Stock Market Liberalizations and Efficiency: The Case of Latin America

Transcription

1 MPR Munich Personal RePEc rchive Sock Marke Liberalizaions and Efficiency: he Case of Lain merica João Paulo Vieio and Wing-Keung Wong and Sheung Chi Chow 06 Online a hps://mpra.ub.uni-muenchen.de/68949/ MPR Paper No , posed 3 February 06 7:6 UC

2 Sock Marke Liberalizaions and Efficiency: he Case of Lain merica João Paulo Vieio School of Business Sudies Polyechnic Insiue of Viana do Caselo Wing-Keung Wong eparmen of Economics Hong Kong Bapis Universiy Chow Sheung Chi eparmen of Economics Hong Kong Bapis Universiy

3 bsrac his invesigaion is among he firs o examine he impac of sock marke liberalizaion on he efficiency of Lain merican sock markes. I is also among he firs o apply he maringale hypohesis es and a sochasic dominance approach o sudy he issue of efficien markes. aily sock indices from Lain merican counries, including Brazil, Mexico, Chile, Peru, Jamaica, and rinidad and obago, are used in our analysis. o examine he impac of sock marke liberalizaion on efficiency, we employ several approaches, including he runs es, Chow-enning muliple variaion raio es, Wrigh variance raio es, he maringale hypohesis es and he S es, he sock marke indices of he counries above. We find ha sock marke liberalizaion does no significanly improve sock marke efficiency in Lain merica. Key words: Marke Liberalizaion; Marke Efficiency; Sochasic ominance, Lain merica. JEL Classificaions: G4, G5. Inroducion

4 he move oward financial liberalizaion in Lain merica has no been a coninuous process bu one wih a bump during he 980s as a resul of financial crisis. Financial liberalizaion in Lain merica has no been he resul of isolaed policy iniiaives bu has always been implemened as he componens of wide-ranging srucural reforms and sabilizaion programs. hese kinds of programs were se up in he region in he second half of he 970s, and heir implemenaion was mosly compleed in he 990s. uring ha period, Lain merican counries sared he process of sock marke liberalizaion. hese counries underook massive reforms and consequenly reduced he sock marke liberalizaion gap beween hem and indusrial counries. he lieraure noes ha sock marke liberalizaion could lead o an increase in equiy prices in emerging markes (Henry 000b; Bekaer and Harvey 000), liquidiy (Han Kim and Singal 000), and invesmen (Henry 000a), economic growh (Bekaer and Harvey 997; Bekaer e al. 00), he repricing of risk (Chari & Henry 00) and a decrease in he cos of capial (Sulz 999), a decrease in dividends (Bekaer and Harvey, 000), and a reduced equiy premium (himud and Mendelson 986; himud e al., 997). ccording o he efficien markes hypohesis (EMH), he increase he availabiliy of informaion in efficien markes should lead o sock prices ha are more efficienly priced. In oher words, heory suggess ha as informaion becomes more readily available as a resul of liberalizaion and here is increased compeiion, predicabiliy should decline. Examples of research relaed o his opic include Groenewold and riff (998), Kawakasu and Morey (999), Han Kim and Singal (000a, 000b) and Laopodis (004) and Füss (005). he lieraure abou he impac of liberalizaion on marke efficiency is mixed. For example, Groenewold and riff (998) find ha he predicabiliy of sia-pacific sock prices remains he same afer sock marke liberalizaion. Füss (005) finds ha liberalizaion could improve marke efficiency in sian sock markes, and Han Kim and Singal (000a, 000b) analyzed 4 emerging counries sock markes and found find ha hese markes became more efficien afer marke liberalizaion. Bu auhors like Kawakasu and Morey (999), esing he efficiency of nine emerging marke counries, did no find evidence ha hese markes become more efficien afer liberalizaion. Laopodis (004) finds ha Greece s financial marke didn become efficien because he marke was already efficien before liberalizaion. Hence, he impac of liberalizaion on sock marke efficiency remains puzzle in he exising lieraure, especially for Lain merican sock markes. 3

5 his invesigaion is among he firs o examine he impac of sock marke liberalizaion on he efficiency of sock markes and also among he firs o examine he impac of sock marke liberalizaion on he efficiency of Lain merican sock markes. o examine he impac on efficiency and o be rigorous in our invesigaion, we employ several approaches, including he runs es, Chow-enning muliple variaion raio es, Wrigh variance raio es, he maringale hypohesis es, and he S es, o sudying Lain merican sock marke indices. herefore, his sudy could be an imporan reference for hose counries ha wan o improve heir sock markes efficiency hrough liberalizaion, especially hose counries ha have condiions similar o hose in Lain merican counries. his paper is also among he firs o apply he maringale hypohesis es and a sochasic dominance approach o he issue of efficien markes. he paper is organized as follows. Secion describes daa sources and oulines he empirical mehodology used, and secion 3 discusses he resuls. Secion 4 concludes.. aa and Mehodology. aa Our daa consis of daily closing values of sock marke indices for he Lain merican counries (Brazil, Mexico, Chile, Peru, Jamaica and rinidad and obago), including he IBOV, MEXBOL, IPS, IGBVL, JMSMX and SE. hese counries were chosen because hey are imporan economies in he region. he oher counries were excluded from he Lain merican lis because heir sock marke daa are available only afer he dae on which heir sock markes were liberalized. In addiion, we use he MSCI World Index o represen he regional marke index. he MSCI World Index capures large- and mid-cap firms across 3 developed marke (M) counries. Wih,6 consiuens, he index covers approximaely 85% of he free floa-adused marke capializaion in each counry. hese daa are exraced from aasream. he sock marke indices of he Lain merican counries from 999 o 03 are ploed in figure for reference. Figure : Sock marke indices of he Lain merican counries 999 o 03 4

