The Impact of Stock Index Futures Tradng on Daly Returns Seasonalty: A Multcountry Study Robert W. Faff a * and Mchael D. McKenze a Abstract In ths paper we nvestgate the potental mpact of the ntroducton of stock ndex futures tradng on the daly returns seasonalty of the underlyng ndex for seven natonal markets. Ths daly seasonalty testng s performed wth respect to (a) mean returns; (b) return autocorrelatons; and (c) return volatltes usng a modfed GARCH model. It has been prevously argued that the ntroducton of futures tradng should lead to reduced seasonalty of mean returns and generally our results support ths concluson. Ths s partcularly the case wth regard to the general weakenng of the Monday effect n mean returns for the US; Germany; and Swtzerland, and to a lesser extent for the UK. Smlarly for Japan and to a lesser extent for Australa, the Tuesday effect n mean returns s no longer n evdence. Whle we detect daly seasonalty n return autocorrelatons and volatltes that s largely related to Monday and Tuesday observatons, ths seasonalty does not seem to be affected by the ntroducton of ndex futures contracts. Key Words: Day-of-the-Week Effect; Stock Index Futures; Seasonalty; GARCH Modelng. JEL Reference: G12; G15. * Correspondng author a School of Economcs and Fnance, RMIT Unversty, GPO Box 2476V, Melbourne, Australa, 3000. Emal address: robert.faff@rmt.edu.au
The Impact of Stock Index Futures Tradng on Daly Returns Seasonalty : A Multcountry Study Abstract In ths paper we nvestgate the potental mpact of the ntroducton of stock ndex futures tradng on the daly returns seasonalty of the underlyng ndex for seven natonal markets. Ths daly seasonalty testng s performed wth respect to (a) mean returns; (b) return autocorrelatons; and (c) return volatltes usng a modfed GARCH model. It has been prevously argued that the ntroducton of futures tradng should lead to reduced seasonalty of mean returns and generally our results support ths concluson. Ths s partcularly the case wth regard to the general weakenng of the Monday effect n mean returns for the US; Germany; and Swtzerland, and to a lesser extent for the UK. Smlarly for Japan and to a lesser extent for Australa, the Tuesday effect n mean returns s no longer n evdence. Whle we detect daly seasonalty n return autocorrelatons and volatltes that s largely related to Monday and Tuesday observatons, ths seasonalty does not seem to be affected by the ntroducton of ndex futures contracts. 2
I. INTRODUCTION Futures contracts provde nvestors wth a relatvely low cost way of tradng on new nformaton and for hedgng aganst adverse prce movements. The prce of futures contracts s fundamentally determned by the prce of the underlyng asset on whch the futures contract s based. Thus, the ntroducton of futures tradng may mpact on the market for the underlyng asset and a body of lterature has evolved whch attempts to emprcally valdate the nature of ths relatonshp. One major area of ths lterature has consdered the mpact of futures tradng on the volatlty of the underlyng asset. For example, n the case of fnancal futures ths lterature s well represented by Fglewsk (1981); Morarty and Tosn (1985); and Edwards (1988a); whle for commodty futures see Workng (1960); Powers (1970) and Cox (1976). Further, n the case of stock ndex futures the lterature ncludes Stoll and Whaley (1987); Edwards (1988a and 1988b); Harrs (1989); Damodaran (1990); Hodgson and Ncholls (1991); Bessembnder and Segun (1992); Kamara, Mller and Segel (1992); Lee and Ohk (1992); Robnson (1994); Antonou and Holmes (1995); Kamara (1997); Hrak, Maberly and Taube (1998); and Antonou, Holmes and Prestley (1998). 1 In general, ths lterature provdes mxed evdence as to the volatlty mpact of futures tradng. Ths emprcal ambguty s not all that surprsng snce the theoretcal lterature proposes both a destablzng forces hypothess whch predcts ncreased volatlty and a market completon hypothess n whch decreased volatlty s predcted. For the former hypothess, t s argued that the nflow and exstence of speculators n futures markets may produce destablzng forces, whch among other thngs create undesrable bubbles. 2 However, the contrary vew s that the ntroducton of futures tradng leads to more complete markets, enhancng nformaton flows and thus mprovng nvestment choces facng nvestors. 3 Moreover, futures may brng more (prvate) nformaton to the market and allow for a qucker dssemnaton of 1 A parallel lterature also exsts for the case of the mpact of opton lstng on the underlyng stock s return behavor. See, for example, Conrad (1989); Sknner (1989); Damodaran and Lm (1991); and Kumar, Sarn and Shastr (1998). 2 See, for example, Harrs (1989); Edwards (1988a & 1988b); and Sten (1987 & 1989)). 3 See, for example, Ross (1977); Hakansson (1978); Breeden and Ltzenberger (1978) and Ardtt and John (1980)). 3
nformaton. Further, speculatve actvty may be transferred from the spot to the futures market whch can dampen spot market volatlty. The prncpal am of the current study s to extend the segment of ths lterature whch has nvestgated the mpact of ndex futures ntroducton. Whle the vast majorty of these studes have focussed on US markets [see for example, Harrs (1989) and Kamara, Mller and Segel (1992)], only a lmted amount of work has been drected toward other markets [for example, n the case of the UK see Robnson (1994), Antonou and Holmes (1995), and Antonou, Holmes and Prestley (1998); n the case of Australa see Hodgson and Ncholls (1991); and n the case of Japan see Hrak, Maberly and Taube (1998)]. Accordngly, the general argument of Leamer (1983) regardng the concern about data snoopng and that of Lo and MacKnlay (1990) n the context of fnance research, oblge us to nvestgate alternatve datasets n order to assess the robustness of these fndngs. 