Conditional Skewness of Aggregate Market Returns: Evidence from Developed and Emerging Markets

Transcription

1 Global Economy and Fnance Journal Vol. 7. No.. March 04. Pp. 96 Condonal Skewness of Aggregae Marke Reurns: Evdence from Developed and Emergng Markes Anchada Charoenrook and Hazem Daouk Ths paper examnes wheher condonal skewness of reurns a he marke level s predcable and nvesgaes he economc mechansms underlyng hs predcably. We analyze aggregae marke reurns n 57 counres. onemonh reurns predc condonal skewness of daly reurns durng he followng monh. Reurns are more negavely skewed followng an ncrease n sock prces and reurns are more posvely skewed followng a decrease n sock prces. Ths relaon beween skewness and lagged reurns s economcally and sascally srong across boh developed and emergng counres. We are able o dsngush dfferen heores by esng posve lagged reurn and negave lagged reurns predcably of skewness and volaly separaely and esng predcably of adjused-rend urnover neracon wh shor-sale consran daa from Charoenrook and Daouk (003). The evdence shows ha he radonal explanaons of skewness such as he leverage effec he volaly feedback effec he sock bubble model (Blanchard and Wason 98) and he flucuang uncerany heory (Verones 999) exs n he daa bu are no he only economc mechansms drvng he asymmery n sock reurns. We fnd no evdence of Hong and Sen (003). Our resuls are conssen wh Coval Coval and Hrshlefer (00). Our fndngs have mplcaons for fuure heorecal and emprcal models of me-varyng marke reurn dsrbuons opmal asse allocaon and rsk managemen. Feld of Research : Fnance Economcs JEL classfcaon code: G C. Inroducon The characerscs of he dsrbuon of secury reurns such as skewness play a sgnfcan role n fnancal heory and pracce. If sock reurn dsrbuons are skewed hen asse prcng models ha accoun for he presence of hgher momens should produce more accurae valuaons. When nvesors have preferences over he asymmery of her porfolo reurns Kraus and Lzenberger (976) Rubnsen (973) Harvey and Sddque (000) and Dmar (00) exend he CAPM o show ha expeced reurns nclude a compensaon for negave sysemac coskewness. They also presen emprcal evdence ha suppors he models. Paon (004) shows ha accounng for skewness mproves performance of opmal asse allocaon. Brunnermeer Goller and Parker (007) develop an asse prcng model ha accouns for some human behavor rades whch resuls n preference for skewness whch suggess skewness s a sysemac rsk. Harvey Lechy Lechy and Muller (00) buld on he Markowz porfolo selecon process by ncorporang hgher order momens and predcve Dr. Anchada CharoenrookThammasa Busness school Thammasa Unversy Prachan rd. Bangkok 000 Thaland Emal: workada@lve.com Phone: Dr. Hazem Daouk Deparmen of Appled Economcs & Managemen Cornell Unversy 446 Warren Hall Ihaca NY Emal: hd35@cornell.edu

2 asse reurns. They fnd ncorporang hgher order momens n porfolo selecon ncreases expeced uly. Furhermore accurae predcon of he condonal reurn dsrbuon especally a he hgher momens sgnfcanly mproves he valuaon of conngen clams and he effecveness of rsk managemen. Thus nvesgang asymmery n sock reurn dsrbuons s predcably and wha causes s mporan for mulple faces of fnance. Some heores pos ha condonal skewness may be predcable by lagged reurns and rend-adjused urnover. A he frm level here s some emprcal evdence of hs predcably. Harvey and Sddque (000) documen ha skewness vares among porfolos of dfferen sze and book-o-marke levels. Chen Hong and Sen (00) (hence forh CHS) repor ha rendadjused urnover and lagged reurns predc skewness of daly reurns of ndvdual socks n he US sock marke. Langlos (03) use lagged rend-adjused urnover lagged reurn and oher frm-specfc varables o predc expeced skewness of ndvdual sock reurns. A he marke level Harvey and Sddque (999) documen me-varaon n condonal skewness. Bal Mo and Tang (008) use models ha allow for me-varyng skewness o beer f reurns for rsk managemen. La (0) uses he S u -normal dsrbuon o model he dynamc behavor n of skewness of en nernaonal aggregae sock ndces. The sudy fnds negave reurn shock skews he me-varyng dsrbuon o he rgh for maure markes bu o he lef for emergng markes. Whle me-varyng skewness has been documened and modeled n he US sock marke here are no sudes of predcably of skewness a he marke level wh large numbers of nernaonal marke reurns whch also dsngushes he dfferen heores of reurn dsrbuon skewness. The mos noable paper o documen predcable skewness and aemps o dsngush beween dfferen heores of condonal skewness s Chen Hong and Sen (00).They repor predcably a he frm level US sock marke. They fnd some predcably a he marke level bu s no sascally sgnfcan. Ther fndngs suppor Hong and Sen (003) (hence forh HS) heory bu do no dsngush he many oher heores of condonal skewness and hey do no es he mporan assumpon n he HS model whch s he shor-sale consran. Ths sudy examnes wheher he condonal skewness of aggregae marke reurns s predcable by lagged reurns and rend-adjused urnover and nvesgaes wha economc mechansms are responsble for he predcably of skewness. We analyze aggregae marke reurns n 57 counres. We presen new evdence ha condonal skewness of aggregae marke reurns s predcable. one-monh reurns predc condonal skewness of daly reurns durng he followng monh. Reurns are more negavely skewed followng an ncrease n sock prces and reurns are more posvely skewed followng a decrease n sock prces. Ths relaon beween skewness and lagged reurns s economcally and sascally srong across boh developed and emergng counres. We fnd smlar resuls usng lagged reurns over 3 monhs 6 monhs and monhs. In conras we fnd ha rend-adjused urnover does no predc marke reurns. We are able o dsngush dfferen heores by esng posve lagged reurn and negave lagged reurns predcably of skewness and volaly separaely and esng predcably of adjused-rend urnover neracon wh shor-sale consran daa from Charoenrook and Daouk (003). 97

