The Systematic Tail Risk Puzzle in Chinese Stock Markets: Theoretical Model and Empirical Evidence

Transcription

1 The Sysemac Tal Rsk Puzzle n Chnese Sock Markes: Theorecal Model and Emprcal Evdence Absrac: Dfferen from he marke bea ha measures common rsk, sysemac al rsk maers n ha he al rsk of he marke porfolo conrbues o he al rsk of one sock and may play an mporan role n asse prcng. Ths paper frsly employs Chnese consumpon and dvdend daa o calbrae he DTragla and Gerlach (2013) heorecal model s parameers. The calbraon resuls show ha, unlke U.S. marke, dvdend growh rae volaly s much hgher han consumpon growh rae volaly n Chna, whch causes negave relaonshp beween sysemac al rsk and expeced sock reurns. Secondly, by nroducng he condonal value a rsk (CoVaR) measures sysemac al rsk, hs paper emprcally examnes he relaonshp beween sysemac al rsk and he cross-seconal expeced reurn n Chnese sock markes. The emprcal resuls sugges: (1) Esmaed by Quanle Regresson, he CoVaR dffers from he oher wo sysemac al rsk measures ncludng lower al dependence (LTD) and al bea. I conans mporan nformaon ha affecs sock prce, and has a beer prcng effec on equy prces. (2) There s a sgnfcanly negave relaonshp beween sysemac al rsk and cross-seconal expeced reurn ( sysemac al rsk puzzle ), even when conrollng for bea, sze, book-o-marke rao, momenum, shor-erm reversals, lqudy, co-skewness, dosyncrac volaly, co-skewness, co-kuross, dosyncrac skewness, dosyncrac kuross, LTD, al bea and so on. Ths sudy has mporan mplcaons for asse prcng research and nvesmen pracce. Key words: Sysemac al rsk; CoVaR; Quanle regresson; Cross-seconal reurn predcably; asse prcng

2 1. Inroducon The relaonshp beween rsk and reurn s a cenral opc n fnancal research. The classcal capal asse prcng model (CAPM) beleves ha he expeced sock reurns are deermned by marke rsk (bea). However, a growng number of emprcal sudes fnd ha he prcng effec of bea s no sascally sgnfcan. In fac, nvesors wll pay more aenon o al rsk han marke bea. Snce nvesors have dsaser avodance moves, hey generally avod holdng asses ha are lkely o suffer enormous losses even f he lkelhood s relavely low (Rez, 1988). Numerous sudes demonsrae ha al rsk has a powerful explanaon ably for macro fnancal opcs such as he equy premum puzzle (Barro, 2006; Gabax, 2012; Wacher, 2013), provng as a poenal prcng facor. Tal rsks of socks are no only affeced by s frm-specfc facors (dosyncrac al rsk), bu also by he common facors n he markes (sysemac al rsk). If sock markes crash, mos of sock prces would fall, wh some socks fallng sharply and some else less han before, and some ohers even rse agans he markes. For example, durng he crash of Chnese sock markes n 2015, bank socks prces rse agans markes declnng. I can be seen ha when sock markes suffer from al rsk, he dfferen performances of ndvdual sock reurns are deermned by sysemc al rsks. Van Oord & Zhou (2016) defnes he sysemac al rsk as al bea, whch s he sensvy of ndvdual socks o he marke porfolo when he al rsk occurs n he marke, ndcang he prces of lower al bea of socks reman frm durng he exreme marke downurns. Smlarly, Bal e al. (2014) decompose sock al rsk no hree componens: a sysemac componen (sysemac al rsk), an sock-specfc componen, and a hybrd componens. Among hose, hey argue ha sysemac al rsk maers n ha he al rsk of he marke porfolo conrbues o he al rsk of he overall porfolo. Then, wha s he relaonshp beween sysemac al rsk and expeced sock reurns? There are only a small number of papers n hs area, and mos of hem are emprcal sudes. Ther conclusons are far from conssen. One srand of leraures show ha sysemac al rsk s sgnfcanly posvely relaed wh expeced sock reurn (Chab-Yo e al., 2018; Kelly & Jang, 2014). Second srand of leraures demonsraes ha he relaonshp beween he wo s negave. Tha s, he lower he sysemac al rsk of ndvdual socks, he hgher he fuure reurn (DTragla and Gerlach, 2013). Thrd srand of papers ndcae ha here s no sgnfcan relaonshp beween sysemac al rsk and expeced sock reurn (Bal e al., 2014; van Oord & Zhou, 2016). In summary, here are wo major shorcomngs n exsng leraures. Frs, due o he dfferen measures for sysemc al rsk and he varey on sock markes daa samples and perod spans, emprcal conclusons are nconssen. Second, mos sudes are only emprcal

3 sudes whou heorecal models. Alhough DTragla & Gerlach (2013) consrucs a heorecal model, he conclusons of he heorecal model conradc her emprcal evdences. Our sudy nvesgaes wheher sysemac al rsk has effec on equy prces n he Chnese sock markes. On he one hand, we propose a heorecal model based on DTragla & Gerlach (2013) o examne hs queson. From he heorecal model, we conclude ha he relaonshp beween sysemac al rsk and expeced sock reurns s deermned by he nvesor rsk averson coeffcen, he probably and scale of al rsk occurrence, he consumpon change relave o he dvdend change and some oher parameers. Employng he Chnese marke consumpon and dvdend daa o calbrae he model parameers, resuls ndcae ha, conrary o he concluson of DTragla & Gerlach (2013) n he US markes, here s a negave relaonshp beween sysemac al rsk and expeced reurn rae, due o he fac ha he dvdend growh rae flucuaon n he Chnese marke s much larger han he flucuaon of he consumpon growh rae. On he oher hand, for he frs me nroducng a novel and suable sysemac al rsk measures (CoVaR proposed by Adran and Brunnermeer (2016)), we employ wo quanave mehods (porfolo-level analyss and Fama-MacBeh (1973) cross-seconal regresson) o emprcally examne he role of sysemac al rsk on asse prcng n Chnese sock markes. The resuls are as follows: (1) CoVaR conans nformaon affecng asse prces whch are no refleced by exsng sysemac al rsk measures such as lower al dependence (LTD, Chab-Yo e al.,2018) and al bea (van Oord & Zhou, 2016)., and have a greaer asse prcng effec; (2) Sysemac al rsk s sgnfcanly negavely relaed o he cross-seconal expeced sock reurns n Chnese sock markes (.e. he " sysemac al rsk puzzle"). Ths phenomenon can neher be explaned by exsng sysemac al rsk proxy varables such as he lower al dependence and he al bea, nor could be accouned for by a seres of common rsk facors such as marke rsk, sze, book-o-marke rao, momenum and reversal facors. our heorecal and emprcal resuls sugges ha here s a "sysemac al rsk puzzle" n Chnese sock markes, whch has grea sgnfcance for exsng asse prcng heory sudy, nvesmen decson-makng and rsk managemen pracce. Ths sudy makes hree man conrbuons. Frs, we choose daa sample from Chnese sock markes, whch supple new evdence o nernaonal sudy abou hs ssue. Comparng wh developed markes, he occurrence of al rsk n Chnese sock marke s more frequen. For example, from md-june 2015 o January 2016, Chnese sock markes arse several crash evens, even lead o a lqudy crss and caused huge losses for nvesors. The frequen occurrence of al rsk, hgh urnover and volaly along wh a large number of speculave radng n Chnese sock markes provde a naural expermen for examnng he prcng effec of sysemac al rsk. The conclusons of hs

