THE IMPACT OF CUBES ON THE MARKET QUALITY OF NASDAQ 100 INDEX FUTURES

Transcription

1 Invesmen Managemen and Financial Innovaions, Volume 3, Issue 3, THE IMPACT OF CUBES ON THE MARKET QUALITY OF NASDAQ 100 INDEX FUTURES Seyfein Unal, M. Mesu Kayali, Cuney Koyuncu Absrac Using Hasbrouck (1993) mehodology and ick-by-ick inraday daa, his paper invesigaes he marke qualiy of Nasdaq 100 Index fuures afer Cubes sared rading on March 10, Marke qualiy is measured by he variance of pricing error. Pricing error is he deviaion of acual ransacion price from he unobserved implici efficien price. By employing a vecor auoregression model, we found a lower pricing error variance in pos-cubes period relaive o ha of pre-cubes period. This finding indicaes an improvemen in he marke qualiy of Nasdaq 100 Index fuures. Key words: Nasdaq, Cubes, index fuures, marke qualiy, pricing error. JEL Classificaion: G14, C Inroducion Exchange Traded Funds (ETFs) are designed o race he performance of an index, in urn allowing he purchase and sale of an enire index in a single ransacion. They also help esablishing a spo posiion a considerably low coss. This will draw invesors aenion owards index racking socks, and lead o a higher rading volume in boh fuures and ETFs. Therefore, we can expec o see a close pricing relaionship beween he spo and fuures prices afer he inroducion of ETFs. While mispricing and low qualiy are aribued o coss associaed wih he spo marke, rading in Cubes may resul in reduced mispricing and increased marke qualiy of Nasdaq 100 Index fuures conracs. As a new invesmen insrumen in spo marke, Cube carries he feaures ha enable i o rack he performance of he Nasdaq 100 Index quie precisely 1. The rading of Cubes on he American Sock Exchange jus like a common sock may le arbirageurs easily esablish an index arbirage posiion a relaively lower coss. Thus, arbirageurs may buy (sell) Cubes, and a he same ime sell (buy) index fuures o ake advanage of arbirage opporuniies. As a resul, index fuures prices may respond more quickly o he new informaion and move oward he efficien price. Finally, his is expeced o reduce pricing error variance and improve he marke qualiy. So far in he lieraure, ample researches have been conduced on he efficiency and he qualiy of fuures markes. These sudies generally employ cos of carry model and bid-ask spread measures (e.g., see Dwyer, Locke, and Yu, 1996; Huang and Soll, 1997). Hasbrouck (1993), on he oher hand, proposes an alernaive marke qualiy measure. By using vecor auoregression (VAR) mehodology, in his sudy, Hasbrouck (1993) compues pricing error variance o analyze he marke qualiy for a sample of NYSE socks. This pioneer sudy of Hasbrouck is widely acceped and followed in he lieraure o analyze marke efficiency (e.g., see Tse and Erenburg, 2003; Kumar, Sarin, and Shasri, 1998). By applying he same echnique wih Hasbrouck and using inraday ick-by-ick daa, his paper invesigaes he marke qualiy of Nasdaq 100 Index fuures in 100-day periods before and afer he incepion of Cubes on AMEX, on March 10, We hypohesize ha he inroducion of Cubes enhances he marke qualiy of Nasdaq 100 Index fuures conracs. Despie he fac ha he innovaors and issuers of ETFs emphasize he advanages of hese insrumens in erms of diversificaion, ransacion coss and ax efficiency, here are few sudies addressing he effec of ETFs on he qualiy of index markes paricularly by uilizing high- 1 Cubes provide several advanages in execuing index arbirage. Firs, insead of dealing wih a porfolio of 100 securiies, he index arbirage involves only he rading of Cubes. Second, Cubes are exemp from he upick rule. Hence by easing he cash-leg of arbirage posiion, he exempion faciliaes shor selling. Seyfein Unal, M. Mesu Kayali, Cuney Koyuncu, 2006

