–Zinutility contains many popular utility functions suchas
power utility as special cases.
In Section C, the preference for random variables with the order relations of
stochasticdominanceareconsidered.HanochandLevy(1969)showthatstochastic
dominance can be defined by classes of utilities as characterized by higher order
derivativesoftheutility,withu(k)beingthekthderivative.Thedominancedescribed
is for a single period, usually the final period of accumulated capital. However,the
capitalisaccumulatedfrominvestmentsovertimeandthetrajectorytofinalwealth
could be important in the assessment of utility. Levy and Paroush (1974) extend
the notions of stochastic dominance to the multi-period case. With additive utility
the stochastic dominance result is extended to multiple periods. Levy and Paroush
also consider the geometric process where the final return is the product of period
returns and give necessary conditions for first order dominance.
Efficient investment strategies, where risk is minimized for specified return, are
the topic of Section D. A major advantage of Markowitz’mean-varianceanalysis is
the relative ease of computing optimal strategies and as such it is a practical tech-
nique. The paper by Ziemba, Parkan and Brooks-Hill (1974) considers the general
risk-return investment problem for which they propose a 2-step approach: the first
step is to find the proportions invested in risky assets using a fractional program;
the second step is to determine the optimal ratios of risky to non-risky assets.
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Preface ix
Ziemba (1975) considers the computation of optimal portfolios when returns
have a symmetric stable distribution. The normal is a stable distribution when the
variance is finite, but the stable family is more general with dispersion replacing
variance and has four rather than two parameters.
The typical utility function in the investment models is concave to reflect risk
aversion. There are aspects of risk aversion which are not captured by concavity.
In the paper by Pratt (1964),an additional property of utility, decreasing absolute
risk aversion,is introduced.
Rubinstein (1973)develops a measure ofglobalrisk aversionin the context ofa
parameter-preference equilibrium relationship. Some properties of this measure in
the context of risk aversion with changing initial wealth levels appear in Kallberg
and Ziemba (1983). Kallberg and Ziemba establish an important property of the
globalrisk measure:Investors with the same risk have the same optimal portfolios.
Chopra and Ziemba (1993) consider the relative impact of estimation errors at
variousdegreesofriskaversiononportfolioperformance,withtheestimateofmean
return being most important. MacLean, Foster and Ziemba (2007) use a Bayesian
framework to include the covariance in an estimate of the mean. In essence, the
return on one asset provides information about the return on related assets, and
thesharingofinformationthroughthecovarianceimprovesthequalityofestimates.
Expected utility may not be the right theory for many risk attitudes, and does
not explain the modest-scale risk aversion observed in practice. Rabin and Thaler
(2001)intheirpaperproposethattherightexplanationincorporatestheconceptsof
lossaversionandmentalaccounting.Theyarguethatlossaversionandthetendency
to isolate each risky choice must both be components of a theory of risk attitudes.
Part II
The basic components of risk are (i) the chance of a potential loss and (ii) the size
of the potential loss. F¨ollmer and Knipsel (2012) view the financial risk of X as
the capital requirement ρ(X) to make the position X acceptable, with the corre-
sponding acceptance set of positions for measure ρ. With reference to acceptance
sets, Rockafeller and Ziemba (2000) have established the following result: There is
a one-to-one correspondence between acceptance sets Aρ and the risk measures ρ.
Theconceptofcapitalrequirementtocoverthe lossesfrominvestmentcaptures
thefinancialriskidea,buttheprobabilityoflossisnottakenintoaccount.Detailson
measures which use the distribution are provided in the papers of Krokhmal et al.
(2011) and Fo¨llmer and Knipsel (2012). Deviation measures are a generalization
of variance. There is a one-to-one relationship between averse risk measures and
deviation risk measures.
A variationis to consider the averageof the values at risk (AVaR). F¨ollmer and
Knipsel show how AVaR is a building block for law-invariant risk measures.
Since convexity is the desired property of a risk measure, the class of convex
risk measures is considered in F¨ollmer and Knispel (2012), following Rockafeller
and Ziemba (2000). Fo¨llmer and Knispel also raise the issue of model uncertainty