The Profitability of Index Futures Arbitrage: Evidence from Bid-Ask Quotes

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1 The Profiabiliy of Index Fuures Arbirage: Evidence from Bid-Ask Quoes Kee-Hong Bae a Kalok Chan b Yan-Leung Cheung a a Deparmen of Economics and Finance Ciy Universiy of Hong Kong Hong Kong b Deparmen of Finance Hong Kong Universiy of Science & Technology Clearwaer Bay, Hong Kong May 1998 We hank Ira Horowiz, H.K. Fung, Lilian Ng, Ghon Rhee, K.C. Chan, wo anonymous referees, and seminar paricipans a he Hong Kong Universiy of Science and Technology, he Korea Securiies Research Insiue of he Securiies Dealers Associaion and he Korea Insiue of Finance for heir helpful commens and K.F. Wong for his capable research assisance.

2 Absrac Previous sudies invesigaed he profiabiliy of sock index fuures based on ransacion price daa, and could oversae he frequency of arbirage opporuniies and size of arbirage profis. We obain a daabase for he Hong Kong index fuures and index opions marke ha conains boh real-ime ransacion prices and bid-ask quoes, and examine he bias of idenifying arbirage opporuniies based on ransacion prices. We find ha he percenage of observaions violaing no-arbirage bounds is significanly reduced when we employ bid-ask quoes insead of ransacion prices. This suggess ha sudies which implemen arbirage sraegies based on ransacion prices employ prices from he wrong side of he spread. We find a relaionship beween he frequency of violaions (evaluaed from ransacion prices) and he size of bid-ask spreads in he fuures and opions markes. This indicaes ha a larger mispricing, which may arise when he bid-ask spread is wider, does no necessarily imply profiable arbirage opporuniy. 2

3 1. Inroducion This paper sudies he profiabiliy of arbirage sraegies beween sock index fuures and sock index opions in Hong Kong. While hese index fuures and index opions are quie new and heir rading volumes are relaively ligh compared wih heir counerpars in he Unied Saes, he daabase is ineresing as i conains real-ime bid-ask quoes as well as ransacion prices, so ha we are able o sudy he effec of bid-ask spread on arbirage profiabiliy. Our resuls have general implicaions for sudies ha examine profiabiliy of arbirage sraegies for sock index fuures and opions markes. Numerous sudies have invesigaed he arbirage profiabiliy for sock index derivaive markes, including S&P 500 index fuures (MacKinlay and Ramaswamy (1988)), MMI index fuures (Chung (1991)), Nikkei 225 fuures (Bailey (1989)), Brenner, Subrahmanyam and Uno (1989), and Chung, Kang and Rhee (1993)), and S&P 500 index fuures and opions (Lee and Nayar (1993)). All of hese sudies idenify mispricings based on ransacion prices. Despie he fac ha hese sudies acknowledge he imporance of ransacion coss when evaluaing he profiabiliy of arbirage sraegies, none of hem consider he direc effec of bid-ask spreads on arbirage profiabiliy simply because bid-ask quoaions are no available. 1 There are wo biases in evaluaing arbirage profiabiliy based on ransacion prices. 2 Firs, he frequency of arbirage opporuniies is oversaed. Suppose ha a fuures ransacion akes place a he bid price and based on he bid price, we conclude ha he fuures is underpriced. Therefore, he arbirage sraegy is o buy he underpriced fuures. However, he price ha we could buy a is he ask, no he bid. If we use he correc price (he ask), here migh be no arbirage opporuniy. Second, he 1 While he New York Sock Exchange (NYSE) and he Chicago Board Opions Exchange (CBOE) mainain hisorical records of all ransacion prices and bid/ask quoes, fuures exchanges such as he Chicago Board of Trade (CBT) and he Chicago Mercanile Exchange (CME) record imes and sales daa, which conain only he ime and price of a ransacion if he price is differen from he previously recorded price. Bid and ask quoes appear in his file only if he bid quoe exceeds or if he ask quoe is below he previously recorded ransacion price. Therefore, sudies ha examine sock index fuures do no have a complee record of bid-ask quoes. 2 Phillips and Smih (1980) had a deailed discussion of he effec of bid-ask spread on arbirage profis. 1