4 In the current paper ths s acheved by analysng seven separate markets n whch ndex futures have been ntroduced. Stock market ndex futures typcally have a face value of a gven multple (e.g. 100) tmes the value of a predetermned natonal stock market ndex. Thus, the value of these futures contracts fluctuates as the value of the underlyng ndex changes reflectng the machnatons of the overall market. It s commonly hypotheszed that the ntroducton of such stock ndex futures may have an mpact on the return characterstcs of the ndex tself. Whle much of the relevant lterature has solely focused on the (uncondtonal) volatlty mpact of such an event, other related but under-researched areas of nterest have recently been dentfed. Of partcular relevance to the current paper, s the potental mpact that the ntroducton of ndex futures tradng has on the daly seasonalty of the underlyng ndex returns. 4 A smlar data-snoopng justfcaton has been used elsewhere to examne non-us data see for example, Jagannathan, Kubota and Takehara (1998) who use Japanese data to test a labor-ncome based CAPM [of Jagannathan and Wang (1996)] and Clare, Prestley and Thomas (1998) who use UK data to test the CAPM usng a one-step procedure. 4
Daly seasonalty n mean returns s a phenomenon that has been documented n many asset return seres ncludng numerous natonal stock market ndces [see for example, Osborne (1962); Cross (1973); French (1980); Gbbons and Hess (1981); Jaffe, Westerfeld and Ma (1989); Wlson and Jones (1993); Chang, Pnegar and Ravchandran (1993); Agrawal and Tandon (1994); Dubos and Louvet (1996); Wang, L and Erckson (1997); Bachller, Blasco and Espta (1998) and Coutts and Hayes (1999)]. In most markets t s has generally been observed that to some degree a Monday effect s n evdence namely, that the Monday mean return s sgnfcantly negatve and less than the average return found for all other days. However, n a smaller subset of markets such as Japan and Australa, a Tuesday effect has been documented, n whch t s the mean Tuesday return whch s found to be sgnfcantly negatve and less than the average return for all other days. Although daly seasonalty n return autocorrelatons and return volatlty has also attracted some research attenton, they are far less extensvely nvestgated than ther mean returns counterpart. Wth regard to the daly seasonalty n return autocorrelatons, Bessembnder and Hertzel (1993) and Hggns and Peterson (1999) are representatve of the lterature. For example, Bessembnder and Hertzel (1993) examned a large set of US equty and futures markets data. Generally, they found that the return autocorrelaton between Monday (Tuesday) and the prevous tradng day s unusually hgh (low) and postve (and n many cases negatve) compared to other day of the week autocorrelatons. Wth regard to the daly seasonalty n return volatlty, Fama (1965); Gbbons and Hess (1981) and Agrawal and Tandon (1994) are good examples of ths lterature. Generally, these papers have found that the Monday return varance tends to be hgher than for all other days of the week. Recently an nterest has emerged n nvestgatng whether, and to what extent, daly return seasonalty s mpacted by the ntroducton of ndex futures tradng. Specfcally, Kamara (1997) consdered the mpact of the ntroducton of an S&P 500 ndex futures contract on the daly mean return seasonalty of the US market ndex return. Usng data sampled over the perod 1962 to 1993, the author fnds evdence to suggest that the daly seasonal effect n the S&P 500 declned sgnfcantly n the postfutures tradng perod. The author argued that the observed declne n the daly seasonal s consstent wth the fact that futures tradng greatly reduces the obstacle to arbtragng t, due to the consderable reducton n transacton costs. Further, smlar 5
analyss of ths ssue for the Japanese market s reported n Hrak, Maberly and Taube (1998). In ther paper, the authors found that tradng of the NIKKEI 225 stock ndex futures had mpacted on daly ndex returns seasonalty. Specfcally, whle the Tuesday effect was found to dsappear n the post-tradng perod, a Monday effect seemed to take ts place. The authors argue that such effects are the result of heghtened nformaton flows whch result from futures ndex tradng. Accordngly, the specfc purpose of the current paper s to supplement and enhance the lterature whch consders the mpact of the ntroducton of a stock ndex futures contract on the daly returns seasonalty of the underlyng aggregate natonal stock market ndex. In contrast to the prevous work whch has confned ts scope for analyss to a sngle natonal ndex, ths study wll emprcally scrutnze a wde range of markets. Specfcally, n addton to the US and Japan cases whch were the subject of analyss n Kamara (1997) and Hrak et al (1998) respectvely, we present evdence on the effect of stock ndex futures tradng on daly returns seasonalty for the Australan, German, Spansh, Swss and UK markets. The use of a broad range of countres for analyss has dstnct advantages. For example, t allows the experences of each country to be compared and any common pattern to be uncovered, thus helpng to allevate the data snoopng concern dscussed above. Further, the ncluson of the US and Japan cases allows comparsons to be made between the new methodology appled n ths paper and the results of the earler lterature. As pre-empted n the precedng paragraph, the current paper employs a dfferent (and arguably superor) testng methodology compared to prevous studes that have nvestgated the mpact of futures tradng. Specfcally, as far as we are aware our methodology for the frst tme unquely brngs together three major elements, namely: (a) the mpact of futures tradng; (b) the ncdence of daly seasonalty; and (c) the GARCH modelng framework. 5 Accordngly, wthn ths framework we make two major contrbutons to the exstng lterature. Frst, the use 5 Interestngly, whle (to our knowledge) these three features have not ever before been combned together n one unfed analyss, t s true that each parwse combnaton has been prevously explored. In the case of (a) GARCH modelng and the mpact of futures ntroducton, see for example, Antonou and Holmes (1995); and Antonou, Holmes and Prestley (1998); (b) the mpact of futures ntroducton and daly seasonalty, see for example, Kamara (1997) and Hrak et al (1998); and (c) GARCH modelng and daly seasonalty, see for example, Connolly (1989) and Easton and Faff (1994). 6