4 paper ndcae ha he relaonshp beween rsk and reurns vares across dfferen markes. (2) o bes of our knowledge, hs s he frs paper o nroduce CoVaR as a measure of sysemac al rsk, and examne s prcng effec. Prevous emprcal research adops wo measures of sysemac al rsk: one s he lower al dependence coeffcen (Chab-Yo e al., 2018) and anoher s he al bea (van Oord & Zhou, 2016; Bal e al., 2014). The former measures he al probables of ndvdual socks condonal on he sock markes are n exremely downsde saes (al even). The laer measures he sensvy of ndvdual socks o al even of sock markes. CoVaR (condonal value a rsk), whch s proposed by Adran & Brunnermeer (2016) for measurng fnancal sysemac rsk, reflecs he rsk spllover of fnancal nsuons (or fnancal sysems) when a fnancal nsuon (or fnancal sysem) al rsk occurrng. As we see, CoVaR s conssen wh he noaon of sysemac al rsk proposed by Bal e al. (2014). However, dfferen from lower al dependence and al bea, CoVaR drecly provde he magnude of sysemac al rsk of one sock suffers from he al rsk occurrng of he sock markes. Fnally, followng he heorecal model of DTragla & Gerlach (2013), we for he frs me employ he consumpon and dvdend daa of he Chnese markes o calbrae he parameers of heorecal model. The resuls are suppored by our emprcal resuls, whch makes our sudy on he relaonshp beween sysemac al rsk and expeced sock reurns more rgorous and he conclusons much more belevable. The remander of he paper s organzed as follows. Secon 2 presens he heorecal model. Secon 3 s varable selecon and research desgn, whle Secon 4 descrbes daa and emprcal resuls. And Secon 5 s he concluson. 2. Theorecal Model DTragla & Gerlach (2013), based on he models of Rez (1998), Barro (2006) and Gabax (2012), consruc a heorecal model of he relaonshp beween sysemac al rsk and expeced reurn rae. Usng he al shock (dsaser) of consumpon as he marke sysemac rsk, he change of dvdends when he consumpon al rsk occurs as he asse sysemac al rsk, and proceedng from he nvesor's maxmzaon of hs uly funcon, hey, on he bass of presumng consumpon and dvdend change equaon, conclude ha he relaonshp beween sysemac al rsk and he expeced reurn rae s relaed o a seres of parameers such as he nvesor rsk averson coeffcen, he probably and scale of he dsaser, he consumpon change magnude relave o he change n dvdends, and so on. Ths secon follows he model of DTragla & Gerlach (2013) o carry ou research.

5 2.1 Model Seup Assumng ha a represenave economc person consumes C a me and has a power uly funcon (CRRA) wh consan relave rsk averson, he dvdend of sock a me s D, hen he sock prce a equlbrum s: j C D j1 C D P D e E (1) 1, 1 [( ) ], where s he coeffcen of relave rsk averson, s he rae of me preference, In each perod here s a small probably p of a consumpon al rsk (also known as consumpon dsaser). No Consumpon Dsaser: Consumpon Dsaser; C 1 e( 1 C 1) (2) C 1 C e( 1B) (3) Wh expeced consumpon growh rae. represens flucuaons n consumpon (no caused by consumpon al rsk), and s ndependen and dencally dsrbued wh mean zero. B sands for scale of consumpon al rsk wh a proporon and B. For dvdend, when no dvdend dsasers occur: D 1 D e( 1 1) (4) Wh expeced growh rae. represens random flucuaons n he dvdends of sock (no normal flucuaons caused by al rsk), whch s also mean zero, ndependen and denfcally dsrbued over me. We make a reasonable assumpon beween consumpon flucuaon and dvdend flucuaon :we allow correlaon beween and. If here s no consumpon al rsk, D here wll be no dvdend al rsk; whereas f a consumpon dsaser occurs, sock I experences a dvdend dsaser wh probably (ha s, he al correlaon beween consumpon and dvdend, whch represens he sysemac al rsk experenced by sock when suffers macro consumpon crss); also when a dvdend al rsk occurs, he reducon scale n sock dvdend s an exogenous fxed rao. Dvdend Dsaser: F D 1 e( 1F D ) (5) 0B 1 Where F represens he reducon scale n dvdend of sock durng a dvdend al rsk

6 occurrence, wh a proporon 0 F 1且 -F. Based on(2) ( 3) (4)and(5), we have 1 C E[( C 1 ) D, 1 D ] e {(1 (1 ) p) E[ ] (1 ) 1 F p[ ]} 1 B (6) Pung (6) no (1), and proceedng recursvely by he law of eraed expecaons, we have 1 P D {1 e [(1 p) ( ) p(1 F )(1 B) ]} 1 (7) Where, respec o (1 ) ( ) E (8) (1 ) Snce and are d over me, does no depend on. Dfferenang wh P, we have 1 e e To calculae expeced reurns, we allow [(1 p) ( ) p(1 F )(1 B ) pf (1 B ) represens he rao beween prce and dvdend, whch depends only on, no. From (7), we have K ( ) u u ( ) 1 1 [(1 ) ( ) (1 )(1 e p p F B ) ] 1 D 2 ] 0 (9), whch (10) Dvdend rae of sock a me +1 can be calculaed as K ( ) P / D P 1 / D 1 ( P 1 / D 1) D 1 D 1 K ( ) 1 D 1 R 1 ( P / D ) D K ( ) D (11) And have: D 1 E e (1 pf ) D (12) Combnng (12) and (11), we have expeced reurns as 1 pf E ( R, 1) e (13) (1 p) ( ) p(1 F )(1 B ) Dfferenang n (13), we have E [ R 1] (1 B) ( ) e p(1 p) F 2 [(1 p) ( ) p(1 F )(1 B) ] (14)