4 size of arbirage profis is oversaed. Suppose he fuures is underpriced, so ha he arbirage sraegy is o purchase fuures (a he ask). If only ransacion prices are observed, we migh misakenly use a sale price (a he bid) for a fuures purchase, so ha he purchase price is undersaed and he arbirage profi is oversaed. To correc for he bias, a common approach is o obain an esimae of he bid-ask spread, and adjus he ransacion cos for he esimaed bid-ask spread. This mehod, however, assumes ha he bid-ask spread is consan. An ineresing feaure of he daase for Hong Kong index opions and fuures is ha i conains bid-ask quoes as well as ransacion price daa. This allows us o examine he size and frequency of arbirage opporuniies based on bid-ask quoaions and compare wih hose based on ransacion prices. The analysis is divided ino hree pars. In he firs par, similar o previous sudies, arbirage profiabiliy is evaluaed based on ransacion prices. This will be used as a benchmark case for comparison. The second par is o examine arbirage profiabiliy based on bid-ask quoaions. We consider bid-ask spreads explicily, and require arbirage ransacions o ake place a he righ side of he order (purchases a he ask and sales a he bid). In he hird par, we use ransacion prices bu classify he rades as buyer- or seller- iniiaed based on quoaion informaion. Since rades ofen ake place inside he quoes, he ransacion price an arbirageur could rade a is no necessarily equal o he quoed prices. Evaluaion of arbirage opporuniy will be based on ransacion prices which are of he correc rade direcion. Resuls show ha he frequency of arbirage opporuniies is very sensiive o differen approaches. For example, assuming a ransacion cos of 20 index poins, he percenage of observaions violaing no-arbirage bounds is 18.01% for shor sraegy (sell overpriced fuures and creae synheic long fuures) and 16.45% for long sraegy (buy underpriced fuures and creae synheic shor fuures) when ransacion prices are used. The percenages decline o 2.27% (shor sraegy) and 2.15% (long sraegy) when bid-ask quoaions are used, and o 2.62% (shor sraegy) 2

5 and 4.87% when ransacion prices of correc rade direcion are used. Therefore, using ransacion prices generally oversaes he frequency of arbirage opporuniies by several imes. We find a relaionship beween he likelihood of an arbirage opporuniy (evaluaed based on ransacion prices) and he size of bid-ask spreads in he fuures and opions markes. This suggess ha a larger mispricing, which may arise when he spread is wider, does no necessarily imply profiable arbirage opporuniy. The res of he paper proceeds as follows. Secion 2 develops he basic pricing relaionship beween fuures and opions conracs, and discusses he arbirage sraegy when he pricing relaion is violaed. Secion 3 inroduces insiuional feaures of index opions and fuures in Hong Kong. Secion 4 describes daa and presens empirical resuls. Secion 5 concludes. 2. Profiabiliy of Arbirage beween Index Fuures and Opions 2.1 Fuures-Pu-Call Pariy Boh Hang Seng Index fuures and opions are based on he same underlying sock index and maure on he same expiraion dae. Therefore, a sock index fuures conrac can be replicaed hrough a combinaion of he call, he pu and he riskless asse. In an arbirage-free marke, he fuures price equals he price of he replicaing porfolio. Suppose here is no ransacion cos, he effecs of marking-o-marke procedures are negligible, and ha he index fuures and index opions expire a ime T. Consider a long posiion in he fuures conrac a ime wih a fuures price of F expiring a ime T. The payoff a ime T would be ( S F ), where S T is he sock index price a ime T. I can be shown (Panel A of Table 1) T ha his payoff equals ha of a porfolio consising of a long posiion in he call opion, a shor posiion in he pu opion and a shor posiion of ( F X) (1 ) ( T + r ) in he riskless bond, 3 where X denoes he exercise price of boh index call and pu opions and r denoes he risk-free rae. 3

