The Econometrics of Financial Markets

627 Pages·1996·18.38 MB·English

by  John Y. Campbell

The Econometrics of Financial Markets
John Y. CamPgeU
AndrewW.Lo
I
A. Craig MacKinJay
Princeton University Press
Princeton, New Jersey
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(:"U1l'lwl\, John Y.
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Contents
List of Figures xiii
List of Tables xv
Preface xvii
Introduction 3
1.1 Organization of the Book 4
1.2 Useful Background. . . . {)
1.2.1 Mathematics Background {)
1.2.2 Probability and Statistics Background (j
1.2.3 Finance Theory Background 7
1.3 Notation................ H
1.1 Prices, Returns, and Compollnding . 9
1.1.1 Defmitions and Conventions. 9
1.4.2 The Marginal, Conditional, anclJoint Distribution
of Returns. . . . . . . . . . . . . . . . . . . . . . .. 13
I.:) Market Efliciency . . . . . . . . . . . . . . . . . . . . . .. 20
1.5.1 Efficient MarkrL~ and the l.aw of Iterated
Expectations .. . . . . . . . . ..... 22
Is Market EffIciency Testable? 24
TIle Predictability of Asset Returns 27
2.1 The Random Walk Ilypotheses ..... . . . . . . . . 2R
2.1.1 The Random Walk I: lID Incremenl~ . . . . . . 31
2.1.2 The Random Walk 2: Independent Increment!! 32
2.1.3 The Random Walk 3: Uncorrclated Increments 33
Tests of Random Walk I: lID Increlllents .
2.2.1 Traditional Statistical Tests .....
2.2.2 SCf)uences and Reversals, and Runs
viii
COII/m!.1
2.~ 2T.e3s.1ts ofF Riltaenrd Roulllle Ws al.k .2:. I.n.de.p.c.nd.e.nt. I.n.cr.em..en.ts . 41
2.3.2 Technical Analysi~ .............. .
2,4 Tests of Randolll Walk :\: Ul\cond.\led Incremcnts
2.4.1 Autocorrelation Coeflicients
2.4.2 Portmanteau Statistics
2.'1.3 Variance Ralim . . . . . . .
2.!:i Long-Ilorizon RelllrBs . . . . . . . ·IH
2.G T22:.e:t>si..t1ls FoEPrxr oLablolllnepgml-esRs awonfitg Ihe. o LDnOgel-lpgRe-1an n[dgoecrni zlckocpn c .I/ nl.cf cl.c rne. nc.cn :. s .. !!::">)/,:!7l)l
2.7 2U.6n.i2l ROTOhle T Hesutsr sl.- M. a.n c. lc. lb. r.o t Rescaled·Rangc Statistic li2
2.H Reccnt EmpiriC<l\ Evidellce . li4
2.S.1 AUlOcorrclations .. Ii:>
2.8.2 Variance Ratios . . . titi
2.n C22..88,o.43 nTCcersolt5sus U-Assuiintoogc Lnoror.nc.gh.l-lH.io.ol.rlSi.z .'o\.Inl.( \R. LC.el.laI.fd.lI-.SL. a g Rc::IatiollS K77tiOH48
3 Market Microstructure
3.1 {I~ 33N..11o..n12s ynAEcx hMtreoonndsoieolll noss fT a NrnaOdd lilGnSgeyn nec.!rtar.loi.lzlao.tui.so .Tnsr. a.di.n g. K8\H:3>
3.2 I The Bid-Ask Spre'ld. . . . . . . . . . . . . ~)H
3.3 'Ij!IIII 3333M3.....33322o.....132d12 e liTRMCRnohgoiodme utT-p iAnOvOrdasannkinteni lsloBtga\nr occ<L tu~d.iinon .ocncPlfsr.rl o\tD.ahb.rea.ir.tt i a\.e.M) r.i ..Mod.-d..Aoe.~..dlk. e. ..Sl s.p.. .re.ad . 111lWi100!n)4K7~\)
3.4 33R..44e..c12e ntEN Esomtnimpsyiarnticicniatglr oFtlhilleoH lEllisfn fTgesrc ati.dvi.en .gB. id.-.A ..s k Sprcad . I111:222HKH2
3.4.3 Transactions Data
•'}• .•r,1 \I (', oncI IIS'IO I1 ••....• 11:4I!4i
4 EveJStudy Analysis
4.\ ; Outline of an Evellt Study ......... .
'I.~ All Example of an Evcnt Study ....... .
