Price distortion induced by a flawed stock market index

Transcription

1 Price disorion induced by a flawed sock marke index Koaro Miwa a and Kazuhiro Ueda b Absrac Despie he inroducion of sophisicaed sock marke indice invesors ofen rade porfolios of he flawed indices o change heir exposure o he marke. In his sudy we show ha hese ransacions cause significan disorions in individual sock price especially during periods of significan marke movemen. As an influenial albei flawed sock index we focus on he Nikkei 5. We find index consiuens ha are excessively weighed on he index experience excessive buying (selling) pressure when he sock marke surges (falls) and experience price correcions afer such periods of change. In conra non-consiuen socks do no experience such rading pressure. Keywords: Sock marke index; Price-weighed index; Trading pressure; Price disorion. JEL classificaion: G; G4; G7; G3. Inroducion Capializaion-weighed or cap-weighed indices have been considered o be adequae ools o evaluae broad marke performance for more han 50 years (Markowiz 959; Sharpe 965; Arno e al. 005). Thu cap-weighed indices have been regarded as represenaive in many sock marke and cap-weighed porfolios have been raded by invesors o increase or decrease heir marke exposure. Laely some sock marke indice such as he S&P 500 and TOPIX have changed o floa-adjused cap weighing which provides a more accurae reflecion of marke movemens. On he oher hand he oudaed and flawed index is sill influenial in some sock markes: Invesors no only consider his ype of oudaed index o be represenaive of he marke hey also rade index porfolios o change heir levels of sock marke exposure. One represenaive example is he price-weighed sock marke index. The value of a price-weighed index is generaed by adding he prices of each of he socks in he index and dividing hem by he oal number of socks. Since he weighing scheme is easy o calculae radiional sock marke indice e.g. he Dow Jones Indusrial Average and Nikkei 5 are calculaed on he basis of his scheme. However he price-based weighing sysem has several drawbacks. Capializaion-weighing assigns he greaes weighs o he larges companie which are ypically among he larges in erms of sale book value cash flow dividend and oal employmen (Arno e al. 005). Conversely price-based weighing seeks o assign he greaes weighs o socks wih high share price even hough firms wih higher share prices do no necessarily make greaer conribuions o he economy. Therefore he price-weighed index can be regarded as less adequae o measure marke performance. Furher while larger-cap socks are likely o be more liquid socks wih higher share prices do no always have greaer liquidiy. Thu he price-based weighing sysem is grealy disadvanageous relaive o he cap-weighing sysem in erms of reducing he price impac of index porfolio ransacions. Considering ha even he ransacions of cap-weighed marke porfolios have a cerain price impac (Barberi e al. 005 and Boyer 0) i is highly likely ha he ransacions of hese flawed index porfolios have an price impac especially on socks ha are excessively weighed on he index also known as overweigh socks. Specifically since invesors ofen rade hese index porfolios o change heir levels of sock marke exposure a sock marke rises (falls) can be accompanied wih increased (decreased) demands for index porfolios. Thu he ousized price impac on overweigh socks can be observed especially when a sock marke moves. In shor invesors demands of he flawed index porfolios o change heir marke exposure could resul in price disorions during periods of significan marke movemen. Thu in his sudy we explore hese price disorions during periods of significan marke movemen o uncover he problem of ransacions of he flawed index porfolios o change invesors a Corresponding auhor Tokio Marine Asse managemen miwa fk@cs.c.u okyo.ac.jp b The Universiy of Tokyo ueda@gregorio.c.u okyo.ac.jp *Publicaion of his paper was suppored by a gran-in-aid from Zengin Foundaion for Sudies on Economics and Finance.