6 Likewise, he payoff a ime T from a shor posiion in he fuures conrac equals ha of a porfolio consising of a shor posiion in he call opion, a long posiion in he pu opion and a long posiion of ( ) ( ) ( T F X 1+ r ) in he riskless bond. 4 Since he payoffs of fuures and he replicaing porfolio are idenical a ime T, o preven arbirage, he iniial cash flow of seing up he replicaing porfolio (synheic fuures) should be equal o ha of a fuures posiion, i.e., zero. This resuls in he fuurespu-call pariy relaion F X C + P + T ( 1+ r) ( ) = 0 (1) where C and P are call and pu opion premiums, respecively. Equaion (1) could be rewrien as, T F = ( C P )( 1 + r) ( ) + X. (2) A violaion of equaion (2) implies arbirage opporuniy. If fuures is underpriced (observed fuures price is less han he heoreical price), one could arbirage by buying he fuures, selling he call and buying he pu (hereafer called long-arbirage sraegy). If fuures is overpriced (observed fuures price is higher han he heoreical price), one could arbirage by selling he fuures, buying he call and selling he pu (hereafer called shor-arbirage sraegy). An inroducion of ransacion coss will affec he no arbirage relaion in (2) by creaing a band wihin which arbirage is no profiable. Denoe TC as he ransacion coss, a long-arbirage sraegy will generae profis (ne of ransacion coss) only if T F ( C P)( 1 + r) ( ) + X TC. (3) Similarly, a shor arbirage sraegy will generae profis (ne of ransacion coss) only if T F ( C P)( 1 + r) ( ) + X + TC. (4) 2.2 Bid-Ask Spread and Selecion Bias 3 If F is greaer (less) han X, i is borrowing (lending). 4 If F is greaer (less) han X, i is lending (borrowing). 4

7 The arbirage sraegy in he above secion does no ake ino accoun he bid-ask spread. The bid-ask spread is he difference beween he price a which a rader can buy and sell in he marke. Usually, he bid-ask quoes are mainained by he marke makers who provide liquidiy for he marke, and he spread reflecs he cos of immediacy. Marke microsrucure heory suggess ha bid-ask spreads cover hree cos componens: order processing cos, invenory cos, and adverse informaion cos. 5 Any rader who seeks o ransac immediaely in he marke mus incur he cos of he bid-ask spread. Therefore, an arbirageur has o consider he bid-ask spread before he or she decides wheher or no o ake arbirage posiions. For a long-arbirage sraegy (buy a fuures, sell a call, buy a pu), since he purchase akes place a he ask, and he sale akes place a he bid, he long-arbirage ransacions will generae profis only if a b a T F ( C P )( 1+ r) ( ) + X TC (5) where superscrips a and b denoe ask and bid prices, respecively. Equaion (5) demonsraes how he implemenaion of he arbirage sraegy based on ransacion prices will easily lead o selecion bias. Since he sraegy aemps o pick ou undervalued fuures for purchase, and if i is assumed ha he fuures could be purchased a ransacion prices, hen he rading rule will sysemaically pick ou more fuures prices ransaced a he bid raher han a he ask. In oher words, he arbirage rading rules sysemaically use prices from he wrong side of he bid-ask spread (Phillips and Smih (1980)). On he oher hand, he shor-arbirage sraegy (sell a fuures, buy a call, sell a pu), will generae profis only if b a b T F ( C P )( 1 + r) ( ) + X + TC (6) 5 See Demsez (1968) and Tinic (1972) for order processing cos, Soll (1978), Amihud and Mendelson (1980) and Ho and Soll (1981) for invenory cos, and Copeland and Galai (1983) and Glosen and Milgrom (1985) for adverse informaion cos. 5

8 and he sraegy aemps o pick ou overvalued fuures for sale. If we execue he arbirage sraegy based on ransacion prices, he rading rule will sysemaically pick ou more fuures prices ransaced a he ask raher han a he bid. Wihou observing ime-samped bid-ask quoes, here is no saisfacory way o handle he selecion bias problem. A common approach is o obain an esimae of he bid-ask spread, adjus he ransacion coss for he esimaed bid-ask spread, and hen idenify mispricings based on adjused ransacion coss. The bid-ask spread could be esimaed based on a sample of bid and ask quoaions (Phillips and Smih (1980), Yadav and Pope (1990)). In he case where bid-ask quoaions are no observed, esimaors could be derived based on momens of ransacion prices (Roll (1984), Soll (1989) and Smih and Whaley (1994)). A drawback of his approach is ha i assumes he bid-ask spread is consan. If bid-ask spreads differ across ransacions, hen arbirage rading rules sysemaically pick ou ransacions for which he bid-ask spread is large, when he arbirage ransacions may in fac be unprofiable. Therefore, even afer adjusing he ransacion coss wih he average bid-ask spread, he frequency and size of mispricings may sill be oversaed. The selecion bias associaed wih using ransacion prices can be avoided if we evaluae he arbirage opporuniy based on bid-ask quoaions. Arbirage profis will also be appropriaely compued as arbirage ransacions ake place a he righ side of he spread. The frequency and size of mispricings are, hus, expeced o be smaller when bid-ask quoes are used o generae arbirage signals han when ransacion prices are employed. Using bid-ask quoaions, however, may undersae he size and frequency of mispricings. This is because rades ofen ake place inside he quoes, raher han a he quoes. As a resul, he spread ha an arbirageur acually incurs is smaller han he one ha being quoed in he marke. The effecive spread is, herefore, lower han he quoed spread. To correc for his problem, we use ransacion prices and aemp o classify he rades as buyer- or seller-iniiaed based on quoaion informaion. Evaluaion of arbirage opporuniy is based on ransacion prices which are of he correc 6

