Trends in Stock Prices and Range to Standard Deviation Ratio

Transcription

1 Inernaional Journal of Business and Managemen Vol. 6, No. ; January Trends in Sock Prices and Range o Sandard Deviaion Raio Subraa Kumar Mira Insiue of Managemen Technology 35 Km Milesone, Kaol Road, Nagpur 44 5, India Tel: skmira@imnag.ac.in Absrac Hurs exponen (H) measured from R/S raio, is being used as a measure o find predicabiliy of a ime series. The larger he H value, he sronger is he rending rai in he ime series. In his paper, we esimaed R/S raio of several sock indexes of Indian marke for years. Though he overall Hurs exponen values for he seleced series were close o.5, he value varied widely on period-o-period basis. The analysis of R/S raio on a smaller window size of 3 rading day revealed a posiive relaionship beween R/S raio and performance of a moving average based rading rule. Keywords: R/S raio, Hurs exponen, Trading rule, Marke rends, Indian sock marke. Inroducion The Hurs exponen proposed by Hurs (95)for use in hydrological sudies has been applied o many research fields. The use of his exponen has also become popular in he financial sudies largely due o work of Peers (99, 994). The Hurs exponen provides a measure for long-erm memory and predicabiliy of a ime series. The objecive of his paper is o develop some insighs on price movemens in financial markes by comparing Hurs exponen (H) and reurns in Indian Sock marke. The value of Hurs exponen can give some clue wheher presen value of he series depend on pas values of he ime series. H-value of.5 signals presence of Brownian moion. When he value of H lies beween < H <.5, i sugges rend reversing characerisics in he series. Conversely, value of H wihin he range of.5 < H < sugges presence of rend in he series. The power of he rend increases unil value of H reaches is upper ceiling value of one. Hurs observed ha he H-value direcly depends on range o sandard deviaion raio (R/S raio). Thus R/S raio can provide a mehod of classifying ime series, which can be useful in idenifying which markes have greaer predicabiliy. While forecasing a ime series, we need o know wheher he ime series under sudy is predicable or no. If he ime series is random, no forecasing mehod will be successful and herefore, we may focus only o hose ime series ha have some degree of predicabiliy. A ime series wih a large R/S raio has rending characerisics and such series is more predicable han a series wih a low R/S raio. The res of he paper is organized as follows: Secion- describes lieraure survey on applicaion of Hurs exponen in financial markes. Secion-3 deals wih he esimaion procedure of R/S raio and Hurs exponen. Secion-4 hen describes various sock indexes used in he sudy. In Secion-5, resuls of empirical ess in Indian marke are abulaed and relaionship beween R/S raio and Marke reurns are analyzed. Finally, he paper is concluded in Secion 6.. Lieraure Survey Applicaion of Hurs exponen in financial ime series has gained momenum wih he work of Peers (99, 994) who esimaed Hurs exponen for monhly reurns on he S&P 5 from January 95 o July 988. From a sample of individual socks, Peers noed ha Hurs exponens varied from.54 for Consolidaed Edison o.75 for Apple Compuer. As he H-values are greaer han.5, he found persisence among sock reurns han would be expeced if sock prices followed a Brownian moion. Nah () found ha, he R/S analysis signaled of long-erm memory for all-ime lags in Indian sock marke. Wih higher ime lags of more han wo years, here exiss long memory. He inferred ha movemen of sock prices in India does no follow a random walk. Corazza and Malliaris () sudied some foreign currency markes and found ha Hurs exponen was saisically differen from.5 in mos of he samples. Besides, hey also found ha he Hurs exponen is no fixed bu i changes dynamically overime. They inerpreed ha foreign currency reurns follow eiher a fracional Brownian moion or a Pareo-Levy sable disribuion. Published by Canadian Cener of Science and Educaion 3

