African Journal of Business Managemen Vol.6 (9), pp. 870-8736, 5 July, 0 Available online a hp://www.academicjournals.org/ajbm DOI: 0.5897/AJBM.88 ISSN 993-833 0 Academic Journals Full Lengh Research Paper An asymmeric process beween iniial margin requiremens and volailiy: New evidence from Japanese sock marke Sohn, Pando *, Kim, Sungsin and Seo, Ji-Yong Deparmen of Business Adminisraion, Dong-A Universiy, -, Bumin-dong, Seo-gu, Busan 60-760, Korea. Division of Business Adminisraion, Sangmyung Universiy, 7, Hongji-dong, Jongno-gu, Seoul 0-743, Korea. Acceped 8 February, 0 This paper invesigaes on wheher here is he asymmeric relaion beween iniial margin requiremens and volailiy across bull and bear markes as well as normal for he Japanese TOPIX and NIKKEI 5 indices over period of 970 o 990. We use regression in levels o scruinize relaion beween margin requiremens and volailiy. We find ha here is negaive relaion. This resul is confirmed significanly by boosrap simulaion. The findings show ha margin requiremen affecs and causes sock reurn volailiy. Thus higher margin requiremens are associaed wih lower subsequen sock marke volailiy across normal bu bear markes marginally, bu show no relaionship during bull markes from regression and exponenial general auoregressive condiional heeroskedasiciy (EGARCH-M) model wih GED. As a resul, we conclude ha here is an asymmeric process ha is, depyramiding effec regarding bear markes from Japanese sock marke. However, for bull periods, we find ha here is no evidence of asymmeric process. In conclusion, we confirm ha he policy ool of margin requiremens does more effecively work when sock marke is in deep recession, bu no work in bubble sae. Key words: Iniial margin requiremens, pyramiding or depyramiding effec, volailiy, boosrap simulaion, granger causaion, exponenial general auoregressive condiional heeroskedasiciy (EGARCH-M). INTRODUCTION Afer he 987 U.S sock marke crash and also recen 008 U.S. credi crunch in financial field, many governmen regulaors of he sock markes in he world have imposed some resricions abou buying on margin and shor selling because hey believe ha hese invesmen sraegies make sock marke volailiy increase rapidly. Before his argumen, acually many have been hough ha volailiy in sock marke migh be conrolled by hese policies, which means ha margin and shor selling is easy o use o simulae sock price depression when sock marke is in recession; and in urn *Corresponding auhor. E-mail: pdsohn@dau.ac.kr. Tel: 8-5- 00-744. hese policies are ighen o reduce he bubble of sock price when i is in boom. This paper examines wheher margin requiremen could be worked well as he policy ool of sock marke sabilizaion in differen marke condiions such as boom, normal, and recession. To verify hese argumens suggesed in prior sudies, Japanese sock marke allows us o use sample because his marke had been very ofen changed margin requiremen policy. In many previous lieraures, how margin requiremens affec sock prices, sock reurn and reurn volailiy has been coninuously an ineresing quesion among academic research and pracice. Margin requiremens are official resricions on he amoun of borrowing available o invesors from brokers and dealers for he purpose of buying socks. An iniial margin requiremen
Pando e al. 87 policy has been used o proec financial marke sysem when sock marke is so volaile. Thus, i is consrain for individual or insiuional invesor o buy addiional sock a credi, which means high leverage. An iniial margin change also affecs o invesors when sock price is crashed or irraional urbulence. Furhermore, if he margin requiremens are limied, increasing he margin requiremens leads o a decrease in sock volailiy when he invesor is relaively opimisic and in urn, leads o an increase in sock volailiy when invesor is relaively pessimisic. Thus, margin requiremens may sabilize or desabilize he disribuion of sock reurn and volailiy. As a resul, he role of iniial margin requiremens is in fac, designed o preven excess volailiy and fragiliy on marke sysem. However, he resuls of hese sudies are mixed. For insance, some sudies insised ha here is evidence of negaive relaionship beween margin requiremens and sock volailiy (Kupiec, 989; Hardouvelis, 990; Hardouvelis and Perisiani, 990, 99; Hardouvelis and Theodossiou, 00). On he oher hand, oher sudies claimed ha here is no such evidence (Ferris and Chance, 988; Kumar e al., 99; Salinger, 989; Schwer, 988; Hsieh and Miller, 990; Kim and Oppenheimer, 00). Due o conroversial resuls in many previous lieraures, we re-examine he relaionship iniial margin requiremens and reurn volailiy using differen mehodlogy on wheher here is he asymmeric relaionship in differen marke saes ha is, bull, bear, and normal, using Japanese sock marke. This asymmery is also acknowledged hrough U.S. economy policy in hisory. When U.S. Congress insiued firsly an iniial margin requiremens regulaion, i had in mind ha pyramiding-depyramiding process was an asymmeric process: prudenial margin regulaion was hough o be an effecive ool of avoiding he excesses of a bull marke, hus, minimizing he probabiliy of disrupions and also higher margin requiremens were no hough o be effecive ool of smoohing he effecs of disrupions (Garbade, 98; Hardouvelis and Theodossiou, 00). We see his differen role of iniial margin requiremen regulaion across bear and bull markes in he hisorical decisions of he U.S Federal Reserve for changing he level of iniial margin requiremens. For Japanese sock marke, since 95, iniial margin requiremens were inroduced and have been changed 68 imes (including cash) unil 990. We use he sample daa from 970 o 990 because iniial margin requiremens have no been changed since 99. Therefore, because of many changes in iniial margin requiremens, we have a good opporuniy o invesigae his asymmeric relaionship in Japanese sock marke. The remainder of his paper is organized as follows: heoreical issues and relaed lieraure in erms of iniial margin requiremens and volailiy; explanaion of insiuional characerisics; presenaion of daa and some saisic issues; implemenaion of regression analysis in levels; misspecificaion in regression indifference; invesigaion of asymmeric relaion across bull and bear markes; EGARCH model is designed o find he linkage beween margin requiremens and condiional volailiy; discussion of he resuls from EGARCH model; conclusion. THEORETICAL ISSUES AND RELATED LITERATURE I has been known ha he iniial margin requiremens generally are srong and forced policy ool o conrol sharp sock price changes and marke volailiy. From U.S. Securiies Exchange Ac of 934, margin requiremens would discourage he redirecion of credi from business uses o speculaive aciviy, hey would proec invesors and brokers from he risks posed by excessive leverage, and hey would conribue o he sabiliy of sock prices by inervening in he pyramidingdepyramiding process (Forune, 00). Iniial margin requiremens deermine he maximum legal collaeral value of a marginable securiy. Thus, i resrics he amoun of credi ha brokers and dealers can exend o heir cusomers for he purpose of buying socks. In addiion, he consideraions on he effec of iniial margin requiremens are he quesion of which ype of rader is more affeced. If increasing margin requiremens discourages only noise raders, no informed raders, he marke volailiy will be reduced effecively. Bu unforunaely if reversing, i will simulae volailiy. In heory, Kupiec (989) analyzed in hypohesizing a negaive relaionship ha i resrics he rading of desabilizing speculaors, whose rading aciviy creaes excess volailiy. This hypohesis is based on noise rader concep in Delong e al. (987). The average reurn variance on risky asses increases due o noise raders and also he influence of he noise raders causes risky asses o exhibi excess volailiy over ha which is jusified by economic facors. As lowering iniial margins, noise rader s abiliies o leverage heir posiions are higher and creae irraional excess volailiy. This kind of rading behavior is called pyramiding and depyramiding process. In urn, as increasing iniial margin requiremens, he leverage on he noise raders posiions decrease and also he excess volailiy will be smaller. However, on he oher hand, Goldberg (985) hypohesizes a posiive relaionship beween he iniial margin requiremens and sock reurn volailiy by using he deb and ax model of Miller (977). Therefore, hese heories have focused as follows. Some papers evaluae he efficacy of iniial margin requiremens in proecing invesors wihou solving he quesion of marke sabiliy and ohers have sressed on he sabilizaion goal wihou addressing he issue of invesor proecion.