3 Why should condonal skewness be predcable? We caegorzed he heores ha address hs queson no hree groups. We dscuss hem n dealed n he nex secon. v The frs group of heores shows ha more negave skewness should follow sock prce declnes. The earles heory s he leverage effec (Black 976; Chrse 98). A drop n sock prce rases fnancal and operang leverage whch ncreases volaly of subsequen sock reurns. An ncrease n sock prce reduces leverage whch reduces volaly of subsequen sock reurns. Ths relaon beween me-varyng volaly and reurns can generae wha appears o be nonzero skewness because sock reurns measured over an exended perod of me conss of a mxure of condonal reurn dsrbuons. When he mean of hese condonal dsrbuons are declnng a he same me as her volales are ncreasng he reurn over a perod of changng condonal dsrbuons wll have negave skewness. Consequenly he leverage effec can creae a negave relaon beween lagged reurn and skewness. Mos frms have leverage herefore hs effec aggregaes o he marke level. The second heory n hs group s he volaly feedback effec (Pndyck 984; French el al. 987; and Campbell and Henschel 99). Releases of major bad economc news decrease sock prce and ncrease volaly. The ncrease n volaly ncreases expeced reurns whch exacerbaes he sock prce declne. On he oher hand releases of major good economc news ncrease sock prce and also ncrease volaly; he second effec dampens he former. Thus gven he same amoun of nformaon sock marke prce declnes are larger and sock marke prce ncreases. Ths generaes a negave relaon beween lagged reurn and condonal skewness. The hrd heory s one of flucuaon n he level of uncerany (Davd 997; Verones 999). Ths heory s akn o he volaly feedback effec bu s more specfc on how volaly level changes wh unexpeced news. The second group of heores predcs more negave skewness followng prce ncreases or hgh levels of rend-adjused urnover. The sochasc bubble model of Blanchard and Wason (98) predcs larger negave skewness followng a perod of susaned sock prce ncrease. The asymmery here s caused by a sock bubble bursng a low probably of very large negave reurns. Hong and Sen (003) (hereafer HS) propose a model n whch lagged rend-adjused urnover s negavely relaed o skewness. Ths relaon arses because nvesors have heerogeneous belefs and hey canno shor sell socks. The las group s he heory proposed by Cao Coval and Hrshlefer (00) (hereafer CCH). Ther model s based on nformaon blockage due o radng coss. The model predcs negave skewness followng a prce run up and posve skewness followng a prce run down. CCH also predc ncrease n volaly followng large prce changes. We adop a smple ye effecve mehod o dsenangle he effecs of hese heores. We noe ha he relaon beween lagged reurns and condonal volaly and skewness mpled by hese heores depends on he sgn of lagged reurns. Therefore we es he relaon beween lagged reurns and condonal skewness based on sgned lagged reurns. Exsng emprcal sudes do no dsngush wheher hs relaon s symmerc wh respeced o he drecon of lagged reurns. 98

4 Our resuls are able o dsngush beween he compeng heores. Specfcally we fnd ha sock reurns become more negavely skewed followng a posve reurn monh and become more posvely skewed followng a negave reurn monh. We also es condonal volaly relaon wh lagged reurns separaely by lagged reurn sgn.the resul ha negave lagged reurns predc more posve skewness s conrary o he predcons of he leverage effec he volaly feedback effec and he flucuaon uncerany heory. The sochasc sock bubble model does no predc any relaon beween negave lagged reurns and skewness. We do no fnd evdence supporng Hong and Sen (003). The economc mechansm proposed n CCH appears o be more conssen wh our fndngs. The fndngs n hs sudy conrbue o he exsng leraure n varous aspecs. Frs hey sugges he ncluson of predcable skewness n models of conngen clams and rsk managemen. Employng more accurae predcons of condonal skewness should mprove he valuaon of conngen clams on he sock marke and he effecveness of rsk managemen. Second hey sugges ha fuure heorecal and emprcal models of sock marke reurns should allow for predcable condonal skewness. Thrd he predcably of condonal skewness of marke reurns s relevan o he opmal dynamc asse allocaon among socks bonds and oher asses of rsk-averse nvesors. Lasly he fndng ha posve lagged reurns predc more negave skewness and negave lagged reurns predc more posve skewness suggess ha he economc mechansm drvng hs relaon affecs boh buyng and sellng of socks. In CCH radng coss causes he condonal reurn dsrbuon o be asymmerc even when he arrval of nformaon s symmerc ex ane. v The remander of hs paper s organzed as follows. Secon I presens he heores relaed o he predcably of skewness. Secon II descrbes he daa employed n our ess. Secon III repors he es resuls. We dscuss robusness ssues n Secon IV and offer concludng remarks n Secon V.. Leraure Revew Ths secon descrbes exsng heores ha have mplcaons for condonal skewness. Ther effecs are summarzed n Table n he appendx.. The Leverage Effec Volaly Feedback Effec and he Flucuaon of Uncerany Effec When a frm has leverage a drop n sock prce rases fnancal and operang leverage (when deb s consan) whch ncreases s volaly. An ncrease n sock prce reduces leverage whch reduces s volaly. The leverage effec can generae wha appears o be negave skewness because he sock reurn whch s measured over an exended perod of me pcks up a mxure of condonal reurn dsrbuons whose mean are declnng a he same me as her volales are ncreasng. Because leverage s hgher afer sock prces declne he leverage effec cause a negave relaon beween lagged reurn and condonal skewness. Mos frms have fnancal and operang leverage hus he leverage effec should aggregae o he marke level. 99