2 Inernaional Journal of Business and Managemen Vol. 6, No. ; January Lipka and Los () measured he degrees of persisence of he daily reurns of several European sock marke indices. They found he global Hurs exponens, esimaed from wavele muli-resoluion analysis, measured he long-erm dependence of he daa series quie well. They found he FTSE urns ou o be an ulra-efficien marke ha exhibi abnormally fas mean-reversion, faser han heoreically posulaed by a Geomeric Brownian Moion (GBM). Razdan () sudied Bombay sock exchange (BSE) index financial ime series for fracal and mulifracal behavior. He found ha BSE index ime series is mono-fracal and can be characerized by a fracional Brownian moion. Carbone, Caselli and Sanley (4) calculaed he Hurs exponen of some ime series by dynamic implemenaion of a scaling echnique: he derending moving average (DMA). The DMA algorihm allowed hem calculaion of he exponen wihou any prior assumpion on he sochasic process and on he probabiliy disribuion funcion of he random variables Qian and Rasheed (4) analyzed he Hurs exponen for all rading-day periods of he Dow-Jones index from January 93 o May 4. They found ha he periods wih large Hurs exponens could be prediced more accuraely. This suggess ha sock markes do no show random walk in all periods. Some periods have srong rend srucure and his srucure can be learned o benefi forecasing. They classified financial daa series of differen periods and experimened wih back-propagaion neural neworks o show ha series wih large H can be prediced more accuraely. The auhors inferred ha he H provides a measure for predicabiliy. Glenn (7) analyzed of he NASDAQ Composie index in he 36-year period since is beginning in 97. He found ha he probabiliy densiy funcion of -day reurn is highly lepokuroic; he maximum -day loss is more han nine sandard deviaions from he mean. To assess wheher long-erm dependence is presen in he NASDAQ ime series, rescaled range-saisic calculaions were carried ou o find ou he Hurs exponen. I was found ha H was.59 for -day reurns and increased monoonically o a value of.87 for 5-day (annual) reurns. Los & Bing (8) idenified lack of ergodiciy, saionariy, and independence, and i idenified he degree of early persisence of he Chinese sock markes when hey were more regulaed. They used index series are from he Shanghai (SHI) sock marke and Shenzhen A-shares (SZI) and B-shares (SZBI), before and afer he various deregulaions and reregulaions. By compuing he Hurs exponens, hey idenified he markes' laer degrees of persisence. The empirical evidence revealed ha SHI, SZI, and SZBI are moderaely persisen wih Hurs exponens slighly greaer han he Fickian.5 of he Geomeric Brownian Moion. I also shows ha hese sock markes were more persisen before he deregulaions, bu ha hey now move like geomeric Brownian moions, i.e. he markes have become more efficien in recen imes. Singh & Prabakaran (8) examined he various feaures of he logarihmic reurn specrum of he Indian sock markes using various saisical ess for he normaliy of daa. They performed rescaled range analysis and carried on o esimae he Hurs s exponen. They inferred ha he Indian capial markes are no random and herefore, do no form a populaion ha is normally disribued. Furher, geomeric Brownian moion canno accuraely model he sock prices, because of significan memory effec found by lumping observaions ino some sor of clusers, paricularly for reurns ha are found in he ails of he disribuion. Leno (9) ried o find synhesis beween echnical analysis and fracal geomery. He argued ha Hurs exponen (H) was developed from he field of fracal geomery and provides a saisical echnique o idenify he naure of any dependencies in a ime series. Moreover, Technical analysis has developed various rading rules ha are premised on he belief ha pas price daa reveals paerns ha can be used o predic fuure prices. Based on his logic, and furher empirical analysis he found ha ime series wih high H resuled in higher profis in case of rending rading rules and ime series wih low H resuled in higher profis from conrarian rading rules. However, according o some auhors, he R/S es is biased oward finding long-erm memory. Sock marke reurns may follow ime pahs ha are biased and he sandard saisical ess canno disinguish i from random behavior. Though R/S raio can be used o