2 marke exposure. As an example of such a marke index we focus on he Nikkei 5 he bes-known Japanese sock marke and one ha uses he oudaed price-based weighing sysem. In erms of he effec of he Nikkei 5 s weighing sysem on sock price Greenwood (008) performs deailed analyses on he effecs of he weighing sysem. The auhor analyzes sensiiviy (bea) of each sock price o average reurns of index consiuens and marke reurn by ime series regression of sock reurns on boh he average reurns and he marke reurns. The auhor shows ha he price of an overweigh sock has high sensiiviy o he average reurns of Nikkei 5 consiuens raher han marke reurns. This resul suggess ha here are invesors demands for Nikkei 5 porfolio ha are no relaed wih marke movemen and hese demands cause excess comovemen among he index consiuens. Since his excess comovemen indicaes price disorion heir findings migh suppor our predicion ha invesors demands (ransacions) of he flawed index porfolios o change heir levels of marke exposure cause significan price impac and disorion. However hese demands for marke exposure are obviously associaed wih sock marke movemen. On he oher hand Greenwood (008) analyzes on price disorions induced by invesors demands for he index porfolio unrelaed o marke movemen. The findings canno provide any evidence on our predicion. To es our predicion in his sudy we firs evaluae he ime-varying price impac from invesors demands for he index porfolios by analyzing each day s cross secional relaion beween sock reurns and he level of overweighing. Then we analyze he relaion beween he daily price impacs and marke reurns.. Theory Socks wih low uni prices are regarded as disressed socks and are sensiive o marke movemen (Campbell 008). Thu low-priced socks could be sensiive o marke reurns. In oher word high-priced socks migh experience lower (higher) reurns han low-priced socks during periods of a marke surge (fall). However we predic ha overweigh sock which end o be high-priced experience higher (lower) reurns during periods of marke surges (falls) because hese socks could experience price pressure from invesors demands for 5 index porfolios o change he level of heir marke exposures in he following manner. A Nikkei 5 fuures ransacion is considered o be he fases and easies way o change exposures o he Japanese sock marke. Since arbirageurs ake long (shor) posiions on 5 index porfolios and shor (long) posiions on Nikkei fuures if here is a price dispariy beween spos and fuure fuure price movemens can affec he spo index hrough shor-erm adjusmens. In line wih his predicion a considerable number of sudies show ha index fuures reurns end o lead sock marke reurns. In erms of he relaion beween he Nikkei 5 Index and is fuures conrac Tse (995) finds ha fuures prices affec he spo index bu no vice versa. Therefore buying (selling) pressure for Nikkei fuures resuls in buying (selling) pressure on index porfolios. Sock marke movemen could reflec invesors demands for marke exposure; specifically marke surges (falls) could reflec increased (decreased) demands for marke exposure. A increased (decreased) demands for exposure o he marke resul in he buying (selling) of Nikkei 5 fuure which induces buying (selling) pressure on index porfolios. Hence we predic ha overweigh socks will experience srong buying pressure when he sock marke rises and srong selling pressure when i falls. Since sronger buying (selling) pressure resuls in higher (lower) sock reurn we formulae he firs hypohesis as follows. Hypohesis. Overweigh socks experience higher (lower) reurns han oher socks when he sock marke rises (falls). As discussed he price behavior menioned above can be observed only among index consiuens. Specifically we predic ha when he sock marke surges (falls) only he index consiuens ha are assigned grea weigh on he price-based weighing sysem will experience higher (lower) reurn while non-index consiuens assigned grea weigh will experience lower (higher) reurns or a lea will no experience higher (lower) reurns. This leads o he second hypohesis. Hypohesis. Non-index consiuens ha are assigned a grea weigh on he price-based weighing sysem do no experience higher (lower) reurns han oher socks when he sock marke rises (falls). The reurn differences beween overweigh index consiuens and oher socks during periods