5 The volaly feedback effec hnges on he emprcal observaon ha n a perod of sgnfcan news good or bad sock prces become more volale for a perod of me. Increased volaly ncreases he expeced reurn on he sock whch furher exacerbaes a sock declne bu dampens a sock prce ncrease. The volaly feedback effec predcs large sock prce declnes han ncrease gven he same amoun of nformaon ex ane. Ths causes reurns o be more negavely skewed when sock prces declne. A he marke level he news s economc-wde news. Verones (999) proposes a heory n whch here s flucuaon n he level of uncerany of he sae of he economy. Verones (999) models he dvdend process as a Markov swchng process beween a good and a bad economc sae. When nvesors receve a sream of good news hey become more ceran ha he economy s n he good sae. If bad news arrves followng a sream of good news causes a marke prce declne and also makes nvesors more unceran as o wha sae he economy s n. On he oher hand he arrval of good news when nvesors beleve ha he economy s n he bad sae ncreases marke prce bu also ncreases he uncerany abou wha sae he economy s n. Verones shows ha n equlbrum he wllngness of nvesors o hedge agans a change n her own uncerany on he rue sae of he economy makes sock marke prce overreac o bad news and underreac o good news. Consequenly reurns are more negavely skewed when prces declne.. Cao Coval and Hrshlefer (00) In he Cao Coval and Hrshlefer (00) model here are nformed nvesors unnformed nose raders and an unnformed marke maker. All marke parcpans are fully raonal. Invesors ncur heerogeneous radng coss. There s a probably ha a se of nvesors receved a common nosy nformave sgnal abou he valuaon of a secury. The followng chan of evens llusraes he man dea of hs model. There s prvae good news abou a secury and a se of nvesors receve favorable sgnals abou hs secury. Despe recevng a prvae sgnal some nvesors are sdelned and do no rade because of hgh radng coss. Ohers wh lower radng coss buy he secury. Afer observng a sock prce ncrease due o buy rades a favorably nformed sdelned nvesor weghs wo effecs. On he one hand he accuracy of hs sgnal s confrmed bu on he oher hand he sock prce s more expensve o buy. The prce ncrease may no ouwegh he ne gan from radng because he prce s revsed by an unnformed marke maker. Tha s he revsed prce se by he marke maker remans less han he full nformaon prce; he marke maker does no know for ceran ha here s a prvae sgnal. Therefore he marke maker places a hgher probably ha he las rade was from a lqudy rader han he nformed sdelned nvesor who has receved a sgnal hmself. Consequenly more nformed nvesors who were prevously sde lned buy socks because he confrmaon of her sgnals by oher buyers ouweghs her radng coss. Overall sgnfcan prce rse can rgger radng of a favorable nformed nvesor prevously sdelned. Conversely an nformed nvesor wh negave nformaon becomes less confden ha he has receved he correc sgnal and herefore ss ou and does no rade. 00

6 Ths sdelnng of nvesors causes condonal changes n skewness as a funcon of pas reurns. Afer an upward prce rend s lkely ha here are a few sdelned nvesors wh favorable sgnals so ha prces wll rse moderaely hgher. However s lkely ha here are a large number of sdelned nvesors wh adverse sgnals. The evenual enry of sdelned nvesors wh adverse sgnals wll cause a major correcon. The marke maker s aware of hese sdelned nvesors and adjuss prces accordngly when he sees a sell rade. Thus reurns become more negavely skewed followng prce rses even when reurns are ex ane symmerc. The oppose chan of evens occurs when prvae news s negave. In hs case prces declne and sdelned nvesors are more lkely o be he ones ha have favorable sgnals. Thus reurns are more posvely skewed followng a prce declne. Ths mechansm also gves rse o hgh condonal volaly followng eher a large prce ncrease or declne..3 Hong and Sen (003) Hong and Sen (003) propose a model ha generaes a relaon beween lagged urnover and skewness. The asymmerc propery of reurns arses because nvesors have heerogeneous belefs and hey canno shor sell. In her model here are hree raders n he marke: nvesor A nvesor B and arbrageurs. Invesors A and B canno shor sell socks. Arbrageurs can shor sell any amoun of socks a no cos. These hree raders rade one sock whch may be hough of as he marke porfolo. Invesors A and B are assumed o be overconfden and herefore use her prvae nformaon n valung he sock bu neher use he oher s sgnal even when s revealed. Ths assumpon keeps he dfferences of opnon beween he wo nvesors from convergng. Arbrageurs are fully raonal rsk-neural and unnformed. Arbrageurs realzed ha he bes esmae of he sock value s he average of sgnals of A and B. Somemes however he arbrageurs do no observe he sgnal of A or B because A or B may no rade due o shorsale consrans. To see how he model generaes asymmerc condonal skewness consder an example. A me nvesor A receves a pessmsc sgnal such ha A s valuaon s lower han ha of B. Invesor A ss ou of he marke snce he s no allowed o shor sell bu B rades. Arbrageurs observe hs and realze ha A s valuaon s lower han ha of B bu do no know by how much. Thus he sock prce a me does no fully reflec nformaon of A. A dae f B s sgnal s posve hen B rades wh he arbrageurs and A does no rade. The sock prce sll does no reflec A s me nformaon. If however a me B receves a pessmsc sgnal ha s lower han he curren marke valuaon hen B wll sell hs socks whch lowers prce. A hs pon arbrageurs learn somehng by observng f and a wha prce A seps n and sars buyng. Tha s arbrageurs learn abou A s nformaon by observng how A reacs o reduced demand by B. Thus more nformaon of pessmsc nvesors s revealed as sock prce declnes. Ths mechansm generaes a hgher varance as he sock prce declnes causng negave skewness n sock reurns a me. The logc above however s no suffcen o esablsh ha he reurn dsrbuon over me and me s negavely skewed. There s a couner effec of posve skewness a me 0

7 because he negave draws are he ones hdden from he marke a me. Hong and Sen show ha when A s and B s belefs are suffcenly dfferen me- effec domnaes leadng o negave skewness n reurns. Hong and Sen sugges ha he level of dvergence of opnon can be measured by urnover. Thus he model predcs ha reurns wll be more negavely skewed followng an ncrease n urnover. 3. The Mehodology and Model Ths secon descrbes he daa se employed n he emprcal ess whch ncludes measures of condonal skewness and condonal volaly as well as oher conrol varables. The daly reurns and monhly reurns of equy ndces radng volume and marke capalzaon are obaned from Daasream daabase for he perod of January 973 hrough December 00 for 3 developed and 34 emergng markes. The resuls presened here are for gross aggregae marke reurns. We also es aggregae marke reurns n excess of he rsk free rae and fnd qualavely he same resuls. The mos recen asse prcng model ha proposes a relaon beween skewness and pass varables such as reurns and adjused urn-over s Hong and Sen (003). Whle he premse of hs model s ha shor-sale consrans effecs he skewness of sock reurns he ess n Chen Hong and Sen (00) whch evaluaes HS model does no nclude any shor-sale consrans. In order o es HS model on condonal skewness we use daa on shor-sale consran a he marke level of dfferen counres from Charoenrook and Daouk (003) o es HS heory. The shor-sale daa obaned from surveys of exchanges around he world s up o an ncludng 00. Therefore n our analyss we decde o use daa hrough December 00 o equally es all heores. 3. Marke Reurn Varables The condonal skewness n daly reurns sk n n 3 ( ) ( n )( n ) ˆ r sk s compued each monh as r () where ˆ ( n n ) ( r r ). r s he ndex reurn of counry on day n monh r s he average daly reurn for reurns of monh and n s he number of daly observaons n monh. Scalng he raw cenral hrd momen by he sandard devaon s a sandard normalzaon employed for skewness sascs ha allows for a comparson across reurns wh dfferen varances (Greene 993). The condonal volaly of daly marke reurns s he sandard devaon of daly reurns n a monh gven as 0

