The Capital Asset Pricing Model in the 21st Century: Analytical, Empirical, and Behavioral Perspectives

457 Pages·2011·2.95 MB·English

by  Professor Haim Levy

TheCapitalAssetPricingModelinthe21stCentury
Analytical,Empirical,andBehavioralPerspectives
TheCapitalAssetPricingModel(CAPM)andthemean-variance(M-V)
rule,whicharebasedonclassicexpectedutilitytheory(EUT),havebeen
heavilycriticizedtheoreticallyandempirically.Theadventofbehavioral
economics,prospecttheory,andotherpsychology-mindedapproachesin
finance challenges the rational investor model from which CAPM and
M-Vderive.HaimLevyarguesthatthetensionbetweentheclassicfinan-
cialmodelsandbehavioraleconomicsapproachesismoreapparentthan
real. This book aims to relax the tension between the two paradigms.
Specifically, Professor Levy shows that although behavioral economics
contradicts aspects of EUT, CAPM and M-V are intact in both EUT
and Cumulative Prospect Theory (CPT) frameworks. There is, further-
more,noevidencetorejectCAPMempiricallywhenex-anteparameters
areemployed.ProfessionalsmaythuscomfortablyteachanduseCAPM
andbehavioraleconomicsorCPTascoexistingparadigms.
Haim Levy is Miles Robinson Professor of Business Administration at
the Hebrew University of Jerusalem and Dean of the Academic Center
of Law and Business, Israel. He is the author of hundreds of articles in
leadingacademicjournalsandnineteenbooks.Basedonpublicationsin
sixteencorejournalsinfinance,hehasobtainedtherankingofthemost
prolificresearcherinfinancecoveringthefifty-yearperiodthrough2002.
AcoauthorwithNobelLaureatesHarryMarkowitzandPaulSamuelson,
Professor Levy’s major research contributions have been in the field of
stochasticdominanceinfinancialeconomics,whichsetsforththecriteria
for decision making under conditions of uncertainty. He has also devel-
oped economic models for risk management. Professor Levy received
Hebrew University’s Prize for Excellence in Research in 1996 and the
EMET Prize in 2006. He has served as economic adviser to the Bank
of Israel and has held academic positions at the University of Califor-
nia, Berkeley, and the Wharton School, University of Pennsylvania. He
received his Ph.D. from Hebrew University in 1969 and has held a full
professorshiptheresince1976.

The Capital Asset Pricing Model
in the 21st Century
Analytical, Empirical, and Behavioral
Perspectives
HAIM LEVY
HebrewUniversity,Jerusalem
cambridgeuniversitypress
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Levy,Haim.
Thecapitalassetpricingmodelinthe21stcentury:analytical,empirical,
andbehavioralperspectives/HaimLevy.
p. cm.
Includesbibliographicalreferencesandindex.
ISBN978-1-107-00671-3–ISBN978-0-521-18651-3(pbk.)
1.Capitalassetpricingmodel. I.Title.