of a GARCH model allows us to provde new nsghts as we may smultaneously consder the mpact of stock ndex futures tradng on daly returns seasonalty n both the mean and volatlty dmensons. 6 Specfcally, daly seasonalty testng s performed wth respect to (a) mean returns; (b) return autocorrelatons; and (c) return volatltes. Second, as mentoned earler we present a unfed package of evdence spannng a number of natonal boundares that wll help to counter the concern of data snoopng bas. Exstng evdence (and then for mean returns seasonalty only) pertanng to ths general area s currently only avalable for two markets, namely, the US and Japan. Our nvestgaton extends the coverage to seven markets. A bref summary of our major fndngs s as follows. In general, our results suggest that the ntroducton of futures tradng has been assocated wth reduced seasonalty of mean returns. Ths s partcularly the case wth regard to the general weakenng of the Monday effect n mean returns for the US; Germany; and Swtzerland, and to a lesser extent for the UK. Smlarly for Japan and to a lesser extent for Australa, the Tuesday effect n mean returns no longer s n evdence. Ths fndng supports the arguments presented by Kamara (1997) and Hrak et al. (1998) that, for example, futures tradng lowers transacton costs of traders who may be lookng to arbtrage any proftable opportuntes, ncludng daly seasonals. Furthermore, whle we detect daly seasonalty n return autocorrelatons and volatltes that s largely related to Monday and Tuesday observatons, ths seasonalty does not seem to be affected by the ntroducton of ndex futures contracts. Wth reference to the prevous lterature, these results provde an mportant nternatonal extenson of the evdence of seasonalty n return volatlty such as that found n Fama (1965), Gbbons and Hess (1981) and Agrawal and Tandon (1994) and seasonalty n return autocorrelatons as reported n Bessembnder and Hertzel (1993). The rest of ths paper proceeds as follows. Secton II detals the basc testng methodology whch s employed n ths paper. Secton III dscusses detals of the seven natonal stock ndces on whch futures contracts are traded. Further, the estmaton results are presented and dscussed. Fnally, Secton IV presents some concludng comments. 6 Recently, ths general ssue has been found to be mportant n the case of futures (see Antonou, Holmes and Prestley (1998)). 7
II. RESEARCH METHOD A. Daly Seasonalty Modfed GARCH Model Framework Our basc model comprses an Auto-Regressve (AR) mean equaton augmented by dummy varables to capture the day-of-the-week (DOW) seasonalty. 7, 8 The ncluson of autoregressve terms follows Bessembnder and Hertzel (1993), Hggns and Peterson (1999) and Hrak et al. (1998). The latter authors argue that: [f]alure to adjust for the short-term prcng dynamcs n returns may ntroduce bas n the estmates of the DOW coeffcents snce the coeffcent estmates wll attempt to capture some of the effects assocated wth the mssng model components. (p.498) Specfcally, the mean equaton takes the form: R t = MonD Mon ODWD ODW Mon D Mon R t 1 ODWD ODWR t (1) where R t s the return to the stock market ndex; D Mon s a dummy varable whch takes the value unty f the day s a Monday and zero otherwse; D ODW s a dummy varable for the other days of the week (ODW) whch takes a value of unty f the day s a Tuesday, Wednesday, Thursday or Frday and zero otherwse; and ϕ Mon, ϕ ODW, λ Mon and λ ODW are coeffcents to be estmated. It should be noted that for Australa and Japan n whch a Tuesday effect has been documented n the lterature, the role of the Monday dummy n the above specfcaton s supplanted by a Tuesday dummy (D Tue ) and so the ODW dummy n ths case captures Monday, Wednesday, Thursday and Frday. The stochastc error term, ε t n Equaton (1), s modeled as a GARCH process whereby the varance of the error term s attrbuted wth dynamc (autoregressve) propertes. Specfcally, we adopt the GARCH (1,1) specfcaton of Bollerslev (1986), whch has been wdely appled n the lterature. As wth the mean equaton, 7 A verson of the model was nvestgated n whch a dummy varable was ncluded for the stock market crash of October 1987. As the results are robust to ths varaton they are not reported n order to conserve space. 8 In earler versons of ths paper, hgher order autoregressve terms were also employed. In order to keep the specfcaton manageable, only frst order terms are reported here. Importantly, the outcome of the hypothess testng s robust to ths varaton. 8
the GARCH specfcaton of the condtonal varance equaton s also augmented to nclude a matchng set of day-of-the-week dummy varables to capture the potental for daly seasonalty n market volatlty. Thus, the condtonal varance equaton s specfed as: h t = D D h (2) 0Mon Mon 0ODW ODW 1 2 t 1 1 where h t s the condtonal varance of the stochastc error term (ε t ) n the mean equaton, α 1 (ARCH term), β 1 (GARCH term), α 0Mon and α 0ODW are coeffcents to be estmated. As was the case for the mean equaton, n those markets n whch a Tuesday effect has been documented n the lterature (Australa and Japan), the role of the Monday dummy n the above specfcaton s supplanted by a Tuesday dummy (D Tue ) and the ODW dummy captures Monday, Wednesday, Thursday and Frday. 