7 (14) represens he relaonshp beween expeced reurn rae and sysemac al rsk can be seen ha s value depends on he relave magnudes of (1 B) ( ), sock sysemac al rsk he conrary, when 2.2 Model calbraon exercse s smaller, he expeced reurn rae s lower. (1 ) B and ( ). I. When s greaer and he expeced reurn rae hgher. On Followng Barrow (2006) and Gabax (2012), DTragla & Gerlach(2013)make a calbraon exercse on he value of (1 ) B and 1949 o 1999 and esmae ha when ( ) (1 ) B. They use US consumpon and dvdend daa from s approxmaely beween 3 and 4 and ( ) around 1, (14) s above 0, whch ndcaes ha n Amercan sock marke, he greaer he sysemac al rsk, he hgher he expeced reurn rae. Followng DTragla & Gerlach(2013) Barro(2006)and he fndngs of domesc researcher Chen Guojn (2014), we use acual daa from Chna for calbraon exercse. Frs, DTragla & Gerlach(2013)make nvesor rsk averson coeffcen as 3 or 4. Domesc scholars Wang We and Ca Mngchao (2011), based on he daa of Chnese resdens behavor, measure he rsk averson coeffcen of Chnese nvesors beween 3 and 6. Therefore, whou loss of generaly, hs paper dscusses four suaons when =3, 4, 5, and 6. Second, o calbrae B and ( ) DTragla & Gerlach(2013)use daa of average resden consumpon oucome and average dvdend ncome n NIPA (he naonal ncome and produc accouns)respecvely o represen consumpon and dvdend n he heorecal model and manly calculae he ncrease magnude of he varables used n he process. Smlarly, consderng he avalably of Chnese daa, hs paper use he overall consumer consumpon ndex (prevous year = 100) o represen he consumpon level ( C ), he sum of all company dvdends n he Chnese sock marke each year o represen he dvdend level ( D ). The daa are from CSMAR Guoaan daabase. The sample range of consumpon daa s from 1952 o 2015 and he dvdend daa from 1991 o Takng no accoun he need o calculae he change range and he machng of consumpon and dvdend daa o oban ( ), we now have 24 annual observaon values: s, C C D, D The average consumpon growh rae ˆ and average dvdend growh rae ˆ 1 log[ ] ˆ log[ ] C C D D ˆ are (15) (16) From (17) we esmae consumpon growh rae error erm and dvdend growh rae error

8 erm: C ˆ 1 ˆ ˆ 1 e ( e ) C D ˆ 1 ˆ uˆ 1 e ( e ) D (17) Chna's consumpon growh rae error erm and dvdend growh rae error erm are shown n Table 1, and he char s shown n Fgure 1. Table 1 Esmaed resuls of error erm for consumpon growh rae and dvdend growh rae year error erm for consumpon growh rae error erm for dvdend growh rae

9 error erms of consumpon growh(lef) error erms of dvdend growh (rgh) Fgure 1 The rend of error erm for consumpon growh rae and dvdend growh rae Proceedng from (18), we esmae ( ) as: 1 1 ˆ ˆ( ) (18) 24 (1 ) uˆ 1 In addon, we need o calbrae parameer B (he magnude of consumpon reducon durng a al rsk). Based on he hsorcal daa from Barro (2006) 1, DTragla & Gerlach (2013) 1 Barro (2006) adops a sample daa abou economc varables such as real GDP per capa, real sock reurns,

10 esmae he probably of a consumpon al rsk, defned as a conracon n consumpon of a leas 15%, s approxmaely p = whle he value for average rsk sze B=30%. Smlarly, domesc scholar Chen Guojn e al. (2014) use Chna's per capa real GDP daa as he research arge, and nne years of daa wh negave GDP growh rae as he crss year daa, and esmae he al rsk probably o be 0.05, he average annual al sze Lkewse, we ake he daa of Chna's consumpon level growh rae from 1952 o 2015 as he research objec, and calculae he probably of consumpon al rsk occurrence p=0.095, he average consumpon al sze 0.039, and he larges consumpon al sze Consderng he fac ha Chna has fewer daa samples, whch wll poenally underesmae he B value, for he sake of cauon, hs paper consders B=0.039 and B= Through he above-menoned calbraon process, we can compare he sgn for he numeraor ( B ) 1 ) ( erm n (14), ha s, he values of and, and hen derve he relaonshp beween he expeced sock reurn and he sysemac al rsk as s revealed by he heorecal model. The parameer calbraon resuls are lsed n Table 2. Table 2 Parameer Calbraon of Sysemac Tal Rsk and Expeced Sock Reurn R n he Theorcal Model ˆ( ) B (1 ) B (1 B) ˆ ( ) I can be seen from Table 2 ha n a dsaser when he nvesor's rsk averson coeffcen s 3, 4, 5, 6 and he consumpon decrease magnude B 0.039, 0.083, he numeraor erm (1 B) ˆ ( ) of (14) s below 0, whch ndcaes ha for he Chnese marke, he greaer he sock sysemac al rsk, he smaller he expeced reurn rae. Ths concluson s conrary o ha of he US marke. Seen from he parameer calbraon process, hs s manly due o he fac ha neres raes, and so on) of 35 counres (20 OECD counres, 8 Lan Amercan counres and 7 Asan naons)) durng recen 100 years n he 20 cenury around he world.

11 he daa flucuaon n he dvdend growh rae of he Chnese sock marke s much larger han ha of he US sock and he consumpon decrease magnude relavely small when a consumpon al rsk occurs, resulng n a much larger (approxmaely 1.0) and a smaller (1 ) B ˆ( ) han ha of he US marke han ha of he US marke (beween 3 and 4), whch causes an nverse change n he relaonshp beween sysemac al rsk and expeced reurn rae. 3. Varable Selecon and Emprcal Research Mehodologes 3.1. Esmaon of he sysemac al rsk (STR) CoVaR and sysemac al rsk (STR) CoVaR(Condonal Value a Rsk), proposed frsly o measure he sysemc rsk of fnancal nsuons by Adran & Brunnermeer(2016),s mplcly defned as, Where j j C( X ) q, Pr ( X CoVaR C( X )) q represens he VaR condonal on some even CX ( ) of nsuon, q of nsuon. j X j (or he fnancal sysem) s he losses of nsuon j a me s he confdence level. We ofen defne CX ( ) as al even, f happens, we have: Pr ( X VaR ) q. CoVaR s an acually condonal al rsk measure, whch ndcaes he q, al rsk of one varable condonal on he al rsk of anoher varable. Adran and Brunnermeer (2016) manly research CoVaR sysem q, fnancal nsuon), whch represens he fnancal nsuon of he fnancal sysem when he fnancal nsuon also menoned he oppose condonng, (where sysem s he fnancal sysem and CoVaR sysem q, s one conrbue o he sysemc rsk suffers a crss (crash or al even). They, whch answer he queson of whch nsuons are mos a rsk should a fnancal crss occur. In oher words, measure he al rsk of fnancal nsuon sysem. In hs paper, we nroduce he measure CoVaR M q, CoVaR q sysem, suffers from he crss occurrng of he fnancal CoVaR no sock markes, and pu forward he sysem q, ( where represens he sock and M represens he sock markes (or marke porfolo), whch ndcaes he al rsk of sock condonal on he occurrng of al rsk (crash or crss) of he whole sock markes. We can derve M q, Where CoVaR q X s he reurn of sock Pr ( X CoVaR X VaR ) q M M M q, q, a me, CoVaR by: M q, M X s he reurn of sock markes ndex. VaR s he Value a Rsk of sock markes ndex a me a he q confdence level. CoVaR s dfferen from wo exsng measures of sysemac al rsk such as lower al M q, j C( X ), dependence (LTD, Chab-Yo e al.,2018) and al bea (van Oord and Zhou, 2016). Esmaed

