Conditional Skewness of Aggregate Market Returns

Transcription

1 Condonal Skewness of Aggregae Marke Reurns Anchada Charoenrook and Hazem Daouk + March 004 Ths verson: May 008 Absrac: The skewness of he condonal reurn dsrbuon plays a sgnfcan role n fnancal heory and pracce. Ths paper examnes wheher condonal skewness of daly aggregae marke reurns s predcable and nvesgaes he economc mechansms underlyng hs predcably. In boh developed and emergng markes here s srong evdence ha lagged reurns predc skewness; reurns are more negavely skewed followng an ncrease n sock prces and reurns are more posvely skewed followng a decrease n sock prces. The emprcal evdence shows ha he radonal explanaons such as he leverage effec he volaly feedback effec he sock bubble model (Blanchard and Wason 98) and he flucuang uncerany heory (Verones 999) are no drvng he predcably of condonal skewness a he marke level. The relaon beween skewness and lagged reurns s more conssen wh he Cao Coval and Hrshlefer (00) model. Our fndngs have mplcaons for fuure heorecal and emprcal models of me-varyng marke reurn dsrbuons opmal asse allocaon and rsk managemen. JEL classfcaon code: G C Keywords: Condonal skewness Condonal Volaly Predcng Skewness Aggregae marke reurns Inernaonal fnance The Owen Graduae School of Managemen Vanderbl Unversy 40 s. Avenue Souh Nashvlle TN Emal: anchada.charoenrook@owen.vanderbl.edu + Deparmen of Appled Economcs & Managemen Cornell Unversy 446 Warren Hall Ihaca NY Emal: hd35@cornell.edu

2 Inroducon The characerscs of he dsrbuon of secury reurns such as skewness play a sgnfcan role n fnancal heory and pracce. Many asse prcng models such as he CAPM assume mulvarae normal dsrbuons of sock reurns. If sock reurn dsrbuons are skewed hen asse prcng models ha accoun for he presence of hgher momens should produce more accurae valuaons. In a sudy of sock porfolo reurns Harvey and Sddque (000) fnd ha coskewness of porfolo reurns wh he aggregae marke reurns s a deermnan of expeced reurns. Paon (00) shows ha accounng for skewness mproves performance of opmal asse allocaon. Furhermore accurae predcon of he condonal reurn dsrbuon especally a he hgher momens (volaly and skewness) sgnfcanly mproves he valuaon of conngen clams and he effecveness of rsk managemen. Thus nvesgang asymmery n sock reurn dsrbuons 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) repor ha rendadjused urnover and lagged reurns predc skewness of daly reurns of ndvdual socks n he U.S. sock marke. A he marke level whle me varaon n skewness has been documened here are no sudes of he predcably of skewness. 3 Ths paper examnes wheher he condonal skewness of aggregae marke reurns s predcable by lagged reurns and rend-adjused urnover and we nvesgae 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. Lagged one-monh reurns predc condonal skewness of daly reurns durng he followng monh. Ths relaon beween skewness and lagged reurns For example Harvey and Sddque (000) and Dmar (00) develop asse prcng models whch nclude hgher momens lke skewness and kuross. Harvey and Sddque (000) defne coskewness as a measure of he comovemen of he second momens of he porfolo reurns and he second momen of aggregae marke reurns. 3 Harvey and Sddque (999) documen me varaon n he skewness of he S&P500 ndex reurns and four oher nernaonal marke reurns.

3 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. Why should condonal skewness be predcable? We caegorze he heores ha address hs queson no hree groups. We dscuss hem n deal n he nex secon 4. 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 non-zero 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. The second heory n hs group s he volaly feedback effec (Pndyck 984; French e al. 987; and Campbell and Henschel 99). Releases of major bad 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 news ncrease sock prce and also ncrease volaly; he second effec dampens he former. Thus gven he same amoun of nformaon sock prce declnes are larger han sock 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 4 Verones (00) offers a concse bu comprehensve revew of well know heores ha can cause pah dependen condonal skewness.