9 rade direcion. Compared wih oher wo approaches (based on ransacion prices and bid-ask quoes), his approach should yield he smalles bias in esimaing he frequency and size of mispricings. 3. Hang Seng Index Fuures and Index Opions Boh Hang Seng Index (HSI) fuures and opions conracs represen derivaives claims wih he HSI as he underlying index. The HSI is a value-weighed index composed of he 33 larges and mos acive lised companies in Hong Kong. 6 The index is he mos widely quoed in Hong Kong and is used as a proxy for he marke as a whole. In recen years, he HSI has represened 75% of oal marke value and 70% of oal marke urnover. HSI fuures were inroduced by he Hong Kong Fuures Exchange (HKFE) in 1986, and proved o be a huge success. In 1987, he new conrac became he hird mos acively raded index fuures conrac in he world, wih rading volume rising o 3.6 million conracs. The rading volume, however, shrank from he peak of 3.6 million o less han 150,000 conracs afer he marke crash of Ocober As he sock marke began o rise in 1992, fuures rading became acive again wih 1.03 million conracs for he year, and winessed he highes rading volume record of 4.9 million conracs in During ha year, he highes daily volume was abou 42,000 conracs and he average daily volume was abou 17,000 conracs. HSI opions conracs were launched in March The rading was relaively hin in 1993, wih a daily average of only several hundred los. The new conracs gained populariy in he following year and a oal of 600,000 conracs were raded in The highes daily rading volume was abou 9,000 conracs and he average daily volume was abou 2,500 conracs. Table 2 summarises basic feaures of he HSI fuures and opions conracs. There are four mauriy monhs for boh fuures and opions conracs: spo monh, he nex calendar monh, and he nex wo calendar quarer monhs. The las rading day is he business day preceding he las business day of he 6 The HSI is compiled by HSI Services Ld, a subsidiary of Hang Seng Bank. 7

10 monh. The conrac size is HK$50 per index poin. All selemen is in cash, wih he selemen made on he firs business day afer he las rading day. All conracs are subjec o a daily price limi of abou 10 percen of he conrac value. An iniial margin is required when he conrac is opened, and margins can be posed in he form of cash or ineres-rae bearing securiies. There are wo rading sessions for boh conracs from Monday o Friday, 10:00 a.m. - 12:30 p.m. and 14:30 p.m. - 16:00 p.m. (local Hong Kong ime). The rading of boh fuures and opions is conduced in he same rading room, so ha fuures and opions raders see he rading aciviies of each oher. Trading in he fuures marke is conduced by he open oucry sysem, while rading in he opions marke is operaed by he dealership sysem. The curren bid, ask and he las ransacion prices are displayed in he exchange s compuer sysem, being inpu by an HKFE official on a real-ime basis from he quoes on he exchange floor. Several conrac feaures are noeworhy. Firs, he HSI opions are European opions. Therefore, here is no early exercise opion ha will desroy he fuures-pu-call pariy relaion. Second, he HSI fuures and opions conracs expire in he same monh. The arbirage posiion can be, herefore, unwind simulaneously for boh of hem. Third, boh conracs are raded a he same ime, and his avoids complicaions arising from he nonsynchronous rading hours. Since he exisence of ransacion coss may reduce profiable arbirage opporuniies, we will consider he sensiiviy of arbirage profis o differen levels of ransacion coss in empirical ess. For fuures rading, based on conversaions wih floor raders in he HKFE, one-way commission is esimaed o be abou $HK80 per conrac for insiuional invesors. The broker commission includes rading fees charged by he Securiies and Fuures Commission. 7 For index opions ransacions, commission coss vary wih he price of he opion. Minimum commission will be payable on all rades a he lesser of 1) 1 percen of he conrac value rounded up o he neares Hong Kong dollar wih a minimum of $HK30 and 2) $HK100. Index opion rading requires he paymen of commissions 7 The curren rading fees include: 1) Exchange Fee of $HK10.00, 2) SFC Levy of $HK1.00, and 3) Compensaion Fund Levy of $HK0.50, oalling $HK