deec long-erm, nonperiodic cycles in sock marke reurns, if his echnique is no applied correcly, hen i can be influenced by shor-erm biases. These biases can lead o he inaccurae conclusion ha he sock marke has long-erm memory. Lo (99) esed R/S saisic, for daily, weekly, monhly, and annual sock reurns indexes over several differen ime-periods. Conrary o previous findings, he found no evidence of long-range dependence in any of he indexes over any sample period or sub period once shor-erm auocorrelaions are considered. His Mone Carlo experimens suggesed ha he modified R/S es had power agains a leas wo specific models of long-run memory, suggesing ha sochasic models of shor-range dependence may adequaely capure he ime series behavior of sock reurns. 4 ISSN E-ISSN

3 Inernaional Journal of Business and Managemen Vol. 6, No. ; January 3. R/S Raio and Hurs Exponen Hurs was a hydrologis and worked on he Nile River Dam projec for abou 4 years during he early years of he las cenury. He ried o find ou he ideal feaures for reservoir design. An ideal reservoir should discharge cerain amoun of waer every year and should never overflow. However, he inflow of he reservoir varies due o changes in he climaic condiions. If he inflow of he reservoir is oo low hen releasing fixed amoun of waer will make reservoir dry. Thus, he was confounded wih he problem of fixing he waer discharge policy, such ha he reservoir will never be empied nor i will overflow. In developing such a model, Hurs sudied he inflow of waer from rainfall. He measured how reservoir level rises and falls around is average and recorded range of he variaions. If he series were random, he range would increase wih he square roo of ime. To sandardize he analysis Hurs creaed a dimensionless raio by dividing high-low Range of he reservoir by he Sandard deviaion of he ime series (R/S raio). Hurs wached ha many naural phenomena like, rainfall, emperaures, river flow follow a biased random walk, which is a combinaion of random walk, rend and noise. Following Hurs, many auhors have also used R/S analysis o analyze daa on hydrological parameers such as river flow, precipiaion, emperaure, ec. 3. Esimaion of R/S Raio R/S analysis was esablished by Hurs in 95 and he same was furher developed by Mandelbro and Van Ness (968). This concep has found applicaion in a diverse area. I has also been applied o economic price analysis by many auhors. The R/S value is referred o as he rescaled range analysis because he series is convered o a zero mean series and is expressed in erms of sample sandard deviaion. The rescaled series is creaed by firs rescaling or normalizing he daa by subracing he sample-mean: Z X. The rescaled range, or R/S saisic, is esimaed by measuring he range beween he maximum and minimum values of he cumulaive sum of he variable Z and hen dividing his range by he sandard deviaion of he series. Hurs drew up a null hypohesis on Binomial disribuion and developed he following equaion: R n. S n H, where n = number of observaions and H is characerisic consan of he series. According o he heory of Brownian moion, H =.5 implies an independen innovaion process i.e. he evens are muually independen hroughou ime, where pas values do no influence he presen values. A persisen marke reurn series is characerized by presence of a long memory. In a persisen marke, a posiive (negaive) change in a period is likely o be coninued in he same direcion in he following period. The srengh of he rend-reinforcing behavior increases as he value of he Hurs exponen approaches uniy. The closer he Hurs exponen is o.5, he price movemen will appear as random and become unpredicable. Ani-persisen processes are mean-revering, which means ha if he marke has been in a paricular direcion in he previous period, i is more likely o move in he reverse direcion in he following period. The srengh of his mean revering behavior depends on how close he Hurs exponen is o zero. 4. Daa The daa used for his sudy are he daily closing price of various sock indices repored by Naional Sock Exchange, India. The socks are classified ino various major indices and he following indices are analyzed in he sudy. S&P CNX Nify CNX Nify Junior S&P CNX Defy S&P CNX 5 CNX IT Index CNX Bank Index The daily closing values of he above indices were colleced from he websie of he exchange for a period of en years, i.e. from January o April. Brief descripion of hese indexes are given below (based on informaion colleced from he websie of Naional Sock Exchange, Published by Canadian Cener of Science and Educaion 5