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Contents
Preface pagexi
1 Introduction 1
1.1. TheMean-VarianceRuleandtheCapitalAsset
PricingModel:Overview 1
1.2. TheIntensiveUseoftheMean-Varianceandthe
CapitalAssetPricingModelamongPractitioners 7
1.3. TheRoleoftheMean-VarianceandtheCapital
AssetPricingModelinAcademia 18
1.4. Summary 21
2 ExpectedUtilityTheory 23
2.1. Introduction 23
2.2. TheAxiomsandExpectedUtilityTheory 25
a) TheAxioms 25
b) TheExpectedUtilityPrinciple 28
2.3. IsU(A)aProbabilityoraUtility? 30
2.4. VariousAttitudestowardRisk 31
2.5. PreferencewithRiskAversionandRiskSeeking 37
2.6. CriticismsoftheExpectedUtilityTheory 38
a) AllaisParadox 39
b) CriticismoftheCommonlyEmployedUtility
Functions 40
c) CumulativeProspectTheory:Experimental
FindingsthatContradictExpectedUtilityTheory 42
d) Roy’sSafety-FirstRule 44
2.7. Summary 44
3 ExpectedUtilityandInvestmentDecisionRules 46
3.1. Introduction 46
3.2. StochasticDominanceRules 47
v
vi Contents
a) ExpectedUtilityandtheCumulativeDistributions 47
b) TheFirst-DegreeStochasticDominanceDecision
Rule 51
c) TheSecond-DegreeStochasticDominance
DecisionRule 52
d) TheProspectStochasticDominanceDecisionRule 53
e) TheMarkowitzStochasticDominanceDecision
Rule 54
3.3. GraphicalIllustrationsoftheStochasticDominance
Criteria 54
3.4. StochasticDominanceRulesandtheDistribution’s
MeanandVariance 58
a) Mean,Variance,andStochasticDominanceRules 58
b) Mean,Variance,andRiskAversion 60
3.5. Summary 61
4 TheMean-VarianceRule(M-VRule) 63
4.1. Introduction 63
4.2. TheMean-VarianceRule:PartialOrdering 65
4.3. ExpectedUtilityandDistribution’sMoments:
TheGeneralCase 68
4.4. TheQuadraticUtilityFunctionandthe
Mean-VarianceRule 72
4.5. QuadraticUtility:AreThereSharperRulesThanthe
Mean-VarianceRule? 76
Discussion 79
4.6. NormalDistributionsandtheMean-VarianceRule 85
Discussion 91
4.7. TheMean-VarianceRuleasanApproximationto
ExpectedUtility 93
a) TheVariousMean-VarianceQuadratic
Approximations 93
b) Discussion:Mean-VarianceApproximationand
Mean-VarianceEfficientProspects 100
c) AGeneralUtilityFunctionwithNoDARA
Assumption 101
d) ARisk-AverseUtilityFunctionwithDARA 105
e) TheQualityoftheApproximation 108
4.8. Summary 114
5 TheCapitalAssetPricingModel 117
5.1. Introduction 117
5.2. TheMean-VarianceEfficientFrontier 120
a) TheMean-VarianceFrontierwithOneRiskyAsset
andOneRisklessAsset 120
Contents vii
b) TheMean-VarianceFrontierwithn-RiskyAssets 123
c) TheMean-VarianceFrontierwithn-RiskyAssets
andtheRisklessAsset 128
5.3. TheDerivationoftheCapitalAssetPricingModel 134
a) Sharpe’sCapitalAssetPricingModelDerivation 135
b) Lintner’sCapitalAssetPricingModelDerivation 139
c) Discussion 143
5.4. EquilibriumintheStockMarket 149
5.5. Summary 154
6 ExtensionsoftheCapitalAssetPricingModel 156
6.1. Introduction 156
6.2. TheZeroBetaModel 158
6.3. TheSegmentedCapitalAssetPricingModel 164
6.4. Merton’sIntertemporalCapitalAsset
PricingModel 168
6.5. TheHeterogeneousBeliefsCapital
AssetPricingModel 171
6.6. TheConditionalCapitalAssetPricingModel 175
6.7. Ross’sArbitragePricingTheory 179
6.8. Summary 184
7 TheCapitalAssetPricingModelCannotBeRejected:
EmpiricalandExperimentalEvidence 186
7.1. Introduction 186
7.2. TheEarlyTestsoftheCapitalAssetPricingModel:
PartialSupportfortheCAPM 191
(i) TheFirst-PassRegression(Time-Series