87 Afr. J. Bus. Manage. In empirical findings, he resuls on maer of margin requiremens are very mixed and conroversial evidences as follows. Largay and Wes (973) found ha he S and P 500 index rose before margin increases and fell before margin decreases and no significan abnormal reurn on he S and P 500 index eiher on he day a margin change was announced or during he 30 days afer a margin change. This resul is consisen wih he view ha he FRB sysem changed regulaion of iniial margin requiremens in response o recen sock price movemens. Grube e al. (979) also found an asymmery effec in erms of sock reurn and rading volume using an even sudy mehod and furhermore alhough, increasing an iniial margin requiremens significanly reduces rading volume, decreasing an iniial margin requiremens does no affec rading volume. However, Ferris and Chance (988) and Harzmark (986) found no relaionship beween margin changes and price volailiy. This debae was iniiaed by Hardouvelis (988) and i has coninued. Hardouvelis (988, 990) argues ha wih regard o Fed s reacion funcion, he Fed looks o sign boh of high credi use o buy socks and of poenial sock price bubbles when seing margin requiremens. This behavior also is found in Japanese sock marke. He concludes ha speculaive bubbles which mean excess volailiy are a source of volailiy and furhermore he level of excess volailiy is affeced by margin requiremens. Tha is, an increase (decrease) in margin requiremens reduces (increases) excess volailiy. Hardouvelis and Perisiani (99) invesigaed Japanese iniial requiremens using even sudy and conclude ha margin increases (decreases) are negaevely associaed wih sock reurn decreases (increases) saisically and economically. In conras o hese evidences, Kupiec (989, 998), Salinger (989), and Kofman and Moser (00) rejec Hardouvelis evidences and insis ha here is no clear relaionship beween iniial margin requiremens and sock reurn volailiy. In addiion, Seguin and Jarrell (993) documened ha using NASDAQ securiies daa, here is no evidence ha margin aciviy simulaed addiional price down. Tha is, margin-eligible securiies acually fell by % less han he ineligible securiies over bear marke, ha is, he crash of 987. Forune (00) invesigaes margin lending and sock marke volailiy using he jump diffusion model and argues ha a higher level of margin deb ends o raise reurns in a bull marke and induce greaer declines in a bear marke. Thus margin loans seem o aggravae he magniude of sock price changes in eiher direcion. In Forune (00) paper, he economic significance is so low ha i is no able o suppor a reurn o he acive margin policy of he 934 o 974 periods even if margin loan affecs saisically sock reurns and heir volailiy. Kim and Oppenheimer (00) examines relaionship beween iniial margin requiremens and reurn volailiy for he individual invesor using Japanese sock marke daa, and concludes ha here is no relaionship beween iniial margin requiremens and volailiy. Now sill oher sudies sugges ha volailiy is eiher unaffeced by margin requiremens or ha i is posiively or negaively or no correlaed wih margin requiremens. Insiuional characerisics Since June, 95, margin sysem was firsly inroduced in Japanese sock marke. Japanese margin regulaion is similar o regulaion of U.S. sock exchange bu regulaion auhoriy is differen, ha is, U.S. sock exchange conrolled by FRB and Tokyo sock exchange conrolled by he Minisry of Finance. Since 95 imposed firsly, i has changed margin requiremens over 00 imes. We hink ha our sudy using sample daa of Japanese Tokyo sock exchange (TSE) may provide considerable saisical power han sudying U.S. sock exchange because of more frequen of margin requiremens. The Japanese margin sysem incorporaes boh an iniial margin requiremen and a mainenance margin ino is sock marke; and cash or socks can be used o saisfy he iniial margin requiremen. Margin in TSE is defined by collaeral deposied o a securiies firm, when borrowing money or socks needed for margin ransacions. TSE imposes funcion of margin ransacion o provide more deph and secure more liquidiy, and o conribue o he fair and orderly price formaion. Also purpose on margin imposed by TSE is o make profis from a shor-erm capial gain, expecing a rise or fall of sock prices in a shor period ime and o avoid he risks associaed wih a fall in sock prices, selling hedge. Table shows a summary of all margin requiremen changes since 970. Iniial margin requiremens vary beween 30 and 70%. Since Sepember 6, 990, margin requiremens have no changed unil now. Specifically, he firs official level of margin requiremen was se in Ocober 95 a 45% (M =0.45); he curren official level is 30%, a level which has been in effec since Sepember 9, 990. The highes level of he iniial margin requiremen was 70%, which occurred on January 9, 973, May 7, 979, February 7, 987, and Jun 3, 988. The lowes level has been 30%, which is also he curren level. In addiion, for he relaionship beween margin requiremens and volailiy based on daily reurn, he plo is shown in Figures and. DATA AND STATISTICAL ISSUES In his paper, he daily sample ime period over which he model is esimaed is from 970 o 990 alhough, official margin requiremens were inroduced in June, 95. As menioned in earlier par, we do no use daa afer 99 and we canno idenify his relaionship afer his year because iniial margin requiremens had no been changed afer 99.
Pando e al. 873 Table. Summary of iniial margin requiremens changes in Japan since 970. Effecive dae Iniial margin (%) Effecive dae Iniial margin (%) Effecive dae Iniial margin (%) 0/0/ 970 30 07/9//977 30 09/09/98 50 03/06/970 40 03/08/978 40 09/4/98 40 05/0/970 30 03/9/978 50 09/9/98 30 04/3//97 40 04/03/978 60 /6/98 40 04/9/97 50 05/3/978 60 0/8/98 30 08/9/97 40 08/0/978 50 /03/98 40 08/0/97 30 0/0/978 60 07/08/983 50 /7/97 40 03/8/979 50 03/4/984 60 0/08/97 50 05/0/979 60 05/9/984 50 0/9/97 60 05/7/979 70 0/7/985 60 /0/97 60 06/5/979 60 /06/985 50 0/09/973 70 07/3/979 50 03/3/986 60 /05/973 60 0/6/980 60 0/7/987 70 0//973 50 04/0/980 50 0//987 50 /4/973 40 04/6/980 60 03/7/988 60 0/03/974 30 06//980 50 06/03/988 70 0/3/976 40 /7/980 40 06/03/989 60 0/0/976 50 03/4/98 30 0//990 50 07/30/976 40 03/6/98 40 0/7/990 40 //976 50 04/0/98 50 09/06/990 30 0/7/977 60 04/5/98 60 03/5/977 50 06/09/98 50 06/04/977 40 07/03/98 60 Toal 63 imes Source: Tokyo sock exchange. In his paper, we use he daily reurns for TOPIX and NIKKE 5 indices o measure volailiy a weekly frequency. The daily daa are colleced from DATASTREAM. Afer all, he weekly sample based on geomeric daily average is used. Marke reurns are consruced from TOPIX and NIKKEI 5 indices, using he formula R =ln(topix /TOPIX -)*00 and R =ln(nikkei5 /NIKKEI5 -)*00. Calculaed reurns are expressed in a coninuously compounded percenage form and include dividend. Table summarizes he descripive saisics for TOPIX and NIKKEI 5 ime series. As shown in Table, Japanese auhoriy has changed official iniial margin requiremens 63 imes over he sample period in his paper. Because margin requiremen policy is discree variable, i is bounded o ake values from 0.3 (30%) o (00%). The level of margin requiremens which is a discree policy canno be regarded as a random walk process, and hus i may have a uni roo because of being finie variance. Furhermore, if he margin series are differenced in esing model, hey resuls in a new series wih all zeros, excep for 63 cases when he value is non-zero. This