12 al dependence beween socks and markes based on copulas, LTD capures a condonal probably of sock al rsk occurs along wh he markes al rsk happen. Based on exreme value heory, al bea measures he sensvy of socks o exreme marke down urn. However, CoVaR q M, drecly provde he magnude of sysemac al rsk of sock al rsk occurrng of he sock markes. suffers from he Esmaon of Sysemac Tal Rsk based on Quanle Regresson CoVaR s essenally a quanle of a condonal probably. Followng Adran & Brunnermeer(2016), our esmaon s also based on quanle regresson. Unlke ordnary leas squares regresson and approaches based on exreme value heory and Copula, quanle regresson makes no presupposed assumpon abou dsrbuon and he esmaed values are less lkely o be affeced by exreme values. I s especally useful for models wh heeroscedascy and he esmaed resuls are relavely effecve and robus. Our calculaon deals for esmang sysemac al rsk based on quanle regresson are as follows: X M M M M M q q -1 q, X X M M M M M M M q q q -1 q, (19) (20) reurns To capure he me varaon n jon dsrbuon of ndvdual sock reurns M X adjusmens: X and marke and measure me-varyng sysemac al rsk, we make he followng wo Frs, we nclude sae varable M -1 no quanle regresson of (19) and (20), o represen nformaon se wh one-week lag. Our sae varables are weekly sandard devaon, monhly sandard devaon, quarerly sandard devaon of marke reurns and reurns on he one-day lag, one-week lag, one-monh lag and one-quarer lag. These adjusmens allow us o absorb he laes nformaon se when esmang VaR. VaR ˆ ˆ M (21) CoVaR M M M q, q q -1 ˆ ˆ VaR ˆ M (22) M M M M q, q q q, q -1 Second, we adop rollng wndow quanle regresson o capure expeced sysemac al rsk of sock a monh. Based on equaon (19) and (20), a monh, we use daly daa for he pas wo years as a sample perod o conduc regresson and we oban he esmaed coeffcens of ˆ M q M M ˆ ˆM q ˆ q ˆ q q M. Each me we roll forward one monh, and esmae he rsk value of he nex monh. Based on equaon (21), we ge he al rsk of marke ndex VaR M q,.

13 Pung he ndex no equaon (22), we can compue CoVaR qof, sock a each radng day n he nex monh. When we average he resuls across he nex monh, we have he expeced sysemac al rsk for each monh. Where me-varyng d s he number of radng days of sock n monh. By formaon (23), we ge 1 STR ECVaR CoVaR d q, q, d 1 STR whch s he expeced sysemac al rsk of sock a monh. In he nex secon, we wll sudy he relaonshp beween STR and expeced reurns. (23) 3.2 Conrol varables Two Exsng Sysemac Tal Rsk Measures Prevous sudes manly use wo sysemac al rsk measures: al bea (T-bea)and lower al dependence (LTD). Van Oord & Zhou(2016)fnd ha T-bea can predc reurns n exreme marke downurns, bu wh no emprcally sgnfcan premum 但实证上并没有获得显著的溢价. Chab-Yo e al.(2017) and Lu Shengyao e al.(2016)boh use LTD o measure sysemac al rsk. They show ha LTD s sgnfcanly posvely correlaed wh expeced reurns. Followng Oord e al. n calculang T-bea and Lu Shengyao e al. n calculang LTD, we use hem as our sysemac al rsk measures oher conrol varables To conrol he nfluence of he oher facors on he relaonshp beween he sysemac al rsk and cross-seconal expeced reurns, we consder he followng commonly used conrol varables: Marke bea (BETA): he proxy of sysemac rsk suggesed n CAPM.Marke capalzaon (SIZE): he logarhm of he marke capalzaon of he prevous June.Book-o-marke rao (BM): he logarhm of he book-o-marke rao a he end of he las fscal year.momenum (MOM): he sock reurn of he prevous year excludng he mos recen monh.shor-erm reversals (REV): he sock reurn of he prevous monh. Illqudy (Amhud): he absolue monhly sock reurn over monhly radng volume.turnover (Turnover): he number of shares raded n he las monh over oal number of ousandng shares. Idosyncrac volaly (IV): he sandard devaon of he resdual reurns from he hree-facor Fama French model. Downsde bea (Bea_down): he covarance beween ndvdual sock reurns and marke ndex reurns when he marke s gong down. Co-skewness (Coskew): he hrd sandardzed cross cenral momen beween he ndvdual sock reurn and he marke reurn. Co-kuross (Cokur): he fourh sandardzed cross cenral

14 momen beween ndvdual sock reurn and marke reurn. Idosyncrac skewness (Iskew): skewness of he resdual reurns from he hree-facor Fama French model. Idosyncrac kuross (Ikur): kuross of he resdual reurns from he hree-facor Fama French model. 3.3 Research Mehodology We employ unvarae porfolo-level analyss, bvarae porfolo-level analyss and frm-level cross-seconal regressons. These mehods are commonly used n he emprcal asse prcng leraure. We follow Fama and Macbeh (1973) o run he followng frm-level regressons wh monhly daa:, 1 0, 1,, k,,, k, k1 (24) where R, 1 represens he realzed reurn of sock n monh + 1. The ndependen varables are he one-monh lagged values of STR, BETA, SIZE, BM, and oher conrol varables. K R STR Conrol 4.Daa and emprcal resuls 4.1 Daa and descrpve sascs We collec daly and monhly reurns of all socks n Chnese A-share markes beween January 1997 and December 2015 from he CSMAR (Chna Secures Marke & Accounng Research) daabase n WRDS (Wharon Research Daa Servce). The 10% prce lm polcy ook effec a he begnnng of We exclude socks ha have been lsed for less han one year and reurns on he frs day afer he nal publc offerng. We use he value-weghed marke reurn from CSMAR daabase. We use he one-year depos rae as he rsk-free rae. We also oban he urnover, oal marke capalzaon, book-o-marke rao, rsk-free rae, and he daly and monhly Fama French hree-facor daa from he CSMAR daabase. Table 3 repors he descrpve sascs for mporan varables ncludng STR, BETA, SIZE, BM, LTD (lower al denpendence) and T-bea (al bea) across 241,626 frm-monh observaons. The mean, mnmum and maxmum of STR s , and , respecvely. These fgures sugges he average daly sysemac al rsk of sample socks n one monh s 2.99 percenage. The mnmum ndcae some socks prces wll rse wh 2.63 percenage a he me al rsk occurrng of he markes, whle he maxmum means some daly sysemac al rsk of sample socks wh exceed he 10 percenage of prce lm polcy. 1 1 As menoned n Secon 3.1.2, sysemac al rsk n hs sudy s he predcon of average daly CoVaR n nex monh, whch reflecs nvesors expecaon abou fuure al rsk. Therefore, s values can vary below 0 and above he 10% (prcng lm percenage).