4 Inernaional Journal of Business and Managemen Vol. 6, No. ; January 4. S&P CNX Nify S&P CNX Nify is a diversified 5 sock index accouning for secors of he Indian economy. I is managed by India Index Services and Producs Ld. (IISL), which is a join venure beween NSE and CRISIL. Nify socks represen abou 63% of he Free Floa Marke Capializaion as on Dec 3, 9. The oal raded value for he las six monhs of all Nify socks is abou 5% of he raded value of all socks on he NSE Impac cos of he S&P CNX Nify for a porfolio size of Rs. crore is.% 4. CNX Nify Junior The nex rung of liquid securiies afer S&P CNX Nify is he CNX Nify Junior, which is also, formed using 5 socks. I may be useful o hink of he S&P CNX Nify and he CNX Nify Junior as making up he mos liquid socks in India. The mainenance of he S&P CNX Nify and he CNX Nify Junior are synchronized so ha he wo indices will always be disjoin ses; i.e. a sock will never appear in boh indices a he same ime. Therefore, i is always meaningful o pool he S&P CNX Nify and he CNX Nify Junior ino a composie sock index or porfolio. CNX Nify Junior represens abou % of he Free Floa Marke Capializaion as on Dec 3, 9. The raded value for he las six monhs of all Junior Nify socks is abou 5% of he raded value of all socks on he NSE Impac cos for CNX Nify Junior for a porfolio size of Rs. 5 lakhs is.3% 4.3 S&P CNX Defy Insiuional invesor and offshore fund enerprise wih an equiy exposure in India would like o have an insrumen for measuring reurns on heir equiy invesmen in dollar erms. To faciliae his, a new index he S&P CNX Defy-Dollar Denominaed S&P CNX Nify has been developed. S&P CNX Defy is S&P CNX Nify, measured in dollars. Salien Feaures of S&P CNX Defy are as follows: Performance indicaor o foreign insiuional invesors, offshore funds, ec. Provides an effecive ool for hedging Indian equiy exposure. Impac cos of he S&P CNX Nify for a porfolio size of Rs. crore is.6% Provides fund managers an insrumen for measuring reurns on heir equiy invesmen in dollar erms. 4.4 S&P CNX 5 The S&P CNX 5 is India s firs broad based benchmark of he Indian capial marke. The S&P CNX 5 represens abou 9.57% of oal marke capializaion and abou 9.7% of he oal urnover on he NSE as on Sep 3, 9. The S&P CNX 5 companies are disaggregaed ino 7 indusry indices viz. S&P CNX Indusry Indices. Indusry weighages in he index reflec he indusry weighages in he marke. For example if he banking secor has a 5% weighage in he universe of socks raded on NSE, banking socks in he index would also have an approximae represenaion of 5% in he index. 4.5 CNX IT Index Informaion Technology (IT) indusry has been playing a major role in he Indian economy since las decade. A number of large, profiable Indian companies oday belong o he IT secor and a grea deal of invesmen ineres is now focused on he IT secor. To have a good benchmark of he Indian IT secor, IISL has developed he CNX IT secor index. The oal raded value for he las six monhs of CNX IT Index socks is around 83.39% of he raded value of he IT secor. CNX IT Index socks represen abou 8.33% of he oal marke capializaion of he IT secor as on March 3, 9. The oal raded value for he las six monhs of all CNX IT Index consiuens is nearly 8.59% of he raded value of all socks on he NSE. CNX IT Index consiuens represen abou 6.97% of he oal marke capializaion as on March 3, CNX Bank Index CNX Bank Index is an index comprised of he highly liquid and large capialized Indian Banking socks. I provides invesors and marke inermediaries wih a benchmark ha capures he capial marke performance of Indian Banks. The index has socks from he banking secor which rade on he Naional Sock Exchange. The oal raded value for he las six monhs of CNX Bank Index socks is approximaely 96.46% of he raded value 6 ISSN E-ISSN