4 ncrease. The asymmery here s caused by a sock bubble bursng a low probably of very large negave reurns. Hong and Sen (003) propose a model n whch lagged rendadjused urnover s negavely relaed o skewness. Ths relaon arses because nvesors have heerogeneous belefs and hey canno shor sell socks. In he 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 or 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. 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. 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. In conras he 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 3

5 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. 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. I. Background heores Ths secon descrbes exsng heores ha have mplcaons for condonal skewness. Ther effecs are summarzed n Table I. A. 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. 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 larger sock prce declnes han ncreases gven he same amoun of nformaon ex ane. Ths causes reurns o be more negavely skewed when sock prces declne. 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 4

6 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 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 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 prce overreac o bad news and underreac o good news. Consequenly reurns are more negavely skewed when prces declne. B. 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 sdelned 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 5

7 negave nformaon becomes less confden ha he has receved he correc sgnal and herefore ss ou and does no rade. 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. C. Hong and Sen (003) Hong and Sen (003) (hereafer HS) 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 realze 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 shor-sale 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 6

8 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 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. II. Daa 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 he same resuls. A. Marke reurn varables The condonal skewness n daly reurns sk s compued each monh as 7

9 8 = = n r r n n n sk 3 ) ˆ ( ) )( ( τ τ σ () where = = n r r n ) ( ) ( ˆ τ τ σ. r τ s he ndex reurn of counry on day τ 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 = = n r r n ) ( ) ( ˆ τ τ σ. () 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 ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε ε (3)

10 r w s he monhly reurn of he world marke ndex a monh. ε 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. 5 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. 6 B. 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 5 The MSCI World Index s acually an ndex of only developed counres. I begns n December 969. In prncpal he choce of MSCI All-Counry World Index whch ncludes more counres may be beer. In pracce however snce he MSCI All-Counry World Index s avalable only from December 987 and because has a correlaon of wh he MSCI World Index MSCI World Index s a beer choce. 6 Our resuls are no sensve o how we adjus for he rend. We adjus urnover usng he average urnover over a 6 monh perod monh perod and 8 monh perod and fnd he same resuls. 9

11 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. [Inser Table II here] C. 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. III. Emprcal evdence 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. A. Predcably of condonal skewness: ndvdual counres 0

12 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. Table II 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. B. Predcably of condonal skewness: Panel regresson analyss The summary sascs for he varables employed n he panel regressons are presened n Table III. Table IV repors regressons of condonal skewness on lagged rend-adjused urnover and lagged one-monh reurns conrollng for lberalzaon and fxed-counry effecs. Lagged rend-adjused urnover does no predc skewness bu lagged reurn does. [Inser Tables III and IV here] Lagged reurn s negavely relaed o condonal skewness. The slope esmaes of lagged reurns are beween o -0.5 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 III). [Inser Table V here]

13 Nex we es he relaon beween 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 s compued usng Equaon (). The skewness esmaes ha are more han wce he sandard error are hghlghed n bold. Resuls n Table V 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 V 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. [Inser Table VI here] Table VI repors panel regressons of skewness on lagged one monh reurns conrollng for derended 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 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 sdelned 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 VI shows ha he coeffcen esmaes of

14 lagged reurns n emergng counres are hgher han n developed counres. The dfference s sascally sgnfcan a he 5% level. Afer a marke run up 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 I 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 B of Table VI). C. Condonal volaly and lagged 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 descrbed n Secon II. [Inser Table VII here] Table VII repors panel regressons of condonal volaly on lagged 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 VII 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 VII. 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 3

15 relaon beween skewness and lagged reurn s subsumed by oher economc mechansms such as he CCH model. E. Condonal skewness and lagged rend-adjused urnover 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 he 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 sellng n mos markes 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 rendadjused urnover mulpled by SSPO feasbly SSPO feasbly lberalzaon and counry-fxed-effecs. [Inser Table VIII here] The resuls repored n Table VIII show ha rend-adjused urnover does no predc he skewness of reurns. In he all counres sample he regresson coeffcen on lagged rendadjused 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

16 IV. 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 IX 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. [Inser Table IX here] 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 X 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 sandard devaon of monhly skewness esmaes and lagged reurns hus assurng ha he regresson coeffcen esmaes n our analyss are unbased. [Inser Table X here] 5