15 Table 3 descrpon sascs Varables nobs Mnmum Maxmum Mean Medan Sdev Skewness Kuross STR BETA SIZE BM LTD T-bea Table 4 provdes he average cross-seconal correlaons beween STR and he oher rsk measures. The correlaon coeffcen beween STR and marke bea s sascally nsgnfcan posve wh a coeffcen of (-sasc 0.91), whch ndcaes STR and Bea measure wo dfferen aspecs of rsk. STR s he rsk of one sock suffer from he condon on markes exreme downsde, whle bea s he covarance beween one sock and markes a he common suaon. Boh LTD and T-bea have a hghly sgnfcanly posve correlaon wh STR, wh correlaon coeffcens (-sasc 13.17) and (-sasc 20.54). These resuls shows he sysemac al rsk measured by CoVaR n hs sudy s conssen wh exsng measure, as hey all reflec sysemac al rsk of socks. However, how much prcng effecs of STR comparng LTD and T-bea on equy prces and wheher he hree sysemac al rsk measure are equvalen hngs are furher researched n followng pars. Table 4 Cross-seconal average correlaons beween STR and oher rsk measures STR bea SIZE BM LTD T-bea STR *** *** *** *** (0.91) (-14.01) (-14.73) (13.71) (20.54) bea * *** *** (-1.88) (0.73 ) (3.88 ) (6.57 ) SIZE *** (1.47) (1.23 ) (9.03) BM *** (-7.66) (1.05) LTD (0.86 ) T-bea Noe: We compue cross-seconal correlaon coeffcens beween ITR and oher rsk

16 measures each monh from January 1997 o December The monhly averaged correlaon coeffcens and he correspondng Newey-Wes (1987) robus -sascs are repored. 4.2 Unvarae porfolo-level analyss To examne he relaonshp beween sysemac al rsk and cross-seconal expeced sock reurns, We frs look a he unvarae porfolo sors. We form porfolos by sorng socks on he bass of he sysemac al rsk (STR) of he prevous monh. Porfolo 1 (5) s concerned wh socks wh he lowes (hghes) STR. We compue he equally-weghed and value-weghed average monhly reurns, CAPM alphas and hree-facor Fama-French alphas of each qunle porfolos as well as he dfference porfolo beween qunle 5 ( hghes STR) and qunle 1 (lowes STR).Resuls are repored n Table 7. Table 5 Unvarae porfolo-level analyss resuls 1 Low Hgh Hgh-Low Rew 1.62% ** 1.55% ** 1.39% * 1.32% 1.07% -0.55% ** (2.22) (1.99) (1.76) (1.60) (1.28) (-2.19) Rvw 0.81% 0.76% 0.61% 0.66% 0.14% -0.67% * (1.28) (1.07) (0.86) (0.87) (0.18) (-1.76) CAPM alphaew 1.47% ** 1.41% ** 1.24% * 1.16% 0.93% -0.54% ** (2.27) (1.99) (1.74) (1.56) (1.22) (-2.12) CAPM alphavw 0.70% 0.65% 0.49% 0.52% 0.01% -0.69% * (1.25) (1.01) (0.77) (0.76) (0.02) (-1.91) FF3 alphaew 1.66% *** 1.64% ** 1.53% ** 1.48% ** 1.16% * -0.50% * (2.74) (2.47) (2.27) (2.09) (1.71) (-1.74) FF3 alphavw 0.88% 0.83% 0.77% 0.84% 0.35% -0.53% * (1.61) (1.31) (1.22) (1.26) (0.51) (-1.68) Noe: Panel A presens qunle porfolos formed n every monh from January 1997 o December 2015 by sorng socks on he bass of he dosyncrac al rsk (ITR) of he prevous monh. Porfolo 1 (5) s concerned wh socks wh he lowes (hghes) ITR. The able llusraes he average equal-weghed ( R ew)and value-weghed ( Rvw) monhly reurns, he CAPM alphas and he hree-facor Fama French alphas of each porfolo. The las column demonsraes he dfferences boh n monhly reurns and n alphas wh respec o he CAPM model and hree-facor Fama French model beween porfolos 5 and 1. In he brackes he -sascs adjused accordng o Newey-Wes (1987) are repored.

17 From he Table 5, we can see ha he average equally-weghed (value-weghed) porfolo reurns R ew (R vw) declne as STR ncreases. For equally-weghed reurns, he average reurn dfference beween he porfolos wh hghes and lowes ITRs s 0.55%, whch s sgnfcan a he 5% sgnfcance level. All he sascs n our paper are adjused accordng o Newey-Wes (1987). The average dfferences n CAPM alpha and FF3 alpha beween he porfolos wh hghes and lowes STRs are 0.54% and -0.50% respecvely, whch are boh sgnfcan a a convenonal levels. For value-weghed reurns, Table 7 presens smlar resuls, alhough somewha less sascally sgnfcan. These resuls show ha here s a sgnfcanly negave relaonshp beween sysemac al rsk and cross-seconal expeced reurns. In fnance sudy, abnormal rsk-urn radeoff s ofen called puzzle. For nsance, Ang e al.(2006) fnd he dosyncrac volaly s negavely relaed wh expeced sock reurns, whch hey named dosyncrac volaly puzzle. Smlarly, we call he phenomena n our sudy sysemac al rsk puzzle. 4.3 Bvarae porfolo-level analyss In hs secon, we use bvarae sor mehod o nvesgae wheher he sysemac al rsk puzzle found n above secon s robus afer conrollng oher common rsk facors, especally for wo exsng sysemac al rsk measures (LTD and T-bea). We ake he Bea facor for example. Frs, we sor all frms no qunle porfolos based on he bea of each frm. Then, we sor all frms whn each bea porfolo no qunle porfolos based on he STR of each sock. We ge 25 porfolos. Second, we calculae he average equal-weghed (or value-weghed) reurn of each of hese 25 porfolos n he nex monh across all monhs. Las, we calculae he average equal-weghed (or value-weghed) reurns of each of he 5 qunle porfolos by STR across 5 qunle porfolos by bea. We presen hese average reurns n he frs row of he Panel A of Table 6. The las wo columns presen he dfferences n reurns and FF3 alphas beween he porfolos wh he hghes and lowes STRs. We repor sascs o es he sgnfcance of he dfference. We mplemen smlar sudes on he neracon beween he STR and he oher rsk facors. All resuls are presened n Table 6 wh Panel A for equally-weghed reurns and Panel B for value-weghed reurns.