5 Inernaional Journal of Business and Managemen Vol. 6, No. ; January of he banking secor. CNX Bank Index socks represen abou 87.4% of he oal marke capializaion of he banking secor as on March 3, 9. The oal raded value for he las six monhs of all he CNX Bank Index consiuens is approximaely 5.6% of he raded value of all socks on he NSE. CNX Bank Index consiuens represen abou 7.74% of he oal marke capializaion as on March 3, Empirical Analysis Some sandard descripive saisics applicable o he seleced daa series are produced in Table-I and Table-II. The figures repored in Table-I show means, medians, maximum and minimum values of he original series. Table-II repors means, medians, sandard deviaions, skewness, and kurosis of he daily reurns obained from he firs difference of he original index series. Inser Table-I and Table-II here All daily reurn series repored in Table-II, qualiaively show o some degree of deparure from normal disribuion. This is evidenced by he difference beween mean reurns from heir corresponding medians, negaive skewness values, and higher kurosis values. The price chars of hese ime series are given in Char-I Inser Char-I here 5. Saionariy Tess From Char-I, i can be observed ha all seleced series have displayed some kind of rending behavior during las years. I was herefore needed o find ou saionariy of he series. According o some auhors, evidence of long-erm memory could be spuriously caused by non-saionariy in he ime series iself. We herefore, performed augmened Dickey-Fuller (ADF) ess and Phillips-Perron (PP) ess o find saionariy of he daa series boh a levels and a heir firs differences. The resuls of ADF and PP ess are produced in Table-III. Inser Table-III here Boh ADF and PP ess reveal ha null hypohesis of non-saionariy canno be rejeced a he level daa as p-values of mos of he series were above 9%. However, p-values are close o zero, when firs difference of daa is analyzed. The index series a levels are herefore ransformed ino daily reurns series by aking (logarihm) differences. The series comprising of daily sock reurns are herefore saionary. 5. R/S and H Values Given he index level X, X, X, he rae of reurn a ime is esimaed by aking differences of he consecuive logarihm values: x = ln(x ) ln(x - ). To remove any secular rends from he series he daily reurns series are firs de-rended by subracing mean reurn from daily log reurns. Sample mean is calculaed by n averaging reurn of he sample period: x. The rend adjused reurn for period is hus: i n i r x. In he nex sage, a cumulaive rend adjused reurn series is formed: c n r. The rescaled range ( R ) of i i his cumulaive series is calculaed aking differences of maximum and minimum values of c : R m ax( c, c... c ) m in( c, c... c ) The sandard deviaion ( S ) of he series is calculaed: S ( x ) i and finally, he rescaled R/S R S raio of he series is obained by aking raio: R S. I has been noed ha he rescaled R is proporional o S H : R C. S H. The leer exponen H was coined by Mandelbro in honor of Harold Edwin Hurs. He also suggesed a mehod of measuring he srengh of long-range dependence of a series. By aking logarihm, he Hurs exponen can be ransformed from a power Published by Canadian Cener of Science and Educaion 7

6 Inernaional Journal of Business and Managemen Vol. 6, No. ; January exponen o a linear form: R C H log log.log S. When we plo lo g R S versus lo g and fi a sraigh regression line, he slope of he regression line will give he value of H. The plo and regression line for all he seleced series are produced in Char-II. The slope coefficien in he equaion of rend line is he overall Hurs exponen value of he corresponding series. Inser Char-II here 5.3 Relaionship beween R/S Raio and Reurns In Char-II, overall H-values were esimaed using enire years daily daa and i migh be noed ha he H values varied beween.4 and.55 in line wih he expeced value of.5 for a random walk model. Thus on a overall basis, all he sudied series closely followed a random walk and herefore predicion of rend in hese series are no easy. However, mos of he sock marke predicions are done analyzing shor erm flucuaions of he