Call & Put Butterfly preads est of E50 Index Optons Market Effcency and E50 Index Optons Contract Adjustment Woradee Jongadsayakul Abstract hs paper tests the effcency of E50 Index Optons market and nvestgates the mpact of contract adjustment on market effcency. he optons data set I employ to conduct call & put butterfly spreads test of market effcency covers the perod from October 9, 007 to December 0, 06. When I gnore transacton costs, the results report frequent and substantal volatons of prcng relatonshps. For an opton maturng wthn 90 days, sze of volatons tends to be hgher for optons farther from the money or further away from expraton. Almost no volatons reman after consderng the bd-ask spread as transacton costs. herefore, our results support the effcency of E50 Index Optons market before and after the modfcaton of contract specfcaton. Comparng the results before and after contract adjustment, I do not observe any mprovement of market effcency after the modfcaton of contract. Index erms Butterfly spread, ndex optons, market effcency, no arbtrage condton. I. INRODUCION haland Futures Exchange (FEX) was establshed on May 7, 004 as a dervatves exchange n haland. It offers dervatves products such as futures and optons to nvestors, fund managers, fnancal nsttuton and the general publc as tools to manage ther portfolo effectvely. he frst product to be traded on FEX s E50 Index Futures, whch was launched on Aprl 8, 006. FEX has offered several products such as E50 ndex optons, gold futures, slver futures, nterest rate futures, sngle stock futures, crude ol futures, UD futures, sector futures, and rubber futures snce then. Although E 50 Index Optons has been traded snce October 9, 007 as the second product on FEX, t has faced the lqudty problem. o ncrease lqudty n E50 ndex optons, FEX added two contract months but removed the two farthest quarterly months, resultng n four contract months avalable for tradng each day. In addton, strke prce nterval of E50 Index Optons has been ncreased from 0 ponts to 5 ponts, so that E50 Index Optons have n-the-money, at-the-money, and out-of-money. he adjustment reduces the number of contracts and complexty nvolved and should boost tradng lqudty and volume. It s observed that yearly volume of E50 Index Optons has contnued to ncrease snce 0; however, t was just 0.6 percent of the total volume n 06. nce the lqudty of E50 Index Optons depends on ts prcng Manuscrpt receved March, 08; revsed June 6, 08. hs work was supported n part by Department of Economcs, asetsart Unversty. Woradee Jongadsayakul s wth asetsart Unversty, Bangkok, haland (e-mal: fecowdj@ ku.ac.th). effcency, ths paper conducts a call & put butterfly spreads test over the sample perod from October 9, 007 to December 0, 06 to analyze E50 Index Optons market effcency before and after the contract adjustment. I focus on no-arbtrage relatonshps among prces to testng market effcency snce t does not rely on assumptons about traders rsk preferences and market prce dynamcs []. he call & put butterfly spreads test also nvolves only optons. ome earler studes report evdence of msprcng of E50 Index Optons when gnorng transacton costs. However, after ncludng transacton costs, very few volatons of arbtrage prcng relatonshps are reported. Research by [] uses daly data from October 9, 0 to October 0, 04 to examne rskless arbtrage opportunty under put-call-futures party. After ncludng all transacton costs, such as the bd-ask spread and brokerage commsson, a number of rskless arbtrage opportuntes reduce sgnfcantly as % of total avalable data. Reference [] provdes the box spread test of E50 ndex optons market effcency usng daly data from October 9, 0, through March 0, 