6 ae 8/7/99 //99 8/7/99 /9/993 8/6/993 3//994 9/6/994 3/3/995 9/5/995 3//996 9/5/996 4//997 0/6/997 4/0/998 0/5/998 4//999 0/6/999 5//000 /3/000 5/0/00 /4/00 5//00 /5/00 5/30/003 /4/003 6/9/004 /4/004 6/0/005 /3/005 6/9/006 /3/007 7/0/007 /4/008 7/8/008 //009 7/9/009 //00 8/9/00 //0 8/8/0 //0 8/8/0 3/4/03 9/6/ Brazil IBOV Mexico MEXBOL Chile IPS Peru IGBVL Jamaica JMSMX rinidad & obago SE MSCI WORL Noe: For an easier comparison, we se all he sock indices a he same basis of 00 on January, 999 and ake he naural log of hem. We compare he sock reurns of one year before, one year afer, and en years afer liberalizaion for a paricular sock exchange. able liss he dae on which each of he 6 counries firs liberalized is sock marke. We compare sock reurns before and afer liberalizaion, since he reurns could be affeced by he marke reurn. hus, we subsrac he reure of he MSCI World Index from he reurn of each reurn series o obain he excess reurns in order o eliminae he impac of he regional economy. In oher words, we compare he excess reurns beween he pre-liberalizaion period and he pos-liberalizaion period for he six sock indices. In his paper, we adop several ess, including he MV crierion, CPM saisics, he runs es, he muliple variaion raio es, he maringale hypohesis es and he S es, o invesigae wheher sock exchange liberalizaion improved he performance and efficiency of he markes we are analyzing. We illusrae hese ess in he following subsecions. able : Firs sock marke liberalizaion 5

7 Counry ae of firs sock marke liberalizaion Brazil May 99 Mexico May 989 Chile January 99 Peru January 99 Jamaica Sepember 99 rinidad &obago pril 997. Mehodology s Fama (970) menions, he definiion of efficien marke prices ha hey "fully reflec" he available informaion is very general. I is so general ha i has no direc empirically esable implicaions. o make he model esable, we mus define more exacly wha is mean by he erm "fully reflec." Various ess are developed o indirecly es he EMH. In his paper we will firs use he mean-variance crierion and CPM saisics o evaluae he performance of sock marke indices in he Lain merican counries. o ensure a robus resul, we will hen employ a number of hese ess, including he runs es, he muliple variaion raio es, he maringale hypohesis es, and a recenly developed sochasic dominance es, o examine he EMH in boh he pre- and he pos-sock marke liberalizaion period... Performance... he Mean-Variance Crierion For any wo invesmens wih reurns X and Y wih means X and Y and sandard deviaions X and Y, respecively, Y is said o dominae X by he MV crierion for risk averers if Y and Y X wih a leas one inequaliy holds (Markowiz, 95). hus, X he MV rule for risk averers is o check wheher Y X and Y X. If boh are no reeced wih a leas one sric inequaliy relaionship, hen we conclude ha Y significanly by he MV rule. Wong (007) has proved ha if boh X and Y dominaes X belong o he same locaion-scale family or he same linear combinaion of locaion-scale families, and if Y dominaes X by he MV crierion for risk averers, hen risk averers will aain higher expeced uiliy by holding Y han X. he heory can be exended o non-differeniable uiliies (see Wong and Ma (008), for deails).... he CPM Saisics 6

8 We nex apply he CPM analysis, including a bea componen, he Sharpe raio, reynor s index and Jensen s index (alpha), o measure he performance of he sock indices. he bea of he porfolio measures he marginal conribuion of a porfolio o he oal marke porfolio and he sensiiviy of is reurn o he movemen of marke porfolio reurns. he esimaion requires fiing he following CPM equaion for he reurn where i, f, i i m, f, i, R i, of index i a ime : R R R R () i, is he residual assumed o be i.i.d., R m, is he reurn of he marke porfolio, and R f, is he reurn of he risk-free asse a ime. In our paper, we use he reurn of he MSCI World Index o represen he R m, and he reurn of he 3-monh reasury bill as he equaion (), hree performance indices he Sharpe raio ( Jensen s index ( J i ) are hen compued using he following formula: S i R f, ), reynor s index ( i. From ), and S i Ri Rf, ˆ i i Ri Rf and J ˆ ˆ i i ( Ri Rf ) i( Rm Rf ). () ˆ i where ˆi is he esimaed sandard deviaion, and R i, R m and R f are he expeced reurn of index i, he marke porfolio and he risk-free asse, respecively.... egree of Efficiency... Runs es he runs es (Bradley, 968) is a nonparameric es o deermine wheher successive price changes are independen. ccording o Campbell (997), i could be used o examine he number of sequences of consecuive posiive and negaive reurns abulaed and compared agains is sampling disribuion under he random walk hypohesis. If y, y is a ime series of N reurns and N y m is heir median, he series of signs of residuals, sign u,..., sign u N are considered where ui yi ym and i,, N. ha is, a Osermark (99) uses he capial asse pricing model o analyze wo Scandinavian sock markes and finds ha he sandard CPM is unable o exhausively represen he economic forces of capial asse pricing, especially in Sweden. Ferruz gudo and Saro Marzal (004) apply he Sharpe raio o analyze he performance of Spanish invesmen funds. 7