9 B. Daly Seasonalty and Pre/Post Index Futures Tradng Modfed GARCH Model Framework To determne the mpact of the ntroducton of (and, hence, tradng n) an aggregate stock market futures contract on the daly returns seasonalty of the underlyng ndex, the basc model as specfed above, requres modfcaton. Specfcally, the day-of-theweek dummy varables of Equatons (1) and (2) may be splt nto a pre-futures tradng perod and a post-futures tradng perod. Thus, each dummy varable n the pre-tradng era D ( = PreMon and PreODW) wll take on a value of unty on the day(s)-of-theweek to whch t s assgned and zero otherwse. In the post-tradng perod however, they wll take on a value of zero regardless. The converse case s 9 Our focus n ths specfcaton of the varance equaton s on the ntercept term. In prncple, the ARCH and GARCH terms can also be allowed to vary accordng to daly seasonalty, however the nterpretaton of any changes found s not straghtforward. Furthermore, we encountered consderable computaton problems when extendng the specfcaton of our model to allow for such shfts n the ARCH and GARCH terms ndeed the model typcally faled to converge n these cases. Interestngly, n the few cases n whch versons of these models dd successfully estmate, the ARCH and GARCH parameters seemed remarkably smlar clearly unable to reject basc tests of equalty. Accordngly, we feel justfed holdng these parameters constant over the full sample perod. 9
true for day-of-the-week dummy varables assgned to the post-tradng regme, D ( = and PostODW). Accordngly, the fully specfed mean and varance equatons become: Pr eodw PostODW Pr eodw PostODW = t D D D R t 1 R D R t (3) h t Pr eodw PostODW 2 0D 0D 1 1h (4) = In ths specfcaton, all coeffcents wth a PreMon () subscrpt measure the Monday value for that feature n the pre-futures (post-futures) perod. For example, ϕ PreMon measures the mean Monday return n the pre-futures perod. Smlarly, all coeffcents wth a PreODW (PostODW) subscrpt measure the other days of the week value for that feature n the pre-futures (post-futures) perod. For example, ϕ PostODW measures the mean return for all other days (namely, Tuesday, Wednesday, Thursday and Frday) n the post-futures perod. Furthermore, as was the case for the basc model represented by Equatons (1) and (2), for Australa and Japan, the role of the Monday dummy n the above specfcaton s supplanted by a Tuesday dummy (D Tue ) and the ODW dummy captures Monday, Wednesday, Thursday and Frday. C. Test of Man Hypotheses: Daly Seasonalty Effects C.1 Daly Seasonalty Effects n the Mean Return Followng Kamara (1997), our prmary tests relate to the basc seasonal effect that s, for Span, Germany, Swtzerland, the UK and the US; we perform a test of whether Monday returns are sgnfcantly lower than the average return on other weekdays. The analogous test of whether Tuesday returns are sgnfcantly lower than the average return on other weekdays s applcable for Australa and Japan. Hence, n the pretradng case the test s formalzed as (note that the Tuesday verson of the hypothess s presented n parentheses to avod confuson): 10
H1: ϕ PreMon = ϕ PreODW (H1: ϕ PreTue = ϕ PreODW ) Smlarly, the post-tradng counterpart of the above test may be specfed as: H2: ϕ = ϕ PostODW (H2: ϕ PostTue = ϕ PostODW ) C.2 Daly Seasonalty Effects n the Return Autocorrelaton 10 An analogous set of hypothess tests s performed for the return autocorrelatons, followng Bessembnder and Hertzel (1993). That s, n the case of Span; Germany; Swtzerland; the UK; and the US (Australa and Japan n parentheses) the hypothess tested n the pre-tradng perod s: H3: λ PreMon = λ PreODW (H3: λ PreTue = λ PreODW ) Smlarly, the counterpart autocorrelaton hypotheses for the post-tradng perod are: H4: λ = λ PostODW (H4: λ PostTue = λ PostODW ) C.3 Daly Seasonalty Effects n the Return Volatlty Followng Fama (1965); Gbbons and Hess (1981) and Agrawal and Tandon (1994) whch dentfes a seasonal effect n varances, an analogous set of tests s performed for the varance equaton ntercepts. Specfcally, for the pre-tradng perod we have: H5: α 0PreMon = α 0PreODW (H5: α 0PreTue = α 0PreODW ) Whle for the post-tradng perod we have: H6: α 0 = α 0PostODW (H6: α 0PostTue = α 0PostODW ) 10 We thank an anonymous referee for suggestng the modelng of seasonalty n the autocorrelatons. 11
D. Tests of Supplementary Day of the Week Hypotheses In addton to the hypotheses outlned above, some further tests can be performed on a varaton of the model represented by Equatons (3) and (4) n whch ndvdual day of the week dummes are ncorporated. Thus, we defne fve separate day-of-the-week dummy varables n the pre-tradng era (PreMon, PreTue, PreWed, PreThu, PreFr) whch each take on a value of unty on the day-of-the-week to whch they are assgned and zero otherwse. In the post-tradng perod however, they take on a value of zero regardless. The converse case s true for day-of-the-week dummy varables assgned to the post-tradng regme, (, PostTue, PostWed, PostThu, PostFr). Accordngly, the fully specfed mean and varance equatons n ths case become: Pr efr PostFr Pr efr PostFr = t D D DR t 1 R D R t (5) h t Pr efr PostFr 2 0D 0D 1 1h (6) = Ths specfcaton allows us to compare the pre-tradng and post-tradng day-of-theweek effects by testng some null hypotheses framed n terms of equalty restrctons. 11 Specfcally, n the pre-tradng (post-tradng) perod we consder whether the jont hypothess of equalty of the day-of-the-week mpacts has any emprcal support. In the case of the mean returns ths s formalzed as: H7: ϕ PreMon = ϕ PreTue = ϕ PreWed = ϕ PreThu = ϕ PreFr and H8: ϕ = ϕ PostTue = ϕ PostWed = ϕ PostThu = ϕ PostFr Smlarly, n the case of the return autocorrelatons we may test: 12