2 118 Invesmen Managemen and Financial Innovaions, Volume 3, Issue 3, 2006 frequency daa. Unlike he oher sudies in he lieraure, o our bes knowledge, his is he firs sudy which adops Hasbrouck s new echnique for measuring marke qualiy and applies i o Nasdaq 100 Index fuures conracs by using ick-by-ick daa. In line wih he hypohesis, we found a lower pricing error variance in Nasdaq 100 Index fuures for he pos-cubes period compared o he pre-cubes period. The resul is an indicaion of improved qualiy of he index fuures marke afer Cubes sared rading. This improvemen in he marke qualiy is consisen wih he expecaion ha, following a new informaion flow o he Nasdaq 100 Index markes, Cubes would help he adjusmen process of fuures and spo prices by faciliaing index arbirage. The paper proceeds as follows: he second secion provides brief discussion abou sudies on pricing efficiency and marke qualiy. Along wih he hypohesis, he relaionship beween he marke qualiy and pricing error variance is also presened in he second secion. Secion hree describes he daa and he mehodology. Empirical resuls are repored and discussed in he fourh secion. The fifh secion provides some furher analyses. Finally, he paper ends wih he conclusion. 2. Pricing Efficiency and Marke Qualiy Marke Qualiy in Index Markes Firs inroduced in Canada, index racking socks have been a major markeing success. They gained so much populariy ha, in microsrucure lieraure, numerous researches have been conduced abou he effec of index shares on marke efficiency and marke qualiy. By using daily daa, Park and Swizer (1995) invesigae changes in he pricing efficiency of index fuures marke, following he inroducion of Torono 35 Index Paricipaion unis (TIPs). They repor a decrease in he mispricing of Torono 35 Index fuures conracs afer TIPs sared rading. This resul is consisen wih he expecaion ha TIPs ease index arbirage aciviy wih is lower cos. By using inraday daa, Hegde and McDermo (2004) examine he liquidiy in he markes for Diamonds and Cubes, and heir underlying socks. Their findings indicae ha he liquidiy of componen socks shows improvemens afer he inroducion of Diamonds and Cubes. They presen evidence ha boh index shares have significanly lower liquidiy coss over he firs 50 days of rading, compared o he porfolio of heir underlying socks. They aribue his resul o he lower adverse selecion coss he shares incur. Acker and Tian (2000) and Elon, Gruber, Comer, and Li (2002), in heir sudies, found ha SPDRs quie accuraely follow he price behavior of S&P 500 index. In ha sense, SPDRs may be beer alernaives for rading he index porfolio. In urn, hey may lower rading aciviy and marke efficiency in oher markes by divering rading aciviy from hose markes. However, Swizer, Varson, and Zghidi (2000) repor a reducion in posiive mispricing of S&P 500 Index fuures marke afer he inroducion of SPDRs. Employing ick-by-ick daa in heir sudy, Kurov and Lasser (2002) examine he pricing relaionship beween Cubes and he Nasdaq 100 Index fuures conracs. They found ha boh he size and frequency of violaions in fuures price boundaries appear o be reduced afer Cubes sared rading. They also repor an increase in he speed of marke response o observed violaions. These imply ha he inroducion of Cubes has led o an improvemen in he Nasdaq 100 Index fuures pricing efficiency. The researchers aribue hese resuls o he increase in he ease of esablishing a spo marke posiion afer Cubes. In a more recen sudy, Tse and Erenburg (2003) invesigae he price discovery and marke qualiy of Cubes. They base heir analysis on he fac ha he NYSE sared rading Cubes in July This is a new milesone in he NYSE hisory since i is he firs ime i opens is door o rading on a securiy represenaive of socks ha are no lised in he NYSE. The auhors repor ha he bid-ask spread is narrower on he AMEX; whereas, ECNs make he mos conribuion o he price discovery process. They found narrower spreads, and improvemens in marke qualiy and price discovery on all rading plaforms afer Cubes sared rading on he NYSE.

