Applied Economerics and Inernaional Developmen Vol.6-3(006) STANDARD & POOR S DEPOSITARY RECEIPTS AND THE MARKET QUALITY OF S&P 500 INDEX FUTURES CHU, Quenin C. * KAYALI, Musafa Mesu Absrac This sudy examines he marke qualiy of S&P 500 index fuures in 50-day periods before and afer he inroducion of Sandard & Poor s Deposiary Receips, SPDRs, on January 9, 993. In a preliminary es of srucure change, resuls fail o reec he null hypohesis ha he empirical disribuions of daily fuures price changes in he wo periods are he same. Marke qualiy is measured by he deviaion of observed prices from he unobserved implici efficien price. A lower pricing error variance from a vecor auoregression (VAR) model implies beer marke qualiy. Using ick-by-ick inra-day S&P 500 index fuures price daa, we find a lower pricing error sandard deviaion of 0.6 percen in he pos-spdr period han in he pre-spdr period (0.3 percen). This finding indicaes an improvemen in he qualiy of he S&P 500 index fuures marke following he inroducion of SPDRs aribuable o improvemen in he microsrucure of he marke. As SPDRs faciliae index arbirage, adusmen of prices in he index fuures marke akes less ime, leading o lower pricing error variance, or improved marke qualiy. In he pos-spdr period, we apply a vecor error correcion model (VECM) o wo pairs of inra-day (fuures, index) prices and (fuures, SPDR) prices. The VECM approach shows beer qualiy in he S&P 500 index fuures marke from is arbirage relaionship wih SPDRs. We conclude ha i is his arbirage relaionship beween index fuures and SPDRs ha improves S&P 500 index fuures marke qualiy afer he inroducion of SPDRs. JEL Classificaion: G3, G4 Keywords: SPDRs, marke qualiy, index fuures, index arbirage.. Inroducion A recen innovaion in financial markes is he rading of exchange-raded funds (ETFs). As an invesmen vehicle, Fabozzi e al. (00) cie wo advanages for rading ETFs over muual funds. Firs, ETFs are coninuously priced and raded when markes are open. Second, invesors of ETFs have beer conrol over axes. During 993, Sandard & * Quenin C. Chu, Professor of Finance, Deparmen of Finance, Insurance, and Real Esae, The Fogelman College of Business and Economics, The Universiy of Memphis, Memphis, TN 385, U.S.A., and Musafa Mesu Kayali, Assisan Professor of Finance, Deparmen of Business Adminisraion, Faculy of Economics and Adminisraive Sciences, Dumlupinar Universiy, Kuahya, Turkey, e-mail:mesukayali@yahoo.com Acknowledgmen: This work is suppored in par by a gran from he Universiy of Memphis, Fogelman College Summer Faculy Research Program. We would like o hank Rober Wood and Thomas McInish for helpful commens. An earlier version of his paper was presened a he Sock Exchange of Thailand, 00, a Conference on he Economics and Financial Prospecs and Derivaives, Naional Chiao Tung Universiy, Taiwan, 00, and a Inernaional Financial Managemen Associaion (FMA) Meeing, Denver, U.S.A., 003. Any remaining errors are our own.
Applied Economerics and Inernaional Developmen Vol.6-3(006) Poor s Deposiary Receips (SPDRs) became a pioneering ETF represening a porfolio of S&P 500 socks and raded on he American Sock Exchange. Since successful rading of SPDRs over he las decade, ETFs represening various sock indexes have been raded on sock exchanges in he US, UK, Hong Kong, and Taiwan. In his sudy, we examine he marke qualiy of S&P 500 index fuures in he 50-day periods before and afer he inroducion of Sandard & Poor s Deposiary Receips (SPDRs) on January 9, 993. According o Hasbrouck s (993) vecor auoregression (VAR) measure of marke qualiy, he pricing error sandard deviaion of S&P 500 index fuures is lower in he pos-spdr period (0.6 percen) han in he pre-spdr period (0.3 percen). This preliminary finding indicaes an improvemen in he qualiy of he index fuures marke afer he rading of SPDRs. This improved marke qualiy is consisen wih he hypohesis ha SPDRs faciliae index arbirage o adus fuures and cash prices following new informaion in he S&P 500 index markes. SPDRs rack he performance of he S&P 500 index quie precisely, and because hey rade on he American Sock Exchange like shares of sock, arbirageurs can easily engage in index arbirage a relaively low cos. Insead of rading a porfolio of underlying socks, hey simulaneously buy or sell SPDRs and sell or buy index fuures o exploi arbirage opporuniies. The prices of index fuures adus more quickly, moving oward an efficien price. This in urn reduces ransiory pricing error and improves he qualiy of he S&P index fuures marke. Index arbirage has an impac on prices in he cash and fuures markes and moves hem oward he efficien price. I faciliaes inegraion and informaion ransmission across markes. The dynamics of index fuures prices should be considered ogeher wih spo prices, represened by he S&P 500 index or SPDRs, o fully capure he effecs of improvemen in he marke qualiy of S&P 500 index fuures. We inegrae Hasbrouck s (993) marke qualiy measuremen and Hasbrouck s (995) muliple markes seing and propose a measuremen of marke qualiy based on a vecor error correcion model (VECM). The measuremen assumes ha one securiy is raded in wo markes. Therefore, i akes ino accoun he error correcion beween fuures and cash markes. Applying a VECM o fuures prices and he S&P 500 index, we find less pricing error variance