11 wice: a he ime of he iniial rade and a he ime of closing ou he posiion. If an opion posiion expires unexercised, only one-way commission is required. If an opion is exercised on expiraion day, an exercise fee of $HK10 per conrac is required. As a conservaive esimae, a maximum commission of $HK150 is assumed. Given he above assumpions regarding brokerage commission, and ignoring marke impac coss, each arbirage sraegy requires abou $HK540 commission coss (10.8 index poins), which include $HK 80 for fuures posiion, and $HK 460 for call and pu opion posiions. 8 Since margins can be posed in he form of ineres-bearing securiies, we ignore he ineres forgone on margin deposis. Empirical analysis on arbirage profiabiliy will be conduced for differen levels of ransacion coss ranging from 10 o 80 index poins 4. Empirical Resuls 4.1 Daa and Preliminary Saisics The daa are obained from he Hong Kong Fuures Exchange (HKFE) for Hang Seng Index (HSI) fuures and opion conracs for he sample period from Ocober 1, 1993 o June 30, The daabase comprises rade-and-quoaion records for he HSI fuures and opions of all differen mauriies and exercise prices. All rade-and-quoaion records are ime-samped o he neares second. The rade records conain he prices and number of shares raded for all ransacions. The quoaion records conain he complee hisory of bid and ask prices recorded in he sequence hey are quoed. Since HKFE inpus ransacion prices and bid-ask quoes ino a compuerized price reporing sysem as soon as hey are called ou on he marke floor, he reporing lag is believed o be only a few seconds. 8 Since he arbirage sraegy calls for he exercise of eiher a call or pu opion alone, only one exercise fee is incurred. 9

12 For he risk-free ineres rae ha is required for fuures-pu-call pariy, we employ he Hong Kong Iner-Bank Offered Rae (HIBOR) mauring on he day closes o he expiraion dae of he fuures and opion conrac. Table 3 repors he percenage disribuion of bid-ask spreads (in index poins) for HSI fuures and opions. For index fuures, 80.83% of observaions have a spread of less han 5 index poins, and he median spread is 5 poins. For boh pus and calls, he disribuion is more evenly disribued, and he median spread is 20 index poins. Therefore, pus and calls have higher dollar spreads han fuures. Since he prices of opions are generally smaller han hose of fuures, his suggess ha he percenage bid-ask spreads for pus and calls are much higher han for fuures Arbirage Sraegies based on Transacion Prices We will firs evaluae arbirage profiabiliy based on ransacion prices. We creae a sample of observaions for fuures, pus and calls ha are mached in he expiraion dae and exercise price (for opions). The sample is consruced so ha whenever a new ransacion price observaion comes in from eiher a pu or call, he price is mached wih he mos recen ransacion prices of he oher wo markes. To miigae he sale price problem, he maching ransacion prices are required o be wihin en minues of each oher. Suppose we have Ocober fuures raded a 2:58 p.m. and 3:08 p.m., Ocober call raded a 2:59 p.m. and 3:10 p.m., and Ocober pu raded (wih he same exercise price) a 3:04 p.m. and 3:26 p.m. We will hen have wo valid observaions as we mach 1) pu a 3:04 p.m., call a 2:59 p.m. and fuures a 2:58 p.m.; 2) call a 3:10 p.m., pu a 3:04 p.m. and fuures a 3:08 p.m. For he pu ransacion a 3:26 p.m., since here is no fuures rade wihin 10 minues of he rade, no valid observaion is obained. This maching process resuls in 2,560 observaions, which will be examined for arbirage opporuniies. A long-arbirage sraegy will be implemened for undervalued fuures by buying a fuures, selling a call and buying a pu, and he ne profi (arbirage profi ne of ransacion coss) is compued as 10