Regression) 191
(ii)TheSecond-PassRegression(Cross-Section
Regression) 191
a) TheStudybyLintner 192
b) TheStudybyMillerandScholes 195
c) TheStudybyBlack,Jensen,andScholes 196
d) TheStudybyFamaandMacBeth 199
e) TheRoleofBetaandtheVarianceasExplanatory
Variables 200
7.3. TheSecondCycleofTests:MainlyRejection
oftheCAPM 202
a) TheSmallFirmEffect 203
b) TheThree-FactorModelofFamaandFrench 205
c) TheStudyofGibbons,Ross,andShanken:A
MultivariateTestofAlphas 207
7.4. Roll’sCritiqueoftheEmpiricalTests 209
viii Contents
7.5. ShortPositionsEverywhereontheFrontier:
AllegedlyProvidesEvidenceagainsttheCapital
AssetPricingModel 212
7.6. TheCapitalAssetPricingModelCannotBeRejected
onEmpiricalGroundAfterAll 214
a) ConfidenceIntervaloftheβ Approach 215
b) APositivePortfolioExistswithEx-AnteMeans 219
c) ReverseEngineering:TheApproach
ofM.LevyandR.Roll 221
d) TheSmallFirmEffectandtheInvestmentHorizon 224
7.7. ExperimentalStudiesoftheCapital
AssetPricingMarket 233
7.8. Summary 237
8 TheoreticalandEmpiricalCriticismof
theMean-VarianceRule 239
8.1. Introduction 239
8.2. DistributionofReturns:TheoreticalApproach 242
8.3. TheEmpiricalDistributionofReturn:TheParetian
VersustheNormalDistribution 249
8.4. AHorseRacebetweenVariousRelevant
Distributions:TheCharacteristicsoftheVarious
DistributionsandtheMethodology 255
8.5. ShortInvestmentHorizonandtheLogistic
Distribution 261
a) TheEmpiricalResultfortheRelativelyShort
Horizon 262
b) TheHorizonEffectonVariousParameters 265
c) TheLogisticDistribution:TheM-VRuleIs
Optimal 270
8.6. GoodnessofFit:InvestmentHorizonLonger
ThanOneYear 275
8.7. EmployingtheMean-VarianceRule:
TheEconomicLoss 280
8.8. NormalDistribution:IsMarkowitz’s
EfficientSetTooBig? 286
8.9. Summary 296
9 ProspectTheoryandExpectedUtility 299
9.1. Introduction 299
9.2. ProspectTheoryandExpectedUtility 303
a) ProspectTheoryandExpectedUtility
Maximization 304
b) AssetIntegration 308
c) RiskAversion 311
Contents ix
9.3. TheValueFunction 316
a) TheShapeoftheValueFunction 316
b) LossAversion 317
9.4. TheDecisionWeightFunction 323
9.5. TheProsandConsofProspectTheory
DecisionWeights 327
a) Drawback:First-DegreeStochasticDominance
Violation 327
b) SomeAdvantages 329
9.6. Summary 330
10 CumulativeDecisionWeights:NoDominanceViolation 333
10.1. Introduction 333
10.2. Rank-DependentExpectedUtility 336
10.3. CumulativeProspectTheoryDecisionWeights 340
10.4. TheValueandtheDecisionWeightFunctionsas
SuggestedbyCumulativeProspectTheory 345
10.5. TheVariousDecisionWeights:
FormulasandEstimates 347
a) LeftTailIrrelevance 353
b) CumulativeProspectTheory’sUnreasonable
DecisionWeights:TheEquallyLikely
OutcomeCase 354
c) IrrelevancyoftheAlternativeProspects 356
10.6. TheSuggestedProspect-DependentDecision
WeightsModel 357
10.7. First-DegreeStochasticDominanceViolations
DuetoBoundedRationality 366
10.8. Summary 370
11 TheMean-VarianceRule,theCapitalAssetPricingModel,
andtheCumulativeProspectTheory:Coexistence 372
11.1. Introduction 372
11.2. GainsandLossesVersusTotalWealth 374
a) TheWealthEffectontheMean-Variance
EfficientFrontier 375
b) TheWealthEffectontheCapitalAsset
PricingModel 378
11.3. RiskAversionVersustheS-ShapeValueFunction 380
a) DiversificationIsNotAllowed 380
b) DiversificationbetweenRiskyAssetsIsAllowed 383
c) DiversificationIsAllowedandaRiskless
AssetExists 390