9 posiive change + is assigned o each reurn y i ha is greaer han he median, a negaive change is assigned when he reurn is less han he median, and he reurn is omied when i equals he median. run is he number of sequences of same signs. For example, he series of signs gives 4 runs. o perform his es, we le n and n be he number of runs of + and, respecively and le U be he observed number of runs. oo many or oo few runs in he sequence are he resuls of negaive and posiive auocorrelaion, respecively. Under he null hypohesis of randomness or independence, by comparing he observed number of runs (U) wih he expeced number of runs ( U ), he es of he randomness hypohesis can be consruced. I has been shown ha, for large sample sizes where boh n and n are greaer han weny, he sandardized es saisic is Z U U, U where nn, U n U n n n n n n n and n n n. We noe ha Z is approximaely normally disribued under he null hypohesis of randomness or independence. If Z Z / ( Z Z / ), we reec he null hypohesis and conclude ha Y i is no random and no independen, and hus, we can conclude ha Y i is negaively (posiively) auocorrelaed.... Variaion Raio es Variance raio ess have been widely used and are paricularly useful for examining he behavior of sock prices or indices in which reurns are frequenly no normally disribued. Suppose we have he ime series X X X, X,..., 0, X saisfying X, (3) where X is he sock index and μ is an arbirary drif parameer. he residual saisfies 8

10 E 0 and E 0when 0 for all. Lo and MacKinlay (988) provide ess of he null hypohesis of randomness. Variance raio ess focus on he propery ha under a random walk wih uncorrelaed incremens in X, he variance of hese incremens increases linearly in Var for any posiive ineger q. he observaion inervals such ha X X qvar X X he variance raio is hen given by q VR q Var X X q Var X X q q. (4) Under he null hypohesis ha X follows he random walk model saed in (3), we have VR q. Lo and MacKinlay (998) generae he asympoic disribuion of he esimaed variance raios and provide wo es saisics, Z q and asympoic sandard normal disribuions under he null hypohesis. assumpion ha he disurbances of equaion (3) are homoscedasic, while Z Z q Z, 3 boh of which have q is derived under he q reas hem as heeroscedasic. he laer es saisic is no only sensiive o he changes in sock prices, bu i is also robus o many general forms of heeroscedasiciy and non-normaliy. he random walk hypohesis implies ha VR q for any ineger q. o improve on he work of Lo and MacKinlay (998), Chow and enning (993) show how conrolling es size faciliaes he muliple variance raio ess. For a single variance raio es, under he null hypohesis ha of m ess q i,,, m i. Under he null hypohesis of a random walk, here are muliple subhypoheses Mr q VR q 0, we follow Chow and enning (993) o consider a se M q i,,, m associaed wih he se of aggregaion inervals r i 3 Readers may refer o Lo and MacKinlay (999) for he formula. 9

11 0i r i i r i H : M q 0 for all i,,, m; H : M q 0 here exiss any i,,, m. (5) Reecion of a leas one H 0i for i,,, m implies reecion of he random walk. For he homoscedasic siuaion, we use he es saisics heeroscedasic siuaion, we adop he es saisics Z q i,,, m i i, whereas, for he Z q i,,, m. Since he random walk hypohesis is reeced if any of he VR q consider he Z q and Z q, where i is significanly differen from one, we only max,, Z q Z q Z q, i i i m i,. (6) If Z q ( Z q ) is greaer han he SMM (α, m, N), hen he random walk hypohesis is reeced under he homoscedasic (heeroscedasic) assumpion, where SMM is he upper α poin of he sudenized maximum modulus disribuion (Richmond, 98) wih parameer m and N (sample size) degrees of freedom. In addiion, Wrigh (000) indicaes wo poenial advanages of rank- and sign-based ess.... Rank-Based Variance Raio ess Suppose ha Y is a ime series of he asse reurns wih sample size. Le ry be he rank of Y among Y, Y,, Y. efine r ry and r ry, (7) where is he inverse of he sandard normal cumulaive disribuion funcion. 0

12 he series r is a simple linear ransformaion of he ranks and is sandardized o have zero mean and uni variance. he series r, known as he inverse normal or van der Waerden scores, also has zero mean and uni variance. Wrigh (000) subsiues r and r in place of he reurn ( X ) in Lo-MacKinlay s definiion of he variance raio es saisic (assuming X q homoscedasiciy). he rank-based variance raio es saisics R and R are defined as r r r k k k k k R 3k r /, (8) R r r r k k k k k 3k r /. (9)... Sign-Based Variance Raio ess For any series of reurn and / oherwise. Le s uy Y, le uy, q Y q 0.5. So,,0,0. Clearly, s uy is / if Y is posiive is an independen and idenically disribued (i.i.d.) series wih zero mean and uni variance. Each s is equal o wih probabiliy / and is equal o oherwise. he sign-based variance raio es saisic S is defined as s s s k k kk k S 3k s /. (0) he criical values of R, R, and S can be obained by simulaing heir exac disribuions Maringale Hypohesis es

