An Econometric Analysis of Market Anomaly - Day of the Week Effect on a Small Emerging Market

Transcription

1 Inernaional Journal of Academic Research in Accouning, Finance and Managemen Sciences Vol., No., January 0, pp. 4 ISSN: HRMARS An Economeric Analysis of Marke Anomaly - Day of he Week Effec on a Small Emerging Marke Julijana ANGELOVSKA Faculy of Economics and Adminisraive Science, Inernaional Balkan Universiy, Tasko Karaga bb, Skopje, Macedonia, Tel: , Fax: julijana.angelovska@yahoo.com Absrac The research abou he exisence of seasonal behavior in reurn and volailiy of Macedonian Sock Exchange is done. Under differen model specificaions he hypohesis if mean reurns are significanly differen in he five rading days is esed. The evidence of exisence of predicable paern or marke inefficiency can be used for profiable marke sraegy or forecasing of he predicable movemens in asse prices can provide invesors wih opporuniies o generae abnormal reurns. The resuls differ under differen model specificaions. While simple single ANOVA model and dummy variable regression using OLS mehodology, could no find enough evidence o rejec he null hypohesis, or mean reurns are no significanly differen in he five rading days, he more advanced models like GARCH (,), EGARCH and modified M-GARCH (,) and M-EGARCH, found evidence abou exisence of a day of he week effec on Thursday. Key words Efficien marke, marke anomaly, day of he week effec, GARCH, EGARCH. Inroducion Discovery commences wih he awareness of anomaly, i.e., wih he recogniion ha he naure has somehow violaed he paradigm-induced expecaions ha govern normal science. Thomas Kuhn (Thaler, 987) Togeher wih raional expecaions models, anoher major approach o explain sock marke aggregae reurn behavior has been developed. I is so-called behavioral approach. Marke anomalies in sock markes should be relaed o invesors rading sraegies, which are based on heir psychologies along wih oher facors. According o Efficien Marke Hypohesis prices conain all relevan informaion (Eugene Fama, 965). An acive area of invesigaion in finance lieraure is o explore he exisence of a paern in sock reurns. A predicable paern is evidence agains marke efficiency. Seasonal effecs in securiy markes have araced much ineres among boh academics and praciioners, as exisence of seasonal effecs in equiy markes can be evidence agains Efficien Marke Hypoheses, as he predicable movemens in asse prices provide invesors wih opporuniies o generae abnormal reurns. Even if he paern does no seem o affec he sock reurns direcly, i can provide useful guideline o invesors concerning heir invesmen decision. I ries o widen he range of analyic ools wih which o approach he processes of decision making. Broadly speaking, calendar effecs occurs when he reurns of financial asses display specific characerisics over specific days, weeks, monhs or even years. A daa se from a small European capial marke, namely he Macedonian sock marke is considered in his research. Emerging markes provide an ineresing "ou of sample" es of he exisence of calendar anomalies, since many well-known calendar anomalies do no exis in he emerging sock markes (Claessens e al., 995). The objecive of his research is o find ou wheher he day of week effec exiss in Macedonian capial marke or no. Researches on day of he week effec have been carried ou under differen model specificaions and he following hypohesis is esed:

2 Inernaional Journal of Academic Research in Accouning, Finance and Managemen Sciences Vol. (), pp. 4, 0 HRMARS Ho: Mean reurns are no significanly differen in he five rading days. H: Mean reurns are significanly differen in he five rading days. To es he hypohesis several economeric models are used: single facor ANOVA, dummy variable regression (OLS mehodology), GARCH (,), M-GARCH(,), EGARCH, M-EGARCH.. Lieraure review There is undoubedly an exensive lieraure on sock marke anomalies referred o seasonal effecs. Researchers firs observaion abou he day of he week effec was he belief ha securiies marke reurns on Mondays are less han he oher days of he week, and are ofen negaive on average. Sudies on such sock marke anomalies sared since he lae 90 where Kelly (90) revealed he exisence of a Monday effec on he US markes where he reurns urned ou o be negaive. From here on, researchers have documened findings in suppor of he low Monday reurns in he US markes. This effec has been observed in boh American and foreign exchanges. Even hough sudies have documened Monday effec since he 90s, no heory has adequaely explained he reasons i exiss. While he Monday effec in he US sock marke is exensively documened during he 980.s, [(French 980), (Gibbons and Hess 98), (Rogalski 984), and (Keim and Sambaugh 984)], laer some papers presen evidence ha he Monday effec in he US and UK sock markes has gradually disappeared. Forune (998) shows ha afer 987 here is no evidence of a negaive weekend reurn. Mehdian and Perry (00) show ha in he period Monday reurns are no significanly differen from reurns during he res of he week for he SP500, DJCOMP and NYSE (large-cap) indexes. Cous and Hayes (999) and Seeley (00) also show empirically ha he Monday effec exiss bu is no as srong as has been previously documened for he UK sock indices. Wang, Li, and Erickson (997) show ha he Monday effec (negaive reurns) occurs primarily in he las wo weeks of he monh for a number of sock indices consisenly over he period 96-99, while reurns for he firs par of he monh are no saisically significanly differen from zero. Similar kinds of effecs have been found in oher capial markes. Jaffe and Weserfield (985a,b) es for he weekend effec and find ou significan negaive mean reurns on Mondays in he US, Canada and he UK sock markes, and significan negaive Tuesday reurns in he Japanese and Ausralian sock markes, whereas Broca (99) found he Wednesday effec in he Indian capial marke. Similarly, DuBois and Louve (996) find negaive reurns on Mondays and Tuesdays and posiive reurns on Wednesdays for eleven indices in nine counries from 969 o 99, whereas Tong (000) repored his sock marke anomaly in weny hree sock markes which include European, Asian and Norh American markes. In addiion, Aggarwal and Rivoli (989) repored a negaive Monday and Tuesday effecs on four Asian emerging markes. Likewise, Choudhry (000) esed he day of he week effec on emerging Asian markes using a GARCH model approach wih he resuls suggesing he presence of significance day of he week effec even hough of differen magniude across he markes. Moreover, Nah and Dalvi (004) examined he week day effec in he Indian equiy marke and found evidence of Monday and Friday effecs before he rolling selemen in 00. Furhermore, Al-Loughani and Chappell (00) documened on he exisence of he day of he week effec in he Kuwai Sock Exchange. On he oher hand some researchers found no evidence of day of he week effec, Malaikah (990) and Aybar (99) did no find any evidence of he day of he week paern in he capial markes of Saudi Arabia, Kuwai, and Turkey, Sanemases (986), Pena (995) and Gardeazabal and Regulez (00) have documened on insignifican week day effecs on he Spanish sock markes. Plaev, Lyroudi and Kanaryan (00) invesigaed he exisence of he day-of-he-week effec in eigh Cenral European sock markes: Romania, Hungary, Lavia, Czech, Russia, Slovakia, Slovenia and Poland for he period Sepember, 997 o March 9, 00. They found mixed resuls in heir sudy. They found ha he Czech and Romanian markes have significan negaive reurns on Monday and he Slovenian