problem is discussed in Hardouvelis and Theodossiou (00). Hardouvelis and Theodossiou (00) insis ha using such a variable as an explanaory variable of he condiional volailiy series is equivalen o esing for emporary blips in volailiy a each insance margins were changed and would make i difficul o uncover he long-run relaionship beween level of margin requiremens and volailiy. According o weak of sample ime series in his paper as menioned earlier, before implemening regression analysis in levels, we conduc a uni roo es for margin series because infrequen margin changes could lead o produce an auocorrelaion funcion similar o one originaing from a sochasic series wih a uni roo. To check margin original ime series saionary, we employ a simple Phillips and Perron (988) and Augmened Dickey and Fuller (979) es mehod. Le M he level of margin requiremens a he end of week and he firs-difference operaor. As employed by Hardouvelis and Theodossiou (00), we esimae he k h -order auoregressive model as follows: M = a + bm + a M + e 0 p p m, p= k We chose lag k=, 4, 6, o eliminae any serial correlaion in he residuals and es he null hypohesis ha b =0 for each lag k. We expec ha less change of margin requiremens make he coefficien b close o zero. However, in empirical es of uni roo, he esimaed coefficien value of b is -0.03 wih -value of-3.36 for k=; -0.03 wih - value of -3.45 for k=4; -0.037 and - value of -3.47 for k=6; and - 0.057 and -value of -.45 for k=. All coefficiens are significan saisically a he %. As unexpecedly, we confirm ha here is no uni roo in margin series. Thus, we conclude ha he uni roo hypohesis is saisical rejeced significanly and so he margin series are saionary o es addiional analysis. We also look a he volailiy series in TOPIX and NIKKEI 5 indices and run Phillips and Perron and Augmened Dicky-Fuller es a weekly frequency by using he sandard deviaion of daily reurns during week. Le σ d, he sandard deviaion of reurns a end of week based on he sandard deviaion of daily reurns. is he firs-difference ()
874 Afr. J. Bus. Manage. Topix weekly Sd 0 Topix sd Margin rae Margin Rae 0.8 9 0.7 8 0.6 7 6 0.5 5 0.4 4 0.3 3 0. 0. 0 970 970 97 97 97 973 974 975 975 976 977 977 978 979 980 980 98 98 98 983 984 985 985 986 987 987 988 989 990 990 99 99 993 993 994 995 995 996 997 998 998 999 Time period 0 Figure. TOPIX volailiy and margin rae. NK5 weekly Sd 0 Margin Rae 0.8 NK5 STD Margin rae 9 0.7 8 0.6 7 6 0.5 5 0.4 4 0.3 3 0. 0. 0 970 970 97 97 97 973 974 974 975 976 977 977 978 979 979 980 98 98 98 983 983 984 985 986 986 987 988 988 989 990 990 99 99 993 993 994 995 995 996 997 997 998 999 Time period 0 Figure. NIKEEI 5 volailiy and margin rae. operaor as well. The auoregressive model is as follows: σ = a + bσ + a σ + e d, 0 d, p d, p d, p= k () For TOPIX, we chose k=, 4, 6, and es he null hypohesis ha b =0. The esimaed coefficien value, b is -0.998(-value= -7.8) for k=; -0.538(-value=-6.9) for k=4; -0.8(-value=-6.45) for k=6; -0.784(-value=-6.) for k=. For NIKKEI5, we also chose k=, 4, 6, and es he null hypohesis ha b = 0. The esimaed coefficien value, b is
Pando e al. 875 Table. The summary of descripive saisics based on weekly ime series by daily average. Variable Mean Median Sd Min Max Skewness Kurosis TOPIX reurn (%) 0.0330 0.0475 0.4755-3.36.677-0.6835 5.339 NIKKEI 5 reurn (%) 0.030 0.05 0.548-3.554.094-0.639 5.54 Margin requiremens Rae (%) 43.05 40 3.8 30 70 NA NA 0.536(-value= -0.08) for k=; -0.78(-value=-8.07) for k=4; - 0.987(-value=-7.3) for k=6; -0.03(-value=-5.97) for k=. As he same over, he uni roo hypohesis is rejeced definably in TOPIX and NIKKEI 5 series. Because a uni roo in boh he margin series and volailiy series does no appear, we sugges ha he model specificaion in level which relaes he wo variables is proper and his specificaion give us robus resuls saisically. Neverheless, as menioned in Hardouvelis and Theodossiou (00), and Granger and Newbold (974), because here is he near-uni-roo behavior of he margin series ogeher wih he high serial correlaion in he volailiy series, spurious regression resuls could be produced beween he levels of he wo series, ha is, biased coefficien esimaes. Because of possibiliy of hese phenomena, many previous researchers examine he relaion beween margin requiremen series and volailiy series in firsdifference form. Laer, we handle and es his issue in more deails, and also compare wih he resuls of each model. THE RESULT OF REGRESSION ANALYSIS IN LEVELS In his area, we analyze a linear regression in level form o find he relaionship beween margin requiremens and volailiy. The volailiy used in his paper is proxy by he sandard deviaion of daily reurns during each week. Overlapping daa, which means ha auhoriy changes over wice a same week, is averaged in margin requiremens. The daa overlapping issue generaes serious problem which is arificial serial correlaion and he informaion effec on he margin requiremens would be disappeared or oversaed. As Hardouvelis and Theodossiou (00), he general form of regression model is as follows: σ = + σ + σ + R d, 0 d, d, 3 d, + R + M + ( R M ) + e M where 4 d, 5 6 d, d, = + σ + σ + R d, 0 d, d, 3 d, + R + M + ( R M ) + ε 4 d, 5 6 d, d, σ d, (3) (4) is weekly sandard deviaion based on daily M σ, σ, reurn; is margin requiremen level; d and d are weekly sandard deviaion based on daily reurn a (- R ) and (-), respecively; d, is he volailiy shock a (-) measured by he absolue value of he average daily Rd, reurn wihin he week, and is he weekly reurn a (-) by averaging daily reurns o conrol for leverage M effec on volailiy, is he level of margin requiremens Rd, M a (-), and is he cross produc or ineracion erm a (-) o capure a possible asymmeric relaion beween margin requiremens and volailiy. Firs of all, in order o decide which one influences o oher one, ha is, causaion relaion beween margin level and volailiy, we do Granger causaliy es using wo equaions specified in Equaions 3 and 4. In he es resul, he null hypohesis which saes ha margin rae does no Granger cause volailiy is rejeced and saisically significan a % wih F-value of 6.6568 and 5.075 for TOPIX and NIKKEI 5 respecively. Finally, we make sure ha margin requiremen level affecs sock reurn volailiy in boh indices. In Equaion 3, volailiy as dependen variable is analyzed and esimaed based on OLS wih Newey-Wes HAC. Especially he main goal in his regression is o make sure wheher or no here is a bias in he esimaed coefficiens of hese variables because esimaed resuls of OLS could be originaing from Granger-Newbold spurious regression. As menioned earlier, addiionally, we run boosrap simulaion o confirm wheher findings of OLS are robus or no. Average coefficiens esimaed in boosrap simulaion are produced using,000 boosrap samples each generaed randomly from he empirical disribuion of he OLS residuals of he model as implemened in Hardouvelis and Theodossiou (00). We ry o confirm wheher he resuls of OLS are robus by using boosrap simulaion mehod. The empirical resuls are summarized in Table 3. Model of Table 3 shows he mulivariae OLS of weekly volailiy based on he daily reurn. Tha is, model in Table 3 is enhanced by adding wo lags of volailiy, σ d, σ d,,, and one lag of he volailiy shock as Rd, proxy. We confirm no serial correlaion from DW (Durbin Weson auocorrelaion es) in model. For model, he 5 margin requiremen coefficiens, s for boh markes are negaive and significan a he %, respecively.