8 03 n r r n ) ( ) ( ˆ. () We also es he sandard devaon esmaes of daly reurns ha correcs for nonsynchronous radng as n French Schwer and Sambaugh (987) and fnd smlar resuls (no repored here). We examne he volaly of monhly reurns esmaed usng he followng ARCH model:. 0 0 ~ w w w w w w w w w w w w w w h h h h N a b h a b h a b h c r c r (3) r w s he monhly reurn of he world marke ndex a monh. s he nnovaon n monhly reurn of he sock marke ndex of counry a monh. h w s he condonal varance of he world ndex a me. h s he condonal varance of he monhly reurn of he sock marke ndex of counry a monh. The condonal volaly of monhly reurns s he square roo of h. h w s he condonal covarance of he monhly reurns of he sock marke ndex of counry wh he monhly reurn of he world ndex a me. The weghs of he lagged resdual vecors of he model n (3) are aken o be / /3 and /6 as n as n Engle Llen and Robns (987). The consans a b and c are consraned o be dencal for every counry-world par. We use he Morgan Sanley Capal Inernaonal Inc. (MSCI) value-weghed world ndex as proxy for he world marke porfolo. v We esmae he model n (3) usng he maxmum lkelhood esmae. Turnover s defned as he rao of volume of dollar rade per monh o dollar marke capalzaon a he end of he monh. To mgae he effec of oulers whch occur because he denomnaor s small n some counres we ake he naural logarhm of hs rao. As n Chen Hong and Sen (00) we use rend-adjused urnover o es he predcons of Hong and Sen (003). The adjusmen elmnaes any componen of urnover ha s relaed o a fxed counry characersc. Here he adjusmen s done by subracng from urnover he average of urnover durng he prevous sx monhs. v

9 3. Daa on he Legaly and Feasbly of Shor Sellng and Exsence of Pu Opons We consruc a measure of shor-sale consrans usng survey daa on he feasbly of shor sellng and pu opon radng from Charoenrook and Daouk (003). Charoenrook and Daouk (003) repor survey daa on legaly and feasbly of shor sellng and pracce of pu opon radng of counres. We use feasbly raher han legaly of shor sellng because as repored n Charoenrook and Daouk (003) some counres do no have rules prohbng shor sellng and a he same me no shor sellng akes place because of lack of nsuonal facles. On he oher hand some counres prohb shor sellng bu shor sellng rounely akes place va off-shore markes. Columns and 3 of Table II repor he feasbly of shor sellng and pu opon radng n each of he 57 counres n our sample daa. The measure of shor-sale consrans varable SSPO feasbly equals f eher shor sellng or pu opons radng s feasble and equals 0 oherwse. For example Chle sared pu opon radng n 994 and shor sellng n 00 hus he varable SSPO feasbly for Chle equals n January 995 and hereafer. 3.3 Conrol Varables Bekaer and Harvey (000) and Henry (000) emprcally show ha lberalzaon has an effec on lqudy and volaly. We conrol for he confoundng effecs of lberalzaon n all our ess. The ndcaor varable lberalzaon n Bekaer and Harvey (000) and Henry (000) changes from zero o one n he monh afer he offcal lberalzaon. Offcal lberalzaon daes used here are obaned from Table I n Bekaer and Harvey (000) for counres repored. For some of he counres no repored n Bekaer and Harvey (000) we use he lberalzaon daes from Bae Baley and Mao (003). In addon o lberalzaon n regresson specfcaons of ess of condonal volaly we nclude lagged volaly o conrol for auocorrelaon n volaly. 4. Emprcal Resuls We are neresed n examnng he paerns of condonal skewness n he aggregae marke reurns of he U.S and oher nernaonal markes and fndng ou wha economc mechansms drve hese paerns. We examne boh me seres regressons of ndvdual counres and pooled cross-secon and me seres panel regressons. All he regressons are correced for auocorrelaon and heeroskedascy n he resdual erm. All panel regressons nclude a counry-fxed-effec dummy whch s no repored. 4. Predcably of Condonal Skewness: Indvdual Counres Table II presens ndvdual counry es resuls. The uncondonal skewness and volaly are esmaed as n Equaons () and () excep ha each counry s sample daa s employed o calculae a sngle skewness or volaly esmae raher han monhly esmaes. Lke prevous sudes we fnd ha he uncondonal skewness of he U.S marke porfolo s negave. Negave skewness s common n developed markes; egheen ou of weny hree developed markes have negave skewness. Ths s no he case n emergng markes; only foureen ou of hry four emergng markes exhb negave skewness. 04