marke has significan posiive reurns on Wednesday and has insignifican negaive reurns on Fridays. They also concluded ha he Polish and Slovak markes have no day-of-he week effec anomaly. Aly e. al (004) resul sugges no evidence of day of he week effec in he Egypian sock marke. Their findings indicae ha while Monday sock reurns are significanly posiive, hey are no significanly differen from reurns during he res of he week. Since hey found ha he reurns on Monday are significanly more volaile han he reurns from Tuesday o Thursday, hey conclude ha he significanly posiive reurns on Monday are associaed wih reurns ha are more risky. Rahman, (009) using GARCH (,) model found saisically significan 5

3 Inernaional Journal of Academic Research in Accouning, Finance and Managemen Sciences Vol. (), pp. 4, 0 HRMARS negaive coefficiens for Sunday and Monday and saisically significan posiive coefficien for Thursday dummies in Dhaka Sock Exchange in Bangladesh. Agahee (008) invesigaed he exisence of day of he week effec in he emerging marke of Mauriius using observaions from Sock Exchange of Mauriius for a period of 006. The sudy found ha he Friday reurns are higher relaive o oher rading days. The sudy also concluded ha he mean reurns across he five week days are joinly no significanly differen from zero. Leonisis and Siriopoulos (007) presen a forecasing mehod based on chaos heory aking ino accoun he specific calendar characerisics, and hey give empirical resuls for NASDAQ Composie Index and TSE 00 Composie Index. Their sudy shows ha here is a grea deal of improvemen on ou-of-sample forecasing resuls, for calendar-correced ime series. On he oher hand, if he ime series does no show any calendar affecion a all, he forecasing is no improved a lo. This fac was clearly shown on he resuls regarding he TSE 00 Cmp resuls. In a second paper Leonisis and Siriopoulos (006) presen a way o incorporae some of he mos significan calendar effecs on forecasing by neural neworks. The main advanage of heir mehod is ha i gives no correcion o ime series ha do no show calendar effecs. Finally, hey indicae ha calendar effecs may be hidden in indices, which represen low-risk socks. 6. Daa and mehodology The daa se used o invesigae he day of he week effecs in Macedonian Sock Marke consiss of daily closing values for he major Macedonian Sock Exchange index, he MBI0 Index, in he period from January 4, 005 o December, 009. MBI0 is a weighed index using closing prices and published by he Macedonian Sock Exchange. Prior o January 006, sock rading in Macedonian capial marke ook place from Monday o Thursday. Uncondiional logarihmic reurns ha amoun o,90 observaions are calculaed as follows: R P log x00 P = () Where P and R refer o MBI0 price of index and reurn of MBI0 index on day, respecively. In order o es he saed hypohesis single facor ANOVA is used. The sandard F-saisic is calculaed as following: BSS dfb F = () WSS df w Where, BSS is beween sums of squares, WSS is wihin sum of squares and df b is degrees of freedom beween groups and df w is degrees of freedom wihin groups. BSS and WSS are calculaed as follows: ( x ) ( ) ( ) x n x x n xn BSS = n () n x Where, n, n n n is he sample size of every working day from Sunday o Friday, x, x x n, is he mean reurn of every working day from Monday o Friday, and x is he populaion mean. ( n ) SD + (n )SD (n WSS = (4) n )SDn Where, n, n n n is he sample size of every working day from Sunday o Friday, SD,SD... SDn, is he sandard deviaion of reurns of each working day from Monday o Friday. To deec he presence of day of he week he following dummy variable regression is used: R = β + β D + β D + β D + β D + β D + ε (5) o Where R is he daily reurn as defined earlier; D hrough D 5 are dummy variables such ha:

4 Inernaional Journal of Academic Research in Accouning, Finance and Managemen Sciences Vol. (), pp. 4, 0 HRMARS D = if is a Monday, hen D = and D =0 for all oher days; D = if is a Tuesday, hen D = and D =0 for all oher days; D = if is Wednesday, hen D = and D =0 for all oher days; D 4 = if is a Thursday, hen D = and D =0 for all oher days; D 5 = if is a Friday, hen D = and D =0 for all oher days; β -β 5 are coefficiens o be esimaed using ordinary leas squares (OLS). The sochasic disurbance erm is indicaed by ε. The hypohesis o be esed is: β = = (6) β = β = β4 β5 Mos of he sudies repored in he finance lieraure invesigae he day of he week effec in mean reurns by employing he convenional OLS mehodology on appropriaely defined dummy variables. However, his mehodology has wo limiaions. Firs, he error erms may no be whie noise due o auocorrelaion and second, heeroskedasiciy problems resuling o misleading inferences. To address he firs drawback, we include lagged values of he reurn variable in a model wih he following sochasic equaion: R 4 5 n 5 + I= = β D + β D + β D + β D + β D βr (7) i The final predicion error crierion (FPEC) specifies he lag order n such ha i eliminaes auocorrelaion in he residual. For he second limiaion progress can be made by using models of family GARCH, as variaions in volailiy are second very imporan par. I is imporan o know wheher a cerain day of he week high (low) reurns are associaed wih respecively high (low) volailiy in a given day. Hsieh (988) modified Engle (98) и Bollerslev (986) GARCH (,) model: R = μ + φr + ε (8) σ - + = ω + αε βσ (9) r N(0,) σ By including day of he week effecs, adding dummy variables for days of he week in he variance equaion (9), he new variance equaion is: σ = ω + ω D + ω D + ω D + ω D + ω D + αε βσ (0) Acually allows reurn condiional variance o vary for each day of he week by modeling he condiional variance from he mean equaion as modified GARCH. Thus he second specificaion (0) incorporaes he effec of he day of he week for boh equaions. GARCH models acceped by Davidson and Peker (996), Clare, Ibrahim and Thomas (998), Foo and Kok (000), Kok (00) and Kok and Wong (004) assume symmerical behavior of marke reacions o posiive and negaive news. Bu in realiy, mos commonly seen is ha he negaive reurns are followed by higher volailiy han posiive. Anomalies of he day of he week furher will be invesigaed wih EGARCH model, which can hi a possible asymmery in he behavior of he capial marke. EGARCH process (Nelson, 99, Brooks, 00): ( ) ( ) ( ) ( ) ( ) u = u lnσ ω β*lnσ α* δ* () σ σ /π i + 7

5 Inernaional Journal of Academic Research in Accouning, Finance and Managemen Sciences Vol. (), pp. 4, 0 HRMARS 8 4. Empirical resuls Macedonian capial marke is represened by he Macedonian Sock Exchange. The modern hisory of he capial marke is associaed wih srucural changes in he 990s, crossing he counry's ransiion o free marke economy. The process of privaizaion has already resuled in he formaion of more join sock companies which have imposed he necessiy of creaing he markeing infrasrucure for ransfer of newly creaed securiies. Alhough many regional markes passing hrough he same ransiion period were esablished earlier, he consiuion of he Macedonian Sock Exchange launched in Sepember 995. However, he official sar of rading on he Macedonian Sock Exchange is considered March 8, 996, when he firs sock bell rang wih a very modes amoun of rading (Angelovska 0). Macedonian Sock Exchange as small and developing marke, during he period , winessed is firs bull and bear marke in is shor hisory. Descripive saisics in Table shows high volailiy provided by posiive firs order auocorrelaion. Table. Summary of Maximum/Minimum Reurns/Sandard Deviaions of he MBI0 for he period January 4, 005-December, 