3 of significan marke movemen canno be jusified by cross-secional differences in sock fundamenals. Therefore i is highly possible ha overweigh socks are overvalued when he sock marke surges and are undervalued when he marke falls: Trading pressure induced by he ransacions for 5 index porfolios could resul in disorions in individual sock price during periods of significan marke movemen. Since misvalued socks are likely o experience price correcions in subsequen period overweigh socks could experience lower (higher) sock reurn especially afer he marke rises (falls). This leads o he hird hypohesis. Hypohesis 3. Overweigh socks experience lower (higher) reurns han oher socks in a subsequen period of a marke surge (fall). 3. Daa and definiions 3. Sample consrucion We obain our sample from he TSE daabase service (hisorical daa is available from he end of July 993). We collec daa from TOPIX consiuen securiie which cover all domesic common socks lised on he Firs Secion of he TSE. We uilize daily daa from he end of July 993 o he end of 03. We divide he sample ino hree sub-periods (July 993 o o 006 and 007 o 03) and perform sub-period analysis. On average here are approximaely 500 firms in our sample for each day. For marke reurn we use he capializaion-weighed reurns of TSE Firs Secion socks. Marke reurns coincide wih TOPIX reurns unil he end of Ocober 005. Afer he end of Ocober 005 TOPIX ransiioned o a free-floa capializaion weighing index. To mainain consisency regarding he definiion of he marke index we calculae unadjused capializaion-weighed index reurns from he beginning of November 005 as marke reurns. 3.. Effec of he price-based weighing sysem The value of he Nikkei 5 is deermined by adding he sock prices of is consiuen divided by heir presumed face values FV muliplying by a consan and dividing he oal by he index divisor. Thu he index weigh w N5 is proporional o he share prices divided by heir face value as follows: 5 Pi Pi w N5 i FV /50 i FV /50 To evaluae he effec of he price-based weighing sysem on cross-secional reurn following he sudy of Greenwood (008) we firs calculae he raio of each sock s weigh in he Nikkei 5 (w ) o is weigh in a capializaion-weighed index (w ). Then we define overweighing (denoed by ) as he log of one plus he raio menioned above (log( + w /w )). As discussed in Greenwood (008) his is no only an inuiive measure of overweighing relaive o he weigh in he cap-weighed index bu also of he price impac from index porfolio ransacions because sock capializaion is posiively associaed wih liquidiy. Then we evaluae he effec of overweighing (he weighing sysem of he Nikkei 5) on cross-secional sock reurns by regressing sock reurns on one-day lagged ( for he previous working day). We repor he effecs of overweighing by separaely regressing he sock reurns of all domesic common socks lised on he Firs Secion of he TSE and consiuens of he Nikkei 5. In analyzing he domesic common sock reurn since he Nikkei index weigh is zero for non-consiuen securiie is zero for approximaely 80% of socks. Thu migh capure no only he effec of he price-based weighing sysem bu also he effec of he consiuen selecion sysem of he Nikkei 5 (he reurn spread beween Nikkei index consiuens and non-consiuens). Therefore when we evaluae he effec of overweighing (he price impac of ) we conrol for he effec of inclusion in he Nikkei 5 (he effec of he consiuen selecion sysem) by including a binary variable (denoed by NK) ha has a value of one if a sock is a Nikkei 5 consiuen and zero oherwise. In addiion we include a cap-weighing facor ha is defined by he log of one plus he weigh of he cap-weighed index (denoed by MW) o conrol for he effec of he denominaor of. We also conrol for he liquidiy effec and measuremen errors in price i.e. bid-ask spreads in securiie in he following ways. To conrol for he liquidiy effec we include he illiquidiy indicaor of Amihud (00) denoed by ILLIQ which is defined as he -rading days average 3