13 ( )( ) ( T C P 1+ r ) + X F TC (7) where TC is he assumed ransacion cos. A shor-arbirage sraegy will be implemened for overvalued fuures by selling a fuures, buying a call and selling a pu, and he ne profi is compued as T F ( C P)( 1 + r) ( ) X TC. (8) Table 4 repors he percenage violaions and ne profis of hese arbirage sraegies for a range of ransacion coss from 0 o 80 index poins. No surprisingly, when a zero ransacion cos is assumed, he percenage violaions for he long sraegy and he shor sraegy add up o almos 100%. This is because unless he prices conform exacly o he fuures-pu-call pariy, he fuures conrac is eiher overvalued or undervalued. A ransacion coss of 20 index poins, he percenage violaion is 18.01% for shor sraegy and 16.45% for long sraegy. Even when ransacion coss of 40 index poins is assumed, he frequency of violaions is sill economically significan % for shor sraegy and 6.13% for long sraegy. As for arbirage profis, boh mean and median are repored. Since here are some ouliers, median profis are more reliable for inference. The median profis range from poins o poins for shor sraegy, and from poins o poins for long sraegy, depending on levels of ransacion coss assumed. Overall, arbirage opporuniies are abundan. This may reflec he fac ha we do no consider he impac of bid-ask spread, and ha arbirage ransacions ake place a he wrong side of he spread. We will herefore evaluae he arbirage sraegies based on bid-ask quoaions. 11

14 4.3 Arbirage Sraegies based on Bid-Ask Quoes This secion examines arbirage opporuniy based on bid-ask quoaions. To keep he sample size he same, for every ransacion price used in Secion 4.2, we idenify he neares bid and ask quoes. Since a shor arbirage sraegy requires selling a fuures (a bid), buying a call (a ask) and selling a pu (a bid), while a long arbirage involves buying a fuures (a ask), selling a call (a bid) and buying a pu (a ask), he maching crieria are very specific abou wheher he bid or ask quoe is used. A valid observaion has o be eiher an observaion comprising fuures bid price, call ask price and pu bid price, or an observaion comprising fuures ask price, call bid price and pu ask price. The ne profi o he long-arbirage sraegy is deermined by b a T a ( )( ) ( C P 1 + r ) + X F TC, (9) while he ne profi o he shor-arbirage sraegy is deermined by b a b T F ( C P )( 1 + r) ( ) X TC. (10) Table 5 repors he percenage violaions and ne profis o arbirage sraegies. Compared wih Table 4, he frequency of arbirage opporuniies dramaically declines. A ransacion coss of 20 index poins, he percenage violaion is 2.27% for shor sraegy and 2.15% for long sraegy. A ransacion coss of 40 index poins, he percenage is 0.94% for shor sraegy and 1.02% for long sraegy. These represen abou 80% reducion from hose repored in Table 4. We could compare Tables 4 and 5 o examine he effeciveness of he approach ha evaluaes arbbirage opporuniy based on ransacion prices and akes ino accoun he impac of bid-ask cos hrough esimaed spread. Wihou observing real ime bid-ask quoes daa, previous sudies (Phillips and Smih (1980)), Yadav and Pope (1990) and Lee and Nayar (1993)) obain an esimae of bid-ask spread, and adjus he one-way ransacion cos for a half of he bid-ask spread. In his sudy, since he median bid-ask spreads are 5, 20 and 20 index poins for fuures, pu and call, one-half of he oal spread is abou 22.5 index poins. Therefore, if we assume ha he oher ransacion cos (e.g. commission cos) is 10 index poins, hen adding 22.5 index poins will increase he oal ransacion 12