10 Table : Indvdual counres Ths able repors he feasbly of shor sellng and pu of opon radng and properes of he reurn dsrbuon of 57 ndvdual counry ndces. Columns 3 and 4 repor he uncondonal skewness and uncondonal volaly of reurns. Uncondonal skewness s compued as n Equaon () employng all observaons for each counry. Uncondonal volaly s he sandard devaon of daly reurns compued usng all observaons for each counry. Regresson I repors regressons of condonal skewness of daly reurns on lagged rend-adjused urnover and lagged one monh reurn. Regresson II repor regresson of skewness on lagged one monh reurns. We conrol for lberalzaon n boh regressons. NA denoes no avalable due o he unavalably of volume daa. T-sascs are repored n parenhess. Counry Exsence Exsence Uncondonal Uncondonal Regresson I Regresson II of of pu skewness volaly Ind. varable: skewness Ind. varable: skewness shor sale opons Inercep lagged lagged Inercep lagged rend-adjused reurn reurn urnover column no. () () (3) (4) (5) (6) (7) (8) (9) Emergng counres ARGENTINA No (0.3798) (0.085) (0.730) (0.4303) (0.539) BAHRAIN No No NA NA NA NA NA NA (0.0846) (0.4556) BRAZIL No (0.0608) (0.84) (0.47) (0.08) CHILE (0.0443) (0.97) (0.709) (0.064) (0.36) CHINA No No (0.5039) (0.073) (0.309) (0.4973) (0.883) COLOMBIA No No (0.649) (0.3599) (0.640) (0.4393) CZECH Yes No (0.955) (0.34) (0.90) (0.975) (0.497) EGYPT No No NA NA NA NA NA NA (0.6494) (0.5746) GREECE No (0.0009) (0.0547) (0.5706) (0.000) (0.760) HUNGARY No (0.039) (0.0033) (0.986) (0.0347) (0.7898) INDIA No (0.039) (0.475) (0.9783) (0.07) (0.869) INDONESIA No N/A (0.3755) (0.737) (0.368) (0.457) (0.5330) ISRAEL No (0.0069) (0.03) (0.3044) (0.06) (0.46) JORDAN No No NA NA NA NA NA NA (0.640) (0.5) SOUTH KOREA No (0.0730) (0.054) (0.005) (0.0593) (0.009) MALAYSIA Sared n 996 sopped n

11 Counry Exsence Exsence Uncondonal Uncondonal Regresson I Regresson II of of pu skewness volaly Ind. varable: skewness Ind. varable: skewness shor sale opons Inercep lagged lagged Inercep lagged rend-adjused reurn reurn urnover column no. () () (3) (4) (5) (6) (7) (8) (9) Emergng counres MEXICO Yes N/A (0.988) (0.4366) (0.00) (0.077) (0.04) MOROCCO No No NA NA NA NA NA NA (0.009) (0.79) NIGERIA NA No NA NA NA NA NA NA (0.6766) (0.038) OMAN No No NA NA NA NA NA NA (0.5005) (0.9998) PAKISTAN No No (0.986) (0.540) (0.08) (0.9058) (0.083) PERU No No (0.970) (0.9654) (0.839) (0.956) (0.835) PHILIPP No No (0.0646) (0.7099) (0.046) (0.060) (0.596) POLAND No (0.085) (0.064) (0.0986) (0.056) (0.7465) RUSSIA Yes (0.684) (0.535) (0.855) (0.708) (0.833) SAUDI No No NA NA NA NA NA NA (0.404) (0.8794) SLOVAKIA No No NA NA NA NA NA NA (0.38) (0.333) SOUTHAFRICA Yes (0.547) (0.8890) (0.359) (0.54) (0.3577) SRILANKA No No NA NA NA NA NA NA (0.74) (0.5343) TAIWAN No No (0.0006) (0.84) (0.4094) (0.000) (0.0666) THAILAND 998 No (0.590) (0.0563) (0.079) TURKEY 995 No (0.009) (0.3763) (0.89) (0.303) (0.845) VENEZUELA No No NA NA NA NA NA NA (0.34) (0.9440) ZIMBABWE No No NA NA NA NA NA NA (0.450) (0.694) 06

12 Counry Exsence Exsence Uncondonal Uncondonal Regresson I Regresson II of of pu skewness volaly Ind. varable: skewness Ind. varable: skewness shor sale opons Inercep lagged lagged Inercep lagged rend-adjused reurn reurn urnover column no. () () (3) (4) (5) (6) (7) (8) (9) Developed conres AUSTRALIA Yes (0.8853) (0.6630) (0.0445) (0.06) (0.77) AUSTRIA Yes (0.066) (0.7348) (0.404) (0.6673) (0.5854) BELGIUM Yes (0.87) (0.744) (0.03) (0.0349) (0.568) CANADA Yes (0.4004) (0.46) (0.5) (0.334) (0.300) DENMARK Yes (0.46) (0.9477) (0.9666) (0.7058) (0.399) FINLAND No (0.7457) (0.93) (0.8534) (0.99) (0.584) FRANCE Yes (0.7807) (0.85) (0.98) (0.9698) (0.967) GERMANY Yes (0.6693) (0.035) (0.958) (0.8766) (0.0633) HONG KONG (0.373) (0.403) (0.005) (0.94) (0.00) IRELAND Yes No (0.387) (0.897) (0.94) (0.6757) (0.607) ITALY Yes (0.397) (0.547) (0.340) (0.007) (0.807) JAPAN Yes (0.0053) (0.565) (0.3753) (0.0586) LUXEMBURG 99 No (0.403) (0.94) (0.787) (0.303) (0.79) NETHERLANDS Yes (0.650) (0.308) (0.5) (0.880) (0.749) NEWZEALAND No No (0.60) (0.443) (0.99) (0.6) (0.679) NORWAY (0.0309) (0.75) (0.009) (0.089) (0.045) PORTUGAL Yes (0.4) (0.89) (0.5704) (0.99) (0.7948) SINGAPORE Yes N/A (0.000) (0.7744) (0.36) (0.0657) SPAIN No (0.4565) (0.064) (0.857) (0.383) (0.793) SWEDEN (0.67) (0.0943) (0.0807) (0.380) (0.0843) SWITZERLAND Yes (0.764) (0.36) (0.0378) (0.634) (0.094) UK Yes (0.009) (0.7569) (0.77) (0.4448) (0.09) US Yes (0.07) (0.9599) (0.0495) (0.0) (0.0469) 07