3 Invesmen Managemen and Financial Innovaions, Volume 3, Issue 3, Pricing Error Variance as a Measure of Marke Qualiy Hasbrouck (1993) has proposed a new mehod for measuring he qualiy of a securiy marke. His approach decomposes ransacion prices in wo pars, namely random-walk and saionary componens. The random walk is considered o be he unobserved implici efficien price, and he saionary par o be he pricing error. In his approach, pricing error is regarded as he implici cos of rading incurred by raders. Insead of paying is fair value for a securiy, if raders pay he ransacion price, he difference beween he ransacion price and he efficien price should reflec he implici cos of rading. Therefore, he dispersion of his pricing error erm is a naural measure of marke qualiy. This new approach suggess ha he pricing error variance measures how accuraely he ransacion price follows he efficien price. In oher words, he lower he pricing error variance is, he higher he marke qualiy will be. In his sudy, Hasbrouck (1993) deecs lower average sandard deviaion of pricing error for acively raded shares of larger firms. This finding is parallel o he asserion ha acive rading resuls in less pricing error variance, and leads o an improvemen in marke qualiy. Using Hasbrouck s (1993) mehod of marke qualiy, Dunne (1996) compues he pricing error variance of he Irish Gil marke for periods before and afer he inroducion of marke making. In his analysis, he repors ha he Irish Gil marke has become raher compeiive, as evidenced by a lower pricing error variance under he pos-marke-making rading regime. In anoher sudy, using Hasbrouck s mehodology, Kumar, Sarin, and Shasri (1998) examine wheher opions rading affecs he marke qualiy of he underlying securiy. They find a narrowing pricing error variance for he underlying securiy afer he incepion of opions rading. Their resul, similar o Hasbrouck s (1993) finding, shows an increase in rading volume along wih an improved marke qualiy. Examining he impac of he FTSE 100 Index fuures ransfer from oucry marke o elecronic marke on marke qualiy, Tse and Zaboina (2001) repor ha spreads are lower in he elecronic marke, implying higher marke qualiy. Conradicing wih his finding, he pricing error variance measured based on Hasbrouck s (1993) mehod is larger, implying a lower marke qualiy. As a resul of his, i may be concluded ha bid-ask spread alone may no be a good measure of marke qualiy. Hypohesis Cubes provide invesors wih a new low-cos insrumen in racking he performance of he porfolio of Nasdaq 100 socks. Insead of using a limied number of socks for mimicking he Nasdaq 100 index, especially raders can implemen arbirage posiions by carrying ou ransacions on Cubes, represenaive of he spo marke. The rading of Cubes may conribue o he qualiy of he Nasdaq 100 Index fuures marke by easing he index arbirage ransacion. Trading Cubes in he Nasdaq 100 Index markes faciliaes arbirage in general and especially shor arbirage since arbirageurs can ake a shor spo posiion in Cubes and simulaneously a long posiion in index fuures. Hence prices may absorb he new informaion more rapidly. Fung and Draper (1999) noe ha he exisence of consrains on shor selling in a marke is a cause of mispricing. Reducion in he consrains on shor selling should reduce he magniude and frequency of mispricing in he marke. This will lead prices o reflec full-informaion values and beer efficiency across markes. Employing he marke qualiy measuremen obained from a mix of VAR and VMA models, we esed he hypohesis wheher he qualiy of he Nasdaq 100 Index fuures marke enhances afer he incepion of Cubes. 3. Daa and Mehodology The analysis employs ick-by-ick daa for Nasdaq 100 Index fuures conracs raded on he Chicago Mercanile Exchange (CME). The esimaion period in his sudy consiss of wo disinc ime periods splied in accordance wih he incepion of Cubes. The firs period covers 100