of S&P 500 index fuures in he pos-spdr period han in he pre- ETF producs include QQQ and Diamonds raded on he American Sock Exchange, TraHK racking Hong Kong Hang Seng index, iftse00 represening FTSE00, and he rading of Taiwan 50 Index on Taiwan Sock Exchange saring June 30, 003. Hasbrouck (993) decomposes he ransacion price of a securiy ino a random-walk componen and a ransiory saionary componen. The random-walk componen may be viewed as he efficien price. The ransiory componen is ermed he pricing error. He proposes he pricing error (ha is, he deviaion of observed ransacion prices from he unobserved implici efficien price) as an alernaive measure of he implici ransacion coss incurred by raders. The variance of he pricing error deermines how closely acual ransacion prices rack he implici efficien price. I is hus a naural measure of marke qualiy; a lower pricing error variance implies beer marke qualiy. 08
Chu, Q.C. and Kayali, M.M. S&P Deposiary Receips and Marke Qualiy of Index Fuures SPDR period. This resul confirms our preliminary finding from VAR analysis ha he qualiy of he index fuures marke improves afer he inroducion of SPDRs. 3 In one final analysis of he source of improved qualiy in he S&P 500 index fuures marke, we apply he VECM analyses o pairs of inraday prices (fuures, index) and (fuures, SPDR) for a 50-day pos-spdr period from March hrough Sepember 30, 993. Pricing error variance is much lower for he pair of (fuures, SPDR) prices. The empirical resuls sugges ha he prices of fuures and SPDRs are more closely relaed. We conclude overall ha i is he index arbirage relaionship beween he fuures and SPDRs markes ha reduces he deviaion of fuures prices from he efficien price and improves he qualiy of he S&P 500 index fuures marke.. Lieraure review SPDRs and Pricing Efficiency. The insiuion of exchange-raded index shares ha closely rack movemens of an underlying index a relaively low cos has promped evaluaion of he improvemen of qualiy in he index markes. Acker and Tian (000) and Elon e al. (00) provide evidence ha SPDRs rack he S&P 500 index quie precisely. To he exen ha hey provide a beer subsiue for rading he marke porfolio, hey may diminish rading aciviy and derac from marke efficiency in oher index producs. Swizer, Varson, and Zghidi (000) analyze pricing efficiency in he S&P index fuures marke before and afer he inroducion of SPDRs using daily and hourly daa. They find ha posiive mispricing is reduced following he inroducion of SPDRs. This resul indicaes ha he index fuures marke has become more efficien. We address he issue by sudying he qualiy of he S&P 500 index fuures marke since inroducion of SPDRs, using Hasbrouck s (993, 995) mehodology o measure marke qualiy. Chu and Hsieh (00) also sudy pricing efficiency and he arbirage relaionship beween SPDRs and he S&P 500 index fuures using rade-by-rade daa. They repor a reducion in boh frequency and duraion of lower boundary violaions since he rading of SPDRs. This indicaes a close price relaionship beween index fuures and SPDRs. These findings are consisen wih he view ha SPDRs faciliae index arbirage in general and shor arbirage in paricular. Fremaul (99) conecures ha index arbirage improves liquidiy by providing buying and selling suppor o correc emporary order imbalances across markes. This argumen implies ha pricing error and is variance will diminish and marke qualiy will improve as a resul of improving efficiency in index arbirage. Pricing Error Variance and Marke Qualiy. Hasbrouck (993) has developed a measure of marke qualiy. In his model, ransacion prices are composed of he implici efficien price and he pricing error. The pricing error is he deviaion of he acual ransacion price from he implici efficien price. He considers pricing error o be he implici cos of rading. If raders should pay fair value, bu hey acually pay he observed ransacion prices insead, he difference beween rade prices and he efficien price should reflec he implici ransacion coss. The variance of he pricing error 3 This finding should no be a surprise. SPDRs offer numerous advanages in execuing index arbirage. Firs, insead of dealing wih a porfolio of 500 securiies, he index arbirage involves only he rading of SPDRs. Second, SPDRs are exemp from he upick rule. The exempion faciliaes shor selling he underlying baske of securiies. 09
Applied Economerics and Inernaional Developmen Vol.6-3(006) measures he precision of racking he efficien price. Thus, he pricing error variance is a summary measure of marke qualiy; a lower variance implies higher qualiy. Hasbrouck (993) shows ha pricing error average sandard deviaions are lower for acively raded larger firms socks. This finding suppors he view ha acive rading induces less pricing error variance and hus leads o beer marke qualiy. Kumar, Sarin, and Shasri (998) analyze he impac of opions rading on he marke qualiy of he underlying securiy. Using Hasbrouck s (993) mehod o measure marke qualiy, hey find ha pricing error variances diminish for he underlying securiy afer opions sar rading. Like Hasbrouck (993), hey observe an increase in rading volume in addiion o enhanced marke qualiy. Hasbrouck (995) invesigaes he price discovery funcion for a securiy raded on muliple markes. Even hough he focuses on he price innovaion in he permanen componen of he securiy price, Hasbrouck (995) noes ha he marke qualiy measuremen relaed o he ransiory componen of pricing error can be exended o a muliple-marke seing. This moivaes our proposed VECM marke qualiy measuremen. 