17 When measuremen error s ndependen of he regressors n he regresson analyss he pon esmaes of he regresson coeffcens are unbased bu he sandard error esmaes are nflaed. In hs case he regresson s led agans fndng sgnfcance. We fnd srong sascal sgnfcance ha lagged reurn predcs skewness despe measuremen error. We also examne f our man resuls are drven by a few oulers. We rank he daa based on skewness. We elmnaed he daa pons n he hghes.5 percenle and he daa pons n he lowes.5 percenle and es he relaon beween lagged posve reurn and lagged negave reurn wh skewness. The resuls reman sascally sgnfcan. V. Conclusons Ths paper examnes wheher condonal skewness of aggregae marke reurns are predcable. Exsng heores sugges ha skewness may be relaed o lagged reurns and lagged rend-adjused urnover. We fnd a srong negave relaon beween condonal skewness and lagged reurns. We fnd no relaon beween skewness and lagged rendadjused urnover. Ths paper furher nvesgaes wha economc mechansms drve he relaon beween lagged reurns and skewness. A number of heores explan hs relaon. We noe ha some of hese heores dffer n her predcons of hs relaon wh respec o he sgn of lagged reurns. They also dffer n her predcons of he relaon beween lagged reurns and volaly. Thus o assess he emprcal valdy of hese heores we examne he relaon beween lagged reurns and skewness or volaly condonal on he sgn of lagged reurns. We fnd ha sock reurns become more negavely skewed followng a posve reurn monh and become more posvely skewed followng a negave reurn monh. The relaon beween lagged reurns and skewness s slghly sronger for negave lagged reurns. We also fnd ha hgher volaly follows a large prce change n eher drecon. The ncrease n volaly s hgher followng a sock prce declne han followng a prce ncrease. Our volaly fndngs are conssen wh he leverage effec he volaly feedback effec and flucuaon uncerany effec. In parcular he leverage effec and he volaly feedback effec are so closely ed o fundamenal fnance heores ha would be surprsng 6

18 f we dd no fnd n he daa. On he oher hand our emprcal evdence concernng condonal skewness appears o conradc hese heores. Our fndngs ndcae ha here are sronger economc mechansms whch drve he predcably of condonal skewness of aggregae marke reurns. These mechansms seem o economcally domnae he leverage effec and he volaly feedback effec. The economc mechansm proposed n CCH appears o be he mos conssen wh all our emprcal fndngs especally wh our fndngs on condonal skewness. Our fndngs have a number of mplcaons for fuure research. Frs snce skewness of aggregae marke reurns are predcable fuure economerc modelng of aggregae marke reurns should be flexble enough o allow condonal skewness o be affeced by lagged reurns and oher varables such as urnover. Second fuure heores of he sock reurn generang process should accoun for he predcably of condonal skewness a a markewde level. In parcular hey should accoun for boh negave skewness followng prce ncreases as well as posve skewness followng prce declnes. Ths should mprove fuure sock marke conngen clams valuaon models. Lasly he predcably of condonal skewness of marke reurns s relevan o he opmal asse allocaon beween socks bonds and oher asses. 7

19 Reference: Bae Kee-Hong Warren Baley and Conne X. Mao 003 Sock Marke Lberalzaon and he Informaon Envronmen workng paper Cornell Unversy. Bekaer G. and C. Harvey 000 Foregn Speculaors and Emergng Equy Markes Journal of Fnance Black F. 976 Sudes of Sock Prce Volaly Changes Proceedngs of he 976 Meeng of Amercan Sascal Assocaon Busness and Economcal Sascs Secon Blanchard O. J. and Wason M. W. 98 Bubbles Raonal Expecaons and Fnancal Markes In: Wachel P. (Ed.) Crses n Economc and Fnancal Srucure Lexngon Books Lexngon MA Campbell J. Y. and R. Henschell 99 No News s Good News: An Asymmerc Model of Changng Volaly n Sock Reurns. Journal of Fnancal Economcs Cao H. Henry Joshua D. Coval and Davd Hrshlefer 00 Sdelned Invesors Tradng- Generaed News and Secury Reurns Revew of Fnancal Sudes Charoenrook Anchada and Hazem Daouk 003 The World Prce of Shor Sellng workng paper Vanderbl Unversy. Chen Joseph H. Hong J. C. Sen 00 Forecasng Crashes: Tradng Volume Pas Reurns and Condonal Skewness n Sock Prces Journal of Fnancal Economcs Chrse A. A. 98 The Sochasc Behavor of Common Sock Varances Value Leverage and Volaly n Sock Reurns Journal of Fnancal Economcs Davd A. 997 Flucuang Confdence n Sock Markes: Implcaons for Reurns and Volaly Journal of Fnancal and Quanave Analyss Dmar Rober F. 00 Non-lnear Prcng Kernels Kuross Preference and Evdence from he Cross Secon of Equy Reurns Journal of Fnance Engle R. D. Llen and R. Robns 987 Esmang Tme Varyng Rsk Prema n he Term Srucure: The ARCH-M Model Economerca French K. W. Schwer and R. Sambaugh 987 Expeced Sock Reurns and Volaly Journal of Fnancal Economcs Greene W. H. 993 Economerc Analyss Macmllan New York. Harvey Campbell R. and Akhar Sddque 999 Auoregressve Condonal Skewness Journal of Fnancal and Quanave Analyss Harvey Campbell R and Akhar Sddque 000 Condonal Skewness n Asse Prcng Tess Journal of Fnance Henry P. 000 Sock Marke Lberalzaon Economc Reform and Emergng Marke Equy Prces Journal of Fnance Hong Harrson and Jeremy C. Sen 003 Dfferences of Opnon Shor-Sales Consrans and Marke Crashes Revew of Fnancal Sudes