13 Table also presens resuls from regressons of condonal skewness on lagged rendadjused urnover and lagged reurn and on lagged reurn alone conrollng for lberalzaon (no repored). The coeffcens ha are sgnfcan a approxmaely 0% or lower are hghlghed. In ndvdual counry regressons when he regresson coeffcens of skewness are sgnfcan hey are all negave excep for regresson. Thus here appears o be a negave relaon beween skewness and lagged reurns. 4. Predcably of Condonal Skewness: Panel Regresson Analyss The summary sascs for he varables employed n he panel regressons are presened n Table 3. Table 4 repors regressons of condonal skewness on lagged rend-adjused urnover and lagged one-monh reurns conrollng for lberalzaon and fxed-counry effecs. rend-adjused urnover does no predc skewness bu lagged reurn does. reurn s negavely relaed o condonal skewness. The slope esmaes of lagged reurns are beween o n all equaon specfcaons and counry groupngs. All coeffcens are sascally sgnfcan a lower han he % level. The relaon of lagged reurns and skewness s also economcally sgnfcan. From regresson (3) a one sandard devaon change n lagged reurn predcs a 0.64 change n skewness of reurns whch equals 85% of he sandard devaon n he dsperson of condonal skewness n our sample (0.79 n Table 3). Table 3: Summary sascs Ths able presens summary sascs for varables employed n he regressons. Skewness s he condonal skewness calculaed as n Equaon () usng daly marke reurns for each monh. Turnover s he logarhm of he rao of volume of dollar rade per monh o dollar marke capalzaon a he end of he monh. Trend-adjused urnover s urnover mnus he average of urnover durng he prevous sx monhs. SSPO feasbly s a bnary varable ha equals one f eher shor-sellng or pu opon radng s feasble n ha counry durng ha monh (n pracce). The ndcaor varable lberalzaon changes from zero o one n he monh afer he offcal lberalzaon dae whch was obaned from Bekaer and Harvey (000). Volaly s he sandard devaon of daly reurn durng a monh. Varable name Mean Sandard Maxmum Mnmum devaon Skewness rendadjused urnover SSPO feasbly Monhly Reurn Lberalzaon Volaly

14 Table 4: Condonal skewness Ths able repors panel regressons of condonal skewness of daly reurns on lagged rend-adjused urnover lagged one-monh reurns conrollng for lagged skewness lagged volaly lberalzaon and a counry-fxed-effec dummy (no repored). Turnover s he logarhm of he rao of volume of dollar rade per monh o dollar marke capalzaon a he end of he monh. Trend-adjused urnover s urnover mnus he average of urnover durng he prevous sx monhs. reurn s he ndex reurn durng he prevous monh. skewness s he skewness durng he prevous monh. volaly s he sandard devaon of daly reurns durng he prevous monh. The ndcaor varable lberalzaon changes from zero o one n he monh afer he offcal lberalzaon dae whch was obaned from Bekaer and Harvey (000). All regresson coeffcen esmaes are correced for auocorrelaon and heeroskedascy n he resdual erm. P-value s repored n parenhess. All counres Developed counres Emergng counres Regresson () () (3) (4) () () (3) (4) () () (3) (4) Independen varables rendadjused urnover (0.65) 0.57 (0.7) (0.63) (0.038) (0.9) (0.0966) 0.64 (0.885) 0.73 (0.57) 0.66 (0.774) reurn (0.000) skewness (0.0369) (0.056) (0.650) volaly.4656 (0.0384) (0.0664).94 (0.0857) Lberalzao n (0.740) (0.893) (0.90) (0.8804) (0.955) (0.9705) (0.8675) (0.840) (0.700) (0.8370) (0.8734) (0.8549) 09

15 Table 5: The relaon beween lagged reurn and skewness We sor he sample daa accordng o lagged reurns no decles of equal number of observaons. We use he daly reurns n each decle o compue a skewness esmae and he sandard error for each esmae. The skewness s compued usng Equaon (). The correspondng sandard error = / n where n s he number of observaons. The condonal skewness esmae ha s more han wce he sandard error s hghlghed n bold. Developed counres Emergng counres Decle reurn Condonal skewness Sandard error reurn Condonal skewness Sandard error Nex we es relaon of skewness and lagged reurns condoned on he sgn of lagged reurns. We sor he sample daa by lagged reurns no decles of equal observaons. We use he daly reurns n each decle o compue a sngle skewness esmae and he sandard error for he esmae. The skewness esmaes ha are more han wce he sandard error are hghlghed n bold. Resuls n Table 5 ndcae ha when lagged reurns are negave and become more negave condonal skewness becomes more posve and when lagged reurns are posve and become more posve skewness becomes more negave. The las row of able 5 repors he skewness of decle 0 mnus he skewness of decle. The dfference beween he skewness of he wo decles s sascally sgnfcan a he 5% level. 0

16 Table 6: Condonal skewness and lagged reurns Ths able repors panel regressons of condonal skewness of daly reurns on lagged rend-adjused urnover lagged one-monh reurns conrollng for lberalzaon and a counry-fxed-effec dummy (no repored). The daa se employed n panel A (B) ncludes only daa pons when lagged reurns are posve (negave). Turnover s he logarhm of he rao of volume of dollar rade per monh o dollar marke capalzaon a he end of he monh. Trend-adjused urnover s urnover subraced by he average of urnover durng he prevous sx monhs. reurn s he ndex reurn durng he prevous monh. The ndcaor varable lberalzaon changes from zero o one n he monh afer he offcal lberalzaon dae whch was obaned from Bekaer and Harvey (000). All regresson coeffcen esmaes are correced for auocorrelaon and heeroskedascy n he resdual erm. P- value s repored n parenhess. Panel A: Daa sample ncludes only posve lagged reurns Regresson specfcaon Independen varables All counres Developed counres Emergng counres () () (3) () () (3) () () (3) rendadjused urnover (0.3847) (0.507) (0.780) 0.60 (0.8900) (0.4005) (0.475) reurn (0.063) (0.038) (0.038) (0.0059) (0.53) (0.430) Lberalzaon (0.0073) (0.3830) (0.30) (0.307) (0.5890) (0.706) (0.038) (0.37) (0.375) Panel B: Daa sample ncludes only negave lagged reurns Regresson specfcaon Independen varables All counres Developed counres Emergng counres () () (3) () () (3) () () (3) rendadjused urnover 0.53 (0.059) 0.08 (0.0763) (0.0999) -.99 (0.040) 0.4 (0.037) (0.038) reurn (0.0009) (0.006) (0.000) (0.000) Lberalzaon (0.004) (0.936) (0.9307) 0.8 (0.487) (0.55) (0.848) (0.009) (0.758) (0.7740) Table 6 repors panel regressons of skewness on lagged one monh reurns conrollng for rend-adjused urnover lberalzaon and counry-fxed-effecs for he sample ha ncludes posve and negave lagged reurns separaely. In he regressons ha nclude only posve lagged reurns he coeffcen of lagged reurns are negave and sgnfcan a he 5% level. In