4.:-1 Mo<iels for Meas\lrillg Normal I'crfOnll'<lIlCC
4.3.1 Constant-Mcan-Return Mockl
4.3.2 Markct Model ............ .
CCJllifll 1.1 ix
'1.:~.3 Other Statistical Mlldds I:)~
,1.::1.'1 Ecollomic Modds .... 15ti
4..1 Me;\sul'illg and AnalYl.illg Abl\ormal Retlll"lls . [57
4.4.1 Estimation of the Market Model .... 15H
'1.4.2 Statistical Properties of Ahllonnal Rellll'lls 159
4.4.:~ Aggregation of AIlllormal Returns .... . IGO
4.4.4 Sensitivity to Nor11lal Rl'llll'l\ Modd ... . IG~
4.4.5 CARs for the Eamiligs-Allllolllll'l'ment Example 1U3
4A.G Inferences with Cilisterillg ltiG
4.:> Moclifying the NullllYl'othesis 107
Hi Allalysis of Power . . . IGH
4.7 Nonparametric Tests . 172
4.K Cross-Sectional Models 173
4 .~l Further Issues . . . . . 175
4.9.1 Role of the Sampling lntel'val 175
4.9.2 Inferences with Evelll-Date Uncertainty 176
4.9.3 Possible Biases. 177
4.10 Conclusion 178 I
5 The Capital Asset Pricing Model 181
:1.
I Review or the CAI'M .. . IHI
S.~ Results from Efficient-Set Mathematics ..... . 184
:>.:~ Statistical Framework for Estimatioll and Testing. IH8
5.3.1 Sharpe-Lintner Version IH9
:l.:t2 nlack Versioll 1%
:>.4 Size of Tests ......... . 203
5.:> Power of Tests ........ . 204
S.li Nonnormal and Non-lID Returns 208 •
:>.7 Implementation of Tests ..... 211
:>.7.1 Summary of Empirical Evidence 211
5.7.2 Illustrative Implementation 21~
:l.7.~ Unobservability of the Market Portfolio 213
?i.H Cross-Sectional Regressions 215
:).~l Conclusion ..... 217
6 Multifactor Pricing Models 219
G.I Theoretical Background ............ . 219
(;.2 Estimation and Testing ............. . 222
1;.2.1 Portfolios as Factors with a Riskfrcc A.sset 223
li.2.2 Portfolios as FaClors without a Riskf'ree Asset 224
ti.~.:~ Macroeconomic Variables as Factors ..... 226
(i.!!A Factor i'ortfillios Spallllilll-\" the l\kall-V;triance
Frolllicr ..' ..... . .22H
IU Estimation of Risk PrellIia and Expcelcd Returns
li,4 Sdcelion of FaclOrs . . ....
li.'1.1 Statistical Approaches ..
li..l.~ NlImher of FaCiors ...
{i.'l.:\ TllI'oretical Approach('s
1i5 Empirical R('sults ....... .
li.li Interpreting Deviations from Exact Factor Pricing
{i.{i.1 Exael Factor Pricing Models, Mean-Variance Anal-
ysis, and the Optimal Orthogonal Portfillio
li.li.2 Squared Sharpc' Ratios ............. .
(i.fi.:~ Implications fi)J' Sc'parating Altcrnativc Th('mil's
1i.7 Conclusion .................... .
7 Present-Value Relations 253
7.1 The Relation I)('twec'n Prices, Dividends, and Returns ~:I·1
7.1.1 'I'lli'I .inear Pn'sc'nt-Value- Relation with Constant
Expected Relllnls ................... ~:);)
7.1.~ Rational Blibbles .... . . . . . . . . . . . . .. :!:.~
7.1.:1 All Approxilllalc'l'n'sc'nl-Vahlc Relation wilh Tillle-
Varying Exp('cled R('lurns ............... <'(ill
7.1.4 Prices and Retul'lls in a Simple Example ~(i·1
7.'2 Present-ValliI' Relations and US Stock Pricc Ikhavior ~(i7
7.~.1 I.ollg-iioriwil Regressions . . . ~(;7
7.~.'2 Volatility 'Ii'sts . . . . . . . . . . n:;
7,'23 Vector AlilOregn'ssive Mc,tllOds
Conclilsion
8 Intertemporal Equilibrium Models 291
H.I The-Stochastic Discounl FaCIOI' . . . . . . . . . . . . 2~l:\
H.I.I Volatility BOllncls ... . . . . . . . . . . . . . 2%
H.'2 Consumptioll-Basl'd Asset Pricing with Pown Utility. :10,\
H.:!. I Powc'r Utility ill a I.ogllol'lnal Model. . . . :1(Hi
H.'2.'2 Power lItility and (;('ll\'rali'.cll Method of
MOlllents . . . . . . . . . . . . . . . . . . . ..... :q 4
Market Friel ions
H.:I.l Market FriClion~ and Il;ulsclI:)agalinathan
Boullds . . . . . . . . . . . . . . . . . . . . . :11:.