3. Hypoheses. SPDRs provide an excellen insrumen o rack he value of he underlying S&P 500 baske of securiies. Their racking performance is documened in Acker and Tian (000). Raher han use a limied number of securiies o emulae he marke value of he S&P 500 index, arbirageurs can esablish arbirage posiions by rading SPDRs as a proxy for he cash marke. The rading of SPDRs would faciliae he index arbirage procedure and improve he qualiy of he S&P 500 fuures marke. Diamond and Verrecchia (987) noe ha he presence of shor sales consrains in a marke may affec he behavior and he willingness of raders o rade in a paricular marke. Thus, shorselling resricions may impede rading and slow he adusmen of prices o new informaion. Markes wih shor sales consrains are hus less efficien in ha i akes hem longer o reflec full-informaion values. The availabiliy of SPDRs in he S&P 500 index markes faciliaes shor sales as arbirageurs can engage in shor arbirage by aking a shor cash posiion in SPDRs and buying index fuures. This would speed up he price adusmen process o new informaion. Applying a measuremen of marke qualiy derived from a ime series VAR model, we posi: Hypohesis I: The qualiy of he S&P 500 index fuures marke improves afer inroducion of SPDRs. Hasbrouck (993) considers pricing error variance, or marke qualiy, for a single marke in isolaion from oher markes. Index markes, however, are closely linked in he long run by index arbirage, and prices presumably rack a common implici efficien price. Consequenly, we argue ha index fuures prices be sudied no in isolaion from bu ogeher wih cash prices in an invesigaion of he impac of index shares on he marke qualiy of index fuures. Considering hem oinly and accouning for a coinegraion relaionship beween cash and fuures markes enables us o capure he dynamics of index arbirage and is effecs on marke qualiy. Mos sudies ake he spo index value as a cash marke proxy o examine he marke efficiency of index fuures afer index shares sar rading. Park and Swizer (995), Swizer, Varson, and Zghidi (000), and Chu and Hsieh (00) show evidence of improved pricing efficiency, using a cos-of-carry model 0
Chu, Q.C. and Kayali, M.M. S&P Deposiary Receips and Marke Qualiy of Index Fuures and he spo index as he cash marke proxy. We hypohesize less pricing error in a VECM seing for fuures and cash prices: Hypohesis II: Assuming an arbirage relaionship beween fuures and index prices, he qualiy of he S&P 500 index fuures marke improves afer inroducion of SPDRs. Using a cos-of-carry model, Chu and Hsieh (00) examine he pricing efficiency of S&P 500 index markes in he pos-spdr period. They find a very close price relaionship beween SPDRs and index fuures as evidenced by rare ex-ane arbirage profis. These findings suppor he view ha arbirageurs rade SPDRs insead of rading a porfolio of underlying securiies o exploi price discrepancies beween fuures and cash markes hrough index arbirage. To furher idenify he source of any improvemen in he pos-spdr period, we compare marke qualiy measuremens based upon arbirage relaionships beween fuures and he index as well as beween fuures and SPDRs. Therefore, sudying he dynamics of index arbirage beween fuures and index and beween fuures and SPDRs separaely, we hypohesize ha: Hypohesis III: In he pos-spdr period, he marke qualiy of S&P 500 index fuures based on an arbirage relaionship beween fuures and SPDRs will be beer han ha based on an arbirage relaionship beween fuures and he index. 4. Daa and mehodology Daa. We use ick-by-ick daa for S&P 500 index fuures conracs raded on he Chicago Mercanile Exchange (CME), quoe daa for Sandard & Poor s Deposiary Receips raded on he American Sock Exchange (AMEX), and inraday daa for he repored S&P 500 index values. The sample covers a 50-day period from March hrough Ocober, 99, before he inroducion of SPDRs, and a 50-day period from March hrough Sepember 30, 993, afer he inroducion of SPDRs. We choose similar imes of he year in he wo periods o avoid seasonal effecs ha migh have an impac on our empirical resuls. The S&P 500 index values and fuures daa are obained from he Fuures Indusry Insiue Daa Cener (FII). The index daa include dae, ime, and index values provided a approximaely 5-second inervals. We do no apply any adusmen o he repored index value, which represens he value of S&P 500 index baske of securiies. The fuures daa include icker symbol, dae, ime of he ransacion samped o he neares second, expiraion monh of he conrac, and he fuures rade price. Trade prices of fuures conracs are usually recorded afer a change in price. Each year, here are four regular S&P 500 index fuures conracs expiring in March, June, Sepember, and December. For every rading day, only he conrac wih he mos rades is considered. Abou one week before expiraion of he mos acive conrac, i becomes less acive, and he nex nearby conrac becomes he new mos acive conrac. 4 4 Fuures rades marked as cancelled, correced, or insered are removed from he daa se. Observaions repored ou of ime sequence are also eliminaed, as hey are likely o conain errors.