06. he box spread arbtrage strategy s approprate for testng the E50 ndex optons market effcency when E50 ndex s not traded because the strategy nvolves only the rsk free asset and two pars of call and put optons havng the same expraton date and underlyng asset, but not underlyng asset tself. he results show that the market frctons mposed by the bd-ask spread, along wth brokerage commssons, exchange fees, and nterest on ntal margn depost, appear to have a sgnfcant effect on arbtrageurs abltes to take advantage of the msprcng of the box spreads. he box spread arbtrage opportuntes drop to less than % when usng bd-ask prces, and none of them s perssted on the followng tradng day. Over the same sample perod from October 9, 0, through March 0, 06, [4] and [5] use the nternal effcency test of call optons alone or put optons alone to nvestgate the exstence of arbtrage opportuntes n E50 Index Optons market. Usng the bd-ask prces as transacton costs, there s no arbtrage opportunty for call optons tradng. he arbtrageurs can earn rskless profts when employng put butterfly spread, but ther opportuntes drop to 0.04% [4], [5]. here s only 0.0% for put spread arbtrage opportuntes [5]. In addton to provdng new results on the effcency test of the E50 Index Optons market, ths paper extends the sample perod to cover both before and after the E50 Index Optons contract adjustment. I nvestgate whether E50 Index Optons are prced correctly relatve to one another for the two sample perods, before and after the contract adjustment, by testng both call & put butterfly spreads do: 0.878/jtef.08.9..597 06
together. A group of prevous studed conduct market effcency test by usng no-arbtrage approach, ncludng call & put lower boundary condtons (e.g., [], [6]), put-call party condton (e.g., [], [7]-[9]), call & put spread condtons (e.g., [], [0], []), call & put convexty condtons (e.g., [], [0], []), and box spread condton (e.g., [], [0]-[]). However, as of my knowledge, ths s the frst paper combnng both call and put butterfly spreads to test market effcency. he paper proceeds as follows. A bref revew of theoretcal framework s gven n ecton II. he descrpton of the data and a dscusson of the testng methodology follow n ecton III. he test results are presented n secton IV, and ecton V concludes. II. HEOREICAL FRAMEWOR he condton of call & put butterfly spreads nvolves call and put optons characterzed by ) three dfferent exercse prces, / ; ) the same underlyng asset; and ) the same expraton date. Defne C and P, the premum of European call and put optons wth exercse prce ;, the prce of underlyng asset; r, the rsk-free rate; t, years remanng untl opton expry. Based on the put-call party by [], optons prcng relatonshps are as follows: rt C P e () rt C P e () rt C P e () ubtractng twce () from the sum of () and (), I have C C C P P P e /, then 0. he condton of call & put butterfly spreads used n ths paper s then as follows: If rt C C C P P P (4) If (4) s volated, arbtrage profts can be generated by employng the followng strateges. A. Long Call Butterfly pread and hort Put Butterfly pread (LCP) trategy If the left-hand sde of (4) s less than the rght-hand sde of (4), an arbtrager can earn rsk-free proft by combnng long call butterfly spread and short put butterfly spread. A long call butterfly spread s a combnaton of a bull call spread (purchase of a call wth exercse prce and sale of a call wth exercse prce ) and a bear call spread (sale of a call wth exercse prce and purchase of a call wth exercse prce ). A short put butterfly spread s a combnaton of a bear put spread (sale of a put wth exercse prce and purchase of a put wth exercse prce ) and a bull put spread (purchase of a put wth