4 absolue value of he sock reurn divided by he average rading value in millions of yen as one of he conrol variables. When here is considerable fund flow o/from he Japanese sock marke illiquid socks could be subjec o a sronger price impac. Thu cross-secional differences in illiquidiy could resul in cross-secional variaions in sock reurn especially when he sock marke moves. Furhermore o conrol for he effec of he bid-ask bounce we include he bid-ask spread (denoed by SPREAD) as a conrol variable. Since he bid-ask spread daa for Japanese socks is no available for over he enire sudied period we esimae he bid-ask spread following he mehodology of Corwin and Schulz (0). Several sudies (e.g. Roll 984 Akins and Dyl 990) demonsrae and sugges ha a daily cross-secional paern is parly aribuable o he exisence of bid-ask spreads in securiies. Therefore for each day we firs regress he daily reurns of sock i over day ( ) on he lagged (overweighing measures as of day -) and he four variables menioned above (lagged NK MW ILLIQ and SPREAD) among all domesic common socks lised on he Firs Secion of he TSE: 0 i NK i β MW i βilliq ILLIQ i βspread SPREAD 0 NK0 MW0 0 0 i () i0 represens he effec of overweighing (he weighing sysem) on sock reurns a day 0 ( ); hu we refer o as he effec of overweighing. A posiive (negaive) indicaes ha overweigh socks experience higher (lower) reurns. In addiion o examine he longer-erm effecs of he price-based weighing sysem s-day-ahead reurns (s= 3) are regressed on as follows: s s i NK NK s i βmw MW s i βilliq ILLIQ s i βspread SPREAD i () i represens he effec of overweighing (he weighing sysem) on he s-day-ahead sock reurn (we refer o i as he s-day-ahead effec of overweighing ). We also repor he effecs of overweighing by regressing he sock reurns of Nikkei 5 index consiuens. In his case does no capure he effec of inclusion in he Nikkei 5. In addiion limiing he invesigaed socks o Nikkei 5 index consiuens can reduce he possibiliy ha he price behavior of non-index consiuens will affec he esimaion of he coefficien of. Therefore we also regress he reurns on among Nikkei 5 consiuens as follows: s s i βmw MW s i βilliq ILLIQ s i βspread SPREAD i (s=0 3) (3) i can be regarded as a proxy for he s-day-ahead effec of overweighing a day. To es hypohesis we also evaluae he price impac of he price-based weighing sysem on non-consiuens. We should esimae weighs for non-index consiuens based on he price-based weighing sysem of he Nikkei 5. As explained he weigh is basically deermined by he share price denominaed by he face value of he share price. However since 00 Japanese socks have no had official face values. Thu he deemed face value which is prediced by considering pas face value corporae even and oher index consiuen has been used o calculae he Nikkei 5. Since we do no esimae face value for non-consiuens sock we uilize he non-face-value adjused weigh for non-consiuens ha are correlaed wih heir share prices. Similar o he definiion of he overweighing facor for Nikkei 5 consiuen we hen calculae he raio of he weigh o is weigh in he capializaion-weighed index; finally we define an overweighing facor for non-consiuen N as he log of one plus he raio 3. To evaluae he effec of N he reurns are regressed on N in addiion o he four conrol variables (NK MW ILLIQ and SPREAD) for socks lised on he Firs Secion of he TSE: N N s i W i β MW i β ILLIQ i β SPREAD N0 3 O 0 MW30 ILLIQ30 SPREAD30 i (4) Ni 0 The effec is also evaluaed by regressing N among non-index consiuen as follows: N N Ni βmw4 MWi βilliq4 ILLIQi βspread4 SPREADi (5) N i0 Approximaely he number of rading days over one monh. The unadjused weighs are likely o be highly correlaed wih face-value adjused weighs; he unadjused weighs for Nikkei 5 consiuens have an approximaely 0.8 correlaion wih official index weighs. 3 N has a value of zero for Nikkei 5 consiuens. 4

5 β and β can be regarded as he effecs of he price-based weighing sysem on non-consiuens. Posiive (negaive) values for β and β mean ha non-consiuen which are assigned greaer weighs in he price-based weighing sysem experience higher (lower) reurns. 