H3.'2 Markc,t Frictions and Aggre-gatc Consllmption
Data . . . . . . . . . . . . . . . . . . . . . . . :1 I Ii
HA More (;('nnall1tility FunC'lions ...... .
H..t.1 Iiallit Forillation .......... .
H.·I.'2 Psychological Mockls or Pr('fucnc('s
( :ondllsion
9 Derivative Pricing Models 339
9.1 Brownian Motion . 341
9.1.1 Constructinr; Brownian Motion . 341 I
9.1.2 Stochastic Differential Equations 346 [
9.2 A Brief Review of Derivative Pricinr; Methods. 349 .
9.2.1 The Black-Scholes and Merton Approach . 350
9.2.2 The Martingale Approach . . . . . . . . . 354
!1.3 Implementing Parametric Option Pricing Models 355
9.3.1 Parameter Estimation of Asset Price Dynamics 356
9.3.2 Estimating in the Black-Scholes Model . . . 361
(j
9.3.3 Quantifying the Precision of Option Price
Estimators ........................ 367
9.3.4 The Effects of Asset Return Predictability. 369
9.3.5 Implied Volatility Estimators . . . . . . . . . . .. 377
9.3.G Stochastic Volatility Models. . . . . . . . . . . .. 379
9.4 Pricing Path-Dependent Derivatives Via Monte Carlo Sim-
ulation ............................. 382
9.1.1 Discrete Versus Continuous Time . . . . . 383
9.1.2 How Many Simulations to Perform .... 384
9.4.3 Comparisons with a Closed-Form Solution 384
9.4.4 Computational Efficiency . 386
9.1.5 Extensions and Limitations. 390
Conclusion '" 391
10 Fixed-Income Securities 395
10.1 Basic Concepts . 396
10.1.1 Discount Bonds 397
10.1.2 Coupon Bonds 401
10.1.3 Estimating the Zero-Coupon Term Structure 409
10.2 Interpreting the Term Structure of Interest Rates 413
10.2.1 The Expectations Hypothesis ...... 413
10.2.2 Yield Spreads and Interest Rate Forecasts 418
10.3 Conclusion .................... 423
11 Term-Structure Models 427
11.1 Affine-Yield Models . 428
11.1.1 A Homoskedastic Single-Factor Model 429
11.1.2 A Square-Root Single-Factor Model 435
11.1.3 A Two-Factor Model ........ . 438
11.1.4 Beyond Affine-Yield Models ... . 441
11.2 Fitting Term-Structure Models to the Data 442
11.2.1 Real Bonds, Nominal Bonds, and Innation 442
11.2.2 Empirical Evidence on Affine-Yield Models 445
xii (.'U/I 11'11 1.1
11.3 Pricing Fixed-Incomc Dcrivativc Sccuritics ..
11.3.1 Filling the Currcnt Terlll Structure Exactly
11.3.2 Forwards and Futures ........... .
11.3.3 Optioll Pricing in a Tcrlll-Structure Modc1
11.4 Conclusion .................... .
12 Nonlinearities in Financial Data 467
12.1 Nonlinear Structure in Univari<lte Timc Scric~ . 11iK
12.1.1 Some Paramctric Models . . . . . . . . . 470
12.1.2 Univariatc Tcsts for Nonlincar Structure 47:)
12.2 Modc\s of Challgill~ Volatility 479
12.2.1 Univariatc Models ............ . 4HI
12.2.2 Multivariatc Models. . . . . . . . . . . . 490
12.2.3 Links between First and Second Moments 494
Nonparametric Estilllation ..... . 49K
12.3.1 Kernel Regression. . . . . . . !",oo
12.3.2 Optimal Bandwidth Selcction :)02
12.3.3 Average Derivative Estimators 504
12.3.4 Application: Estimating State-Price Densities !i07
12.4 Artificial Neural Nctworks . . :)12
I 12.4.1 Multilayer PerccptfOns ... . 512
12.4.2 Radial Basis Functions ... . :) I Ii
12.4.3 Projcction Pursuit Regression 51H
12.4.4 Limitations of Learning Networks !ilK
\
I 12.4.5 Application: l.earning thc Bbck-Scholes FOflllllla 51\1
1~ .5 Overfllting and Data-Snooping :)~:{
12G Conclusion .... . . . .... :,24
1
Appendix
I
A Linear Instrumelllal Variablcs . . . . . . . . . .
A.2 Generalized Mcthod of MOlllcnts ....... .
A.3
Serially Correlated and f Icteroskeoastic Errors.
A.4 GMM and MaximulII Likelihood ....... .
References 541
Author Index 587
Subject Index 597