876 Afr. J. Bus. Manage. Table 3. The resul of regression analysis in levels for TOPIX and NIKKEI 5. Coefficien Panel A. TOPIX Panel B. NIKKEI 5 Model Model Model 3 Model 4 Model Model Model 3 Model 4 0 0.3346 *** 0.4064 *** 0.3984 *** 0.46 *** 0.5470 *** 0.5486 *** 0.5384 *** 0.5545 *** (6.64) (8.37) (8.3) (8.37) (9.) (9.44) (9.3) (9.53) 0.39 *** 0.40 *** 0.87 *** 0.306 *** 0.8 *** 0.5 *** 0.449 *** 0.575 *** (7.77) (7.5) (6.95) (7.4) (9.) (7.7) (7.43) (8.08) 0.360 *** 0.694 *** 0.698 *** 0.673 *** 0.555 *** 0.76 *** 0.79 *** 0.694 *** (4.78) (5.88) (5.88) (5.8) (5.83) (6.5) (6.9) (6.07) 3 0.5397 *** 0.469 *** 0.4837 *** 0.4595 *** 0.46 *** 0.453 *** 0.4654 *** 0.4453 *** (6.50) (6.66) (6.7) (6.54) (4.9) (5.35) (5.38) (5.33) 4-0.394 *** -0.386 *** -0.775 *** -0.408 *** (-6.68) (-3.49) (-6.57) (-3.64) Boosrap( 4 ) -0.40 *** -0.995 *** -0.09-0.4055 *** {-4.8} {-.98} {-4.8} {-3.7} 5-0.343 ** -0.85 *** -0.584 *** -0.3670-0.438 *** -0.4860 *** -0.64 *** -0.3868 (-.4) (-.49) (-5.99) (-.46) (-3.90) (-4.4) (-6.7) (-.54) Boosrap ( 5) -0.065 *** -0.37 *** -0.96 *** -0.9 *** -0.3566 *** -0.394 *** -0.3345 *** -0.9 *** {-3.50} {-3.8} {-3.8} {-3.80} {-4.70} {-5.7} {-4.} {-3.80} 6-0.39 ** -0.546 ** -0.400 *** -0.4560 *** (-.94) (-.6) (-3.6) (-4.07) Boosrap( 6 ) -0.558 *** -0.3697 *** -0.3809 *** -0.4806 *** {-3.83} {-.75} {-5.05} {-.4} Adj. R 0.764 0.3086 0.305 0.3094 0.36 0.3533 0.346 0.3539 F-Value 48.46 *** 38.8 *** 34.9 *** 6.3 *** 79.4 *** 69.75 *** 64.54 *** 4.0 *** DW..5.4.6.0.5.3.5 This able shows he regression resul of weekly volailiy from daily daa on margin requiremen. The regression wih Newey-Wes HAC sandard error is esimaed during 970-990. σ d, Esimaed model in his paper is as follows: = 0 σ d, σ d, 3 R d, 4 R d, + + + + + 5M 6 ( Rd, M ) + e d, σ d, +. The dependen variable is weekly sandard deviaion based on daily reurn. Parenheses, ( ) is -value for regression wih Newey-Wes HAC and bracke, { } is -value from boosrap simulaion wih replacemen. ***, **, * are significan a he, 5, and 0% level, respecively.
Pando e al. 877 However, because here are posiive auoregressive coefficiens and all are significan a he %, ha is, = 0.39 and = 0.36 for TOPIX; and = 0.8 and = 0.555 for NIKKEI 5, as menioned in Hardouvelis and Theodossiou (00), i indicaes ha, following a permanen change in margins, he cumulaive long-run associaion beween margins and volailiy remains approximaely he same. Thus, his long run associaion is 5 /( ) = - 0.343/ (-0.39-0.360) = -0.3707 for TOPIX, and /( ) 5 =-0.438/ (-0.8-0.555) =-0.768 for NIKKEI 5. In boosrap simulaion for model of Table 3, he afore-menioned resuls are also confirmed, bu average coefficien, -0.065(-value=-3.50) and - 0.3566(-value=-4.70) for boh markes are smaller han - 0.343 (-value=-.4) and -0.438(-value=-3.90) in OLS wih same sign or direcion excep smaller coefficiens and bigger -values. Hence, we sugges ha he Granger-Newbold spurious regression problem does no affec esimaed coefficiens of OLS. The same conclusion is found in model, 3, and 4, respecively. This evidence is no only for he, bu 6 also for he coefficiens 4 and. Hence, inference from he -value of OLS is no affeced by he Granger- Newbold spurious problem. As suggesed by Hardouvelis (990), he weak saisical significance wih smaller - values of he margin requiremen coefficiens in model of Table 3 could be due o he lack of he appropriae conrol variables in he regressions. In logical process, margin requiremens or sock price movemens affec he decision of Japanese financial auhoriy o change margin requiremens and in urn could be correlaed wih volailiy. For model of Table 3, we conrol for average daily sock reurn a (-), d, based on prior lieraure ha sock reurns a (-) are also negaively associaed wih volailiy a ime. The 4 esimaed coefficiens, s wih -0.394(-value=-6.68) for TOPIX and -0.775(-value=-6.57) for NIKKEI 5 in model of Panel A and Panel B are negaively associaed and significan saisically a %. Thus, hese resuls are consisen wih prior sudies. R Afer conrolling for d,, a saisical power of 5 coefficien( ) for boh in models is boosed slighly, which means ha -values are from -.4 o -.49 for TOPIX and from -3.90 o -4.4 for NIKKEI 5. The long run relaion beween margins and volailiy in model of Table 3 is 5 /( ) = - 0.85/(- 0.4-0.694) = - 0.47 for TOPIX, and 5 /( ) = - 5 R 0.486/ (-0.5-0.76) =-0.84 for NIKKEI 5. These findings imply ha he percenage change in volailiy wih respec o a percenage in erms of long run elasiciy is approximaely -0.05% (=- 0.47(0.4305 /0.989)) for TOPIX and -0.36%(=-0.84(0.4305/.488) for NIKKEI 5, where 0.4305 is he average margin requiremens during 970 o 999; and 0.989 and.488 are he average daily volailiy in boh indices. As a maer of fac, ineresingly, his evidence documens ha he effec of margin requiremens on volailiy is bigger in NIKKEI 5 han in TOPIX. Bu hese effecs are smaller han as -0.35% in U.S by findings of Hardouvelis and Theodossiou (00). Now we invesigae on wheher here is a possible asymmeric relaion beween margin requiremens and volailiy or no. Model 3 is o es presence of an asymmery in erms of he sign and size of he price change weekly a (-). Model 3 could enhance model hrough including he ( R ineracion erm, d, M ) R d, insead of. The associaion beween margin levels and volailiy is now refleced in he composie coefficien ( 5 + 6 ) and variaion according o boh he sign and he size of he earlier sock price change is also allowed. Boh coefficiens 5and for TOPIX and NIKKEI 5 are - 0.584 wih -value= -5.99 and -0.39 wih -value= -.94, respecively for TOPIX; and -0.64 (-value= -6.7) and -0.400 (-value=-3.6), respecively for NIKKEI 5. They are negaively significan a he % or 5% in boh markes. This evidence implies ha he relaion of margin levels o volailiy could be nonlinear. We will check his resul using E-GARCH model. The negaive sign value of suggess ha he negaive sensiiviy of volailiy o Rd, margins ges larger in absolue erm, he higher d, he reurn a (-). We include wo erms, and ( Rd, M ) o model 4 because ineracion erm, ( Rd, M ) could be dominaed by he informaion in Rd,. If he leverage effec dominaes he informaion in ( Rd, M ), hen 4 should be significan and 6 insignifican as well (Hardouvelis and Theodossiou, 00). Conversely, if he informaion in he ineracion ( R erm, d, M ) shows mainly an asymmery effec, hen 6 should coninue o be significan despie he presence of d, in regression (Hardouvelis and Theodossiou, 00). We find ha 6 6 R R 6 is sill being negaive and significan in
878 Afr. J. Bus. Manage. boh indices as before despie he presence of in he regression. We conclude ha boh he leverage effec and he asymmery effec are no behind he informaion ( R M ) d, in. Rd, Is here a misspecificaion in regression in firsdifference? In he earlier model es, we idenified ha regression model in levels is correcly specified. Neverheless, regression model in firs-difference has been used in many previous papers and heir papers give lile evidence of a negaive relaionship beween volailiy and margin requiremens. Thus, i is worhwhile o esimae he regression in firs-difference form in order o compare he resuls of regression in levels form and idenify he source of heir differen empirical resuls. To enhance comparison, model in Table 3 is chosen by incorporaing he leverage effec, and we faciliae i by adding second lag of margin requiremens, M -, as an independen variable. Then general regression in levels form for boh TOPIX and NIKKEI 5 indices is as follows: σ = + σ + σ + R + R + M + M + e d, 0 d, d, 3 d, 4 d, 5 6 d, ` (5) Where he noaions in his equaion are same as defined in Equaion 5. Due o he problem ha he M series are highly auo