18 Table 6 Bvarae porfolo-level analyss resuls Panel A:Equally-weghed porfolos TR Conrol 1 Low Hgh H-L Reurn dfference Hgh-Low FF3 alpha Bea 1.54% ** 1.46% * 1.47% * 1.31% 1.11% -0.43% * -0.35% * (2.09) (1.89) (1.84) (1.62) (1.37) (-1.79) (-1.68) BM 1.61% ** 1.41% * 1.38% * 1.32% 1.18% -0.43% * -0.33% * (2.21) (1.81) (1.72) (1.63) (1.46) (-1.78) (-1.66) SIZE 1.82% ** 1.59% ** 1.36% * 1.25% 0.92% -0.90% *** -0.73% *** (2.42) (2.04) (1.73) (1.53) (1.10) (-4.11) (-3.17) MOM 1.60% ** 1.49% * 1.42% * 1.29% 1.13% -0.46% ** -0.40% * (2.18) (1.92) (1.78) (1.58) (1.36) (-2.10) (-1.73) REV 1.71% ** 1.52% ** 1.44% * 1.29% 0.98% -0.73% *** -0.65% ** (2.34) (1.97) (1.82) (1.56) (1.15) (-2.92) (-2.52) Amhud 1.78% ** 1.59% ** 1.39% * 1.24% 0.94% -0.84% *** -0.67% *** (2.40) (2.04) (1.77) (1.51) (1.13) (-3.60) (-2.66) LTD 1.67% ** 1.52% * 1.40%* 1.26% 1.08% -0.59% ** -0.43% * (2.27) (1.95) (1.77) (1.55) (1.29) (-2.50) (-1.66) T-bea 1.61% ** 1.53% ** 1.42% * 1.31% 1.07% -0.54% ** -0.43% * (2.15) (1.96) (1.80) (1.61) (1.29) (-2.54) (-1.90) Panel B:value-weghed porfolos TR Conrol 1 Low Hgh H-L Reurn dfference Hgh-Low FF3 alpha Bea 0.89% 0.73% 0.88% 0.75% 0.44% -0.45% * -0.32% (1.38) (0.99) (1.20) (1.03) (0.55) (-1.72) (-1.63) BM 0.93% 0.64% 0.65% 0.66% 0.51% -0.42% * -0.30% * (1.44) (0.89) (0.88) (0.89) (0.64) (-1.75) (-1.69) SIZE 1.68% ** 1.43% * 1.15% 1.01% 0.63% -1.05% *** -0.87% *** (2.37) (1.89) (1.50) (1.28) (0.78) (-4.65) (-3.67)

19 MOM 0.92% 0.79% 0.79% 0.79% 0.44% -0.47% * -0.46% * (1.41) (1.09) (1.07) (1.04) (0.56) (-1.72) (-1.78) REV 1.14% * 0.94% 0.78% 0.80% 0.26% -0.88% *** -0.80% ** (1.75) (1.30) (1.07) (1.08) (0.32) (-2.62) (-2.54) Amhud 1.50% ** 1.39% * 1.11% 1.03% 0.50% -1.00% *** -0.84% *** (2.19) (1.89) (1.50) (1.34) (0.63) (-3.91) (-3.13) LTD 1.02% 0.75% 0.68% 0.61% 0.32% -0.70% ** -0.55% * (1.60) (1.04) (0.92) (0.82) (0.40) (-2.13) (-1.68) T-bea 1.02% 0.81% 0.77% 0.73% 0.29% -0.73% ** -0.63% ** (1.48) (1.11) (1.06) (0.98) (0.38) (-2.66) (-2.30) Noe: In hs able, we sor all frms no qunle porfolos based on each conrollng rsk facor. Then, we sor all frms whn each porfolo no qunle porfolos based on he STR of each sock. We ge 25 porfolos n each bvarae sor. We compue he average reurns of each of he 5 qunle porfolos by STR across 5 qunle porfolos by each of he oher rsk facors. Qunle 1 (5) ncludes socks wh he lowes (hghes) STR. We also repor he dfferences n reurns and FF3 alphas beween porfolos wh hghes and lowes STR. For Panel A, porfolo reurns are compued n an equally-weghed way, whle for Panel B n a value-weghed way. We repor n brackes he -sascs adjused accordng o Newey-Wes (1987). From he frs wo rows of Panel A n able 6, afer conrollng for bea, he equally-weghed average reurn dfference beween he low STR and hgh STR porfolos s abou -0.43% per monh wh a Newey Wes -sasc of The H L dfference n he hree-facor Fama-French alphas s -0.35% per monh wh a -sasc of For value-weghed porfolos afer conrollng for bea, as show n Panel B of able 6, he raw reurn and alpha dfferences are sll negave, bu hey are less sascally sgnfcan. Thus, marke bea does no fully explan he hgh (low) reurns o low (hgh) STR socks. From able 6, smlarly, afer conrollng for marke capalzaon, book-o-marke rao, momenum, shor-erm reversals, llqudy, urnover, he raw reurn and alpha dfferences are sascally sgnfcan negave a 10% condonal level. The resuls show hese rsk facors canno fully accoun for he negave relaonshp beween STR and expeced sock reurns. Specally, from he las wo rows of Panel A n Table 6, he H-L reurn dfference beween he hghes and lowes STR porfolos conrollng for LTD and T-bea s -0.59% (-sasc -2.50) and -0.54% (-sasc -0.54%) per monh respecvely. Smlarly resuls wh hose n Panel B. These resuls sugges ha he exsng sysemac al rsk measures LTD and T-bea canno fully

20 explan he negave effec of STR, even hough as we see from he secon X.XXX here are hghly correlaons among hem. In oher words, he STR measure nroduced from CoVaR does conans new nformaon abou fuure prce ha LTD and T-bea may no. Overall, he sysemac al rsk puzzle n Chnese sock markes s robus exsng when conrollng for oher rsk facors such as marke bea, marke capalzaon, book-o-marke rao, momenum, shor-erm reversals, llqudy, urnover, lower al dependence, and al bea. 4.4 Frm-level cross-seconal regressons So far we have esed he sgnfcance of he sysemac al rsk (STR) as a deermnan of he cross-secon of fuure reurns a he porfolo level. Ths porfolo-level analyss has he advanage of beng non-paramerc n he sense ha we do no mpose a funconal form on he relaon beween STR and fuure reurns. The porfolo-level analyss also has wo poenally sgnfcan dsadvanages. Frs, hrows away a large amoun of nformaon n he cross-secon va aggregaon. Second, s a dffcul seng n whch o conrol for mulple effecs or facors smulaneously. Consequenly, n hs secon we examne he cross-seconal relaon beween STR and expeced reurns a he frm level usng Fama and MacBeh (1973) regressons. We classfy all rsk facors no caegores ha measure sysemac al rsk, classcal rsk, radng characerscs, sysemac rsk and dosyncrac rsk. Panel A, B, C, D and E of Table 7 presen he resuls for regressons ncludng STR and he oher rsk measures. Table 7 Frm-level cross-seconal regresson resuls Model 1 Model 2 Model 3 Model 4 Model 5 Model 6 Model 7 Model 8 Model 9 Model 10 Model 11 Panel A: Sysemac al rsk STR *** *** *** *** ** ** *** ** *** (-2.60) (-3.83) (-3.13) (-3.35) (-2.06) (-2.24) (-2.38) (-2.29) (-2.43) LTD *** *** *** (-2.53) (-2.64) (-2.68) T-bea (-0.93) (-0.70) (-0.77) Panel B: Classcal rsk bea * (-0.22) (0.80) (-1.82) (0.78) (0.04) (-0.29) (-0.17) (0.06) (0.09) (0.12) SIZE *** *** *** *** *** *** *** *** *** *** (-4.13) (-3.58) (-4.11) (-4.12) (-3.50) (-3.42) (-3.49) (-3.49) (-3.54) (-3.53) BM (-0.49) (0.94) (0.46) (-0.14) (0.79) (0.86) (0.86) (0.78) (0.79) (0.79) Panel C: Tradng characerscs

