The Econometrics of Financial Markets John Y. CamPgeU AndrewW.Lo I A. Craig MacKinJay Princeton University Press Princeton, New Jersey PPClu"iIbn'ylciresi\h\(lt),·hI"It . h ©Ny e Pw1'r, )Ji9ne7rc sehetyyo In\'l riUillrln)c~ie\vllt O"rlsli lUy l(l'ifwI''"'.i l4y1 IW'ni'l"li ,,," SII ,'('1. WIne t.ht eS ul~int"itXe tl Kingdonl; prinCt.'tlln Unil't'"ity 1'1'''. Cltid,,·,t<·,. library of Congress Cataloging·in.Publication Data (:"U1l'lwl\, John Y. W. 1.0. A'r. hCrr .ti'"\c\ oMnaoclHKt."intrliany .o f Hnand.,\ 1Il .• rkt,t!\o / John Y. C;.nnpht·U. AIl(\t"t'W p. em. Inchl(k~ bitJliographic-.1 ,ek't''''''s ,\lid index. ISBN t).tj~I.()4~()I.!1 (dutll : alk.I',I[>el) 1W\(t;'I4I.[C,:hDjIJ(.; CU<lI7'):. ' ,lIIpI!.i tmaMl laJclaKriknelta-yE. cAorlclhoilll.l' cCt,r;i\(i ~,," uI,%l .. fh,.- I. 1I.1ll1., ATlildtkre. w W. \AlltI' ('w 3~2'.tl!I114-<lr~1\ I : TIfl,t iT.\, lhrOtl'~l "\ ''OV;;U" I,( '" 'R''pooadse. ,M1 lilnl lIliTle\:l \No., I'"I. 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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