correlaed, which is firs-order auocorrelaion coefficien is 0.9879 in he weekly sample, here may be severe mulicollineariy and endogenous problem beween M - and M - in he regression Equaion 5. For TOPIX, esimaed coefficien values are =0.4048(-value=8.33), =0.73(-value=7.56), =0.678(-value=5.83), 3 =0.4748(-value=6.78), and 4 =-0.479(-value=-7.0). For NIKKE 5, esimaed coefficien values are 0 =0.465(-value=7.7), =0.378(-value=5.98), =0.35(-value=5.5), =0.4879(-value =5.75), and = -0.34(-value = -6.79). These esimaed values are close o hose in model of Table 3. The esimaed coefficiens for he lagged values of margins are 5=0.7793(-value=.38) and = -.075 (-value= -.84) for TOPIX; and = 0.603 (- 0 3 4 6 5 6 value=0.84) and = -.0406(-value = -.34) for NIKKEI 5. Due o mulicollineariy, he wo coefficiens for boh indices are pushed ino opposie direcions. The cumulaive shor run associaion of margins wih volailiy 6 5 6 is 5+ = -0.38 for TOPIX and + = -0.4374 for NIKKEI 5 and hese numbers are close o he in model of Table 3. Similarly, he long run associaion is ( 5 + 6) /( ) = -0.38/ (-0.73-0.678) = - ( 0.3938 for TOPIX, and 5 + 6) /( ) = - 0.4374/ (-0.378-0.35) = -0.857 for NIKKEI 5. These numbers are also close o he -0.47(= -0.85/ (- 0.4-0.694)) and -0.84(= -0.486/ (-0.5-0.76)), long run associaion respecively in model of Table 3. Based on Equaion 5, he volailiy and he margin variables in firs difference form are included in model 6. 5 σ = + ( + ) σ σ + R + R d, 0 d, d, 3 d, 4 d, + ( + ) M M + ed 5 6 6, (6) Tha is, Equaion 6 includes he lagged levels of boh margin requiremens and volailiy as regressors. As explained in Hardouvelis and Theodossiou (00), if hese lagged levels from he regression are omied, model would resul in misspecificaion error. Mos previous paper employed regression in firs difference form o examine he relaion beween margin requiremens and volailiy and omied hese addiional level erms. Therefore, esimaed regression model could be misspecified. As poined in Hardouvelis and Theodossiou (00), Equaion 6 is seup o compare Equaion 5. Panel A and Panel B of Table 4 repor regression esimaes for Equaion 6. Models and of Table 4 are similar o model used previously o invesigae he relaionship beween margins and volailiy, excluding he lagged levels of margin requiremens and volailiy as addiional explanaory variables. These models, however, have serial auocorrelaion problem in he residual evidenced by DW saisics due o excluding σ d,-, which is iself indicaive of model misspecificaion. The coefficiens of M - in hese models are posiive value wih.665 (-value =.) and.684 (-value =.80) for TOPIX; and.38
Pando e al. 879 Table 4. The resul of regressions of changes in TOPIX and NIKKEI 5 volailiy on margin requiremen. Panel A. TOPIX Panel B. NIKKEI 5 Coefficien Model Model Model 3 Model Model Model 3 0.0004-0.083 0.406*** -0.000-0.09 0.5474*** 0 (0.05) (-.05) (8.35) (-0.00) (-0.65) (9.46) ( + -) - -0.6049*** -0.5756*** (-7.9) (-3.9) -0.403*** -0.673*** -0.43*** -0.696*** (-3.5) (-5.8) (-4.09) (-6.05) 3 0.05 0.475*** 0.0706 0.4574*** (.3) (6.78) (0.9) (5.44) 4-0.9*** -0.470*** -0.54*** -0.846*** (-4.88) (-6.98) (-5.05) (-6.85) ( 5 + 6) - 6-0.406*** -0.4374*** (-.8) (-3.9).665.684*.077*.38.774*.030 (.) (.80) (.83) (.8) (.80) (.47) Adj. R 0.004 0.84 0.3773 0.0044 0.869 0.3703 F-value 7.43*** 88.*** 56.95*** 6.75*** 88.50*** 50.77*** DW.79.9.6.78.9.5 This able represens he resul of weekly volailiy changes from daily daa on margin requiremen for TOPIX and NIKKEI index. The esimaed regression wih Newey-Wes HAC is as follows: σ d, = 0 + ( + ) σ d, σ d, + 3 Rd, + 4 R d, + ( 5 + 6) M 6 M + ed, This equaion is based on equaion (5) and is firs difference operaor. Parenheses, ( ) is -value for regression wih Newey- Wes HAC. ***, **, * are significan a he %, 5%, and 0% level, respecively. (-value =.8) and.774 (-value =.80) for NIKKEI 5, respecively. These values all are posiive and, he coefficiens in models and 3 for TOPIX, and model for NIKKEI 5 are saisically significan a 0% as well. Hardouvelis and Theodossiou (00) argue ha esimaing models and of Table 4 would wrongly conclude ha he relaion beween margins and volailiy is posiive, when in fac, according o Equaion 6, he esimaed coefficien is acually he coefficien, - 6, denoing - even in hese misspecified models - a negaive associaion beween margins and volailiy. In model 3 in Table 4, he lagged levels of margins and volailiy are included. Thus, model 3 provides a more appropriae specificaion of he relaions beween margins and volailiy. From his model, he sum of he ( + ) 5 6 coefficiens of M - and M -, = -0.406, - 0.4374, respecively in boh indices is close o -0.38 for TOPIX and idenical o -0.4374 for NIKKEI 5 esimaed in Equaion 5. In urn, hese values are also close o - 0.343 and -0.438, which implies he resuls of he more correc specificaion of model in Table 3. As maer of fac, we are able o approximaely replicae he resuls of regressions in levels even if he model in firs-difference is used. In fac, many researchers had previously used regression model in firs-difference form and could mos likely omi he lagged levels of volailiy and margin requiremens. Based on our findings, he rue associaed wih margin requiremens and volailiy is deeced and appeared from regression model in levels. An asymmeric effec on across bull and bear markes Here, we invesigae he possible exisence of an asymmeric relaion beween margin requiremens and sock marke volailiy across bull, bear, and normal
8730 Afr. J. Bus. Manage. markes. In earlier discussion, we found he possibiliy of an asymmery according o he magniude and sign of he price change of pas week. Acually a bull or bear marke defined is a period of consecuive weekly increases or decreases in sock marke a ime horizon. To define which marke is bull or bear, we use ime horizon of four weeks and longer. As defined in Hardouvelis and Theodossiou (00), we define a bull or a bear marke as follows: a period during which here are a leas N consecuive weekly sock reurns wih same algebraic sign. We chose he horizon N aking hree possible values, N=4, 5, and 6 weeks. Table 5 repors he resuls esimaed for hese periods. For N=4 in Panel A, here are 38 disjoin bull periods, which means periods consising of a leas four consecuive posiive weekly reurns. These periods conain 88 weekly observaions, or.5% of he sample. The bear marke periods are 5 and number of observaions is 73, or 4.7% of he sample. Oher N is same as saed earlier. We see ha as he horizon N increases, he numbers of bull and bear periods decline. To invesigae a possible asymmery effec across bull and bear periods, wo dummy variables, BULL and BEAR are defined as follows: We ake he value of during bull and bear periods, respecively and he value 0 oherwise. Subsequenly, in model of Table 3, we include wo ineracion erms, (BULL * M - ) and (BEAR * M - ). Model is chosen because i conrols he leverage effec. The general regression equaion is as follows: σ = + σ + σ + R + R + M d, 0 d, d, 3 d, 4 d, M + B u l l M + B e a r M + e M B u l l M B e a r d, (7) Table 5 presens he regression resuls esimaed for all hree bull and bear periods. For bull periods, he coefficiens are posiive for boh markes, implying ha he margin requiremens are posiively correlaed o volailiy and hese coefficiens are saisically significan a he, 5, and 0%. Tha is, when marke is in bull, if Japanese governmen auhoriy of sock marke increases margin requiremens o avoid high volailiy, hen sock marke volailiy will be even increased, and evenually marke will be unsable in bull period. Moreover, he sum of M + MBull, is close o 0 for TOPIX and NIKKEI 5 as N goes o 6, suggesing ha