20 Paon Andrew J. 004 On he Ou-of-Sample Imporance of Skewness and Asymmerc Dependence for Asse Allocaon Journal of Fnancal Economercs Pndyck Rober S. 984 Rsk Inflaon and he Sock Marke Amercan Economc Revew Verones P. 999 Sock Marke Overreacon o Bad News n Good Tmes: A Raonal Equlbrum Model Revew of Fnancal Sudes Verones P. 00 Dscusson of Sdelned Invesors Tradng-Generaed News and Secury Reurns Revew of Fnancal Sudes

21 Table I: The dfferen effecs on condonal volaly and skewness Theory Condonal volaly Condonal skewness Leverage Volaly ncreases (declne) when sock prce declnes (ncreases) Lower or more negavely skewed reurns follows a sock prce declne Volaly feedback And Verones (999) Volaly ncreases wh large prce ncrease or decrease Lower or more negavely skewed reurns follows a sock prce declne Sock Bubble Lower or more negavely skewed reurns follows a perod of sock prce ncrease Cao Coval and Hrshlefer (00) Volaly ncreases wh large prce ncrease or decrease Lower or more negavely (posvely) skewed reurns follows a perod of sock prce ncrease (declne) Hong and Sen (003) Lower or more negavely skewed reurns follows hgh rend-adjused urnover 0

22 Table II: Indvdual counres Ths able repors he feasbly of shor sellng and pu 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. Counry Feasbly Exsence Uncondonal Uncondonal Regresson I Regresson II of of pu skewness volaly Dep. varable: skewness Dep. 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 (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 sopped n 997 (0.0060) (0.59) (0.078) (0.0059) (0.047)

23 Counry Feasbly Exsence Uncondonal Uncondonal Regresson I Regresson II of of pu skewness volaly Dep. varable: skewness Dep. 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 (0.988) (0.4366) (0.00) (0.077) (0.04) MOROCCO No No NA NA NA NA NA NA (0.009) (0.79) NIGERIA No 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) PHILIPPINES 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 ARABIA 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) SOUTH AFRICA Yes (0.547) (0.8890) (0.359) (0.54) (0.3577) SRI LANKA No No NA NA NA NA NA NA (0.74) (0.5343) TAIWAN 998 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)

24 Counry Feasbly Exsence Uncondonal Uncondonal Regresson I Regresson II of of pu skewness volaly Dep. varable: skewness Dep. 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) NEW ZEALAND 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 (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) 3

25 Table III: 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 Lagged rend-adjused urnover SSPO feasbly Monhly Reurn Lberalzaon Volaly

26 Table IV: 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. Lagged reurn s he ndex reurn durng he prevous monh. Lagged skewness s he skewness durng he prevous monh. Lagged 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. Regresson specfcaon All counres Developed counres Emergng counres () () (3) (4) () () (3) (4) () () (3) (4) Independen varables Lagged 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) Lagged reurn (0.000) Lagged skewness (0.0369) (0.056) (0.650) Lagged volaly.4656 (0.0384) (0.0664).94 (0.0857) Lberalzaon (0.740) (0.893) (0.90) (0.8804) (0.955) (0.9705) (0.8675) (0.840) (0.700) (0.8370) (0.8734) (0.8549) 5

27 Table V: 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 = 6 / 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 Lagged reurn Condonal skewness Sandard error Lagged reurn Condonal skewness Sandard error

28 Table VI: 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). 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. Lagged 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 A: Daa sample ncludes only posve lagged reurns Regresson specfcaon Independen varables All counres Developed counres Emergng counres () () (3) () () (3) () () (3) Lagged rendadjused urnover (0.3847) (0.507) (0.780) 0.60 (0.8900) (0.4005) (0.475) Lagged 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) Lagged rendadjused urnover 0.53 (0.059) 0.08 (0.0763) (0.0999) -.99 (0.040) 0.4 (0.037) (0.038) Lagged 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) 7