exercse prce and sale of a put wth exercse prce ). he LCP strategy nvolves a postve ntal nflow, C C C P P P, and zero payoff at expraton (see able I). B. hort Call Butterfly pread and Long Put Butterfly pread (CLP) trategy If the left-hand sde of (4) s greater than the rght-hand sde of (4), an arbtrager can earn rsk-free proft by combnng short call butterfly spread and long put butterfly spread. A short call butterfly spread s a combnaton of a bear call spread (sale of a call wth exercse prce and purchase of a call wth exercse prce ) and a bull call spread (purchase of a call wth exercse prce and sale of a call wth exercse prce ). A long put butterfly spread s a combnaton of a bull put spread (purchase of a put wth exercse prce and sale of a put wth exercse prce ) and a bear put spread (sale of a put wth exercse prce and purchase of a put wth exercse prce ). he CLP strategy nvolves a postve ntal nflow, C C C P P P, and zero payoff at expraton (see able II). Prce Range at Expraton Call wth ABLE I: PAYOFF FROM HE LCP RAEGY Payoff from hort Payoff from hort Calls wth Call wth Put wth Puts wth Payoff from hort Put wth otal Payoff 0 0 0 0 Prce Range at Expraton Payoff from hort Call wth ABLE II: PAYOFF FROM HE CLP RAEGY Payoff from hort Calls wth Call wth Put wth Payoff from hort Puts wth Put wth otal Payoff 0 0 0 0 07
III. DAA MEHODOLOGY Optons on the E50 has been traded on the FEX snce October 9, 007. hey are European-style optons. As s usual for ndex optons, prces of E50 Index optons are n ndex ponts. he contract sze s 00 baht per ndex pont. he optons data set I employ to test call & put butterfly spreads conssts of closng prces, bd prces, and ask prces n the perod from October 9, 007 to December 0, 06 for a total of 0,69 observatons. o study how the contract modfcaton affects the effcency of the E50 Index Optons market, I splt a gven data set nto perods, before and after contract adjustment on October 9, 0. he market effcency tests were carred out under the assumpton of both zero and postve transacton costs. Closng prces (CL) are used under the assumpton of zero transacton costs. Wth the bd-ask spread as transacton costs, an opton can be purchased at the ask prce (A) and sold at the bd prce (B). Under two assumptons, wthout and wth transacton costs, able III and able IV show the arbtrage condtons of the LCP strategy and the CLP strategy, respectvely. he arbtrage condtons must be multpled by 00 to express n terms of baht nstead of ndex pont. When the arbtrage opportuntes are detected, the comparson of the sze of arbtrage profts (Y) n E50 Index Optons prcng relatonshps before and after change n contract specfcaton on October 9, 0 s analyzed by usng t-test at sgnfcance level of 5 percent. ABLE III: ARBIRAGE CONDIION OF HE LCP RAEGY Assumpton Arbtrage Condton Wthout Y CL CL CL CL CL CL C C C P P P 00 0 transacton costs Wth transacton B A A B B A Y costs C C C P P P 00 0 ABLE IV: ARBIRAGE CONDIION OF HE CLP RAEGY Assumpton Arbtrage Condton Wthout Y CL CL CL CL CL CL C C C P P P 00 0 transacton costs Wth transacton B B A A A B Y C C C P P P costs 00 0 IV. E REUL On each tradng day durng the test perod, the arbtrage condtons of the LCP strategy and the CLP strategy are tested. he percentage and sze of volatons of the condtons are tabulated for the two sample perods, before and after the contract adjustment to ndcate the effect of contract adjustment on E50 Index Optons market effcency. able V report the percentage and sze of volatons n arbtrage prcng relatonshp. I also nvestgate whether the baht value of volatons decreases after the contract adjustment. o do so, I use a t-test of the null hypothess that the mean baht volaton s equal before and after contract