he whole shor-run relaionship beween margin requiremens and volailiy weakens marginally during bull periods for boh marke indices. This finding implies ha here is no pyramiding effec in bull periods of Japanese sock marke. Therefore, when marke is in bull sae, he governmen policy ool of margin requiremens is useless. Unlike bull periods, for bear periods, he saisical srengh associaed wih margin requiremens and volailiy is srenghen marginally relaive o normal periods for only N=6 for TOPIX, ha is, he coefficien, MBear MBull is negaively significan and he negaive shor-run of relaion beween margins and volailiy srenghens marginally relaive o normal periods. In conras o bull periods, he sum of M +, is diverge for boh markes as N goes o 6, implying ha he oal shor-run associaion on margin requiremens and volailiy urns o negaive. In normal sae, however, iniial margin policy works. Tha is, he coefficien of MBear M is negaive and significan a he % level for boh marke indices, indicaing ha as he iniial margin requiremens increases a ime -, he volailiy of marke decreases a ime. Therefore, we conclude ha here is evidence of he effec for iniial margin policy during he only deep bear period for TOPIX, bu no evidence during bull periods in Japanese sock markes (TOPIX and NIKKEI5). This finding is inconsisen wih resuls of Japanese sock marke in Hardouvelis and Perisiani (99) sudy, of U.S. marke in Hardouvelis and Theodossiou (00) sudy, and bu is consisen o he resul by Kim and Oppehneimer (005) sudy for esing Japanese sock marke based on he individual invesor. When he marke is in normal, our resul is consisen wih in Hardouvelis and Perisiani (99, 00), bu inconsisen wih Kim and Oppehneimer (005). Specially, i is in conras o wha Hardouvelis (990), and Kupiec and Sharpe (99) poin ou hose margin requiremens are supposed o primarily purpose and deep recession marginally in Japanese sock marke. An EGARCH model for esing asymmeric effec Here, we adap a complemenary model as EGARCH which can explain he asymmeric effec in order o invesigae he relaionship beween iniial margin requiremens and he condiional mean and variance of weekly sock marke reurns. To do his, we employ he exended version of Nelson s (99) EGARCH model as condiional volailiy model implemened by Kupiec (989) and Hardouvelis and Theodossiou (00).
Pando e al. 873 Table 5. The resuls of margin requiremens and TOPIX and NIKKEI 5 volailiy across bull and bear markes. Panel A. TOPIX Panel B. NIKKEI 5 N=4 N=5 N=6 N=4 N=5 N=6 Obs. of Bull 88(.5%) (7.8%) 80(5.7%) 6(0.4%) 95(6.4%) 59(3.9%) Bull periods 38 4 6 3 9 Obs. of Bear 73(4.7%) 34(.9%) 4(0.90%) 70(4.5%) 37(.39%) 9(.3%) Bear periods 5 7 3 4 7 4 0 0.457*** 0.438*** 0.43*** 0.5688*** 0.5768*** 0.565*** (9.35) (8.36) (8.58) (0.0) (0.7) (9.70) 0.04*** 0.*** 0.35*** 0.464*** 0.466*** 0.494*** (7.) (7.03) (7.7) (7.59) (7.54) (7.66) 0.687*** 0.693*** 0.7*** 0.77*** 0.674*** 0.754*** (5.83) (5.89) (5.93) (6.3) (5.98) (6.) 3 0.4655*** 0.466*** 0.479*** 0.4543*** 0.4530*** 0.456*** (6.48) (6.65) (6.69) (5.35) (5.34) (5.35) 4-0.499*** -0.375*** -0.54*** -0.86*** -0.836*** -0.839*** (-6.87) (-6.70) (-6.84) (-6.78) (-6.8) (-6.69) M -0.354*** -0.699*** -0.8*** -0.53*** -0.536*** -0.480*** (-3.49) (-.33) (-.46) (-5.33) (-5.53) (-4.5) MBull 0.3* 0.99** 0.307** 0.349*** 0.5406** 0.384*** (.00) (.3) (.46) (.6) (.4) (.9) MBear 0.570 0.5939-0.895** 0.875 0.6584** 0.07 (.07) (.55) (-.30) (.) (.09) (0.) Adj. R 0.340 0.39 0.3 0.358 0.3634 0.3553 DW.6.5.6.6.4.5 F value 0.06 *** 00.98 *** 00.6 *** 4. *** 6.9 ***.48 *** This able repors margin requiremen effec on volailiy based on daily daa across bull and bear and normal markes. The esimaed regression wih Newey-Wes HAC is as follows: σ d, = 0 + σ d, + σ d, + 3 R d, + 4 R d, + M M + MBullBull M + MBear Bear M + e d, σ The dependen variable, d, is he weekly sandard deviaion based on daily reurn. Parenheses, ( ) is -value for regression wih Newey-Wes HAC. ***, **, * are significan a he, 5, and 0% level, respecively. Condiional mean of sock marke reurns In he poin of view wih saisical consideraions, an moderaing speculaive behavior by imposing a cos impedimen. This explanaion may be fied o only normal empirical model of sock marke reurn and volailiy should allow he condiional expeced excess reurn o be linear relaed o condiional non-diversifiable risk. As specified by Hardouvelis and Theodossiou (00), he condiional mean for sock marke reurns is specified as follows: r = µ + e m, m, E( r Ω ) µ m, m, N m, = 0 + MM + nrm, n + n= µ γσ (8)
873 Afr. J. Bus. Manage. r, µ where m m, E( rm, Ω ) is sock marke reurns, is he condiional mean of sock marke reurns a ime based on informaion se available up o ime (-),, e is an error erm used as proxy for marke shocks, M - denoes he level of iniial margin requiremen a ime -, r -n are hisorical reurns up o (-n), and σ var ( rm, Ω ) is he condiional variance of r m, Ω based on. Lagged reurns, r m,-n, employed reduce serial correlaions whenever hey exis and he error erm, is inended o capure a possible linkage beween he condiional mean and variance of he disribuion of sock marke reurns, and he lagged margin requiremen variable, M - is inended in order o capure a possible influence of margin requiremens on he risk premium hrough is possible associaion wih volailiy. Furhermore, if higher margin requiremens reduce he volailiy of fuure unwarraned sock price movemens, he reurn ha invesors require in order o inves in he sock marke may be diminished. The condiional variance of sock marke reurns Given he asymmery in he marke volailiy, we specify he exended Nelson s (99) EGARCH-M model on he generalized error disribuion (GED) wih some modificaion. This model allows for a possible nonlinear and asymmeric associaion beween margin requiremens and condiional volailiy: ln( σ ) = a0 + am M + ambear Bear M + ambull Bull M + θ g( z ) + γ ln( σ ) g( z Where ) = z E z + δ z, M In Equaion 9, erm capures he influence of a change in margin requiremens during normal periods. Bear Also each erms for ( M Bull ) and ( M ) allow o a differen relaionship beween margin requiremens and volailiy during bull and bear periods. e z (9) Ω σ σ g( z is and he funcion ) is an asymmeric z nonlinear funcion of and can be viewed as a proxy funcion for pas volailiy shocks. Assuming ha he uncondiional means of g( z ) is [ ] zero, ha is, E g ( z ) = 0 g( z ) under saionary of he condiional variance has a ransiory impac on curren condiional volailiy and no impac on uncondiional volailiy (Hardouvelis and Theodossiou, 00). Generally, we expec ha here is a posiive relaionship beween pas volailiy shocks and presen θ g( z volailiy, which is ) >0. Also he funcion g( z ) is consised of boh a symmeric z E z as par of pas innovaions, and δ z as an asymmeric par. This funcional form imposes a differenial impac of pas volailiy shocks on curren condiional volailiy. For example, if he asymmery coefficien, is negaive, hen ( z negaive pas innovaions < 0) would have a greaer impac on curren volailiy han posiive innovaions of he same magniude. As a resul, a δ negaive implies ha he volailiy rises more following bad news han good news. THE RESULTS FROM EGARCH MODEL Here, we esimae EGARCH-M wih GED disribuion. The resuls are shown in Tables 6 and 7. Panel A presens he esimaes of he condiional mean equaion, and Panel B shows he esimaes of he condiional volailiy equaion. The esimaion resul from he condiional mean equaion of sock reurns We inerpre he esimaed resuls for he TOPIX and NIKKEI 5 weekly reurn series. When weekly sock marke reurns are modeled as AR (), he esimaed coefficien for AR () is no significan a all. Thus, he second erm of AR in reurn series is dropped and we seup EGARCH-M model wih AR () in Tables 6 and 7. Panel A of Tables 6 and 7 for TOPIX and NIKKEI 5 indices shows ha he coefficien for condiional variance is posiive bu no saisically significan in Model and for TOPIX and also in Model for NIKKEI 5, implying ha here is very weak posiive linkage beween condiional means reurns and condiional sock marke volailiy. From his evidence, we drop condiional volailiy erm in incorporaing model 3, 4, 5, and 6 in Table 6. However, Model, 3, 4, and 5 of Table 7 show ha his σ linkage is sronger in including in he condiional mean equaion. This evidence implies ha here is significan posiive relaionship beween condiional volailiy and sock marke reurns if pas margin variable is included o condiional mean model. This suggess ha margin requiremens play an imporan role in condiional δ λ