13 he disincion beween a maringale difference sequence (MS) and uncorrelaedness is crucial when nonlinear dependence is presen, as commonly happens wih financial daa. For processes wih bounded second momens, an MS is an uncorrelaed sequence, bu an uncorrelaed sequence is no necessarily an MS. So we should poin ou ha a random walk is a srong form of he efficien marke hypohesis and furher one may be ineresed in esing he maringale hypohesis ha X is a maringale wih respec o some filraion equally o es wheher he reurn sequence r X X forms a maringale difference ( Er F ). o do so, ominguez and Lobao (003) derive consisen ess for he null F n ; or hypohesis ha he ime series process r has consan condiional expecaion given he informaion se F composed of he curren value of some exogenous variables and by a finie number of pas values of boh he own process and some exogenous variables. Since he asympoic disribuion of he considered es saisic depends on he specific daa-generaing process, sandard asympoic inference procedures are no feasible. hey show ha a modified wild boosrap procedure properly esimaes he asympoic null disribuion of he es saisic. ha is, hey use he wild boosrap Cramer-von Mises es saisic (denoed as Cp) and wild boosrap Kolmogorov-Smirnov es saisic (denoed as Kp) (ominguez and Lobao, 003) o es wheher he reurn r is a maringale difference sequence. Since here are no oher exogenous variables, informaion se is provided by z,,, p r r p null hypohesis is: 0, p, p H : E r z a. s.. o es r, z be an ergodic and sricly saionary process ha saisfies and ha r given condiioning argumen. H 0. hus, he considered here we need some assumpions. Le E r 4 for some 0, z, phas a bounded condiional densiy funcion ha is coninuous on any he proposed es is based on he following equivalence H R for almos all 0 0 p R, where R E r I z, p s I u df s, u he oin disribuion funcion of he vecor r, z F s u is in which,, p. Le F n denoe he empirical disribuion funcion of r, z, p and r he sample mean n r n r.

14 he esimae of he funcion R given by is sample analog n R s r I u df s, u r r I z, and he wo paricular es n n p n saisics considered here he Cramer von Mises es saisic is n n, C nr df r r I z z p, n n n, p, p n where F, lim F s,, and he Kolmogorov Smirnov saisic is n s n n K max nr z max r r I z z. () p, n n i, p, p i, p i,, n i,, n n ominguez and Lobao (003) provide he 0%, 5% and % criical values hrough a boosrap procedure. In pracice, we us need o calculae he value of C pn, or/and K, pn (), and compare hem o he corresponding criical value. If he value of he es saisic is larger han he corresponding criical value, we will reec he null hypohesis. We denoe he wo maringale difference ess Cp and Kp as M and display he ess resuls in able 5. Readers may refer o ominguez and Lobao (003)) for more deails and discussions on esing he maringale hypohesis and he conecure of he maringale propery ha generalizes he random walk conecure in he concep of efficien marke...3 Sochasic ominance es Le X and Y represen wo series of excess reurns ha have a common suppor of [ ab, ], where a b wih heir cumulaive disribuion funcions (CFs), F and G, and heir corresponding probabiliy densiy funcions (PFs), f and g, respecively. efine H0 x h, H x H d b and a H x H d (3) x for h f, g ; H F, G ; and,,3. We call he inegral he inegral and 3 and for H H he -order ascending cumulaive disribuion funcion (CF), and H he -order descending cumulaive disribuion funcion (CF), for =, Fand G. 3

15 We define he S rules as follows (see Quirk and Saposnik, 96; Fishburn, 964; Hanoch and Levy, 969): X F dominaes Y by FS (SS, S), denoed by x G x ( F x G x, F x G 3 x inequaliy holds for a leas one value of x. X 3 ) for all possible reurns Y ( X Y, X 3 x Y ) if and only if, and he sric he S heory for risk seekers has also been well esablished in he lieraure. Whereas S for risk averers works wih he CF, which couns from he wors reurn ascending o he bes reurn, S for risk seekers works wih he CF, which couns from he bes reurn descending o he wors reurn (Wong and Li, 999). Hence, S for risk seekers is called descending S (S). We have he following definiion for S (see Hammond, 974; Wong and Li, 999): X dominaes Y by FS (SS, S)) denoed by if F x G x ( F x G x, F x G3 x inequaliy holds for a leas one value of (second-order, hird-order) descending S. and Y We briefly describe he es in he following: Le {( f i, g i X 3 ) for all possible reurns x Y ( X Y, X 3 Y ) if and only x, he sric, where FS (SS, S) denoes firs-order )} ( i,..., n) be pairs of observaions drawn from he random variables X, wih disribuion funcions F and G, respecively, and wih heir inegrals F G x defined in (3) for,,3. For a grid of pre-seleced poins x, x,, x k x and, Bai e al. (0) modify he saisic developed by avidson and uclos (000) o obain he following -order es saisic for risk averers, : ˆ ( ) ˆ F x G ( x ) ( x) (4) ˆ V ( x ) where ˆ ˆ ( ) ( ) ˆ ( ) ˆ V x V x V x V ( x); F G FG H x x z N ˆ ( ) ( i), N( )! i 4

16 Vˆ x x z H x H F G z f g N ( ) ˆ H ( ) ( ) ( ),, ;, ; i N N(( )!) i N ˆ ( ) ( ) ˆ ( ) ˆ VFG x x f ( ). i x si F x G x N N(( )!) i I is no possible o es empirically he null hypohesis for he full suppor of he disribuions. hus, Bishop e al. (99) propose o es he null hypohesis for a pre-designed finie number of values x. Specifically, for all i,,..., k; he following hypoheses are esed: H : F ( x ) G ( x ), for all x ; 0 i i i H : F ( x ) G ( x ) for some x ; i i i H : F x G x for all x, F x G x for some x ; i i i i i i H : F x G x for all x, F x G x for some x. i i i i i i (5) In order o es S for risk seekers, he saisics for risk averers are modified o be he descending es saisic,, such ha: ˆ ( ) ˆ F x G ( x) ( x) (6) ˆ V ( x) Where ˆ ˆ ( ) ( ) ˆ ( ) ˆ V x V x V x V ( x); F G FG H x z x N ˆ ( ) ( i ), N( )! i Vˆ x z x H x H F G z f s N ( ) ˆ H ( ) ( ) ( ),, ;, ; i N N(( )!) i N ˆ ( ) ( ) ˆ ( ) ˆ VFG x f ( ) ; i x si x F x G x N N(( )!) i where he inegrals F x and following hypoheses are esed for risk seekers: G x are defined in (3) for,,3. For i,,..., k, he 5