H9: λ PreMon = λ PreTue = λ PreWed = λ PreThu = λ PreFr and H10: λ = λ PostTue = λ PostWed = λ PostThu = λ PostFr Fnally, n the case of the varance equaton we have a smlar par of tests relatng to the pre-tradng and post-tradng perods, respectvely: 12 H11: α 0PreMon = α 0PreTue = α 0PreWed = α 0PreThu = α 0PreFr and H12: α 0 = α 0PostTue = α 0PostWed = α 0PostThu = α 0PostFr III. RESULTS A. Data In the current paper, the mpact of the ntroducton of stock ndex futures tradng on seven natonal stock market ndces s nvestgated. Specfcally, the markets analysed are Australa; Span; Germany; Japan; Swtzerland; the UK and the US. Daly stock market ndex data were collected from the Datastream database from the earlest avalable date to the end of January 1999. The longest sample perod nvolved the US S&P 500 ndex for whch the ntal observaton occurs n January 1969. 13 Accumulated ndexes were chosen for analyss except for Japan, Swtzerland and the US for these countres a prce ndex seres was employed to allow a longer perod to be analyzed. 14 Detals of the stock ndexes used, the date on whch the futures contracts began tradng as well as the begnnng of each sample perod are presented n Table 1. 11 Estmaton results of the model represented by Equatons (5) and (6) wll not be reported only the outcome of the hypotheses outlned n ths secton wll be reported to conserve space. The full set of estmaton results s avalable from the authors upon request. 12 A seres of further hypotheses were tested wth regard to the equalty of ndvdual day of the week measures (mean, autocorrelaton and volatlty) n the pre- and post-futures tradng perod. These results do not greatly enhance those dscussed n the text and, hence, are not reported n order to conserve space. 13 As s common n studes that model condtonal heteroskedastcty, we use long sample perods [for example, see Jones, Lamont and Lumsdane (1998, p. 319)]. 14 In the case of the countres n whch both prce and accumulaton are avalable, we checked the senstvty of our results, wth regard to whether the type of ndex matters. Whle not reported here, we fnd that the basc thrust of our conclusons s robust to ths varaton n data. The detals are avalable from the authors upon request. 13
[TABLE 1 ABOUT HERE] The returns for each ndex were estmated as the log prce relatve and some basc descrptve statstcs are reported n Table 2. It can be seen that the average daly returns vary between 0.015% for Japan (captal returns only) to 0.064% for Span. Further, whle all market returns reveal some degree of negatve skewness, as expected n daly data there s strong evdence of leptokurtoss, partcularly for Australa and the US. [TABLE 2 ABOUT HERE] B. Daly Seasonalty and the Pre/Post Index Futures Tradng Modfed GARCH Model: Mean Equaton Results The modfed GARCH (1,1) model represented by Equatons (3) and (4) was ftted to the stock market ndex returns data for each of the seven countres n our sample and the mean equaton results are presented n Table 3. 15 Accordng to Panel A of the table, wth respect to the pre-tradng perod, as expected (gven the exstng lterature), a Tuesday effect s n evdence n both Australa and Japan. Specfcally, we see that the Tuesday mean return s negatve and lower than the mean return of all other days for these two cases. Of the remanng countres, Germany, Swtzerland, and the US reveal a Monday effect that s, a sgnfcant negatve return (at the 5 % level) on Monday that s lower than the mean return for all other days of the week. Further, the UK reveals a sgnfcantly negatve mean Monday return at the 10 % level. In addton, t can be seen that durng the pre-tradng perod, average returns on all other days of the week are postve and hghly sgnfcant n all cases (except Span). Ths agan s generally consstent wth prevous evdence documentng daly seasonalty across nternatonal markets [see for example, Dubos and Louvet (1996)]. 15 It should be noted, consstent wth the arguments of Nelson (1990a, 1990b) and others, that the thrust of our mean equaton results s robust to the specfcaton of the varance equaton. Indeed, the conclusons we draw based on the mean equaton results are vald even (a) n the case where the varance equaton contans no daly seasonal dummy varables and (b) n the case where the varance equaton s omtted altogether. Further detals are avalable from the authors upon request. 14
[TABLE 3 ABOUT HERE] The post-futures tradng perod average day-of the-week returns are also reported n Panel A of Table 3. The most notable fndng here s that the sgnfcant negatve Monday and Tuesday returns documented n the pre-tradng perod analyss have dsappeared. Specfcally, consstent wth the fndngs of Dubos and Louvet (1996); Kamara (1997) and Hrak et al. (1998); the US Monday effect and the Japanese Tuesday effect, respectvely, are no longer n evdence. In the case of the US the average pre-tradng Monday return was 0.18 % (wth a t-statstc of 5.80), compared to ts average post-tradng perod counterpart of 0.03 % (wth a t-statstc of 1.35). Smlarly, for Japan the average pre-tradng Tuesday return was 0.08 % (wth a t-statstc of 2.90), compared to ts average post-tradng perod counterpart of 0.09 % (wth a t-statstc of 2.45). Interestngly, the unreported estmaton results for Equatons (5) and (6) whch allow ndvdual estmates of each day of the week separately, reveals that the average pre-tradng perod Monday return s 0.14 % (wth a t-statstc of 3.03), compared to ts post-tradng perod counterpart of 0.03 %. Ths supports the suggeston of Hrak et al. (1998), that the Tuesday effect n Japan has changed to a Monday effect n the post-tradng perod. Thus, the exstng fndngs n the lterature [Kamara (1997) and Hrak et al. (1998)] are strongly confrmed n the context of our more general expermental desgn based on a modfed GARCH model framework. Our fndngs however, extend much further than smply confrmng known outcomes for the US and Japanese markets. Specfcally, we fnd that a smlar dsappearance of the daly seasonal effect n mean returns s n evdence for Australa (where the prevously documented Tuesday effect s now absent n the post-tradng perod analyss); and for Germany, the UK and Swtzerland (where the prevously documented Monday effect s now absent n the post-tradng perod). For example, n the case of Germany the average pre-tradng Monday return was 0.12 % (wth a t- statstc of 4.07), compared to ts average post-tradng perod counterpart of -0.02 % (wth a t-statstc of 0.50). Fnally, as was the case for the pre-tradng perod, t s evdent that average other day of the week returns for the post-tradng perod are postve and sgnfcant across all countres. 15