Pando e al. 8733 mean reurn. For he associaion of margin requiremens and condiional mean reurns in Model of Tables 6 and 7, ineresingly he coefficiens,, are even posiive wih 0.86(TOPIX) and 0.3076(NIKKEI 5). Also all coefficiens of in Model are posiively significan a and 5%, implying ha here is very srong posiive linkage beween margin requiremens and condiional mean reurns in Japanese sock marke. Moreover, his finding also shows ha he effec of margin requiremens on sock marke reurn affecs srongly more power in NIKKEI 5 han in TOPIX. As a resul, his evidence indicaes ha an increase in margin requiremens is associaed wih an increase in he required rae of reurn on he aggregae sock marke. As menioned by Hardouvelis (990), he financial auhoriy raises margins requiremens because i anicipaed furher unusual increases, no declines, in sock prices. I is no consisen wih findings of Hardouvelis and Perisiani (99) for Japanese sock marke, and of Hardouvelis and Theodossiou (00), and of Zhang e al. (005) for U.S. sock marke. The esimaion resul from he condiional volailiy equaion of sock reurns wihou margin policy Panel B in Tables 6 and 7 shows he esimaed resuls for he condiional variance of sock marke reurns. Firsly, we exclude he margin variable from he Model. In he Tables 6 and 7, an EGARCH (, ) model fis he daa bes, meaning ha he condiional volailiy equaion includes one own-lag and one lag of pas volailiy shocks. We observe ha all coefficiens for he logarihm of pas condiional variances are close o uniy, suggesing high persisence of volailiy over ime. For level of persisence in volailiy, NIKKEI 5 reurn series are sronger han TOPIX. All persisence coefficiens are saisically significanly a he %. Specifically, he coefficiens, γ M =0.970 for TOPIX and =0.9734 for NIKKEI 5 indicae ha i would ake approximaely 76=ln (0.)/ln (0.970) for TOPIX and 85=ln (0.)/ln (0.9734) business days for he influence of curren volailiy on fuure volailiy o diminish o oneenh he size of is influence on nex period s volailiy. For he asymmery effec, all asymmery coefficiens, s from model wihou margin for TOPIX and NIKKEI 5, are negaive and saisically significan a he %. This resul confirms ha he pas negaive shocks on he condiional mean have a sronger associaion wih curren condiional volailiy han pas posiive shocks. The esimaion resul from he condiional volailiy equaion of sock reurns wih margin policy In Tables 6 and 7, for he Japanese sock marke reurns, M γ δ we add he margin as an explanaory variable in he condiional variance equaion. Thus esimaed coefficiens are presened for he in all models. Also, in model 4 for TOPIX and model 3 for NIKKEI 5, bear M, Bear and bull periods (, ) are ineracion erms separaed respecively o disinguish each effecs on margins requiremens and volailiy. Coefficien capures he associaion beween he level of margin requiremens and volailiy during normal period and α α M, Bull M, Bear and also idenify he relaionship beween he margin requiremens and volailiy for each bear and bull periods In Tables 6 and 7, all coefficiens, are negaive and saisically significan a he, 5, and 0% for boh marke indices. These evidences indicae ha in he normal periods, he pas margin requiremens affec curren condiional volailiy negaively for TOPIX and NIEEI 5. These findings confirm ha he higher margin requiremens reduce he volailiy. Also, during bear periods, in model 6 for TOPIX and in model 5 for NIKKEI α M Bear 5. are negaive and saisically significan a he and 5% marginally and respecively bu excep no significan in Model 3 for boh marke indices. In model 3, 5 of TOPIX and model 3, 5 of NIKKEI 5 he M M, Bear ineracion erm sum of coefficien is -0.39, -0.069, -0.468, and -0.559, respecively. This means ha margin requiremen policy plays an imporan role in volailiy, he higher margin, he lower volailiy, hus his is consisen wih depyramiding hypohesis ha margin requiremens end o push sock prices down in bear periods and he couner-cyclical characerisics of volailiy: in bear marke, volailiy is higher raher han in bull marke. However, he associaion of margin wih volailiy during bull periods is subsanially weaker, even posiive effec. Thus, i does no play a key role in volailiy for model 4 and 5 of TOPIX and model 4 and 5 of NIKKEI 5, he higher margin, he higher volailiy. This resul implies ha if Japanese financial auhoriy inends o increase margin level o reduce volailiy during bull periods, unexpecedly, he volailiy would be even higher. Also his finding implies ha he margin policy only affec volailiy in bear periods during shor ime as week. In bear sae, a lower margin requiremen would decrease he liquidiy needs of invesors and lessen he downward pressure on prices, hus, reduce volailiy. Conclusions α α M, Bull α M α M α + α α M From he original Hardouvelis (990) and Hardouvelis
8734 Afr. J. Bus. Manage. Table 6. The resul of EGARCH model of TOPIX index wih margin requiremens. Coefficien Model Model Model 4 Model 5 Model 6 Panel A: Condiional mean of reurns 0 0.03 *** -0.06 ** -0.0476 * -0.0476 * -0.0464 * (3.5) (-.9) -(.89) (-.89) (-.85) M 0.86 *** 0.73 *** 0.73 *** 0.703 *** (3.47) (3.9) (3.3) (3.7) 0.394 *** 0.404 *** 0.399 *** 0.399 *** 0.400 *** (.09) (.09) (.4) (.4) (.6) λ 0.0054 0.085 (0.40) (.3) Panel B: Condiional variance of reurns α 0-0.74 *** -0.043 *** -0.743 *** -0.759 *** -0.98 *** (-8.09) (-3.56) (-3.9) (-3.39) (-4.3) α M -0.0449 *** -0.0738 ** -0.0769 *** -0.039 * (-.0) (-3.45) (-3.63) (-.88) α M,BEAR -0.040-0.0678 ** (-.0) (-.97) α M,BULL 0.0955 *** 0.0996 *** (5.06) (5.38) θ 0.68 *** 0.744 *** 0.45 *** 0.46 *** 0.69 *** (8.4) (8.4) (7.99) (7.97) (8.7) δ -0.08 *** -0.085 *** -0.0978 *** -0.0959 *** -0.0866 *** (-0.36) (-0.7) (-.87) (-.87) (-0.54) γ 0.970 *** 0.9663 *** 0.975 *** 0.977 *** 0.9696 *** (64.47) (34.43) (78.97) (8.48) (46.67) GED(v).987 ***.94 ***.958 ***.954 ***.905 *** (77.56) (74.54) (76.35) (77.05) (74.) Lik. Raio -8383-8376 -8365-8370 -838 Adj. R 0.043 0.068 0.09 0.03 0.03 F-value 6. *** 4.97 *** 0.66 ***.84 ***.85 *** DW.0.0.0.0.0 Panel C: Model diagnosics Mean for z -0.03-0.000-0.000-0.0070-0.00 Max 6.558 6.574 6.494 6.53 6.558 Min -.447 -.7-3. -3.4 -.45 Sd.035.04.040.040.035 Skewness -0.6655-0.68-0.69-0.70-0.666 Kurosis.8943.8.46.57.894 Jarque Bera 486 *** 64 *** 8076 *** 876 *** 487 *** This able repors exended EGARCH-M model resul of TOPIX weekly volailiy on margin requiremens. Parenheses, ( ) is -value of EGARCH(,) esimaion. Esimaed model is as follows: rm, = 0 + M M + rm, + λσ + ε ln( σ ) = α0 + α M M + α M, Bear ( Bear M ) + α M, Bull ( Bull M ) + θ z E z + δ z + γ ln( σ ) ***, **, * Are significan a he %, 5%, and 0% level respecively. and Theodossiou (00) paper, which finds he evidence of a negaive relaion beween iniial margin requiremens and volailiy, mos sudies conclude ha margin is unrelaed o volailiy.