21 Mom (-1.09) (-0.31) (-0.17) (-0.29) (-0.28) (-0.37) (-0.35) Rev *** *** *** *** *** *** *** (-5.60) (-5.49) (-5.43) (-5.40) (-5.52) (-5.51) (-5.54) amhud ** *** *** *** *** *** *** (2.10) (2.59) (2.52) (2.73) (2.44) (2.64) (2.49) urnover *** *** *** *** *** *** *** (-7.81) (-8.36) (-8.24) (-8.19) (-8.33) (-8.28) (-8.24) Panel D: Sysemac rsk Bea_dn ** * * (1.21) (1.58) (1.57) (1.81) (1.53) (1.77) (1.73) Coskew (-0.23) (-0.24) (-0.26) (-0.16) (-0.35) (-0.23) (-0.34) Cokur (1.41) (-0.90) (-0.23) (-0.76) (-0.53) (-1.05) (-0.69) Panel E: Idosyncrac rsk IV *** *** *** *** *** *** *** (-3.19) (-2.76) (-3.63) (-3.66) (-2.73) (-2.83) (-2.80) skew (0.00) (-1.08) (-0.44) (0.63) (-0.81) (-1.04) (-0.79) kur (-0.77) (-0.12) (0.10) (0.19) (-0.21) (-0.45) (-0.55) Max *** (-2.50) (-1.39) (-1.56) (1.49) (-1.43) (-1.35) (-1.40) monhs Adj R Noe: For each monh from January 1997 o December 2015, we run a frm-level cross-seconal regresson accordng he Eq. (24). In each column, he me-seres averages of he cross-seconal regresson slope coeffcens and her assocaed Newey-Wes (1987) adjused -sascs (n brackes) are repored. The las row repors each regresson Adj.R 2.,, and denoe sgnfcance a he 10%, 5%, and 1% level, respecvely. In Model 1 of able 7, we only nclude he STR as he ndependen varable. In Model 2-11, nclude BETA, SIZE and BM n he models. Specally n Model 2, we nclude STR as well as BETA, SIZE and BM for conrollng her effec on he relaonshp beween STR and cross-seconal expeced reurns. In Model 3-5, we nclude STR, BETA, SIZE, BM and one of hree caegores of rsk measures (radng characerscs, sysemac rsk and dosyncrac rsk). In Model 6, we conrol all he rsk measures excep for oher wo sysemac al rsk (TDC and Tal Bea) From Model 1-6, we can see ha all he coeffcens of STR are sascally sgnfcanly

22 negave a 5% level. Conssen wh our porfolo analyses, he resuls furher ndcae a sgnfcanly negave relaonshp beween he sysemac al rsk and cross-seconal sock reurns. The common Fama-French facors and he oher rsk measures canno fully accoun for he sysemac al rsk puzzle n Chnese sock markes. Moreover, he average coeffcens on some conrol varables are also as expeced he sze effec s sgnfcanly negave. And socks exhb shor-erm reversals, and llqudy s prced. The average coeffcens on BETA s negave and sascally nsgnfcan excep for Model 5, whch conradcs he mplcaons of he CAPM bu s conssen wh pror emprcal evdence. Conssen wh he U.S evdence of Ang e al.(2006), he average coeffcens on dosyncrac volaly (IV) s sgnfcanly negave a convenonal levels, whch shows he dosyncrac volaly puzzle exs n Chnese sock markes. Noably, he sgn of coeffcens on urnover n all model s sgnfcanly negave, whch s conssen wh Long e al. (2018). The laer fnd an dosyncrac a rsk puzzle n Chnese sock markes ha can be fully explaned by he urnover, whle n hs sudy we sugges ha urnover canno accoun for he sysemac al rsk puzzle any more. For ease of comparng he prcng effec of STR wh oher wo sysemac al rsk measures (LTD and T-bea), We nclude STR and eher LTD or T-bea or boh, as well as oher rsk facors, n our regresson equaons n Model In he Model 7, Model 9 and Model 11, he average coeffcen esmaes of LTD are all , wh Newey-Wes -sasc of -2,53,-2.64,-2.68, respecvely. Ths fndng ndcaes, he same wh STR, he LTD s also a negavely prcng facor. Bu hs resuls conradc he Chab-Yo e al. (2018) fndng ha LTD has a posve premum n he US sock markes as nvesor are crash-averse. We beleve ha hs conradcon may due o he dfferen radng sysem and nvesors' sophscaon beween USA and Chna. he average coeffcens on T-bea (al bea) n Model 8, Model 10 and Model 11, are sascally nsgnfcan a convenonal levels. Ths fndng s conssen wh he fndngs repored n Van Oord and Zhou (2016) ha fnd no evdence of a premum assocae wh al bea n USA. Mos mporanly, as shown n Model 9-10, he average coeffcens on STR are all sgnfcan a 5% sgnfcance level. These resuls sugges ha boh TDC and al bea canno accoun for he sgnfcanly negave relaon beween STR and cross-seconal expeced reurn n Chnese sock markes. In summary, conssen wh our porfolo analyss resuls, he cross-seconal regresson resuls show ha he negavely relaonshp beween sysemac al rsk measured by CoVaR and expeced sock reurns (,e, sysemac al rsk puzzle ) n Chnese sock markes canno be explaned by a seres of oher rsk facors such as marke bea, marke capalzaon, book-o-marke rao, momenum, shor-erm reversals, llqudy, urnover, downsde bea, co-skewness, co-kuross, dosyncrac volaly, dosyncrac skewness, dosyncrac kuross,