009 Mean Skewness Maximum Kurosis Minimum Jarque-Bera Sd. Dev Probabiliy Observaions 90 Firs order AC 0.5 Source: MSE Reurns for each day of he week separaely are calculaed for each year as well as for he whole period. Table provides summary saisics for daily index reurns hrough differen ime periods. The coefficien of variaion CV is a measure of reurn obained per uni of risk, which is useful for comparison of risk-reurn exchange hrough he days and years oo. The mean reurn for he enire period is negaive on Monday, which could indicae he presence of he Monday effec similar o mos of he empirical evidence on he capial marke in America. The highes mean reurn for he same period is on Wednesday. Volailiy for he enire period does no differ across days of he week, excep Friday when he volailiy is smalles, bu i is he resul of fewer observaions for 005, when Friday was a non-rading day. Coefficiens of variaion are no significanly differen and very low, which is an indicaion of low reurns or high risk, or boh. Table. Summary Saisics of Daily Reurns by rading days of he MSE in he period of Monday Observaions 49,00 49,00 49,00 49,00 47,00 4,00 Average 0,0 0,09 0,9-0,4-0,5-0,0 Sandard Deviaion,7,09,6,7,99,9 Coefficien of Variaion 0,08 0,08 0,8-0,8-0,08-0,0 P-value 0,00 0,0 0,00 0,00 0,5 0,00 Tuesday Observaions 48,00 50,00 48,00 5,00 49,00 47,00 Average 0,5 0,8 0, -0,58 0,08 0,0 Sandard Deviaion,,45,67,0,,9 Coefficien of Variaion 0,4 0,9 0,4-0,9 0,04 0,0 P-value 0,00 0,00 0,00 0,00 0,5 0,00 Wednesday Observaions 5,00 49,00 5,00 49,00 5,00 5,00 Average 0,47 0,08 0,7-0,57 0,6 0, Sandard Deviaion,9,05,69,0,0,8 Coefficien of Variaion 0,4 0,08 0,6-0,8 0,8 0,07

6 Inernaional Journal of Academic Research in Accouning, Finance and Managemen Sciences Vol. (), pp. 4, 0 HRMARS P-value 0,00 0,06 0,55 0,00 0, 0,00 Thursday Observaions 49,00 5,00 49,00 49,00 50,00 49,00 Average 0,46 0, 0,5-0,79 0,09 0,09 Sandard Deviaion,9 0,9,07,8,0,97 Coefficien of Variaion 0,4 0,5 0, -0, 0,04 0,05 P-value 0,00 0,6 0,00 0,00 0,00 0,00 Friday* Observaions 5,00 49,00 50,00 46,00 96,00 Average 0,6 0,45-0,9 0,7 0, Sandard Deviaion 0,80,5,8,0,67 Coefficien of Variaion 0,0 0,9-0,6 0,08 0,07 P-value 0,68 0,4 0,00 0,00 0,00 *Essenially, he MSE has been rading on a daily basis for he full year as from 006. Annual analyses hrough he rading days of he week show inconsisency in erms of he direcion and magniude of reurns. Such inconsisen sample may sugges ha reurns are random and as such can reduce suppor for any argumen in favor of a day of he week effec. For ha reason in order o es he hypohesis, single facor ANOVA is used and he sandard F-saisic is calculaed. Tess for equaliy of mean reurns are made and resuls across years are provided in Table.The null of equaliy of mean reurns canno be rejeced ha is in accordance wih he resuls of mean reurns across day of he week repored in Table. Bu even hough es of equaliy in means canno be rejeced, hey differ in variance raios. This finding is significan o invesigae risk-reurn rade-off in financial markes. Table. Tes of equaliy of mean reurns in he days of he week F-статистика 0,4 0,5 0, 0,9 0,58 0, P-вредност 0,87 0,7 0,97 0,8 0,68 0,9 To deec he presence of day of he week, furher on, he mos exploied mehodology - dummy variable regression, equaion (5) is used. If he daily reurns are drawn from an idenical disribuion, hey will be expeced o be equal. The null hypohesis will indicae a specific paern in he sock reurn hus he presence of day of he week anomaly. The same regression is repeaed for each individual year and for he whole period. Table 5 provides β -β 5 dummy variables coefficiens. Saisically significan coefficien provides evidence of he effec of day of he week. In 006 here is evidence of day of he week