Chapter 3. The Data and Methodology. Estelar. The major objectives of the study are as follows:

Transcription

1 Chaper 3 The Daa and Mehodology In he previous Chaper a survey of exising lieraure was conduced wih a view o idenify he research gaps. Based on his survey, he research objecives and mehodology are se for he presen sudy. This Chaper presens an overview of he mehodology used Objecives of he Sudy The major objecives of he sudy are as follows: 1. To examine he exisence of he day-of-he-week, urn-of-he-monh, monh-of-he-year and oher calendar anomalies in - (i) aggregae sock reurns, (ii) individual sock reurns, (iii) rading volume, (iv) volailiy of sock prices and oher parameers of sock marke behaviour in India. 2. To es he saisical and economic significance of he calendar anomalies. 3. To explore he facors conribuing he calendar anomalies. 4. To sudy he impac of sock marke reforms and changes in marke microsrucure on calendar anomalies and hereby on he markeefficiency Broad Hypoheses Some of he major null-hypoheses of he sudy are as follows: 1. There is no significan difference among he mean sock reurns for differen days of he week. 2. There is no significan difference among he mean sock reurns for differen weeks of he monh. 3. There is no significan difference among he mean sock reurns for differen monhs of he year. 29

2 4. There is no significan difference among he mean sock reurns for pre and pos holidays. 5. There is no significan difference among he volailiy of sock prices for differen days of he week. 6. There is no significan difference among he volailiy of sock prices for differen weeks of he monh. 7. There is no significan difference among he volailiy of sock prices for differen monhs of he year. 8. There is no significan difference among he volailiy of sock prices for pre- and pos-holidays. 9. There is no significan difference among rading volume of sock for differen days of he week. 10. There is no significan difference among he rading volume of sock for differen weeks of he monh. 11. There is no significan difference among he rading volume of sock for differen monhs of he year. 12. There is no significan difference among he rading volume of sock for pre- and pos holidays. 13. The behaviour of calendar anomalies has no changed afer he implemenaion of rolling selemen Daa In his sudy we ry o idenify he seasonal ies in hree differen variables: Sock Reurns Volailiy Volume 30

3 Coninuously compounded daily reurns have been used in he sudy, which are defined as he firs difference of (changes in) logarihmic values of closing daily prices. r ln P ln P 1 For primary analysis, he squared reurns have been used as proxy of he volailiy; while for economeric modeling GARCH (1, 1) model has been used o capure volailiy. For he sudy of calendar anomalies in volume, he change in logarihmic value of volume daa has been used. Broadly, he daa covers he sample period of 13 years from January 1995 o December In some cases he acual sample period may differ from his due o non-availabiliy of he daa. The choice of sample period is crucial in a sudy relaing o calendar anomalies because hese anomalies have been observed o change heir naure wih changing marke microsrucure and sage of developmen. Some of he anomalies are more profoundly observed in less liquid and underdeveloped markes. During he period under sudy he Indian sock marke winess he sea changes in is microsrucure. The NSE commenced operaions in November 1994 and soon became he larges sock exchange of India. I was insrumenal in inroducion of many echnological innovaions in marke including demaerializaion of socks, on-line rading, rolling selemen sysem, auomaic risk managemen ec. Foreign insiuional invesors (FIIs) allowed invesing in India since Emergence of collecive invesmen vehicles (muual funds in privae secor) and increasing role of FIIs in changed he marke dynamics remendously. The similar role was played by he inroducion of derivaive producs. These changes are expeced o conribue o he marke efficiency. End of badala sysem and inroducion of rolling selemen is also likely o change he dynamics of price discovery and herefore he possibiliies of he presence of calendar anomalies. We have analyzed he daa in sub-samples o capure he dynamic impac of marke reforms on marke efficiency. This sudy is based on wo-ypes of daa aggregae index daa and company daa. Indices reflec he behavior of he marke as a whole. One benefi of using indices is ha he indices are less noisily han he prices of individual socks; herefore, i is easier o deduc any sysemaic paern in sock reurns a index level. However, 31