Applied Economerics and Inernaional Developmen Vol.6-3(006) In our VECM analysis, we adus fuures prices o make hem comparable o he repored index value. As fuures prices represen he value of he index in he fuure, he adusmen process discouns fuures prices by a facor reflecing componens of financing cos and dividend yield from he underlying baske of securiies hroughou he life of he fuures conracs. The risk-free rae is he hree-monh Treasury consanmauriy ineres raes obained from Federal Reserve Saisical Release H.5. The dividends per share on he S&P 500 index are obained from S&P s Quarerly Dividend Record Annual Issues from 99 o 993. Garbade and Silber (983) make similar adusmens o calculae he cash equivalen of fuures prices. The quoe daa for SPDRs are rerieved from he New York Sock Exchange s Transacions and Quoes (TAQ) daabase. I includes icker symbol, dae, ime of he quoe samped o he neares second, and rade price. We resric our sample o quoes wih posiive bid and ask prices, spreads, and dephs. We furher error-filer he quoe daa o minimize he reporing errors ha migh affec our empirical resuls when we esimae he pricing error variance. Following Huang and Soll (996), we eliminae bid and ask prices ha change more han 0 percen over he previous price recorded. Afer careful examinaion of quoe daa, however, we do no observe such exreme changes in prices. The average number of quoes per day is 49 in 993. Acker and Tian (000) repor a seasonal paern in price differences beween SPDRs and he corresponding S&P 500 index. The seasonal differences include wo componens. The firs componen is he accumulaed dividends received by SPDRs before he dividend paid by SPDRs. The second componen is he managemen fee. On a quarerly basis, he acual dividend paid by SPDRs equals he dividend received by SPDRs minus he managemen fee. We use a linear inerpolaion mehod o adus he observed SPDRs prices by subracing accrued dividend paymens from he observed SPDRs quoe price. During he period sudied, rading in boh fuures and SPDRs akes place from 9:30 a.m. o 4:5 p.m. Easern ime. The S&P 500 index marke, however, closes 5 minues earlier. We use he MINSPAN procedure proposed by Harris e al. (995) o mach prices of fuures and index for esing Hypohesis II as well as fuures, index, and SPDRs for esing Hypohesis III. This procedure involves minimizing he ime span beween prices of markes by looking forward as well as backward in rading ime. I allows us o obain more synchronous prices wih a minimum ime span. Mehodology. Hasbrouck (993) defines he logarihm of he observed ransacion price as he sum of wo componens: p = m + s () m = m + w () The firs componen, m, follows a random walk and can be viewed as he implici efficien price ha is no observable. I is he expeced end-of-rading securiy value condiional on all he public informaion available a ime. The incremen w is zero-mean, independenly and idenically disribued, and uncorrelaed. Tha is, Ew = 0; Ew = σ w ; and Ew w τ = 0 for τ. These innovaions o he implici efficien price reflec updaes o he public informaion se released beween ime and.
Chu, Q.C. and Kayali, M.M. S&P Deposiary Receips and Marke Qualiy of Index Fuures The second componen, s, is he pricing error reflecing he emporary deviaion of he acual ransacion price from he implici efficien price. I is a covariance-saionary sochasic process whose uncondiional expecaion is zero; ha is, Es = 0, wih a finie variance, Es = σ s. The pricing error erm is no required o be serially uncorrelaed, or be uncorrelaed wih w. I capures ransien microsrucure imperfecions such as efficiency in index arbirage, shor sale resricion, invenory conrol, and price discreeness. The variance of pricing error is he focus of our examinaion of S&P 500 index fuures marke qualiy before and afer he inroducion of SPDRs. Vecor Auoregression Model. Hasbrouck (993) measures pricing error variance by implemening a vecor auoregression (VAR) of reurns and rade variables, such as rade indicaor, or signed rading volume. Since here is no rading volume informaion in he S&P 500 index fuures daa se, we use he reurns and a rade indicaor variable in our analysis. To es our firs hypohesis, we measure he pricing error variance or marke qualiy of he S&P 500 index fuures by esimaing a VAR model of reurns and a rade indicaor wih five lags over wo 50-day periods before and afer he inroducion of SPDRs: F = a F + a F +... + a5 F 5 + b x + b x +... + b5 x 5 + v (3) x = c F + c F +... + c5 F 5 + dx + d x +... + d 5x 5 + v (4) where F F F is he reurn, and F is he logarihm of rade price of index fuures a rade ime. x is he rade indicaor variable a rade ime. A value of + indicaes a buy order, and a value of indicaes a sell order. The error erms are serially uncorrelaed wih Var( v ) = σ, Var( v ) = σ, and Cov ( v, v ) = σ. The variance-covariance marix is obained from simulaneous esimaion of he wo equaions in he VAR model. As here are no bid and ask quoes in fuures ick-by-ick daa, we use Lee and Ready s (99) ick es o classify rades as buys and sells. The ick es is applied o