17 H : F ( x ) G ( x ), for all x ; 0 i i i H : F ( x ) G ( x ) for some x ; i i i H : F x G x for all x, F x G x for some x ; i i i i i i H : F x G x for all x, F x G x for some x. i i i i i i No reecing H 0 or H or H implies he non-exisence of any S relaionship beween X and Y, he non-exisence of any arbirage opporuniy beween hese wo markes, and ha neiher of hese markes is preferred o he oher. If H ( H ) of order one is acceped, X (Y) sochasically dominaes Y (X) a he firs order, while if H ( H ) of order one is acceped, asse X (Y) sochasically dominaes Y (X) a he firs order. In his siuaion, and under cerain regulariy condiions, 4 an arbirage opporuniy exiss and any non-saiaed invesors will be beer off if hey swich from he dominaed o he dominan asse. On he oher hand, if H ( H ) [ H ( H )] is acceped a order wo (hree), a paricular marke sochasically dominaes he oher a he second (hird) order. In his siuaion, an arbirage opporuniy does no exis, and swiching from one asse o anoher will only increase he risk averers [seekers ] expeced uiliy, hough no heir expeced wealh (Jarrow, 986; Wong e al. 008). hese resuls could be used o infer ha marke efficiency and marke raionaliy could sill hold in hese markes. 5 In he above analysis, in order o minimize ype II errors and o accommodae he effec of almos S, 6 we follow Gasbarro e al. (007) and use a conservaive 5% cu-off poin in checking he proporion of es saisics for saisical inference. Using a 5% cu-off poin, we conclude ha one prospec dominaes anoher prospec only if we find ha a leas 5% of he saisics are significan. 3. Empirical Resuls and iscussion 4 Refer o Jarrow (986) for he condiions. 5 See Chan e al. (0) and he references conained herein for furher informaion. 6 lmos S allows a small area violaion compued from he compared disribuions o reveal a preference for mos decision makers bu no for all of hem. Readers may refer o Leshno and Levy, 00for more informaion. 6

18 his secion discusses empirical resuls wih differen ess and approaches in various subsecions in deail. 3. Performance o evaluae he performance of he sock indices, we use he MV approach and he CPM saisics o compare he performance of Lain merican socks before and afer sock marke liberalizaion. 3.. Mean-Variance Crierion and CPM Saisics able provides he descripive saisics of four daily sock excess reurns for he pre- and pos-liberalizaion periods. cademics and praciioners are ineresed in esing wheher sock marke liberalizaion could improve he performance of sock markes. One could provide an answer by checking wheher he mean reurn afer merging is higher and he volailiy is smaller. From able, we find ha risk averers prefer he pos-liberalizaion period s sock marke in he case of Brazil, Jamaica and rinidad and obago by he MV crierion, since hey all have a bigger mean and smaller sandard deviaion. However, using he MV crierion for risk seekers, we conclude ha risk seekers would prefer o inves in he pos-liberalizaion period in he case of Mexico, since i has boh bigger mean and sandard deviaion. However, here is no dominance beween he pre- and pos- liberalizaion periods by he MV crierion in he case of Chile and Peru. On he oher hand, from able, he saisics are no significan for all sock marke indices. hus, alhough one may sugges ha marke liberalizaion could, in general, resul in a higher reurn for he index afer liberalizaion, no index significanly improves is performance afer liberalizaion. mong hem, he F-saisic of he reurns beween he preand pos-liberalizaion periods is significanly smaller han uniy only for Brazil and rinidad and obago. his resul implies ha alhough Brazil, Mexico, Jamaica and rinidad and obago are more volaile afer marke liberalizaion, only Brazil and rinidad and obago are significanly more volaile afer marke liberalizaion. 7

19 able : escripive Saisics of he reurns Variable Mean Sdev Skewness Kurosis J-B es F -es F-es year Pre *** *** 39.0 *** *** Brazil year Pos *** *** 0 years Pos *** *** *** *** Mexico Chile Peru Jamaica Pre ***. *** -7.7 *** year Pos *** *** 9.07 *** *** years Pos *** *** *** *** *** Pre *** year Pos *** 6.5 *** *** *** 0 years Pos *** *** *** -.8 *** *** Pre *** 6.59 *** *** year Pos *** 6.57 *** -.60 *** *** 0 years Pos *** *** *** *** Pre ** *** 33. *** -4.3 *** year Pos ***.50 *** *** *** *** 0 years Pos *** *** *** *** *** rinidad & Pre *** *** *** *** obago year Pos *** *** *** -.95 *** years Pos *** *** *** -7.7 *** *** Noes: Lag orders of he F es are deermined based on IC. *, **, and *** denoe significance a he 0%, 5% and % level, respecively. 8