Pando e al. 8735 Table 7. The resul of EGARCH model of NIKKEI 5 wih margin requiremens. Coefficien Model Model Model 3 Model 4 Model 5 Panel A: Condiional mean of reurns 0 0.0395 *** -0.7 *** -0.09 *** -0.046 *** -0.58 *** (3.8) (-3.4) (-3.0) (-3.05) (-3.39) M 0.3076 *** 0.879 *** 0.907 *** 0.3057 *** (4.89) (4.55) (4.60) (4.86) 0.0563 *** 0.0540 *** 0.0533 *** 0.053 *** 0.0543 ** (4.8) (4.66) (4.60) (4.59) (4.65) λ 0.008 0.076 ** 0.05 * 0.08 * 0.07 ** (0.93) (.8) (.8) (.84) (.4) Panel B: Condiional variance of reurns α 0-0.858 *** -0.597 *** -0.64 *** -0.7 *** -0.566 *** (-7.59) (-.) (-0.35) (-0.39) (-.08) α M -0.076 *** -0.0980 *** -0.05 *** -0.0697 *** (-3.4) (-4.8) (-5.05) (-3.) α M,BEAR -0.0488-0.086 *** (-.63) (-.64) α M,BULL 0.58 *** 0.3 *** (7.83) (8.8) θ 0.367 *** 0.445 *** 0.09 *** 0.04 *** 0.409 *** (7.3) (7.40) (5.89) (5.9) (7.7) δ -0.098 *** -0.097 *** -0.098 *** -0.075 *** -0.009 *** (-.66) (-.90) (-4.00) (-3.89) (-.4) γ 0.9734 *** 0.9664 *** 0.9759 *** 0.975 *** 0.9685 *** (30.89) (34.69) (90.97) (9.) (38.48) GED(v)..39 ***.309 ***.3334 ***.337 ***.34 *** (80.58) (76.89) (73.57) (74.88) 75.9 Lik. Raio -956-9549 -9534-9535 -9546 Adj. R -0.0005 0.0007 0.000 0.000 0.0005 F-value 4.5 *** 6.05 *** 0.5 ***.34 *** 3.9 *** DW.05.03.04.04.03 Panel C: Model diagnosics Mean for z -0.047-0.000-0.04-0.000-0.00 Max 6.494 6.533 6.3733 6.49 6.447 Min -3.497-3.5 -.87 -. -3.37 Sd.06.0.00.0.07 Skewness -0.7886-0.8-0.6964-0.7-0.793 Kurosis.9.6 0.49 0.64.85 Jarque Bera 506 *** 6545 *** 7805 *** 855 *** 4808 *** This able shows EGARCH-M model resul of NIKKEI 5 weekly volailiy on margin requiremens. Parenheses, ( ) is -value of EGARCH(,)-M esimaion. Esimaed model is as follows: rm, = 0 + M M + rm, + λσ + ε ln( σ ) = α0 + α M M + α M, Bear ( Bear M ) + α M, Bull ( Bull M ) ***, **, * are significan a he %, 5%, and 0% level respecively. + θ z E z + δ z + γ ln( σ ) Bu Hardouvelis (990) and Hardouvelis and Theodossiou (00) sudies provide he negaive relaion beween margin and volailiy. Also hese findings are aacked from many auhors, which mean ha heir
8736 Afr. J. Bus. Manage. resuls are more likely o bias from he spurious regression phenomenon of Granger Newbold (974). However, Hardouvelis and Theodossiou (00) analyzed o find facs clearly using sophisicaed mehodologies. They provide ha using US sock marke daa, boh he volailiy and he margin series are highly auocorrelaed, bu saionary, and ha he Granger- Newbold bias in he level regressions is neiher economically nor saisically significan. Wih moivaion of heir sudy, we reexamine Japanese governmen policy of sock marke margin o find he associaion beween margin requiremens and volailiy. Using Japanese sock marke daa in order o securiize his relaionship is very unique and good opporuniy o us because here are los of changes in margin policy. We employ several sophisicaed echniques such as regression and condiional volailiy model o invesigae he linkage of margin requiremens and volailiy. In regression analysis, margin requiremens affec volailiy negaively and also here is nonlinear effec for TOPIX and NIKKEI 5. This resul is robus in various mehods and even afer conrolling for addiional variables. Thus we confirm ha higher margin could reduce excess volailiy. Across bull and bear markes, he linkage beween margin requiremens and volailiy is slighly sronger (more negaive) in bear marke for TOPIX bu is weak in bull marke, even posiive associaion for all markes. The afore-menioned resuls are also confirmed by EGARCH-M model wih GED disribuion. In his model, here is also negaive associaion relaion beween margin requiremens and volailiy across only bear and normal markes. These findings indicae when sock prices keep drop as in case of a sharp decline, i would be sabilizing o have higher margin requiremens policy. Conversely, for bull marke, he volailiy would be more volaile if Japanese financial auhoriy inends o raise he level of margin requiremens o reduce he volailiy. These resuls sugges ha for Japanese, governmen policy as ool of sabilizing sock marke has o be scheduled and implemened in only deep bear and normal markes. Therefore, governmen resricion does no work for sabilizing marke urbulence in bull marke, implying ha imposing his financial policy ino all marke saes should be cauious because he effec of his policy could be worked differenially. ACKNOWLEDGEMENT This sudy was suppored by research funds from Dong-A Universiy. In addiion, we acknowledge ha he firs auhors are Kim, Sungsin and Seo, Ji-Yong equally conribuing o his paper, and ha he name order of he firs auhors is depended on only alphabeical one of each las name. REFERENCES DeLong B, Shleifer A, Summers L, Waldman R (987). The Economic Consequences of Noise Traders. NBER. Working paper. Dickey DA, Fuller WA (979). Disribuion of he Esimaors for Auoregressive Time Series wih a Uni Roo. J. Am. Sa. Associaion. 74:47-43. Ferris S, Chance D (988). Margin Requiremens and Sock Marke Volailiy. 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