4 120 Invesmen Managemen and Financial Innovaions, Volume 3, Issue 3, 2006 rading days from Ocober 13, 1998 hrough March 9, 1999, before he inroducion of Cubes, and he second one covers 100 rading days from March 10 hrough July 30, 1999, afer he inroducion of Cubes. The Nasdaq 100 Index fuures daa are obained from he Insiue for Financial Markes (IFM). Ticker symbol, ime of he ransacion, fuures rade price, ransacion dae, expiraion monh of he conrac are included in he daa se for each ransacion. Transacion prices are generally recorded whenever a change in price occurs. Four regular Nasdaq 100 Index fuures conracs expire in March, June, Sepember, and December. In each rading day, only he mos acive conrac wih he mos rades is aken ino accoun. Approximaely one week before he expiraion, he mos acive conrac becomes less acive, and he nex nearby conrac becomes he new mos acive conrac. Considering he likelihood of conaining errors, rades recorded as cancelled, correced, or insered, and observaions repored ou of ime sequence are dropped from he daa se. The selecion of daa and variables used in he sudy are subjec o he availabiliy of daa and aim of he sudy. Hasbrouck (1993) decomposes he logarihm of he observed ransacion price ino wo componens: m p m s, (1) m 1 w, (2) where, m represens unobservable implici efficien price and i follows a random walk process. I is he expeced value of a securiy a he end-of-rading condiional on all publicly available informaion a ime. The innovaion w as he properies: w ~ iid(0, w 2 ) and E(w w ) = 0 for all. These innovaions represen informaion updaes o he public disseminaed beween ime and 1. s is he pricing error which reflecs he ransiory difference beween observed ransacion price and implici efficien price. I is also a covariance-saionary sochasic process wih zeromean and finie variance (i.e., E(s ) = 0, E(s 2 ) = s 2 ). The pricing error erm is no resriced o be serially uncorrelaed wih iself and w. I is considered a proxy for marke imperfecions such as discreeness, invenory conrol, he non-informaion-based componen of he bid-ask spread, he ransien componen of he price response o a block rade, ec., which are no aken ino accoun explicily in he model. Even hough Hasbrouck (1993) uses rading volume in his sudy for measuring pricing error variance, we employ reurn and rade indicaor as variables in our analysis due o he fac ha no volume informaion is provided for he Nasdaq 100 Index fuures by he IFM. For esing he hypohesis, he pricing error variance or marke qualiy of he Nasdaq 100 Index fuures is measured by esimaing a VAR model of reurn and rade indicaor wih five lags over wo 100-day periods before and afer he incepion of Cubes as follows: P P P... P x x... x, (3) x P P... P x x... x, (4) where P P P 1 is he reurn, and P is he logarihm of rade price of index fuures a ime. x is he rade indicaor variable a ime. The value of +1 and 1 indicaes buy and sell 2 orders respecively. The error erms possess he following feaures: Var( 1 ) 1, 2 Var( 2 ) 2, Cov( 1, 2) 12, Cov( 1, 1j) 0, and Cov( 2, 2 j) 0 for all j. The variance-covariance marix also comes from he VAR model. Since he IFM daa se does no provide informaion on bid and ask quoes, in order o idenify buy and sell orders we applied Lee and Ready s (1991) ick es o rade prices. The es classifies a rade as a buy (sell) if i appears on an upick (a downick) or a zero upick (zero downick).

5 Invesmen Managemen and Financial Innovaions, Volume 3, Issue 3, Following Hasbrouck (1993), overnigh reurns are dropped and lagged values of he rades and reurns are se o zero prior o each day s firs ransacion. Similar o Hasbrouck (1991), we assume ha he VAR model is inverible and he reurn and rade indicaor can be represened by a vecor of moving average (VMA) process as below: P......, (5) x (6) Parallel o Hasbrouck (1993), he VMA coefficiens are esimaed by sepping he sysem forward in response o a uni shock. The VMA model is runcaed a en lags. In order o compue pricing error variance, we use he informaion coming from coefficien esimaes of VMA model and he esimaed variance-covariance marix of he VAR model as follows; s j j j j j , (7) where 10 j 10 k and j k k j 1 k j Resuls Firs, using he informaion from VAR model in equaions (3) and (4), and VMA model in equaions (5) and (6), summary measures of he pricing error variance (or marke qualiy) are esimaed as in equaion (7) for he Nasdaq 100 Index fuures over each 100-day period before and afer he incepion of Cubes 1. There are 60,893 rade prices in he pre-cubes period while here are 92,342 rade prices in he pos-cubes period 2. Esimaion resuls are repored in Table 1. Par A in he able conains esimaion resuls of pricing error variances for pre and pos-cubes periods over 100 rading days. As Par A reveals, we idenified a lower pricing error variance of in he pos-cubes period compared o ha of in he pre-cubes period. Hence our findings show ha marke qualiy of Nasdaq 100 Index fuures improves afer Cubes sared rading, implying ha index fuures prices rack he efficien price more