Evdence as to the seasonalty of return autocorrelaton s presented n Panel B of Table 3 and several major features are evdent. Frst, across the fve relevant countres there s a hgh and postve return autocorrelaton between Monday equty returns and those of the pror tradng day. For example, n the case of Span the pretradng perod Monday coeffcent s 0.6788 as compared to a value of 0.0549 for all other days n the pre-tradng perod. Ths s consstent wth the fndngs of Bessembnder and Hertzel (1993) who examned US equty and futures markets data. Second, the fndng of daly seasonalty n return autocorrelatons dscussed above, s also evdent n the post-tradng perod across these fve countres, although to a lesser extent than for the pre-tradng perod. For example, reconsder Span n the post-tradng perod n whch the Monday autocorrelaton coeffcent has fallen to 0.3061 as compared to a value of 0.1011 for all other days n the post-tradng perod. Thrd, n the case of Japan and Australa, there s a tendency for the return autocorrelaton to be low between Tuesday equty returns and those for the pror tradng day n both the pre-tradng and post-tradng perods. For example, n the case of Japan n the pre-tradng perod, the Tuesday return autocorrelaton s 0.054 as compared to a value of 0.1238 for the counterpart all other days case. Ths fndng s also consstent wth the Bessembnder and Hertzel (1993) results. In summary, n terms of the estmated return autocorrelatons reported n Table 3, whle daly seasonalty s generally observed, there s not a strong pattern ndcatng any partcular effect assocated wth the ntroducton of futures tradng n ndex futures contracts. C. Daly Seasonalty and the Pre/Post Index Futures Tradng Modfed GARCH Model: Varance Equaton Results Table 4 presents the estmated coeffcents for the GARCH model varance equaton [Equaton (4)]. It can be seen from the table that the ARCH and GARCH terms are all postve, statstcally sgnfcant and sum to be less than unty, whch ndcates that shocks to the model are not permanent. Wth regard to both the pre-tradng and posttradng perods the predomnant pattern revealed n ths set of results s that the Monday volatlty coeffcents (for Span, Germany, Swtzerland, the UK and the US) are all sgnfcantly postve and predomnantly larger n magntude compared to ther 16
other day of the week (ODW) counterparts. Ths suggests that the volatlty mpact on all other days of the week s lower than the Monday volatlty a form of daly seasonalty n return volatlty that s consstent wth the prevous lterature [see, for example, Agrawal and Tandon (1994)]. Interestngly, for the two markets (Australa and Japan) n whch Tuesday s solated from other days of the week, the reverse volatlty effect s apparent. That s, n these markets the pont estmate of the volatlty mpact tends to be larger n the all other days case relatve to Tuesday. [TABLE 4 ABOUT HERE] D. An Extended Analyss of the US Case Followng Kamara (1997) we extend the analyss of the US market to ncorporate two pre-tradng subperods. Specfcally, May 1, 1975 s dentfed as a potental pont for a structural break relatng to the move from non-negotable to compettve commssons on the NYSE. To the extent that the exstence of the daly seasonal relates to transacton costs, reduced brokerage costs n ths post-nonnegotable commssons perod would suggest a greater ablty of traders to arbtrage any Monday seasonal. Hence, we have three subperods (broken at May 1, 1975 and Aprl 21, 1982) and Kamara (1997) argues (and fnds) that as we move through these subperods, we expect to observe a weakenng of the Monday seasonal. Accordngly, the three subperods are: (a) the non-negotable commssons perod coverng the nterval January 1969 to Aprl 30, 1975 ( Pre1 ); (b) the postnonnegotable commssons perod coverng the nterval May 1, 1975 to Aprl 20, 1982 ( Pre2 ); and (c) the post-s&p 500 futures perod coverng the nterval Aprl 21, 1982 to 31 January, 1999 ( Post ). The outcome of ths extended analyss n the context of our modfed GARCH model s reported n Table 5. The table s parttoned nto three panels Panel A reports the estmaton results for the mean returns, Panel B reports the return autocorrelaton estmates, whle Panel C reports the estmated coeffcents for the varance equaton. [TABLE 5 ABOUT HERE] 17
In Panel A we observe that the average Monday return n the non-negotable commssons perod of 0.25 % (wth a t-statstc of -6.23) s sgnfcant, negatve and lower than the average returns recorded for all other days of the week n that perod. In the second pre-futures tradng subperod ( post-nonnegotable commssons ), the average Monday return of 0.09 % s sgnfcant, negatve and estmated to be lower than the average return for all other days of the week. Further, n the thrd subperod (whch heralds post-futures tradng actvty), the average Monday return (0.03 %) s now postve (although nsgnfcant) and s no longer the lowest across all days of the week (n unreported results the average Thursday return s now lowest). Hence, ths fndng of a general weakenng n the Monday effect over tme strongly confrms the analyss of Kamara (1997) n the more comprehensve settng of the GARCH framework employed n the current paper. Ths confrmaton s mportant as t serves to show that the Kamara (1997) results have not been nduced by neglectng to model tme-varyng volatlty effects n the data or by the omsson of the dynamcs captured by return autocorrelatons n the mean equaton. Panel B of Table 5 reports the outcome for the return autocorrelatons. As was the case above there s a strong tendency for the autocorrelaton to be hgh and postve between Monday and the prevous tradng day