consecuive rade prices. A rade is a buy (sell) if i occurs on an upick (a downick) or a zero upick (zero downick). As in Hasbrouck (993), we eliminae overnigh reurns and se lagged values of he rades and reurns o zero before he firs observaion of each day. Assuming inveribiliy of he VAR model, he reurn and rade indicaor may be expressed as a vecor moving average (VMA) represenaion: F = a0 v + a v +... + a0v 0 + b0 v + b v +... + b0v 0 (5) x = c0 v + c v +... + c0v 0 + d 0v + d v +... + d0v 0 The moving average coefficiens are obained by sepping he sysem forward in response o a uni innovaion as described in Hamilon (994). We runcae he VMA a en lags. The pricing error variance or he measuremen of index fuures marke qualiy is compued by using he esimaed coefficiens from he VMA model and he esimaed variance-covariance marix from he VAR model. 9 ( σ = α σ + α β σ + β σ ) s = 0 (6) (7) 3
Applied Economerics and Inernaional Developmen Vol.6-3(006) 0 where α = a k and β = b k. k = + 0 k = + Vecor Error Correcion Model. To es hypoheses II and III, we measure he pricing error variance of he S&P 500 index fuures by esimaing a VECM of fuures and spo reurns wih five lags: F = µ + A F +... + A5 F 5 + B P +... + B5 P 5 + γ ( F P ) + ε (8) P = µ + C F +... + C5 F 5 + D P +... + D5 P 5 + γ ( F P ) + ε (9) where F and P are he logarihm prices of fuures and cash prices a ime, and F ( F F ) and P P P ) are he reurns. Cash prices are represened ( by eiher he index value or he quoe midpoin of SPDRs. γ and γ are he error correcion coefficiens. The model residuals, ε and ε, are zero-mean, serially uncorrelaed disurbances wih variances Var( ε ) = Ω, Var( ε ) = Ω Cov( ε, ) = Ω ε, and covariance. The variance-covariance marix is obained from simulaneous esimaion of he wo equaions in he VECM. Following Hasbrouck (00), we use quoe midpoins of SPDRs insead of rade prices because hey are posed more frequenly. Quoe midpoins of SPDRs and he repored index value are similar because boh are posed even in he absence of rades o reflec he value of he index. Informaion in quoe revisions of SPDRs will conribue o he adusmen of fuures prices. As in Hasbrouck (995) and Hasbrouck (00, 00), price changes are assumed o be covariance-saionary. This suggess ha hey follow he VMA process: F P = A ε (0) 0 + A ε +... + A0ε 0 + B0ε + B ε +... + B0ε 0 = C ε () 0 + C ε +... + C0ε 0 + D0ε + D ε +... + D0ε 0 The pricing error variance of index fuures is compued as: Ω s = 0 9 ( = 0 φ Ω + φ θ Ω + θ Ω ) where φ = A k and θ = B k. k = + 0 k = + () 5. Empirical resuls Preliminary Resuls. Our analysis is based on he assumpion ha he efficien price behaves similarly in he wo periods examined. In order o compare marke qualiy beween wo esing periods, we need o invesigae wheher here is a srucural change in daily fuures prices from he pre-spdr period o he pos-spdr period. For ha purpose, we firs compue he daily fuures price changes in he wo sudy periods. We perform a Kolmogorov-Smirnov wo-sample es for he same empirical disribuions of daily fuures price changes in he wo periods. The es procedure o compare wo empirical disribuions is specified in Conover (980). The es repors a KS-saisic of 0.58 wih a p-value of 0.89. The es saisic fails o reec he null hypohesis ha he disribuions 4
Chu, Q.C. and Kayali, M.M. S&P Deposiary Receips and Marke Qualiy of Index Fuures of he daily price changes in he S&P 500 index fuures marke are no differen in preand pos-spdr periods. This would sugges ha here is no srucural change in daily fuures prices. Any improvemen in he marke qualiy of S&P 500 fuures in he pos- SPDR period would hus be aribuable o improvemen in he microsrucure aspecs of he S&P 500 index fuures marke, such as index arbirage aciviies and he faciliaion of shor sales. Vecor Auoregression Resuls. We firs esimae summary measures of he pricing error variance or marke qualiy of he S&P 500 index fuures over each 50-day period before and afer he inroducion of SPDRs, using Hasbrouck s (993) VAR model of reurns and a rade indicaor specified in equaions (3) and (4). There are 334,589 rade prices in he pre-spdr period and 333,985 rade prices in he pos-spdr period. The resuls of his VAR analysis are repored in Table I, Panel A. In boh pre-spdr and pos- SPDR periods, here are 50 rading days in 99 and 993. The VAR analysis shows a lower pricing error sandard deviaion for S&P 500 index fuures prices in he pos-spdr period (0.6 percen) han in he pre-spdr period (0.3 percen). These resuls indicae ha S&P 500 index fuures marke qualiy improves afer he inroducion of SPDRs. In oher words, he prices of index fuures rack he efficien price more closely. Tess of Hypohesis I. We es hypohesis I regarding comparison of he marke qualiy of S&P 500 index fuures in he pre- and pos-spdr periods using Hasbrouck s (993) VAR mehodology. This ime, however, we esimae he pricing error variance or marke qualiy for each day in he wo periods. The esimaion mehod obains 50 daily pricing error variances in boh pre- and pos-spdr periods. We use hese 300 daily esimaes o es he null hypohesis