effec or saisically significan posiive Tuesday and Thursday are deeced, while in 008 saisically significan negaive again Tuesday and Thursday are found. For he whole period again no day of he week effec is deeced. Table 5. Regression coefficiens esimaed using ordinary leas squares (OLS) from equaion (5) on daily reurns β β β β 4 β 5 R - F-sa ,08 0,5 0, 0, 0,64 (-0,) (,5) (0,9) (0,55) (,6)*** 7, 006 0,0 0,4-0,06 0,9-0,0 0,54 (0,07) (,84)* (-0,45) (,)** (-0,7) (0,0)***, ,05 0,04 0,6 0,0 0, 0,55 (0,5) (0,) (0,79) (0,48) (,55) (0,)*** 4, ,9-0,50-0,8-0,5 0,00 0,7 (-,06) (-,8)* (-,4) (-,86)** (0,0) (6,4) 4,79 9

7 Inernaional Journal of Academic Research in Accouning, Finance and Managemen Sciences Vol. (), pp. 4, 0 HRMARS β β β β 4 β 5 R - F-sa ,4 0, 0, 0,07 0,008 0,4 (-0,84) (0,76) (,9) (0,6) (0,0) (5,58)***, ,08 0,09 0,08 0,0 0,09 0,48 (-0,76) (0,9) (0,8) (0,) (0,77) (8,88)*** 77,79 ***,**, and * denoes significance level a %,5% and 0% levels For he second problem or heeroskedasiciy problem, GARCH family models are included: GARCH (,), M-GARCH (,), EGARCH, M-EGARCH and he resuls are presened in Table 6. Thursday is saisically significanly differen from he oher days of he week which means ha day of he week anomaly is deeced on Thursday. The resuls are sable in all models or wih modificaion in variance equaion or wihou, meaning i is no a resul of variaions in he volailiy. Coefficiens of he dummy variables in he modified GARCH equaion variance are saisically insignifican, bu wih he modified EGARCH model hough i is confirmed saisically significan coefficien on Thursday here are as well significance in he variaions of volailiy on Wednesday, and Thursday. 5. Conclusions Table 6. Regression Coefficiens: GARCH, ЕGARCH, М-GARCH and М-ЕGARCH GARCH (,) М-GARCH (,) ЕGARCH (,) М-ЕGARCH (,) β -0.07(-,6) -0.08(-,) -0,0(-0,4) 0,04(0,69) β 0.07(,9) 0.07(-,) 0,04(0,78) -0,06(-0,84) β 0.0(,5) 0.0(,69)* 0,08(,9) 0,04(0,45) β 4 0.0(,96)*** 0.(,49)*** 0,7(,0)*** 0,4(,6)* β 5-0.0(-0,8) 0.00(0.07) -0,09(-,4) -0,(-,4) R (,6) 0.47(,)*** 0,49(,) 0,49(0,5)*** Variance Equaion ω 0.07(7,48)*** -0.0(-0.7) -0,9(-,97)*** -0,9(-,5)*** α 0.7(,)*** 0.8(0,74)*** -0,0(-,4) -0,0(-0,90) β 0.74(5,05)*** 0.7(47,05)*** 0,94(4,7)*** 0,94(9,5)*** δ 0,45(4,59)*** 0,47(,55)*** ω 0.6(.45) 0,7(,) ω 0.9(0.95) -0,(-,69)* ω 0.5(0.60) 0,09(0,8)* ω 4 0.9(0.7) -0,09(-0,9) ω 5 0.4(0.85) 0,04(0,69) ***,**, and * denoes significance level a %,5% and 0% levels Empirical examples idenified as day of he week effec shows ha reurns are no evenly disribued across days of he week. Mos commonly observed are he negaive reurns on Monday called Monday effec. The research using more economeric models o find evidence ha mean reurns are significanly differen in he five rading days was done. The presened daa showed ha he mean reurn for he enire period ( ) is negaive on Monday, which could indicae he presence of he Monday effec similar o mos of he empirical evidence on he capial marke in America. Bu he simple single ANOVA model and dummy variable regression using OLS mehodology, could no find sable evidence of presence of day of he week effec, or o rejec he null hypohesis. The more advanced models like GARCH (,), EGARCH and modified M-GARCH (,) and M-EGARCH, found evidence abou exisence of a day of he week effec in Thursday. The main reason of he ineres of financial heoriss and praciioners o deec some marke anomaly is o use his informaion or marke inefficiency for profiable marke sraegy or o use for forecasing. The predicable movemens in asse prices can provide invesors wih opporuniies o generae abnormal reurns. In addiion many psychologiss believe ha invesor s psychology can play an imporan role in causing he anomaly. 0

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