4 someime micro-srucural inricacies, such as non-synchronous rading, lead-lag effec, smoohing ec may creae some arifacs or may conceal some oher effecs. Therefore, we have also explored he daa a individual company level for possible presence of calendar anomalies. Sudy a individual company level is also useful in deducing he linkage beween he anomalies and individual company characerisics Index Daa Indices from he Bombay Sock Exchange (here afer BSE) and he Naional Sock Exchange (here afer NSE) have been included in he sudy. These indices vary in erms of he numbers and he size (capializaion) of companies included in heir consrucion. Indices from boh he large exchanges are included in he sudy because he calendar anomalies may be affeced by exchange micro-srucure and in some cases hese wo exchanges follow differen microsrucure (e g weekly selemen sysem before 2002 was differen in hese wo exchanges). Calendar anomalies are also observed o follow differen behavior for he indices represening he companies of differen size. In fac anomalies are observed more profoundly for small capializaion companies raher han he large capializaion companies. Therefore, indices represening companies of differen capializaion are included in he sudy. The descripion of he indices included in he sudy is as follow: i BSE Sensex : from January 1995 ii BSE 100 : from January 1995 iii BSE 200 : from January 1995 iv BSE 500 : from November 1998 v BSE Mid Cap : from January 2003 vi BSE Small Cap : from March 2003 vii S&P CNX Nify (Nify) : from January 1995 viii CNX Nify Junior : from January 1997 ix CNX Mid Cap : from 1 January 2001 x Nify mid Cap 50 : from1 January

5 Volume daa was no available a index level; herefore aggregae volume daa for he marke as a whole has been used in he sudy Companies Daa Toal 44 companies have been included in he sudy, which include 16 large caps, 15 mid cap, and 13 small cap companies. Companies of differen capializaion size have been idenified on he basis of heir presence in respecive BSE capializaion index. Only hose companies have been included in he sudy for which he reurn and volume daa is available from 1995 o Table 3.1 presens he lis of he companies included in he sudy. 3.1 Lis of he Companies No. Large cap Companies No. Mid cap Companies No. Small cap Companies 1 A C C Ld. 1 Alas Copco (India) Ld. 1 Aegis Logisics Ld. 2 Ambuja Cemens Ld. 2 Avenis Pharma Ld. 2 Alembic Ld. 3 Bajaj Auo Ld. 3 Bajaj Holdings & Invs. Ld. 3 Amara Raja Baeries Ld. 4 Cipla Ld. 4 Casrol India Ld. 4 Asian Elecronics Ld. 5 Grasim Indusries Ld. 5 Cenury Texiles & Inds. Ld. 6 Hindalco Indusries Ld. 6 Chambal Ferilisers & Chemicals Ld. 7 Hindusan Unilever Ld. 7 Glaxosmihkline Consumer Healhcare Ld. 8 Housing Developmen Finance Corpn. Ld. 8 Hindusan Consrucion Co. Ld. 5 Auomobile Corpn. of Goa Ld. 6 Bannari Amman Sugars Ld. 7 Bihar Causic & Chemicals Ld. 8 Mysore Cemens Ld. 9 I T C Ld. 9 Hoel Leelavenure Ld. 9 Nocil Ld. 10 Larsen & Toubro Ld. 10 Jindal Saw Ld. 10 Premier Ld. 11 Mahindra & Mahindra Ld. 11 Maharashra Seamless Ld. 12 Ranbaxy Laboraories Ld. 12 Nagarjuna Ferilizers & Chemicals Ld. 13 Reliance Energy Ld. 13 Nicholas Piramal India Ld. 14 Reliance Indusries Ld. 14 Orchid Chemicals& Pharmaceuicals Ld. 15 Taa Moors Ld. 15 Orienal Bank Of Commerce 16 Taa Seel Ld. 11 Sandard Indusries Ld. 12 Taa Sponge Iron Ld. 13 Videocon Appliances Ld. 33

6 Only hose companies included which have coninuous series of volume daa. Volume daa of small cap was broken ha s why we could no apply he analysis on rading volume of small cap companies Source of daa: We used Prowess daa base o collec he daa Saisical Tools In his sudy we examine he presence of four mos common anomalies- day-of-heweek effec, urn-of-he-monh effec, monh-of-he-year effec and holiday effec. The saisical echniques applied for his can be divided ino wo sages (i) primary analysis and (iii) confirmaive analysis based on economeric modeling Primary Analysis In he primary Analysis of daa -es and F-es have been used o deec he calendar anomalies in reurns, volailiy (define as he square reurns) and changes in rading volume. To examine he presence of anomaly associaed wih a paricular ime frame or season (day of he week, week of he monh or monh of he year ec), we compare he mean of ha season wih he mean of he res of he period. The differences beween hese means are saisically evaluaed. Two saisical ess have been used for his purpose - (i) he pairwise -es and (ii) he analysis of variances, ANOVA. Boh of hese ess are parameric in naure and based on he assumpion ha variables are normally disribued (as an alernaive we had also used non parameric ess Mann- Whiney U es in case of wo independen samples and Kruskal-Wallis for muliple caegories comparisons; bu he resuls were no much differen from hose produced by parameric ess). The saisical erms and ools we use in he analysis are as follow: 34