15 cos o 32.5 index poins. From Table 4, his implies percenage violaions of 8.95% for shor sraegy and 9.69% for long sraegy (30 index poins). On he oher hand, since using bid-ask quoaions already accouns for he difference beween he purchase and sale price, here is no need o add he bid-ask spread o he ransacion cos in Table 5. Assuming ha he oher ransacion cos is 10 index poins, his implies percenage violaions of 4.73% for shor sraegy and 3.87% for long sraegy. Therefore, he frequency of arbirage opporuniies is sill higher when ransacion prices are used han when bid-ask quoes are used, even if ransacion coss are adjused for he esimaed bid-ask spread. A similar conclusion is reached for oher levels of ransacion coss. A possible reason for his resul is ha he size of he bid-ask spread is no consan bu varies over ime. Furhermore, when he spread is widened, arbirageurs are unlikely o sep ino he marke, so ha he mispricing persis. Therefore, based on ransacion prices, we are likely o pick ou some seeming arbirage opporuniies which are, in fac, no profiable once we consider he cos of he spread. We will explore his possibiliy in laer secions. 4.4 Arbirage Sraegies based on Feasible Transacion Prices Since rades could ake place inside he quoes, raher han a he quoes, he spread ha an arbirageur acually incurs is smaller han ha quoed in he marke. This secion examines arbirage profiabiliy based on feasible ransacion prices, he ransacion prices ha ake place a he righ side of he spread and are feasible for arbirage ransacions. For each ransacion price, we aemp o check he direcion of he rades. Our rade-classificaion scheme is similar o hose used by Lee and Ready (1991) and Easley, O Hara and Srinivas (1994). We compare rade prices wih he bid-ask quoes in neighboring 10-minues. Trades occurring in he lower half of he spread, a he bid or below are classified as sells, and rades occurring in he upper half of he spreads a he ask or above are classified as buys. Trades occurring a he midpoin of he spread are no classified. A summary of he rade classificaion is repored in Table 6. I is ineresing o noe ha for fuures, more han 90% of he 13

16 rades ake place a he bid-ask quoes (46.41% a he ask and 48.98% a he bid). On he oher hand, rades for he pu and call ofen ake place inside he spread. Compared wih fuures, call and pu opions have many ransacion prices whose rade classificaion canno be deermined since hey are equal o he midpoin of he bid-ask spread (7.42% for he pu and 7.62% for he call). This drasically reduces he number of feasible ransacion prices for examinaion. Table 7 repors he frequency of arbirage opporuniies based on feasible ransacion prices. Overall, here are only 267 valid observaions o be examined for he shor sraegy, and 258 valid observaions for he long sraegy. No surprisingly, he percenage violaions are generally larger han hose in Table 5, bu smaller han hose in Table 4. For example, a ransacion coss of 20 index poins, he percenage is 2.62% for shor sraegy and 4.87% for long sraegy. A ransacion coss of 40 index poins, he percenage is 1.50% for shor sraegy and 2.25% for long sraegy. Overall, when we use feasible ransacion prices, arbirage opporuniies are sill slim. 4.5 Sensiiviy Tess Table 8 repors some sensiiviy ess o check he robusness of he resuls when ransacion prices and bid-ask quoaions of fuures and opions are mached based on finer inervals. We require he prices o be wihin 5 minues and 1 minue of each oher respecively. This obviously resuls in fewer observaions. Neverheless, he frequency of mispricing opporuniies varies across differen approaches in a paern similar o before -- he percenage violaions are he highes for ransacion prices, lower for feasible ransacion prices, and he lowes for bid-ask quoaions. 4.6 Relaionship Beween Arbirage Opporuniies and he Size of he Bid-Ask Spread A problem associaed wih using ransacion prices in evaluaing arbirage opporuniy is ha he bid-ask cos is ignored. I is obvious ha when bid-ask spread is wider, a larger deviaion from fuures-pu-call pariy is required o induce arbirageurs o sep ino he marke. Therefore, when 14

17 using ransacion prices, we are likely o pick ou some seeming arbirage observaions ha migh no be profiable once we consider he cos of he spread. To examine his possibiliy, we regress he arbirage profis on bid-ask spreads in fuures and opions markes. The arbirage profis are compued based on ransacion prices and ne of ransacion coss of 10 index poins. Table 9 repors regression resuls for several differen specificaions. We also include number of days o mauriy and moneyness of he opions o conrol for heir possible effecs on arbirage profis. Evidence generally indicaes ha ne arbirage profis are posiively and significanly relaed o bid-ask spreads in fuures and opions markes. Table 10 repors logi regressions of he probabiliy of arbirage opporuniy on he bid-ask spreads, where he binary choice variable equals one if he arbirage profis ne of ransacion coss of 10 index poins is posiive and zero oherwise. Esimaed coefficiens for he bid-ask spreads are all posiive and significan. This is consisen wih he argumen ha he seeming arbirage opporuniy is due o he wider bid-ask spread in he markes. 5. Conclusion This sudy examines he profiabiliy of arbirage sraegies beween index fuures and index opions in Hong Kong. A unique feaure of his sudy is ha we uilize real ime bid-ask quoes in addiion o ransacion prices in evaluaing he profiabiliy of arbirage sraegies. Wih bid-ask quoes, we ake ino accoun he bid-ask spread explicily in idenifying arbirage opporuniies. This circumvens he selecion bias problem inheren in sudies using ransacion prices alone. We evaluae he frequency and size of arbirage opporuniies based on hree approaches: (i) ransacion prices, (ii) bid-ask quoes, (iii) ransacion prices ha are checked for rade direcion using bid-ask quoes. Overall, he percenage of observaions violaing no-arbirage bounds is dramaically reduced under (ii) and (iii) relaive o (I). We also find a relaionship beween he likelihood of arbirage opporuniy (evaluaed based on ransacion prices) and he size of bid-ask spreads in he 15