equty returns. Whle ths feature appears to have weakened over tme, the post-tradng perod n the US stll reveals a relatvely hgh return autocorrelaton for the Monday case (0.2242) as compared to all other days of the week (0.0012). Perhaps even more mportantly, the modfed GARCH framework permts us to detect whether there s some sort of related daly seasonal effect n the volatlty equaton. Accordngly, we now turn our attenton to Panel C of Table 5. Smlar to the precedng analyss, we observe that the estmated Monday volatlty coeffcent n the frst pre-tradng perod (Pre1Mon) s hgher than the estmated average volatlty n all other cases wth the excepton of the Monday volatlty coeffcent n the second pretradng perod (Pre2Mon). A Wald test of equalty between the Pre1Mon and Pre2Mon volatlty coeffcents produces a p-value of 0.7017 whch suggests that these two coeffcents are statstcally ndstngushable from each other. In sum, the precedng analyss of mean and volatlty suggests a paradox - hgher average returns tend to be assocated wth lower return volatlty. The declne n volatlty may smply reflect a declne n nose however, both of whch could be 18
consstent wth an mprovement n effcency. Furthermore, unless nformaton arrval vares by day of the week, a seasonal n volatlty may reflect a seasonal n nose (especally for the Tuesday seasonal snce t does not follow the non-tradng weekend). Moreover, even f nformaton arrval s dfferent on Monday than on other weekdays, unless ths has changed by the ntroducton of futures, a change n the volatlty seasonal followng futures ncepton may reflect a change n the seasonal n nose. 16 E. Tests of Man Hypotheses Daly Seasonal Effects: Mean Equaton Results The above analyss ndcates that a certan degree of varaton s observed when comparng daly seasonalty n the mean and varance equaton n pre-tradng and post-tradng (of share ndex futures) subperods. To further nvestgate the statstcal sgnfcance of these seasonaltes, we nvestgate our man set of hypotheses as outlned n Secton II C, by applyng a seres of Wald tests. Specfcally, for (a) mean returns; (b) return autocorrelatons; and (c) return volatltes; we formally test whether Monday (Tuesday) values are statstcally dfferent from the average values on all other days. The results are presented n Panels A, B and C of Table 6, respectvely. The frst set of analyss presented n ths table conssts of testng the basc seasonalty hypothess as appled to the mean returns case. Ths s represented by Hypotheses H1 and H2 outlned prevously. H1: ϕ PreMon = ϕ PreODW represents the null hypothess that average pre-tradng perod Monday returns equal the average return on other pre-tradng perod weekdays. The alternatve hypothess of nterest here s whether average Monday returns are sgnfcantly lower than the average return on other weekdays. As revealed n Panel A of Table 6, the Monday verson of hypothess H1 s resoundngly rejected for all countres although note that Span presents a perverse case snce the average Monday return s sgnfcantly postve (refer back to Table 3). Lkewse, H1: ϕ PreTue = ϕ PreODW the Tuesday counterpart for the pre-tradng perod s strongly rejected for both countres nvolved Australa and Japan. Interestngly, when we consder the post-tradng versons of these two tests we fnd 16 The authors are most grateful to an anonymous referee for suggestng ths nterpretaton. 19
only Australa (H2: ϕ PostTue = ϕ PostODW ); and Span and the UK (H2: ϕ = ϕ PostODW ) provde a rejecton of the relevant hypothess. Notably, n each case the rejecton s much less convncng than that found for each pre-tradng perod counterpart. [TABLE 6 ABOUT HERE] Overall, the results dscussed thus far suggest that the ntroducton of share ndex futures has at least concded wth a general change n the daly seasonalty n mean returns. Moreover, our evdence largely confrms the fndngs of Kamara (1997) and Hrak et al. (1998) for the US and Japanese markets, and mportantly suggests smlar effects have occurred n other markets such as Germany, Swtzerland and the UK. Further analyss conssts of testng the basc seasonalty hypothess as appled to the return autocorrelatons case. Ths s represented by Hypotheses H3 and H4 outlned prevously and the results are shown n Panel B of Table 6. For H3: λ PreMon = λ PreODW, n all cases except the UK ths hypothess s rejected. Ths therefore supports the earler concluson that the Monday autocorrelaton s sgnfcantly hgher than ts counterpart taken for all other days durng the pre-tradng perod. In the case of Australa and Japan, H3: λ PreTue = λ PreODW shows rejecton only for Japan n ths case drven by a lower Tuesday return autocorrelaton. Furthermore, the counterpart autocorrelaton hypotheses for the post-tradng perod (H4: λ = λ PostODW and λ PostTue = λ PostODW ) reveal smlarly strong rejectons. Generally, these fndngs confrm the belef that the ntroducton of futures tradng has not been assocated wth any major change to the return dynamcs as reflected by daly seasonalty n return autocorrelatons. F. Tests of Man Hypotheses Daly Seasonal Effects: Varance Equaton Results Panel C of Table 6 presents the outcome of the set of Wald tests of the analogous seasonalty hypothess n the varance equaton. Ths s represented by Hypotheses H5 and H6 outlned prevously. Generally, t can be seen n the table that the basc 20