7 Mean Mean is he average and compued as he sum of all observed oucomes from he sample divided by he oal number of evens. In oher words, his is idenical o he equaion: = ( )/N Where N is he number of observaions (a some places is used in he place of n o signify he ime series observaions) Sandard Deviaion Sandard Deviaion is he square roo of he variances, i measure he spread of a disribuion around he mean. More precisely, we measure now for all our measuremens are from he mean, symbol of sandard deviaion is ( ). var = Where, is square roo of variance. To es he saisical significance of resuls we used he following ools: -es The -es is he mos common saisical ool for hypohesis esing. There is several kind of -es bu he mos common is he Two sample -es or Suden s -es or independen sample -es F-es or One-Way ANOVA The F-es or one-way-analysis of variance is used o assess wheher he expeced values of a quaniaive variable wihin several pre-defined groups differ from each oher. This es has been used o examine if here exiss significan difference in reurns (or volailiy or volume) across he differen days (weeks or monhs). 35

8 P-Value The es saisics are inerpreed on he basis of he p-values. p value is a probabiliy ranging from 0 o 1. I is associaed wih a es saisics, if he es saisic really were disribued as i would be under he null hypohesis. p- value signify he probabiliy of Type I error; i is he likelihood of he nullhypohesis o be correc. Smaller he p value, more srongly he es rejecs he null hypohesis. In our sudy null hypohesis is rejeced when p value is less han 0.05 levels. Resuls were highly significan when p valued is less han 0.01 levels. Levene Tes Levene es is used o es if sample have equal variance across caegories. I is used o es he homogeneiy of variances. Some saisical es for example he independen sample -es, assume ha variance are equal across groups. Tes saisics needs some modificaion if his assumpion is no rue. Therefore, Levene es has been used o verify ha assumpion Economeric Models The resuls of saisical ess presened in he preceding secion are valid only when he variable under consideraion is idenically and independenly disribued Gaussian variable. However, his assumpion is no valid for asse reurns because asse reurns are found o be auoregressive and usually depic he phenomenon of volailiy clusering. Therefore, he rue naure of he seasonal anomalies canno be known unless he adjusmen is made for condiional mean and volailiy. We use he AR (1)- GARCH (1, 1) for his purpose and hen include he dummy-variables in mean and variance equaions o examine he presence of anomaly. To avoid he dummy variable rap he number of dummy variables mus be less han he oal number of caegories. Therefore, one caegory is used as reference caegory and dummy variable regression coefficiens show ha changes in oher caegories in comparison o he reference caegory. 36

9 For he examinaion of he Monday effec in reurns and volailiy, one dummy variable represening he Monday is included as follow: R C R 1 u h h u Mon ~ N(0,1) h Mon (3.1) The firs line of he above equaion is called he mean equaion while he hird line is called a variance equaion. The second line esablishes a link beween mean and condiional variance. The mean equaion signify ha he reurn generaing process is assumed o follow AR(1) process; herefore oday s reurn is dependen on yeserday s reurns hrough coefficien. Such dependence is generally observed in empirical research. In variance equaion he condiional variance for a given day h depends on 2 yeserday s squared residuals ( ) hrough coefficien and on yeserday s 1 condiional variance hrough coefficien. In his sandard GARCH(1,1) model, coefficien is called he news coefficien while coefficien governs he persisence of volailiy. To ensure consisency in volailiy esimaion boh of he coefficien should be non-negaive and heir sum mus be less han 1. This sandard AR(1)-GARCH(1,1) model is augmened by a dummy variable Mon. This is Monday dummy and akes he value of 1 Monday and 0 on oher days. In mean equaion coefficien capures he Monday effec. If his coefficien is posiive and significan i implies ha he reurns on Monday are significanly higher han he reurns on oher days of he week. On he oher hand if is negaive and significan i implies ha Monday reurns are lower han he reurns on oher week days. A nonsignifican coefficien signify he absence of Monday anomaly in reurns. Similarly, coefficien capures he Monday effec in volailiy. A posiive and significan value of indicaes ha volailiy increases on Monday while a negaive and significan value of his coefficien is an indicaor of reducion in volailiy on Monday. A non-significan value will show absence of Monday effec on volailiy. 37

10 To es he presence of Monday effec in volume he following economeric model is used: V C V 1 1 u h h h u Mon ~ N(0,1)... (3.2) In his specificaion he Monday dummy is presen only in mean equaion. A significan value of coefficien 1 indicaes he presence of Monday effec while he posiive or negaive sign of his coefficien shows wheher he volume on Monday is higher or lower han he volumes on oher days of he week. Similar economeric models have been used o es oher week day s effecs, urn-ofhe-monh effec and monh-of-he-year effec 3.6. Sofware Packages We have used SPSS 15.1 for he primary analysis of he daa. EVIEWS 6.2 has been used for he economeric modeling. Findings: In his sudy an aemp has been made o examine he presence of he calendar effec in Indian sock marke. 38