17 he regressons ha nclude only negave lagged reurns he coeffcen of lagged reurns are also negave and are all sgnfcan a he % level. These resuls confrm ha he negave relaon beween skewness and lagged reurns are due o boh negave skewness followng a posve reurn monh and posve skewness followng a negave reurn monh. These relaons are nconssen wh he leverage effec he volaly feedback and he flucuaon uncerany model all of whch predcs more negave skewness followng negave reurns. The bubble heory does no predc any relaon beween lagged negave reurns and skewness. Among he heores we consder here CCH s he mos conssen wh he relaon found n he es resuls. The dfference n he magnudes of he coeffcen esmaes of lagged reurns n developed markes and emergng markes furher suppors CCH. In CCH nvesors are sde lned due o radng coss. Snce radng coss are hgher n emergng markes we should observe a sronger relaon beween lagged reurns and skewness n emergng markes. Afer a marke declne sdelned nvesors are more lkely o have favorable nformaon. When hey ener he marke hey buy socks. Panel B of Table 6 shows ha he coeffcen esmaes of lagged reurns n emergng counres are hgher han n develop counres. The dfference s sascally sgnfcan a he 5% level. Afer a marke declne sdelned nvesors are more lkely o have adverse nformaon. When hese nvesors ener he marke hey sell socks. In counres where shor sellng s no possble sdelned nvesors who do no already own socks never ener he marke even when her adverse nformaon s confrmed by observng oher sell rades. Table repors ha 7 ou of 34 emergng counres allow shor sales compared o 0 ou of 3 developed counres. Ths explans he weaker relaon beween lagged posve reurn and condonal skewness n emergng counres compared o developed counres even when radng cos s hgher n emergng markes (repored n Panel A of Table 6). 4.3 Condonal Volaly and Reurns The emprcal evdence on skewness may be nerpreed wo ways: () he leverage effec he volaly feedback effec and he flucuaon uncerany are emprcally nsgnfcan n our daa sample or () he emprcal mpac of hese effecs s subsumed by oher effecs n predcng skewness. To dsngush beween hese wo nerpreaons we examne he relaon beween condonal volaly and lagged reurns. We examne boh he volaly of daly reurns and volaly of monhly reurns of he ARCH model n Secon 3.

18 Table 7: Condonal volaly Ths able repors panel regressons of condonal volaly of daly reurns and monhly reurns on lagged onemonh absolue reurns conrollng for lagged volaly lberalzaon and a counry-fxed-effec dummy (no repored). Volaly of daly reurns s calculaed as he sandard devaon of daly reurn usng daly reurn observaons n each monh. The volaly of monhly reurns s calculaed from a mulvarae ARCH model n Equaon (3). reurn s he ndex reurn durng he prevous monh. The ndcaor varable lberalzaon changes from zero o one n he monh afer he offcal lberalzaon dae whch was obaned from Bekaer and Harvey (000). All regresson coeffcen esmaes are correced for auocorrelaon and heeroskedascy n he resdual erm. P-value s repored n parenhess. Panels A and B repor regressons ha employ daa when lagged reurns are posve and negave respecvely. Panel C also repors he -sascs (n alcs) for he es of he hypohess ha he coeffcens of absolue lagged reurns are equal when lagged reurns are negave han when lagged reurns are posve. Panel A: Daa sample ncludes only posve lagged reurns Dependen varable Independen varables All counres Developed counres Emergng counres Volaly of Daly reurns Volaly of monhly reurns Volaly of Daly reurns Volaly of monhly reurns Volaly of Daly reurns Volaly of monhly reurns absolue reurn (0.000) 0.60 volaly (0.0004) (0.060) (0.000) Lberalzaon (0.005) (0.080) (0.39) (0.0549) (0.008) (0.36) Panel B: Daa sample ncludes only negave lagged reurns Dependen varable Independen varables All counres Developed counres Emergng counres Volaly of Daly reurns Volaly of monhly reurns Volaly of Daly reurns Volaly of monhly reurns Volaly of Daly reurns Volaly of monhly reurns absolue reurn volaly (0.0008) (0.3) (0.00) Lberalzaon (0.383) (0.0630) (0.003) (0.99) (0.4400) 0.00 (0.045) 3

19 Table 7 repors panel regressons of condonal volaly on lagged absolue reurns conrollng for lagged volaly lberalzaon and counry-fxed-effecs. Panel A repors es resuls for he sample of posve lagged reurns and Panel B repors es resuls for he sample of negave lagged reurns. The resuls n Panels A and B of Table 7 show hgher volaly follows hgher lagged reurns when lagged reurns are negave and when lagged reurns are posve. We furher examne he hypohess ha he regresson coeffcens of lagged absolue reurn are he same when lagged reurns are negave or posve. The - sascs correspondng o he es of hs hypohess s repored n alcs n Panel B of Table 7. We fnd ha volaly ncreases more followng a sock prce declne han a sock prce ncrease whch s conssen wh he leverage effec he volaly feedback effec and he flucuaon uncerany heory. Thus we conclude ha hese effecs are presen n our daa bu he relaon beween skewness and lagged reurn s subsumed by oher economc mechansm such as ha presened n he CCH model. 4.4 Condonal Skewness and Trend-Adjused Turnover The HS model predcs a negave relaon beween lagged rend-adjused urnover and condonal skewness. In he HS model a regular nvesor canno shor sell bu arbragers can. The arbragers need o be able o shor sell o absorb he buyng demand of he regular nvesors who canno shor sell because one of he smplfyng assumpons of he model s ha he ne supply of hs sock s zero. When we apply he HS model o our emprcal seng we hnk abou arbragers as a large group of arbragers who have a large nvenory of he sock and herefore can buy or sell from her nvenory bu no acually shor sell. In oher words he arbragers would no have o borrow he socks and sell hem bu jus ake hem from her nvenory and sell hem. Moreover when we classfy a marke as no allowng shor sale n mos marke an nernal borrowng of secures wh a fnancal nsuon may sll be possble. In hs sense he HS model sll apples when counres prohb shor-sellng. In HS he neracon beween shor-sellng consran of nvesors and her heerogeneous belefs causes he negave relaon beween lagged rend-adjused urnover and skewness. To undersand he role of shor-sellng consrans we esmae he regresson of condonal skewness on rend-adjused urnover an neracon erm of lagged rend-adjused urnover mulpled by SSPO feasbly SSPO feasbly lberalzaon and counry-fxed-effecs. The resuls repored n Table 8 show ha rend-adjused urnover does no predc reurns. In he all counres sample he regresson coeffcen on lagged rend-adjused urnover mulpled by SSPO feasbly erm s and s sgnfcan a he 0% level. A negave coeffcen means ha hgher rend-adjused urnover predc more negave skewness n counres where shor sellng s feasble (when SSPO s ) compared o counres where shor sellng s no feasble. Ths fndng s conrary o our nerpreaon of wha HS model predcs. Overall our es resuls do no suppor Hong and Sen (003). 4