seasonalty hypothess for volatlty only fals to be rejected twce out of 14 occasons. Of note s the case of Australa n whch the daly seasonal n volatlty, whle beng strong n the post-tradng perod, was non-exstent n the pre-tradng perod. However, the US reveals the opposte change namely, an extremely strong rejecton of the man volatlty seasonal hypothess n the pre-tradng perod, has become starkly nsgnfcant n the post-tradng perod. Ths latter fndng s consstent wth the earler extended analyss reported for the US. Gven that the volatlty equalty hypothess s only rejected for Australa and the US and then n opposng ways, suggests that ths s unlkely to be drven by the ntroducton of ndex futures tradng. A more plausble concluson relates to nose, as outlned earler. G. Tests of Supplementary Day of the Week Hypotheses Fnally, for (a) mean returns; (b) return autocorrelatons; and (c) return volatltes; we perform an addtonal set of jont tests as outlned n Secton II D namely, the jont equalty of (a) the fve pre-tradng perod day-of-the-week coeffcents and (b) the fve post-tradng perod day-of-the-week coeffcents, for each country. These tests are conducted n the context of the expanded verson of the model outlned n Equatons (5) and (6) earler and the results are reported n Table 7. [TABLE 7 ABOUT HERE] Consultng Panel A of the table wth respect to the mean returns verson of ths hypothess n the pre-tradng perod (H7), except n the case of Span, the day-of-theweek coeffcents are statstcally dfferent from each other. Wth regard to the counterpart jont tests appled to the post-tradng perod (H8), only Australa, Japan and the UK reject the null hypothess. However, n the case of Japan and the UK the strength of the rejecton s much weaker n the post-tradng perod (partcularly for Japan). Whle these results vary slghtly from the man tests reported above, they confrm that n the case of Germany, Swtzerland and the US, a sgnfcant change n the day of the week effect n mean returns concded wth the ntroducton of ndex futures contracts. 21
Panel B of Table 7 reveals the outcome of the supplementary equalty tests appled to the return autocorrelatons. Specfcally, t can be seen that n the pretradng perod (H9) all countres (wth the excepton of Australa) reject the equalty of day of the week return autocorrelatons coeffcents. In the post-tradng perod (H10) t s Germany that presents the only case of a non-rejecton of ths hypothess. These outcomes are largely consstent wth the results of the man hypothess testng reported n the prevous table. Fnally, Panel C of Table 7 reports the results for testng the equalty hypothess as appled to the day of the week volatltes. In both the pre-tradng perod (H11) and the post-tradng perod (H12) an overwhelmng rejecton of the equalty hypothess s revealed. Generally, the outcome of the secondary tests reported n ths subsecton renforce the earler concluson that whle ndex futures tradng has concded wth a change n the mean return daly seasonalty, smlar changes n ether the return autocorrelaton or volatlty seasonalty have not been evdent. 22
IV. CONCLUSION The tradng of futures contracts often has an mpact on the underlyng asset on whch ts value s based. In ths paper, the potental mpact of the ntroducton of stock ndex futures on the daly seasonalty of the underlyng share ndex was examned for a group of seven countres Australa, Germany, Japan, Span, Swtzerland, the UK and the US. Ths daly seasonalty testng s performed wth respect to (a) mean returns; (b) return autocorrelatons; and (c) return volatltes. Each country s ndex return s modeled usng a GARCH model augmented by day-of-the-week dummy varables n both the mean and varance equaton. A varety of Wald tests were performed to assess whether the daly seasonalty n the pre-futures tradng perod was dfferent to that of the post-futures tradng perod. In ths paper two major contrbutons to the exstng lterature are made. Frst, the use of a GARCH model allows us to provde new nsghts as we may smultaneously consder the mpact of stock ndex futures tradng on daly returns seasonalty n both the mean and volatlty dmensons. Second, we present a unfed package of evdence spannng a number of natonal boundares that wll help to counter the concern of a data snoopng bas. Exstng evdence pertanng to ths general area s currently only avalable for two markets, namely, the US and Japan but then only n terms of mean return effects. Our nvestgaton extends the coverage to seven markets. Our major fndngs are as follows. In general, our results suggest that the ntroducton of futures tradng has been assocated wth reduced seasonalty of mean returns. Ths s partcularly the case wth regard to the general weakenng of the Monday effect n mean returns for the US; Germany; and Swtzerland, and to a lesser extent for the UK. Smlarly for Japan and to a lesser extent for Australa, the Tuesday effect n mean returns no longer s n evdence. Ths fndng supports the arguments presented by Kamara (1997) and Hrak et al. (1998) that, for example, futures tradng lowers transacton costs of traders who may be lookng to arbtrage any proftable opportuntes, ncludng daly seasonals. Furthermore, whle we detect daly seasonalty n return autocorrelatons and volatltes that s largely related to Monday and Tuesday observatons, ths seasonalty does not seem to be affected by the ntroducton of ndex futures contracts. Notably however, the general confrmaton 23
(across our sample of seven countres) of seasonalty n (a) return volatlty provdes an mportant nternatonal extenson of the fndngs of Fama (1965); Gbbons and Hess (1981) and Agrawal and Tandon (1994); and (b) return autocorrelatons, provdes an mportant nternatonal extenson of the fndngs of Bessembnder and Hertzel (1993). As such, our analyss suggests that a fndng of a weakenng n daly seasonals that concdes wth ndex futures ntroducton, s not as smple as frst thought. Whle we agree wth the concluson of Hrak et al. (1998, p. 505)...that return seasonalty n tself s a dynamc process and that prevously documented returns patterns are lkely to change whenever there s a major structural change n fnancal markets, our work suggests focusng solely on mean returns may only partally capture ths evoluton. That s, the nterplay between changes occurrng n the frst and second moments of returns presents addtonal challenges for emprcal researchers. Accordngly, we commend ths as a focus for future research n ths area. 24
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