closely 3. A possible explanaion for such a drasic difference in pricing error variances beween he wo periods migh be he learning by rading process. Tha is, as raders are accusomed o he feaures of Cubes and learn how o use hem properly, hey may be able o make beer esimaes of he fair value. Indeed, his process may ake some ime. In ha sense, as he number of rading days exends, i would be normal o observe an increase in he magniude of pricing error variance differences in he boh periods 4. In addiion o compuing pricing error variances for 100-day periods, we also esimaed pricing error sandard deviaions for each day over he wo periods. These esimaes are used o 1 In an aemp o verify ha he resuls are no affeced by he sample size, he analysis is also performed for each 50 and 75-day periods boh before and afer Cubes. Pricing error variances of and are obained for 50-day pre and pos-cubes periods, respecively. Pricing error variances of and are calculaed for 75-day pre and pos- Cubes periods, respecively. These findings are consisen wih hose for 100-day periods, supporing he view ha he qualiy of Nasdaq 100 Index fuures improves following he inroducion of Cubes. 2 The difference in he number of rades beween he wo periods becomes more apparen as moved forward in ime (e.g., 215,607 rades in pos-period versus 114,929 rades in pre-period for 200 rading days). This may suppor he view ha Cubes faciliae index arbirage, which is also consisen wih he findings of Hegde and McDermo (2004), and Tse and Erenburg (2003). 3 See Kayali (2002) and Chu and Kayali (2006) for similar resuls. 4 We compued he raio of pricing error sandard deviaions beween pre and pos-cubes period for 50, 75 and ie.., s 100 rading days. The esimaion resuls are 2.1, 7.2 and 10.1, respecively. These findings, o some exen, suppor our learning by rading argumen. pre s pos

6 122 Invesmen Managemen and Financial Innovaions, Volume 3, Issue 3, 2006 es he null hypohesis ha he mean sandard deviaions in he wo periods are no differen from each oher. The resuls are repored in Par B of he able. The mean sandard deviaion of pricing error is and in he pre-and pos-cubes periods, respecively. The comparison of he mean sandard deviaions using -es yields a -saisic of This indicaes ha he mean sandard deviaions are significanly differen from each oher a he 1 percen level. A non-parameric Mann-Whiney U es, which produced a z-saisic of -5.93, is performed o ensure ha he findings are no sensiive o he assumpion of a specific disribuion. The resuls suppor he hypohesis ha pricing error variance is lower in he pos-cubes period han in he pre-cubes period. This verifies he improvemen in he marke qualiy of Nasdaq 100 Index fuures afer Cubes sared rading. 5. Furher Analysis We also examined wheher our hypohesis is sensiive o srucural change and seasonaliy. The analysis is based on he assumpion ha he efficien price behaves similarly in he wo periods. Thus, o check he validiy of his assumpion, we carried ou a es on if any srucural change exiss in daily fuures prices from one period o he oher. In his case, our null hypohesis is ha he mean daily price changes are no differen in wo periods. The resuls are presened in Par C of he able. The es produces a -saisic of wih a p-value of The es saisic fails o rejec he null hypohesis. This implies ha here is no srucural change in daily fuures prices. Therefore, any improvemen in he marke qualiy afer Cubes may be credied o developmen in he microsrucure aspecs of he Nasdaq 100 Index fuures, such as index arbirage aciviies, he ease of shor sales, ec. Anoher analysis is conduced o es wheher any effec of seasonaliy and sensiiviy o sample period selecion exiss. This is carried ou since he sample periods used in our firs analysis do no cover he same par of he year. Therefore, he same pricing error variance analysis is applied o wo 50-day periods overlapping he same imes of he years. These wo samples cover he daes of Ocober 20 hrough December 31, 1998 for he pre-cubes, and Ocober 21 hrough December 31, 1999 for he pos-cubes periods. The resuls on his analysis are repored in Par D of he able. A lower variance of is compued for pos-cubes period compared o ha of for pre-cubes period. This finding is also consisen wih he previous one ha he marke qualiy improves following he incepion of Cubes. Thus, i can be concluded ha he resuls are no sensiive o seasonaliy and he sample periods seleced. Esimaion Resuls Table 1 Par A: Pre-Cubes Pos-Cubes Time period 98/10/13-99/03/09 99/03/10-99/07/30 Pricing error variance ( s 2 ) Pricing error sandard deviaion ( s ) Number of rade prices 60,893 92,342 Par B: H 0: pre mean H 1: pre mean = pos mean pos mean Mean daily pricing error sd. dev. ( s ) Number of rading days Average number of rade prices per day es = 5.69* Mann-Whiney U es z = -5.93*