adjustment. In the absence of transacton costs, able V shows a sgnfcant number of volatons both before and after contract adjustment. Based on the whole sample of 0,69 observatons, the total of 0,549 breaches of the condton of call & put butterfly spreads s broken down nto 5,0 (49.89%) LCP arbtrage opportuntes and 5,46 (49.6%) CLP arbtrage opportuntes. he average sze of volatons s 897.74 baht for the LCP strategy and 889.8 baht for the CLP strategy. he percentage and baht amount of volatons are hgher n the later tme perod (49.77% and 875.0 baht versus 50.6% and 946.65 baht) for the LCP strategy. he t-test ndcates the dfference n sze of the volatons before and after contract adjustment at a sgnfcance level of 5%. For the CLP strategy, both measures decrease over tme (49.4% and 89.0 baht versus 49.4% and 884.8 baht), though not sgnfcantly so. When the analyss consders the bd-ask spread as transacton costs, the percentage of volatons drops substantally to less than 0.%. I also observe a declne n average sze of volatons to 96.67 baht for the LCP strategy and 40.00 baht for the CLP strategy. he E50 Index Optons market s therefore effcent. Consderng the LCP strategy, the results show an nsgnfcant ncrease n both percentage and baht amount of volatons after contract adjustment (0.0% and 80.00 baht versus 0.% and 555.00 baht). here are no arbtrage opportuntes for employng the CLP strategy and generatng arbtrage profts n a pror perod contract adjustment. After contract adjustment, there are 0.06% of arbtrage opportuntes n the CLP strategy and an average arbtrage proft of 40.00 baht. he results do not provde support for the argument that the E50 ndex optons market effcency mproved after the modfcaton of contract. In addton, the puts are usually overprced relatve to the calls so that the LCP strategy s used more often and, n many cases, generates more arbtrage profts than the CLP strategy before and after contract adjustment, regardless of the assumpton of transacton costs. ABLE V: VIOLAION OF CALL & PU BUERFLY PREAD ransacton Costs Zero Postve Perod Before After Whole Before After Whole Panel A: he LCP strategy Number of Obs. 7,84,45 0,69 7,84,45 0,69 Number of Volatons,65,678 5,0 4 6 Percent of Volatons 49.77 50.6 49.89 0.0 0. 0.06 Volaton ze (baht) 875.0 946.65 897.74 80.00 555.00 96.67 statstc (p-value) -.4674 (0.07) -.00 (0.86) Panel B. he CLP strategy Number of Obs. 7,84,45 0,69 7,84,45 0,69 Number of Volatons,599,647 5,46 0 Percent of Volatons 49.4 49.4 49.6 0.00 0.06 0.0 Volaton ze (baht) 89.0 884.8 889.8-40.00 40.00 statstc (p-value) 0.684 (0.7884) - Furthermore, to see f the volatons are related to factors, such as opton moneyness and tme to maturty, prevously cted n the lterature (e.g., [7], []), arbtrage profts of the LCP strategy and the CLP strategy n the absence of transacton costs are classfed by opton moneyness (M) and tme to maturty (t). he results are reported n able VI for the LCP strategy and able VII for the CLP strategy. As there are three exercse prces (,, and ), opton moneyness s defned n (5) as the weghted average absolute percent dfference between the three exercse prces and the daly closng prce of E50 Index (). M 00 / 4 (5) For a total of 0,69 observatons, there are,695 observatons wth moneyness less than %, 4,59 observatons wth moneyness between % and 4%,,06 observatons wth moneyness between 4% and 6%, 76 08