20 able 3 provides he CPM saisics of four daily sock excess reurns for he pre- and posliberalizaion periods. For he CPM saisics, all Sharpe raios and he Jensen index are negaive. We noe ha he Sharpe raios in he pos-liberalizaion period are bigger han in he pre-liberalizaion period excep for he case of rinidad and obago. he Sharpe (966) raio is he mos convenional formula used in sock evaluaion. he Sharpe raio measures he excess reurn per uni of risk, where he risk is deermined by sandard deviaion. he higher he Sharpe raio value, he beer he porfolio s reurns relaive o is risk or he larger he excess reurn per uni of risk in a porfolio. We find ha he Jensen index raios in he pos-liberalizaion period are bigger han in he pre-liberalizaion period excep for he case of Mexico. higher Jensen index suggess a higher level of reurn given he level of risk (sysemaic or marke) on he invesmen. low Jensen index, such as a negaive number, indicaes inferior performance given he level of risk. On he oher hand, he reynor index has mixed resuls. he reynor index for Brazil, Peru and Jamaica in he pos-liberalizaion period is beer han in he pre-liberalizaion period, while Mexico, Chile and rinidad and obago show he reverse relaionship. he reynor (965) raio akes ino accoun he sysemaic risk or marke volailiy as is measure of risk insead of he sandard deviaion, as in he Sharpe raio (966). reynor (966) noed ha he relaionship of he excess fund reurn o he bea lies along he securiy marke line. In shor, our resuls using he mean-variance approach and he CPM saisics confirm ha marke liberalizaion could resul in he index showing marginally higher reurns and more volailiy afer liberalizaion, while our resuls using he CPM saisics confirm ha he performance of he six sock indices improves afer liberalizaion. 9

21 able 3: CPM Saisics Variable Bea Sharpe reynor Jensen Pre Brazil Year Pos Years Pos Pre Mexico Year Pos Years Pos Pre Chile Year Pos Years Pos Pre Peru Year Pos Pos Pre Jamaica Year Pos Years Pos Pre rinidad &obago Year Pos Years Pos Noes: *, **, and *** denoe significance a he 0%, 5% and % level, respecively. 0

22 3. egree of Efficiency 3.. Runs es he resuls of he runs es for daily excess reurns, which do no depend on he normaliy of reurns, are presened in able 4. From able 4, we see ha all he values of he Z-saisic pre-liberalizaion are saisically significan a he 5 % level in boh he pre- and posliberalizaion periods excep for Brazil, Jamaica and rinidad and obago. he Z-saisics of Brazil and Jamaica are saisically insignifican a he 0 % level in boh he pre- and posliberalizaion periods. he Z-saisics of rinidad and obago on he oher hand are only saisically significan a he 5 % level in he pre-liberalizaion period. he null hypohesis of randomness is reeced in boh he pre- and pos-liberalizaion periods for Mexico, Chile, Peru and rinidad & obago. he resuls also show ha for all counries excep Peru he absolue value of he Z-saisic is smaller in he pos-liberalizaion period. hese resuls could imply ha almos all counries are more efficien afer sock marke liberalizaion.

23 able 4: Resuls of Runs es Variable n n + Year Period 0 Years Period oal Number oal Number Z- p-value n saisic n Cases of Runs + Cases of Runs Z- saisic p-value Brazil Mexico Chile Peru Jamaica rinidad &obago Pre Pos Pre *** *** 0.00 Pos ** *** <0.00 Pre *** *** Pos ** *** <0.00 Pre *** *** 0.00 Pos *** *** <0.00 Pre Pos Pre ** ** 0.03 Pos Noe: his able presens he resuls of he runs es of he excess reurns ha are compued by deducing he reurn of he MSCI World Index from each of he reurn series. *, **, and *** denoe significance a he 0%, 5%, and % level, respecively.

24 3.. Variaion Raio ess he resuls of he muliple variance raio es developed by Chow and enning (993) are presened in able 5. In able 5, boh Z ( q) and Z ( q) of all Lain merican counries are saisically significan a he % level for boh he pre- and pos-liberalizaion periods. hese resuls reec he random walk hypohesis under boh homoscedasic and heeroscedasic siuaions. However, i should also be noed ha he Z-saisics ( Z ( q), Z( q)) of Mexico and Jamaica become smaller in he pos-liberalizaion period, which shows a possible endency o random walk. able 5: Chow-enning (993) Muliple Variaion Raio es Saisics Counry Indexes Year Pre Year Pos 0 Years Pos Z (q) Z (q) Z (q) Z (q) Z (q) Z (q) Brazil *** *** *** *** *** *** Mexico 8.99 *** 5.59 *** 35.9 ***. *** *** 0.49 *** Chile *** *** 38.9 *** 8.7 *** *** *** Peru *** 3.03 *** *** *** *** *** Jamaica 50.3 *** 43.0 *** 4.95 *** 7. *** *** *** rinidad & obago 3.3 ***.38 *** *** 4.8 *** 70.4 *** 5.47 *** Noe: Z (q) is he variance raio es saisic assuming homoscedasiciy. Z (q) is he variance raio es saisic, assuming heeroscedasiciy. *, **, and *** denoe significance a he 0%, 5% and % level, respecively. he 0%, 5% and % criical values are.668, and 3.00, respecively. able 6 describes he rank and sign es developed by Wrigh (000). In order o draw a beer picure of he comparison, we adop he common pracice and selec lags, 4, 8, and 6 in he esing procedure. From able 6, he rank-based es resuls show ha R and R are saisically significan a he % level in boh he pre- and pos-liberalizaion periods. he signbased es resuls are similar o he rank-based es resuls. Overall, for every Lag =,4,8,6, he null hypohesis ha Lain merican sock marke indices are following a random walk is reeced in boh he pre- and pos-liberalizaion periods. 3