7 Invesmen Managemen and Financial Innovaions, Volume 3, Issue 3, Table 1 (coninuous) Par C: Pre-Cubes Pos-Cubes H 0 : pre = pos H 1 : pre pos Mean daily price change saisic = 1.048** p-value p = 0.296** Par D: Time period 98/10/20-98/12/31 99/10/21-99/12/31 Pricing error variance ( s 2 ) Number of rading days * Saisically significan a he 1 percen level. ** Saisically no significan a convenional levels. 6. Conclusion By using Hasbrouck (1993) mehodology and ick-by-ick daa, his sudy invesigaes he effec of Cubes on he marke qualiy of he Nasdaq 100 Index fuures marke for 100-day periods before and afer he incepion of Cubes. We idenified a lower pricing error variance (or beer marke qualiy) for index fuures marke in pos-cubes period compared o pre-cubes period. In parallel o explanaion in he lieraure (e.g., see Fung and Draper, 1999; Fung, Jiang, and Cheng, 2001) ha securiies prices should follow he efficien price more closely as resricions o shor selling of hose securiies are lifed, he incepion of Cubes may ease rading in he spo marke and allow seizing arbirage opporuniies. Tha is, arbirageurs would be able o ake a spo posiion by purchasing or shor selling Cubes. Hence, i can be expeced ha variaion in pricing errors would be lower and in urn he qualiy of index fuures marke would improve afer Cubes sared rading. Our findings are consisen wih his expecaion, and provide supporing empirical evidence. References 1. Acker L.F., Y.S. Tian. Arbirage and valuaion in he marke for Sandard and Poor s deposiory receips // Financial Managemen, pp Chu Q.C., M.M. Kayali. Sandard and Poor s Deposiary Receips and The Marke Qualiy Of S&P 500 Index Fuures // Applied Economerics and Inernaional Developmen, 2006, forhcoming. 3. Dunne P.G. An economeric assessmen of he change in qualiy of he Irish gil marke since he inroducion of marke making // The Economic and Social Review, pp Dwyer G.P., P. Locke, W. Yu. Index arbirage and nonlinear dynamics beween he S&P 500 fuures and cash // The Review of Financial Sudies, pp Elon E.J., M.J. Gruber, G. Comer, K. Li. Spiders: Where are he bugs? // Journal of Business, pp Fung K.W.J., L. Jiang, T.W.L. Cheng. The lead-lag relaion beween spo and fuures markes under differen shor-selling regimes // The Financial Review, pp Fung K.W.J., P. Draper. Mispricing of index fuures conracs and shor sales consrains // Journal of Fuures Markes, pp Hasbrouck J. The summary informaiveness of sock rades: An economeric analysis // Review of Financial Sudies, pp

8 124 Invesmen Managemen and Financial Innovaions, Volume 3, Issue 3, Hasbrouck J. Assessing he qualiy of a securiy marke: A new approach o ransacion-cos measuremen // Review of Financial Sudies, pp Hegde S., J.B. McDermo. The marke liquidiy of Diamonds, Q s, and heir underlying socks // Journal of Banking and Finance, pp Huang R.D., H.R. Soll. The componens of he bid-ask spread: a general approach // The Review of Financial Sudies, pp Kayali M.M. SPDRs and he marke qualiy of he S&P 500 index fuures: A Vecor Error Correcion Model approach o measuring marke qualiy // Unpublished Ph.D. Disseraion, The Universiy of Memphis, U.S.A. 13. Kumar R., A. Sarin, K. Shasri. The impac of opions rading on he marke qualiy of he underlying securiy: An empirical analysis // Journal of Finance, pp Kurov A.A., D.J. Lasser. The effec of he inroducion of Cubes on he Nasdaq-100 indexspo-fuures pricing relaionship // Journal of Fuures Markes, pp Lee C.M.C., M.J. Ready. Inferring rade direcion from inradaily daa // Journal of Finance, pp Park T.H., L.N. Swizer. Index paricipaion unis and he performance of index fuures markes: Evidence from he Torono 35 index paricipaion unis marke // Journal of Fuures Markes, pp Swizer L.N., P.L. Varson, S. Zghidi. Sandard & Poor s deposiory receips and he performance of he S&P 500 index fuures marke // Journal of Fuures Markes, pp Tse Y., T.V. Zaboina. Transacion coss and marke qualiy: Open oucry versus elecronic rading // Journal of Fuures Markes, pp Tse Y., G. Erenburg. Compeiion for order flow, marke qualiy, and price discovery in he Nasdaq 100 Index racking sock // Journal of Financial Research, pp