observatons wth moneyness between 6% and 8%, 7 observatons wth moneyness between 8% and 0%, and 6 observatons wth moneyness greater than or equal to 0%. hus, the majorty of observatons are optons beng near the money. ABLE VI: ARBIRAGE PROFI OF HE LCP RAEGY BY OPION MONEYNE AND IME O MAURIY Perod Before After Whole Volaton % baht % baht % baht Panel A: t 0 days M < % 5.0 600.59 46.56 64.80 49.85 60.75 % M < 4% 5.90 759. 49.5 904.5 5. 799.6 4% M < 6% 48.5 787.80 47.7,05.77 47.99 90.4 6% M < 8% 5.0 86.67 57.95,06.7 55. 97.84 8% M < 0%. 46. 5.5,404. 4.47,040.00 M 0% 47.06,485.00 59.46,70.8 55.56,644.00 Panel B: 0 days < t 90 days M < % 50.95 77.0 48.0 6.5 50. 70. % M < 4% 48.66 89.98 50.98 8.7 49.4 868.5 4% M < 6% 46.8,07.5 5.48,06.0 48.,09.66 6% M < 8% 5.74,06.65 46.67,07.07 5.9,065.0 8% M < 0% 4.86,0.95 50.00,869.5 44.,4.67 M 0% 57.5,409.7 60.87,08.57 57.89,490.58 Panel C: 90 days < t M < % 4.67 968.00 5.6,4.00 5.4,9. % M < 4% 66.67 987.50 46.0,99. 47.8,6.5 4% M < 6% 50.00 700.00 5.94,84.44 5.6,6.00 6% M < 8% 50.00,570.00 40.00,80.00 4.86,0.00 8% M < 0% 00.00 780.00 50.00,00.00 66.67 900.00 M 0% - - - - - - ABLE VII: ARBIRAGE PROFI OF HE CLP RAEGY BY OPION MONEYNE AND IME O MAURIY Perod Before After otal Volaton % baht % baht % baht Panel A: t 0 days M < % 47.88 558.9 5.67 590.00 49.4 567.70 % M < 4% 47.7 75.4 50.4 847.0 48.44 76.4 4% M < 6% 5. 870.5 5.9,08.60 5.68 95. 6% M < 8% 46.0 856.54 4.05,7.0 44.8,048.09 8% M < 0% 66.67,5. 48.65,08.89 57.5,77.4 M 0% 5.94,4.44 7.84,4.86 4.59,78.6 Panel B: 0 days < t 90 days M < % 47.84 770.9 5. 66.58 48.8 77.6 % M < 4% 50.6 9.6 48.4 77.08 49.7 88.6 4% M < 6% 5.,. 45.77 970.87 5.0,08.67 6% M < 8% 45.56,0.5 5.50,54.9 47.08,.7 8% M < 0% 56.,09.55 50.00,409.5 55.04,4.6 M 0% 4.94,45. 9.,5. 4.6,6.0 Panel C: 90 days < t M < % 58. 648.57 44.74 894.7 46.59 85.68 % M < 4%.,445.00 5.97,.94 5.7,0.8 4% M < 6% 50.00 40.00 45.0,5.04 45.6,86.9 6% M < 8% 50.00 740.00 60.00 546.67 57.4 595.00 8% M < 0% 0.00 0.00 50.00 90.00. 90.00 M 0% - - - - - - me to maturty s dvded nto three classes. he class of short-term optons contans all optons maturng wthn 0 days. mlarly, the classes of medum-term and long-term optons consst of all optons wth a tme to maturty between 0 and 90 days and more than 90 days, respectvely. he category contanng long-term optons has only 0 observatons, compared to,9 short-term optons and 6,95 medum-term optons. Consderng the frequency of call & put butterfly spreads volatons by opton moneyness, I do not fnd any consstent pattern of the frequency ncreasng for optons movng away from at-the-money. he frequency of call & put butterfly spreads devatons also does not seem to ncrease as the tme to expraton ncreases. However, for an opton maturng wthn 90 days, t seems that arbtrage opportuntes n both strateges (LCP and CLP) generate more profts when optons are farther from the money. For the LCP strategy, short-term optons wth moneyness less than % generates the lowest mean proft of 60.75 baht, whle short-term optons wth moneyness greater than or equal to 0% generates the hghest mean proft of,644.00 baht. urnng to the CLP strategy, short-term optons wth moneyness less than % generates the lowest mean proft of 567.70 baht, whle short-term optons wth moneyness greater than or equal to 0% generates the hghest mean proft of,78.6 baht. I also do not observe any relatonshp between opton moneyness and sze of volatons for long-term optons. For optons wth moneyness less than 6%, ther arbtrage profts from both LCP and CLP strateges ncrease as tme to maturty ncreases. V. CONCLUION haland Futures Exchange started tradng E50 Index Optons n 007 but lqudty has been low. o boost lqudty, the E50 Index Optons contract has been readjusted to better ft the tradng style of local nvestors snce October 9, 0. hs research utlzes daly data from October 9, 007 to December 0, 06 to test market effcency and nvestgate the effect of contract adjustment on market effcency. he methodology s based on call & put butterfly spreads, whch combne both call and put optons. For