25 able 6: Wrigh (000) Variance Raio es Saisics Ranks and Signs Variables Brazil Year Pre-Liberalizaion Year Pos Liberalizaion 0 Years Pos Liberalizaion Number of Lag (q) R 5.7 *** 4.74 *** 35.4 *** *** 5.60 *** 4.40 *** 34.6 *** *** 50.9 *** 8.45 *** 9.63 *** *** R 5.68 *** 4.66 *** *** *** 5.4 *** 4.00 *** *** 4.9 *** *** *** 8.6 *** *** S 6.03 *** 5.5 *** *** 5.68 *** 6.00 *** 5.46 *** *** 5.57 *** 5.04 *** 8.78 *** 0.50 *** *** Mexico R 5.47 *** 3.86 *** 3.56 *** *** 5.59 *** 4. *** *** 4.60 *** *** 8.40 *** 9.45 *** *** R 5.4 ***.8 *** 9.66 *** 33.7 *** 5.5 *** 3.0 *** 30.3 *** *** 50.7 *** 80.9 *** 8.5 *** *** S 6.00 *** 5.46 *** *** 5.57 *** 6.03 *** 5.5 *** *** 5.68 *** 5.03 *** 8.77 *** 0.48 *** 7.96 *** Chile R 5.88 *** 5.06 *** 35.8 *** 48. *** 5.56 *** 4.8 *** *** *** 50.9 *** 8.36 *** 9.3 *** *** R 5.79 *** 4.8 *** 35. *** 45.4 *** 5.3 *** 3.36 *** 3.44 *** *** 50.7 *** *** 7.68 *** 66.0 *** S 5.9 *** 4.05 *** 34.8 *** *** 5.88 *** 5.3 *** 36.0 *** 50.6 *** *** 8.43 *** 9.79 *** 7.88 *** R 5.67 *** 4.53 *** *** *** 5.85 *** 4.99 *** *** *** *** 8.43 *** 9.5 *** 70. *** Peru R 5.9 *** 3.47 *** 3.6 *** 40.9 *** 5.74 *** 4.74 *** 35. *** 46.5 *** *** 8.34 *** 9.35 *** 70.0 *** S 6.00 *** 5.46 *** *** 5.57 *** 6.00 *** 5.46 *** *** 5.57 *** 5.04 *** 8.78 *** 0.50 *** *** R 5.64 *** 4.70 *** *** *** 5.78 *** 4.79 *** *** *** *** 8.39 *** 9.38 *** *** Jamaica R 5.5 *** 4.38 *** *** *** 5.44 *** 3.98 *** 33.6 *** 4.77 *** *** 8.35 *** 9.33 *** 69.6 *** S 6.00 *** 5.46 *** *** 5.57 *** 6.06 *** 5.56 *** 37.3 *** 5.79 *** 5.04 *** 8.78 *** 0.50 *** *** rinidad & obago R.37 *** 9. *** 6.94 *** *** 5.66 *** 4.64 *** *** 46.7 *** *** 8.53 *** 9.85 *** 7.6 *** R. *** 7.5 *** 4.56 *** *** 5.03 *** 3.59 *** 33.7 *** 4.8 *** 50.7 *** 8.07 *** 8.89 *** *** S 6.03 *** 5.5 *** *** 5.68 *** 6.03 *** 5.5 *** *** 5.68 *** 5.03 *** 8.77 *** 0.48 *** 7.96 *** Noe: R and R are rank-based variance raio es saisics, which are defined in equaions (6) and (7), S is he sign-based variance raio es saisic, which is defined in equaion (8). he *, **, and *** denoe significance a 0%, 5% and % level, respecively. 4

26 3..3 Maringale Hypohesis es he wild boosrap Cramer-von Mises es saisic (Cp) and wild boosrap Kolmogorov- Smirnov es saisic (Kp) by ominguez and Lobao (003) are repored in able 7. For he pre-liberalizaion, excep for Jamaica, we reec he null hypohesis ha he reurn is a maringale difference sequence. hese resuls show ha Jamaica has an efficien sock marke bu he ohers do no. For he pos-liberalizaion, excep for Brazil, we reec he null hypohesis ha he reurn is a maringale difference sequence. his shows ha Brazil is an efficien marke and he ohers are no efficien markes. hus, only Brazil s resuls show ha liberalizaion has improved marke efficiency when we compare he pre-liberalizaion -year period o he posliberalizaion -year period. However, his resul doesn hold when we compare he preliberalizaion -year period o he pos-liberalizaion 0-year period. Overall, our resuls do provide evidence ha liberalizaion has improved marke efficiency in Lain merican sock markes. able 7: ominguez and Lobao (003) es saisics Cp and Kp Variable Year Pre Year Pos 0 Years Pos C p K p C p K p C p K p Brazil *** **.7786 *** Mexico.389 ***.88 *** 0.56 *** *** *** *** Chile ***.335 *** ***.378 *** 8.8 *** 4.07 *** Peru.44 ***.90 ***.559 ***.35 *** *** *** Jamaica *** rinidad.785 ***.58 *** *** & obago Noe: In he wild boosrap Cramer-von Mises es (Cp) and wild boosrap Kolmogorov-Smirnov es (Kp), he number of boosrap replicaions is 500, and he lag value p is. *, **, and *** denoe significance a he 0%, 5% and % level, respecively. 5