4. Resuls 4.. Price impac of overweighing In his secion we show he analysis used o es Hypohesis. Fir we run he following regression o analyze he associaion beween marke reurns and he effec of overweighing: a b e (6) a b e The coefficiens of ( and ) are esimaed using he weighed leas squares (WLS) mehod where he values for he reciprocal of he square of he sandard error of he coefficien in Equaion () and ha of in Equaion (3) respecively are used as weighs. Posiive coefficiens ( b >0 and b >0) indicae ha he price impac caused by he price-based weighing sysem is posiively associaed wih concurren marke reurns. In oher word posiive coefficiens indicae ha overweigh socks experience sronger buying pressure (higher reurns) when he sock marke rises and sronger selling pressure (lower reurns) when he sock marke falls. The resuls are shown in Table shows ha and have a significanly posiive associaion wih marke reurns. This resul can be undersood o indicae ha overweigh socks experience higher reurns han oher socks when he sock marke rises. These findings srongly suppor Hypohesis. Table Effec of overweighing Whole period β (.74) *** 0.33 (4.84) *** 0.35 (6.75) *** 0. (3.8) *** β (3.08) *** 0.48 (4.93) *** 0.56 (6.8) *** 0.43 (8.88) *** 4.. Effec on non-consiuens To es hypohesis we examine wheher he effecs of he price-based weighing sysem on non-consiuen i.e. β and β are no posiively associaed wih concurren marke reurns by regressing hose on. The coefficiens for each regression are esimaed using he WLS mehod where he values for he reciprocal of he square of he sandard error of he coefficiens and in Equaions (4) and (5) respecively are used as weighs. The resuls in Table reveal ha β and β are significanly negaively associaed wih marke reurns ( ). These resuls indicae ha non-consiuen sock which are assigned grea weighs on he price-based weighing sysem experience lower (higher) reurns han oher socks when he sock marke rises (falls). These findings are consisen wih he argumens of Campbell (0) and Liu e al. (0) which show he high-bea characerisic of low priced socks. The findings suppor our view ha high marke sensiiviy of socks ha are assigned a grea weigh on he weighing sysem is only observed among he index consiuen supporing Hypohesis. Table Price impac of overweighing on non-consiuens Whole period βn (9.6) *** (5.07) *** -0.4 (4.84) *** -0.3 (8.5) *** βn (8.00) *** (5.50) *** (4.63) *** -0.3 (8.4) *** 4.3. Price correcion To es Hypohesis 3 we analyze wheher he s-day-ahead effec of overweighing is negaively associaed wih marke reurns ( ). We analyze he one-day-ahead effecs by running he following regressions: 5

6 a a b b b b e e Negaive coefficiens ( <0 and <0) indicae ha overweigh socks experience lower reurns in a subsequen marke surge and higher reurns in a subsequen marke fall. As shown in he previous secion he effec of overweighing is posiively associaed wih concurren marke reurns. Thu he one-day-ahead effecs of overweighing (β and β ) could be associaed wih one-day-ahead marke reurns. As a conrol variable we include one-day-ahead marke reurns. The coefficiens for he models are esimaed using he WLS mehod where he reciprocal of he square of he sandard error of coefficien in Equaion () and ha of coefficien in Equaion (3) are used as weighs. Since he prices migh be slowly correced we also examine he associaion beween marke reurns and he wo- and hree-day-ahead effecs of overweighing by running he following regressions: a b b b e 3 (8) a b b b3 e 3 3 a a 3 3 b b 3 3 b 3 b 3 b3 3 b3 3 The resuls in Table 3 reveal ha he one-day-ahead effecs of overweighing ( and ) have a significanly negaive associaion wih marke reurns ( ). This negaive associaion beween marke reurns and he one-day-ahead effec can be observed in each sub-period. On he oher hand he wo- and hree-day-ahead effecs of overweighing are posiively associaed wih marke reurns. However he absolue values of hese coefficiens are much smaller han ha of he one-day-ahead effec. In sum hese resuls indicae ha alhough sock reurns are higher (lower) for overweigh socks when he marke is up (down) his performance is oally reversed in a subsequen day. This resul can be undersood from he perspecive ha overweigh socks experience srong rading pressure which causes significan individual sock price disorion especially during periods of significan marke movemen and his price disorion is correced on a subsequen day. b4 b e 3 e 3 Table 3 One- wo- and hree-day-ahead effecs of overweighing (a) Regression analysis for Whole period β (.06) *** (6.93) *** -0.8 (6.5) *** -0.0 (4.07) *** β 0.00 (3.00) *** (.0) ** (0.4) 0.04 (.70) *** β (0.3) (3.0) *** (0.0) 0.03 (.48) (7) (9) (b) Regression analysis: β (5.0) *** (6.8) *** -0.9 (5.30) *** -0.5 (9.56) *** β (.74) *** (.33) (0.37) 0.06 (.69) β (0.9) (3.6) *** 0.05 (.) (.56) ** Whole period 5. Conclusion Despie he inroducion of several sophisicaed marke indice some sock marke indices ha apply oudaed flawed weighing sysems are sill influenial and represenaive. Invesors rade he flawed index porfolios o change heir levels of sock marke exposure. In his sudy o highligh he problem of invesors ransacion of he flawed index porfolios o adjus heir exposure o he marke we explore wheher hese ransacion resul in price disorions during periods of significan marke movemen. As a flawed albei influenial marke index we focus on he Nikkei 5 ha uses he oudaed price-based weighing sysem. Invesors demands for Nikkei 5 index porfolios o have he marke exposure could be higher (lower) when marke reurn is higher (lower). In addiion overweigh socks do no always have he

7 higher liquidiy required o beer absorb higher rading pressure han oher socks. Thu overweigh sock i.e. socks ha are overweighed on he index could experience more buying (selling) pressure when he sock marke surges (falls). These excessive rading pressures during periods of significan marke movemen could resul in price disorion for hose socks. Consisen wih our predicion we firs find ha overweigh socks experience higher (lower) reurns when he marke rises (falls). Second hey experience lower (higher) reurns afer such period i.e. heir performance is reversed. These findings sugges ha overweigh socks could experience significan rading pressure resuling in individual sock price disorion when he sock marke moves considerably. In addiion we find ha non-consiuen socks which are assigned grea weigh on he price-based weighing sysem do no experience such rading pressure; his resul suggess ha price disorion among overweigh socks is aribued o price-weighed index porfolio ransacions. The sudy of Greenwood (008) shows ha he exisence of he flawed bu influenial sock indices creaes invesors demands for he index porfolio which are no associaed wih marke movemen and hese demands cause individual sock price disorion. On he oher hand we focus on he demands for he index porfolio o change heir levels of sock marke exposure which are srongly associaed wih marke movemen; our sudy furher exends his argumen by showing ha hese demands for marke exposure also play a key role in he price disorions. In addiion our sudy raises anoher problem regarding he use of oudaed and flawed indices as sock marke indices. The price-weighed index on which we focus as a represenaive flawed index has been regarded as being less adequae o measure marke performance because socks wih higher share prices do no always make greaer conribuions o he economy. In addiion our analyses show ha when he marke is up (down) he index value could be upwardly (downwardly) biased due o he overvaluaion (undervaluaion) of overweigh socks. Thu he daily reurns of he flawed index are biased by no only by he inadequae evaluaion of marke movemen bu also by he price disorion induced by he inadequae weighing sysem. Reference Amihud Y. 00. Illiquidiy and sock reurns: Cross-secion and ime series effecs. Journal of Financial Markes Arno D. Hsu J. and Moore P Fundamenal indexaion. Financial Analyss Journal Akin A. and Dyl E Price reversal bid ask spread and marke efficiency. Journal of Financial and Quaniaive Analysis Barberi N. Shleifer A. and Wurgler J Comovemen. Journal of Financial Economics Boyer B. 0. Syle relaed comovemen: Fundamenals or labels? Journal of Finance Campbell J. Hilscher J. and Szilagyi J In search of disress risk. Journal of Finance Corwin A. and Schulz P. 0. A simple way o esimae bid-ask spreads from daily high and low prices. Journal of Finance Greenwood R Excess comovemen: evidence from cross-secional variaion in Nikkei5 weighs. Review of Financial Sudies Liu Q. Rhee G.and Zhang L. 0. Too good o ignore? A primer on lised penny socks. Working Paper Universiy of Hawaii. Markowiz H Porfolio Selecion: Diversificaion of Invesmens. John Wiley & Son New York. Roll R A simple implici measure of he effecive bid-ask spread in an efficien marke. Journal of Finance Sharpe W sk-aversion in he sock marke: Some empirical evidence. Journal of Finance Tse K Lead-lag relaionship beween spo index and fuures price of he nikkei sock average. Journal of Forecasing