ha he mean sandard deviaions in he wo periods are no differen from each oher. The resuls are repored in Table I, Panel B. The mean sandard deviaion of pricing error is 0.37 percen in he pre-spdr and 0.30 percen in he pos-spdr period. Comparison of he mean sandard deviaions using suden -es yields a -saisic of 7.58. This indicaes ha he mean sandard deviaions are significanly differen from each oher a he percen level. We also conduc a nonparameric Wilcoxon rank sum es o make sure ha he resuls are no sensiive o he assumpion of a specific disribuion, obaining a z-saisic of 6.95. These resuls suppor hypohesis I ha pricing error variance is lower in he pos-spdr period han in he pre- SPDR period, indicaing improved marke qualiy in S&P 500 index fuures afer he inroducion of SPDRs. Our findings are consisen wih he view ha SPDRs faciliae rading in he cash marke as well as in he index fuures marke hrough index arbirage. Hasbrouck (993) argues ha as impedimens o rading are removed, prices should more closely mach he implici efficien price. Since index arbirage via individual S&P 500 securiies is an impedimen o rading in he cash marke, he prices of index fuures diverge from he efficien price more and for longer imes following new informaion in he S&P 500 index markes. Pricing error variances are greaer, and index fuures marke qualiy is poorer before he inroducion of SPDRs. Afer SPDRs sar rading, hese impedimens o rading are removed so ha invesors can easily engage in index arbirage. Taking a cash posiion also becomes much easier wih SPDRs so ha arbirageurs can exploi shor as well as long arbirage opporuniies. Consisen wih his predicion, we find lower pricing error variance and beer marke qualiy in he index fuures marke afer he inroducion of SPDRs. Uni Roo and Coinegraion Tess. To perform VECM analysis, we firs check for inegraion orders for logarihms of fuures and index price series, mached by he 5
Applied Economerics and Inernaional Developmen Vol.6-3(006) MINSPAN procedure suggesed by Harris e al. (995), in he pre-spdr and pos-spdr periods using augmened Dickey-Fuller (979) and Phillips-Perron (988) uni roo ess. The uni roo ess wih five lags indicae ha he wo price series are non-saionary in levels and can be characerized as I() processes. They are saionary in firs differences. We es he coinegraion relaionship using Johansen s (99) coinegraion ess. These resuls show ha fuures and index prices are coinegraed wih one coinegraion relaionship, indicaing here is one common sochasic rend. We also check for inegraion orders of fuures, index, and SPDR prices, mached by he MINSPAN procedure in he pos-spdr period. The resuls indicae ha all hree prices are nonsaionary in levels bu saionary in firs differences. When we es for coinegraion beween he pairs of (fuures index) and (fuures, SPDR) prices, we find ha each pair is coinegraed wih one coinegraion relaionship. Chu, Hsieh, and Tse (999) documen similar coinegraion relaionship among fuures, index and SPDR prices. Vecor Error Correcion Model Resuls. Tess of Hypohesis II. Hypohesis II posulaes ha pricing error variance of S&P 500 index fuures from he arbirage relaionship beween fuures and index will be lower or marke qualiy will improve in he pos-spdr period over he pre-spdr period. We es his hypohesis using a VECM of mached prices of fuures and index. We firs esimae he sandard deviaions of pricing error using he VECM of fuures and index prices for each day in he wo 50-day periods before and afer he inroducion of SPDRs. The averages of sandard deviaions in he wo periods are compued o es he null hypohesis ha hey are no differen from each oher. The average number of price pairs idenified by he MINSPAN procedure is,405 per day for he pre-spdr period and,396 for he pos-spdr period. The average ime span is 4.4 seconds for he pre-spdr period and 4.3 seconds for he pos-spdr period. The resuls are repored in Table II. The averages of he pricing error sandard deviaions are 0.34 ( 0-4 ) in he pre-spdr period and 0.7 ( 0-4 ) in he pos-spdr period. Comparison of hese averages using a sandard -es yields a -saisic of 3.63. This resul implies ha he means of he pricing error sandard deviaions in he wo periods are saisically and significanly differen a he percen level. We also perform a non-parameric Wilcoxon rank sum es. The Wilcoxon z-saisic of 3.97 confirms he resul of he -es, indicaing a saisically significan difference beween he means of he pricing error sandard deviaions in he wo periods a he percen significance level. These findings provide suppor for hypohesis II ha pricing error variances of S&P 500 index fuures from an arbirage relaionship wih he index are lower in he pos-spdr period han in he pre-spdr period. Tess of Hypohesis III. To es hypohesis III, we repea he VECM analysis for he pos- SPDR period only. We firs mach he prices of fuures, index, and SPDRs using he MINSPAN procedure. The procedure obains on average 34 price riples per day wih an average ime span of 8.69 seconds. Then we use each pair of (fuures, index) and (fuures, SPDR) prices in he VECM analysis separaely o direcly deermine which pair racks he efficien price mos closely. We esimae he pricing error variance of S&P 500 index fuures by using he VECM of (fuures, index) or (fuures, SPDR) pair prices for each day in he pos-spdr period. The resuls are repored in Table III. The average of 50 daily pricing error sandard deviaions from he VECM of (fuures, index) prices is 0.5 ( 0 3 ). The average from he VECM of (fuures, SPDR) prices is 0. ( 0 3 ). We es he null hypohesis ha hese averages are no differen. The saisic obained from a 6