27 3..4 Sochasic ominance pproach We will employ he es o examine invesors preference oward liberalizaion, check wheher here is an arbirage opporuniy due o liberalizaion and examine marke efficiency. ables 8 and 9 repor he percenage of significan modified saisics over he negaive domain (losses), posiive domain (gains) and he enire reurn disribuion (boh) for risk averers and risk seekers, respecively. We find ha he pos-liberalizaion excess reurns do no sochasically dominae he pre-liberalizaion excess reurns a he firs hree orders for all six indices. We explain he resuls in more deail below. s can be seen from able 8, no (S and S) is significanly posiive and negaive, indicaing ha pos-liberalizaion excess reurns and e pre-liberalizaion excess reurns do no dominae each oher in he sense of FS. Moreover, he pre- and pos-liberalizaion excess reurns also do no dominae each oher in boh SS and S because boh and 3 (S and S) are no significanly posiive and negaive. he resuls show ha excess reurns in he pre- and pos-liberalizaion period do no dominae each oher a he firs hree orders, implying ha here is no arbirage opporuniy in he pre- and pos-liberalizaion periods and invesors canno ge higher expeced wealh by shifing heir invesmen from he preliberalizaion period o he pos-liberalizaion period and vice versa. his resul, in urn, shows ha all six markes are efficien. o have a beer undersanding of he pre- and posliberalizaion relaionship in he sense of FS, we plo he CFs for Mexico in figure. From figure, we noice ha he CFs for boh he pre- and pos-liberalizaion periods coincide wih each oher. his leads us o suspec ha here is no difference beween pre- and posliberalizaion. Our S resul implies ha risk averers are indifferen beween he pre- and posliberalizaion periods for all indices sudied in his paper; here is no arbirage opporuniy owing o liberalizaion; and he marke is efficien and invesors are raional. las, we noe ha we have applied he S es for risk seekers o analyze he daa and draw he same conclusion ha risk seekers are indifferen beween he pre- and posliberalizaion periods for all e indices sudied in his paper; here is no arbirage opporuniy owing o liberalizaion; and he marke is efficien and invesors are raional. hus, he S es offers no evidence ha sock marke liberalizaion has improved marke efficiency. 6

28 Figure : Plo of he CF of he pre- and pos-liberalizaion periods for Mexico pre-liberalizaion pos-liberalizaion 7

29 able 8: Percenages of Significance of Modified avidson-uclos Saisics Year Period 0 Years Period Variable FS SS S FS SS S F=pre, G=pos % Brazil Mexico Chile Peru Jamaica rinidad & obago > 0 % < 0 % > 0 % < 0 % 3 > 0 % 3 < 0 % > 0 % < 0 % > 0 % < 0 % 3 > 0 % Noe: he numbers in he columns of FS, SS and S indicae he percenages of he modified saisics significanly in he posiive domain (+) and negaive domain (-) a he 5% level. is defined in (4). F is he reurn series for he pre-liberalizaion period, while G is he reurn series for he pos- liberalizaion period. 3 < 0 8

30 able 9: Percenages of Significance of Modified avidson-uclos Saisics Year Period 0 Years Period Variable FS SS S FS SS S F=pre, G=pos % Brazil Mexico Chile Peru Jamaica rinidad & obago > 0 % < 0 % > 0 % < 0 % 3 > 0 % 3 < 0 % > 0 % < 0 % > 0 % < 0 % 3 > 0 % Noe: he numbers in he columns of FS, SS and S indicae he percenages of he modified saisics significanly in he posiive domain (+) and negaive domain (-) a he 5% level. is defined in (6). F is he reurn series for he pre-liberalizaion period, while G is he reurn series for he pos-liberalizaion period. 3 < 0 9

31 4. Conclusion he impac of liberalizaion on sock marke efficiency sill remains a puzzle in he lieraure, especially for Lain merican sock markes. his invesigaion is among he firs o examine he impac of sock marke liberalizaion on he efficiency of sock markes and also among he firs o examine he impac of sock marke liberalizaion on he efficiency of Lain merican sock markes. aily sock indices from Brazil, Mexico, Chile, Peru, Jamaica and rinidad and obago are used for he analysis. We compare sock reurns one year before, one year afer, and en years afer liberalizaion for a paricular sock exchange. We firs employ he mean-variance approach and CPM saisics o evaluae sock indices performance. o es he randomness, in order o have a more reliable resul, we employ several approaches, including he runs es, he Chow-enning muliple variaion raio es, he Wrigh variance raio es, he maringale hypohesis es and he S es, o Lain merican sock marke indices. he runs es implies ha hese markes efficiencies are more or less he same afer liberalizaion. he resuls of he Chow-enning muliple variaion raio es saisics and he Wrigh variance raio es saisics ranks and signs show ha he indices sudied in his paper do no improve heir randomness afer he inroducion of liberalizaion. he maringale hypohesis es shows ha only Brazil s efficiency is improved afer liberalizaion, bu his resul doesn hold when we compare he pre-liberalizaion period wih he period 0 years afer liberalizaion. he resuls from he S es imply ha risk averers and seekers are indifferen beween he pre- and pos-liberalizaion periods for all indices sudied in his paper; here is no arbirage opporuniy owing o liberalizaion; and he marke is efficien and invesors are raional. ll of our ess offer no evidence ha sock marke liberalizaion has improved sock marke efficiency in Lain merica. We believe our resuls are quie reliable, since we use several differen approaches and hey all give he same resul. herefore, one may need o consider ha liberalizaion may no necessarily significanly improve sock marke efficiency when i comes o counries ha are similar o Lain merica. 30

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