the whole sample, the results show that arbtrage opportuntes occur much more frequently n the LCP strategy than n the CLP strategy. In many cases, the LCP strategy generates more arbtrage profts than the CLP strategy. In the absence of transacton costs, the percentage and sze of volatons n the LCP (CLP) strategy are greater after (before) change n contract specfcaton. he dfference n arbtrage profts before and after the contract adjustment s statstcally sgnfcant at 5% level when usng the LCP strategy. In addton, for an opton maturng wthn 90 days, most results show an ncrease n sze of volatons when optons are farther from the money or have more tme remanng to expry. akng the bd-ask spread nto account, the percentage and the sze of the volatons decrease substantally over the whole sample. herefore, our results support the effcency of E50 Index Optons market before and after the modfcaton of contract specfcaton. I also observe an nsgnfcant ncrease n both percentage and baht amount of volatons after contract adjustment. herefore, the results do not provde support for the argument that the E50 09
ndex optons market effcency mproved after the contract adjustment. REFERENCE [] G. Capelle-Blancard and M. Chaudhury, Effcency tests of the french ndex (CAC40) optons markets, presented at the European Fnancal Management Assocaton 00 Annual Meetngs, London, England, June 6-9, 00. [] J. Lertburapa, A test of put-call future party n FEX, presented at the 8th EC Workng Papers Forum, Bangkok, haland, eptember 6, 05. [] W. Jongadsayakul, A box spread test of the E50 ndex optons market effcency: Evdence from the haland futures exchange, Internatonal Journal of Economcs and Fnancal Issues, vol. 6, no. 4, pp. 744-749, 06. [4] W. Jongadsayakul, Arbtrage opportunty n haland futures exchange: An emprcal study of E50 ndex optons, ICE & IEC Proceedngs, pp. 8--8-7, 07. [5] W. Jongadsayakul, he nternal effcency test of E50 ndex optons market: Call optons vs. put optons, Appled Economcs Journal, vol. 4, no., pp. -6, 07. [6] A. Dxt,.. Yadav, and P.. Jan, estng lower boundary condtons for ndex optons usng futures prces: Evdences from the ndan optons market, he Journal for Decson Makers, vol. 6, no., pp. 5-, 0. [7] A. amara and. W. Mller, Jr., Daly and ntradaly tests of european put-call party, Journal of Fnancal and Quanttatve Analyss, vol. 0, no. 4, pp. 59-59, 995. [8]. L, he arbtrage effcency of the nkke 5 optons market: A put-call party analyss, Monetary and Economc tudes, vol. 4, no., pp. -54, 006. [9] Z. Zhang and R. N. La, Prcng effcency and arbtrage: Hong ong dervatves markets revsted, Appled Fnancal Economcs, vol. 6, pp. 85-98, 006. [0] L. F. Ackert and Y.. an, Evdence on the effcency of ndex optons markets, Economc Revew-Federal Reserve Bank of Atlanta, vol. 85, no., pp. 40-5, 000. [] L. F. Ackert and Y.. an, Effcency n ndex optons markets and tradng n stock baskets, Journal of Bankng & Fnance, vol. 5, no. 9, pp. 607-64, 00. [] A. G. Ronn and E. I. Ronn, he box spread arbtrage condtons: heory, tests, and nvestment strateges, Revew of Fnancal tudes, vol., no., pp. 9-08, 989. [] H. toll, he relatonshp between put and call opton prces, Journal of Fnance, vol. 4, no. 5, pp. 80-84, 969. Woradee Jongadsayakul s an assocate professor of economcs at asetsart Unversty, Bangkok, haland. he receved her B.B.A. n fnance from Chulalongkorn Unversty (Bangkok, haland) n 999, M.F. from ant Lous Unversty (Mssour, UA) n 00, M.A. n economcs from Unversty of Colorado at Boulder (Colorado, UA) n 00, and Ph.D. n economcs from Unversty of Colorado at Boulder (Colorado, UA) n 006. Her teachng and research nterests are n busness economcs, fnancal rsk management, and ndustral organzaton. 0