20 Table 8: Condonal skewness and shor-sale consrans Ths able repors panel regressons of condonal skewness of daly reurns on SSPO feasbly lagged rendadjused urnover lagged one-monh reurns he neracon erm SSPO feasbly x rend-adjused urnover conrollng for lberalzaon and a counry-fxed-effec dummy (no repored). SSPO feasbly s a measure of shor-sale consrans. SSPO feasbly s a bnary varable ha equals one f eher shor-sellng or pu opon radng s possble n ha counry durng ha monh (n pracce). Turnover s he logarhm of he rao of volume of dollar rade per monh o dollar marke capalzaon a he end of he monh. Trend-adjused urnover s urnover mnus he average of urnover durng he prevous sx monhs. reurn s he ndex reurn durng he prevous monh. The ndcaor varable lberalzaon changes from zero o one n he monh afer he offcal lberalzaon dae whch was obaned from Bekaer and Harvey (000). All regresson coeffcen esmaes are correced for auocorrelaon and heeroskedascy n he resdual erm. P-value s repored n parenhess. All counres Developed counres Emergng counres Independen varables SSPO feasbly (0.99) rend-adjused urnover 0.77 (0.49) (0.7549) (0.907) (0.0935) 0.85 (0.6) SSPO feasbly rend-adjused urnover (0.0900) (0.368) (0.08) Lberalzaon (0.9967) (0.9430) (0.757) 5. Robusness In hs secon we revew hree ssues relaed o our emprcal analyss: () he robusness of he resuls gven dfferen specfcaons of lagged reurns and rend-adjused urnover () measuremen error n he skewness esmaes and (3) he effec of oulers. Table 9 repors regressons of skewness on lagged reurns and rend-adjused urnover for dfferen specfcaons of lagged reurns and rend-adjused urnover. Tess usng lagged reurns consruced usng he prevous monh 3 monhs 6 monhs and monhs are repored. Trend-adjused urnover s consruced by subracng he rend over he prevous 6 monhs 8 monhs and 30 monhs. The resuls n all regresson specfcaons are qualavely he same as our man resuls. 5

21 Table 9: Condonal skewness and dfferen lagged reurns and rend-adjused urnover Ths able repors panel regressons of condonal skewness of daly reurns on lagged rend-adjused urnover lagged reurns conrollng for lberalzaon and a counry-fxed-effec dummy (no repored). Turnover s he logarhm of he rao of volume of dollar rade per monh o dollar marke capalzaon a he end of he monh. The ndcaor varable lberalzaon changes from zero o one n he monh afer he offcal lberalzaon dae whch was obaned from Bekaer and Harvey (000). The 6 regresson specfcaons dffer n how he rend-adjused urnover and lagged reurn varables were consruced. For regresson () rend-adjused urnover s urnover mnus he average of urnover durng he prevous sx monhs. reurn s he ndex reurn durng he prevous monh. For regresson () rend-adjused urnover s urnover mnus he average of urnover durng he prevous sx monhs. reurn s he ndex reurn durng he prevous 3 monhs. For regresson (3) rend-adjused urnover s urnover mnus he average of urnover durng he prevous sx monhs. reurn s he ndex reurn durng he prevous 6 monhs. For regresson (4) rend-adjused urnover s urnover mnus he average of urnover durng he prevous sx monhs. reurn s he ndex reurn durng he prevous monhs. For regresson (5) rendadjused urnover s urnover mnus he average of urnover durng he prevous 8 monhs. reurn s he ndex reurn durng he prevous monh. For regresson (6) rend-adjused urnover s urnover subraced he average of urnover durng he prevous 30 monhs. reurn s he ndex reurn durng he prevous monh. All regresson coeffcen esmaes are correced for auocorrelaon and heeroskedascy n he resdual erm. P-value s repored n parenhess. Panel A Regresson specfcaon () () (3) (4) (5) (6) Independen varables reurn Condonal skewness Lberalzaon (0.893) (0.9644) (0.9669) (0.874) (0.893) (0.893) Panel B Regresson specfcaon () () (3) (4) (5) (6) Independen varables rend-adjused urnover 0.57 (0.7) (0.38) Condonal skewness (0.804) (0.400) (0.3536) 0.07 (0.45) reurn Lberalzaon (0.90) (0.8448) (0.737) (0.4957) (0.8494) (0.5666) The skewness varable s esmaed each monh from daly reurns hus s measured wh nose. In he case ha he measuremen error s correlaed wh a regressor he pon esmae of he regresson coeffcen on ha regressor s posvely based f he measuremen error s posvely correlaed wh he regressor. The regresson coeffcen s negavely based f he measuremen error s negavely correlaed wh he regressor. To assess wheher our measuremen error s relaed o lagged reurn we sor monhly skewness esmaes by her correspondng lagged reurns no 0 decles and hen calculae he sandard devaon of monhly skewness n each decle. We hen examne f here s any deecable relaon beween he sandard devaon number and he average lagged reurn among he decles. Table 0 repors he sandard devaon and average lagged reurns for he 0 groupngs of monhly skewness for he sample ha ncludes all markes emergng markes and developed markes separaely. The resuls show ha here s no relaon beween he 6