18 fuures and opions markes. This suggess ha he reason for he appearance of some arbirage opporuniies is ha arbirageurs would no sep ino he marke when he spread is large. Therefore, hose seeming arbirage opporuniies migh in fac be no profiable. As far as we know, his sudy represens he firs aemp o examine index arbirage profiabiliy based on bid-ask quoaions. I has a broad implicaion for earlier sudies ha examine profiabiliy of arbirage sraegies for sock index fuures and opions markes. Our resuls underscore biases incurred when ransacion prices are employed o invesigae arbirage opporuniy. Therefore, sudies ha evaluae arbirage opporuniy based on ransacion prices should be cauious in inerpreing heir resuls. 16

19 References Amihud, Y. and H. Mendelson, 1980, Dealership marke: Marke-making wih invenory, Journal of Financial Economics 8, Bailey, W., 1989, The marke for Japanese sock index fuures: Some preliminary evidence, Journal of Fuures Markes 9, Brennan, M. J. and E. S. Schwarz, 1990, Arbirage in sock index fuures, Journal of Business 63, S7- S32. Brenner, M., M. G. Subrahmanyam and J. Uno, 1989, The behavior of prices in he Nikkei spo and fuures marke, Journal of Financial Economics 23, Chung, Y. P., 1991, A ransacions daa es of sock index fuures marke efficiency and index arbirage profiabiliy, Journal of Finance 46, Chung Y. P., J. K. Kang and S. G. Rhee, 1993, Sock marke microsrucure and index-fuures arbirage in Japan, Working Paper, The Universiy of Rhode Island. Copeland, T. and D. Galai, 1983, Informaion effecs on he bid-ask spread, Journal of Finance 38, Demsez, H., 1968, The cos of ransacing, Quarerly Journal of Economics 82, Easley D., M. O Hara and P.S. Srinivas, 1994, Opion volume and sock prices: Evidence on where informed raders rade, Working Paper, Cener for Economic Policy Research, London. Glosen, L. R. and P. R. Milgrom, 1985, Bid, ask, and ransacion prices in a specialis marke wih heerogeneously informed raders, Journal of Financial Economics 14, Ho, T. and H. Soll, 1981, Opimal dealer pricing under ransacions and reurn uncerainy, Journal of Financial Economics 9, Lee, J. H. and N. Nayar, 1993, A ransacion daa analysis of arbirage beween index opions and index fuures, Journal of Fuures Markes 13, Lee, C. and M.J. Ready, 1991, Inferring rade direcion from inraday daa, Journal of Finance, 37, MacKinlay, A.C., and K. Ramaswamy, 1988, Index-fuures arbirage and he behavior of sock index fuures prices, Review of Financial Sudies 1, Phillips, S. M. and C. W. Smih, 1980, Trading coss for lised opions: The implicaions for marke efficiency, Journal of Financial Economics 8, Roll, R., 1984, Inferring he componens of he bid/ask spread in an efficien marke, Journal of Finance 39,

20 Smih, T. and R. Whaley, 1994, Esimaing he effecive bid/ask spread from ime and sales daa, Journal of Fuures Markes 14, Soll, H., 1978, The supply of dealer services in securiies markes, Journal of Finance 33, Tinic, S.M., 1972, The economics of liquidiy services, Quarerly Journal of Economics 86, Yadav, P. and P. Pope, 1990, Sock index fuures arbirage: Inernaional evidence, Journal of Fuures Markes 10,

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31 Figure 1: Average Daily Spreads of Fuures and Opion Conracs Fuures Conracs In Percen Fuures Dae Opion conracs In Percen Pu Call Dae 29

32 Figure 2: Inraday Spreads of Fuures and Opion Conracs FuuresConracs In Percen Fuures Time Opion Conracs in Percen Pu Call Time 30

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