Chu, Q.C. and Kayali, M.M. S&P Deposiary Receips and Marke Qualiy of Index Fuures paired -es comparing he averages is 3.94, and he z-saisic from a non-parameric Wilcoxon signed ranks es is 3.90. Paired -es and Wilcoxon signed ranks es are used o es Hypohesis III because he comparison is beween wo esimaes of pricing error sandard deviaion on a rading day. Boh ess reec he null hypohesis, indicaing ha he mean pricing error sandard deviaions are saisically and significanly differen a he percen significance level. The pricing error variance of index fuures from is arbirage relaionship wih SPDRs is lower han ha from is arbirage relaionship wih he spo index. I is he arbirage relaionship beween fuures and SPDRs ha moves prices oward he efficien price and reduces pricing errors. This in urn enhances he qualiy of he S&P 500 index fuures marke afer he inroducion of SPDRs. 6. Summary and conclusions This sudy examines he effecs of S&P Deposiary Receips rading for marke qualiy in he S&P 500 index fuures marke in 50-day periods before and afer he inroducion of SPDRs on January 9, 993. We find less pricing error variance or beer marke qualiy in index fuures marke in he pos-spdr period han ha in he pre-spdr period. We aribue he improvemen in marke qualiy o increased efficiency in index arbirage wih rading of SPDRs. Hasbrouck (993) conends ha securiies prices should conform more closely o he efficien price as barriers o rading in hese securiies are reduced. Since arbirageurs would ake a cash posiion by purchasing or shor selling a single SPDRs securiy, he presence of SPDRs reduces impedimens o rading in he cash marke and faciliaes index arbirage. I should be expeced ha deviaions of prices from he efficien price (pricing errors) will be lower and he marke qualiy of index fuures will improve afer SPDRs sar rading. Our finding from he VAR analysis using reurns and rade indicaors of index fuures is consisen wih his argumen, and provides empirical evidence o suppor hypohesis I. Using a VECM analysis based on an inegraion of Hasbrouck s (993, 995) models, we find a lower pricing error variance in he index fuures marke from is arbirage relaionship wih he index in he pos-spdr period han in he pre-spdr period. This resul shows improved index fuures marke qualiy, which suppors hypohesis II. Finally, we examine he close price relaionship beween fuures and SPDRs. Firs, we mach he prices of fuures, index, and SPDRs in he pos-spdr 50-day period by he MINSPAN procedure. Then, we implemen he VECM analysis using pairs of (fuures, index) and (fuures, SPDR) prices separaely. We find a lower pricing error variance of index fuures from is arbirage relaionship wih SPDRs han from is arbirage relaionship wih he index. This resul suggess ha he marke qualiy of index fuures improves due o is arbirage relaionship wih SPDRs. We conclude ha i is his arbirage relaionship beween fuures and SPDRs ha moves prices oward he efficien price, diminishes pricing error and is dispersion around he efficien price, and enhances he qualiy of he S&P 500 index fuures marke afer he inroducion of SPDRs. ETFs have been promoed as muual funds for he nex generaion because of heir increasing populariy over he las decade. This sudy provides empirical evidence supporing he impac of ETF rading on efficien pricing in he underlying index markes. Fuure research would invesigae ETFs advanages beyond beer conrol over axes, coninuous rading, faciliaing index arbirage, and improved marke qualiy. 7
Applied Economerics and Inernaional Developmen Vol.6-3(006) Bibliography Acker, L. F., & Tian, Y. S. (000). Arbirage and valuaion in he marke for Sandard and Poor s deposiory receips. Financial Managemen, 9, 7-88. Chu, Q. C., & Hsieh, W. G. (00). Pricing efficiency of he S&P index marke: Evidence from he Sandard & Poor s deposiary receips. Journal of Fuures Markes,, 877-900. Chu, Q. C., Hsieh, W. G., & Tse, Y. (999). Price discovery on he S&P 500 index markes: An analysis of spo index, index fuures, and SPDRs. Inernaional Review of Financial Analysis, 8, -34. Conover, W. J. (980). Pracical nonparameric saisics, second edion (Wiley, New York). Diamond, D. W., & Verrecchia, R. E. (987). Consrains on shor-selling and asse price adusmens o privae informaion. Journal of Financial Economics, 8, 77-3. Dickey, D. A., & Fuller, W. A. (979). Disribuion of he esimaors for auoregressive ime series wih a uni roo. Journal of he American Saisical Associaion, 74, 47-43. Elon, E. J., Gruber, M. J., Comer, G., & Li, K. (00). Spiders: Where are he bugs? Journal of Business, 75, 453-47. Fabozzi, F.J., Modigliani, F., Jones, F.J., & Ferri, M.G. (00) Foundaions of financial markes and insiuions, hird ediion (Prenice Hall, New Jersey). Fremaul, A. (99). Sock index fuures and index arbirage in a raional expecaions model. Journal of Business, 64, 53-547. Garbade, K. D., & Silber, W. L. (983). Price movemens and price discovery in fuures and cash markes. The Review of Economics and Saisics, 64, 89-97. Hamilon, J. D. (994). Time series analysis (Princeon Universiy Press, Princeon). Harris, F. H. deb., McInish, T. H., Shoesmih, G. L., & Wood, R. A. (995). Coinegraion, error correcion, and price discovery on informaionally linked securiy markes. Journal of Financial and Quaniaive Analysis, 30, 563-579. Hasbrouck, J. (993). Assessing he qualiy of a securiy marke: A new approach o ransacioncos measuremen. Review of Financial Sudies, 6, 9-. Hasbrouck, J. (995). One securiy, many markes: Deermining he conribuions o price discovery. Journal of Finance 50, 75-99. Hasbrouck, J. (00). Salking he efficien price in marke microsrucure specificaions: An overview. Journal of Financial Markes, 5, 39-339. Hasbrouck, J. (003). Inraday price formaion in U.S. equiy index markes. Journal of Finance, 58, 375-400. Huang, R. D., & Soll, H. R. (996). Dealer versus aucion markes: A paired comparison of execuion coss on NASDAQ and he NYSE. Journal of Financial Economics, 4, 33-357. Johansen, S. (99). Esimaion and hypohesis esing of coinegraion vecors in Gaussian vecor auoregressive models. Economerica, 59, 55-580. Kumar, R., Sarin, A., & Shasri, K. (998). The impac of opions rading on he marke qualiy of he underlying securiy: An empirical analysis. Journal of Finance, 53, 77-73. Lee, C. M. C., & Ready, M. J. (99). Inferring rade direcion from inradaily daa. Journal of Finance, 46, 733-746. Park, T. H., & Swizer, L. N. (995). Index paricipaion unis and he performance of index fuures markes: Evidence from he Torono 35 index paricipaion unis marke. Journal of Fuures Markes, 5, 87-00. Phillips, P. C. B., & Perron, P. (988). Tesing for a uni roo in ime series regression. Biomerika, 75, 335-346. Swizer, L. N., Varson, P. L., & Zghidi, S. (000). Sandard & Poor s deposiory receips and he performance of he S&P 500 index fuures marke. Journal of Fuures Markes, 0, 705-76. On line Annex a he ournal web sie Journal published by he EAAEDS: hp://www.usc.es/econome/eaa.hm 8
Chu, Q.C. and Kayali, M.M. S&P Deposiary Receips and Marke Qualiy of Index Fuures Annex Table I Summary Esimaes of Marke Qualiy of S&P 500 Index Fuures Before and Afer SPDRs: Resuls Based on Vecor Auoregression (VAR) Model Time period Pre-SPDR 9/03/0-9/0/0 Pos-SPDR 93/03/0-93/09/30 Panel A: Pricing error variance (σ s ) ( 0 4 ) Pricing error sandard deviaion (σ s ) Number of rade prices 0.050 0.3% 334,589 0.067 0.6% 333,985 Panel B: Mean daily pricing error sd. dev. (σ s ) Number of rading days Average number of rade prices per day 0.37% 50,3 0.30% 50,7 -es Wilcoxon rank sum es = 7.58* z = 6.95* Noe: For each 50-day period before and afer he inroducion of SPDRs, we esimae a VAR model wih five lags o measure he variance of he pricing error (σ s ) specified in equaion (7). We es he null hypohesis ha he summary esimaes of he variance of he pricing error (σ s ) in he wo periods are no differen. * Saisically significan a he percen level. Table II Comparison of Marke Qualiy of S&P 500 Index Fuures Before and Afer SPDRs: Resuls Based on Daily Esimaion of Vecor Error Correcion Model (VECM) Using Mached Prices of Fuures and Index Pre-SPDR Pos-SPDR Time period Mean pricing error sd. dev. (Ω s ) ( 0 4 ) Number of rading days Average number of observaions per day 9/03/0-9/0/0 0.34% 50,405 93/03/0-93/09/30 0.7% 50,396 -es = 3.63* Wilcoxon rank sum es z = 3.97* Noe: For each rading day in a 50-day period before and afer he inroducion of SPDRs, we esimae a VECM wih five lags using mached prices of fuures and index o measure he variance of he pricing error ( Ω s ) specified in equaion (). We es he null hypohesis ha he mean pricing error sandard deviaions in he wo periods are no differen. * Saisically significan a he percen level. 9
Applied Economerics and Inernaional Developmen Vol.6-3(006) Table III Comparison of Marke Qualiy of S&P 500 Index Fuures Afer SPDRs: Resuls Based on Daily Esimaion of Vecor Error Correcion Model (VECM) Using Mached Prices of Fuures and Index or Fuures and SPDRs in 993 Mean pricing error sd. dev. (Ω s ) ( 0 3 ) Number of rading days Average number of observaions per day Paired -es Wilcoxon signed ranks es Fuures-Index 0.5% 50 34 Fuures-SPDR 0.% 50 34 = 3.94* z = 3.90* Noe: For each rading day in he pos-spdr 50-day period, we esimae a VECM wih five lags using mached prices of fuures and index or fuures and SPDRs o measure he variance of he pricing error ( Ω s ) specified in equaion (). We es he null hypohesis ha he mean pricing error sandard deviaions from he wo arbirage relaionships are no differen. * Saisically significan a he percen level. 0