23 and oher wo sysemac al rsk ncludng lower al dependence and al bea. Our emprcal conclusons suppor he mplcaons of heorecal model n secon Robusness check The paper adops he followng mehods o check he robusness of he conclusons: (1) Tes based on he excluson of fnancal ndusry socks n he sock sample and es based on he excluson of ST and PT companes. Due o he parculary of he fnancal ndusry's balance shee, many emprcal sudes exclude fnancal socks. Ths arcle re-examnes afer excludng he fnancal ndusry socks every monh and fnds ha he sysemac al rsk combnaon n he one-dmensonal porfolo analyss s hgh. The dfference beween he equally-weghed reurns s -0.63% (Newey-wes value s -2.50), and he coeffcen erm for sysemac al rsk n model 1 n cross-seconal regresson s (Newey-wes value s -2.80), whch shows he value and he sgnfcance of he wo boh rse slghly. Afer excludng he ST and PT companes, he dfference n he equvalence yeld of he sysemac al rsk combnaon n he one-dmensonal porfolo analyss s -0.68% (Newey-wes value s -2.69), n he cross-seconal regresson model 1 The coeffcen erm for sysemac al rsk s (Newey-wes value s -3.77), whch s larger han he prevous wo values and sgnfcance. Ths may be due o he fac ha ST and PT companes ofen encouner prof crss. The volaly s so ferce ha he esmaon of he sysemc al rsk s prone o abnormal values. Afer deducon, he emprcal conclusons of hs paper are more sgnfcan. The resuls of wo-dmensonal group analyss and oher cross-seconal regressons show smlar changes, whch are lmed o he reasons for he space. On he whole, afer he elmnaon of he fnancal ndusry and he elmnaon of ST and PT companes, he negave relaonshp beween he sysemc al rsk and he expeced rae of reurn s more sgnfcan. (2) Tesng Dfferen Sample Perods. We dvde he full sample perod n wo ways. Frs, we evenly dvde no wo perods, one before December 2006, he oher afer December 2006 (namely half 1 and half 2). Second, followng Ang e al.(2006) n makng he medan of marke monhly reurns as he creron for judgng bull marke and bear marke, we dvde he sample perod n wo bull marke perod and bear marke perod and conduc he same emprcal process. Due o he lm of space, we only ls he resuls for model 1, model 2, model 6 and model 11 of H-L dfference and cross-seconal regresson (n Table 7) n he above-menoned one-dmensonal porfolo analyss (Table 5). The resuls are gven n Table 8.

24 Table 8 Resuls of robus check abou dfferen sample perods Perod H-L dfferece model 1 STR model 2 STR model 6 STR model 11 STR All -0.61% *** *** *** ** *** (-2.37) (-2.60) (-3.83) (-2.24) (-2.43) half1-0.85% ** *** * * * (-1.97) (-1.98) (-1.91) (-1.92) (-1.94) half2-0.70% *** *** *** *** ** (-1.88) (-2.21) (-3.66) (-2.83) (-2.15) bear -0.52% * * (-1.52) (-1.75) (-1.87) (-1.48) (-1.50) bull -0.73% ** *** *** ** *** (-2.16) (-2.40) (-3.84) (-2.30) (-2.61) 5. Concluson Wh he developmen of fnancal markes, al rsks occur somemes. Dfferen from he marke bea ha measures common rsk, sysemac al rsk maers n ha he al rsk of he marke porfolo conrbues o he al rsk of one sock and may play an mporan role n asse prcng. Ths paper sudes he relaonshp beween sysemac al rsk and sock expeced reurns n Chnese sock markes from he wo aspecs of heorecal model and emprcal sudy. The conclusons are as follows: (1) The heorecal calbraon resuls show ha, unlke U.S. marke, dvdend growh rae volaly s much hgher han consumpon growh rae volaly n Chna, whch causes negave relaonshp beween sysemac al rsk and expeced sock reurns. (2) To bes of our knowledge, hs s he frs paper o nroduce condonal rsk value (CoVaR) o measure he sysemac al rsk of ndvdual socks, and esmae based on he quanle regresson. We show ha CoVaR dffers from he oher wo sysemac al rsk measures ncludng lower al dependence (LTD) and al bea. I conans mporan nformaon ha affecs sock prce, and has a beer prcng effec on equy prces. (3) our resuls sugges ha here s a sgnfcanly negave correlaon beween sysemac al rsk and sock expeced reurns, ha s, here exss sysemac al rsk puzzle n Chnese sock markes. Ths relaonshp s robus by unvarae porfolo-level analyss, bvarae porfolo-level analyss and cross-seconal regresson ha conrollng for a seres of oher rsk facors. n oher words, he negave prcng effecs of

25 sysemac al rsk can be neher explaned by he exsng sysemac al rsk proxes such as lower al dependence, he al bea, nor he common rsk facors such as marke bea, marke capalzaon, book-o-marke rao, momenum, shor-erm reversals, llqudy, urnover, downsde bea, co-skewness, co-kuross, dosyncrac volaly, dosyncrac skewness, dosyncrac kuross and so on. Moreover, he robusness check demonsraes ha he effec of sysemac al rsk on he expeced sock reurn vares a lle n dfferen markes saes, whch s more sgnfcan n he bull marke han n he bear marke. The conclusons of hs paper have grea reference sgnfcance for asse prcng heory research and nvesmen pracce. From he perspecve of asse prcng heory, sysemac al rsk s a sgnfcan facor affecng expeced sock reurns. The hgher he sysemac al rsk, he lower he expeced reurns. The emprcal asse prcng model can nroduce sysemac al rsk as a prcng facor, whch offers a beer explanaon for he sock cross-seconal reurns. From he perspecve of nvesmen pracce, nvesors can choose socks wh lower sysemac al rsks n a porfolo n order o oban hgher fuure reurns. Alhough we conduc a dealed and rgorous sudy on he relaonshp beween sysemac al rsk and expeced sock reurns and sugges he "sysemac al rsk puzzle" exss n Chnese sock markes, we does no have fully explanaon for hs phenomenon, whch may be furher researched from nvesor s psychologcal behavors or marke mcrosrucure feaures. References Adran, T.& Brunnermeer, M. K. CoVaR[J]. Amercan Economc Revew, 2016, 106(7): Ang, A., Hodrck, R. J.& Xng, Y.e al. The Cross-Secon of Volaly and Expeced Reurns[J]. Journal of Fnance, 2006, 61(1): Bal, T. G., Cakc, N.& Whelaw, R. F. Hybrd Tal Rsk and Expeced Sock Reurns: When Does he Tal Wag he Dog[J]. Revew of Asse Prcng Sudes, 2014, 2(4): Chab-Yo, F., Ruenz, S.& Weger, F. Crash Sensvy and he Cross-Secon of Expeced Sock Reurns[J]. Journal of Fnancal and Quanave Analyss, 2018, 53(3): DTragla, F. J.& Gerlach, J. R. Porfolo selecon: An exreme value approach[j]. Journal of Bankng & Fnance, 2013, 37(2):

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