marke. Though a marke may remain efficien, in general, in a shor inervening period, he marke reurns may deviae from normal disribuion due o various reasons. To analyze he variaions of R/S raio in shor erm, he full daa se is spli ino smaller series; each conains daa of 3 consecuive rading days. We esimaed R/S raios separaely for each of hese smaller periods and found ha R/S raio flucuaed widely from period o period. The dispersion of R/S raio generally remained wihin he range of 4 o 4, barring few ouliers. We herefore, classified each 3-period smaller series based on heir R/S values and presened he classificaion in Table-IV. I is believed ha a series having higher R/S raio shows evidence of rending behavior. When rends are presen in a series, he same can be capured using a rend deecing rule. To evaluae rending characerisic, we used a rading rule using -period moving average. We produced a buy signal when index value was higher han is moving average value and conversely, produced a sell signal when index value was lower han is moving average value. We esimaed heoreical profis based on hese buy and sell rading signals. However, o make analysis simpler, we did no consider ransacion coss in esimaing profis. We presen he resuls of comparison beween esimaed R/S values wih reurns gained in each sub-period in Table -IV. Inser Table-IV here We also presen he resuls of our analysis in Char-III aking R/S raio on x-axis and reurn value in y-axis. I is apparen from he chars ha higher reurns are associaed wih higher R/S raios as all he rend-lines displayed upward slope. To analyze significance of slope values, we compared coefficien values wih is sandard errors and obained p-values. The observaions are abulaed in Table-V Inser Char-III and Table-V here I is obvious from Table-V ha all slope values are no only posiive bu also significan a % level. This confirms associaion of R/S values in he reurn making process of he sock markes. From Char-III, i can be inferred ha periods having high R/S raio have yielded higher reurn. Ineresingly, during periods of low R/S raio, mos of he rend lines enered ino he negaive erriory. This implies ha rend following rading rule have failed o generae correc rading signals during periods of low R/S raio. As per Hurs s original inerpreaion, low R/S signals mean reversal phenomena, negaing presence of any rend. The resuls of his sudy also suppor mean reversal phenomena as a rend following rading rule generaed negaive profi during periods of low R/S raio. 6. Conclusion All he sock indices sudied in his paper show a Hurs exponen ha is close o.5, which reconfirms random behavior of marke reurns and marke efficiency. However, he R/S raio in he inermediae 3-period rading window is found o vary dynamically overime, wihin a wide range of 4 o 4. I is also found from he analysis ha whenever he R/S values were high, he average reurns obained from a moving average based rading rule were also high and vice versa. These observaions lead o he conclusion ha R/S raios are relaed o he reurn generaing process in he Indian sock marke. Since R/S raio provided a measure of predicabiliy of a financial series, his raio can be used as a guide for daa selecion while analyzing rend and deciding a rade. Some aspecs migh have influenced he resuls of he sudy. The daa is subdivided in smaller block period of 3 rading days. Change in block size may have some 8 ISSN E-ISSN

7 Inernaional Journal of Business and Managemen Vol. 6, No. ; January impac on he resuls. Besides, we used only one rading rule based on moving average, using oher rading rules may presen more insighs ino he issue. References Carbone, A., Caselli, G., & Sanley, H. E. (4). Time-dependen Hurs exponen in financial ime series, Physica A: Saisical Mechanics and is Applicaions, 344, Corazza, M., & Malliaris, A.G. (). Mulifracaliy in Foreign Currency Markes. Mulinaional Finance Journal, 6, Glenn, L.A. (7). On Randomness and he NASDAQ Composie, SSRN Working Paper, [Online] Available: hp://ssrn.com/absrac=499 Hurs, H. (95). Long-erm sorage capaciy of reservoirs, Transacions of he American Sociey of Civil Engineers,, Leno, C. (9). A Synhesis of Technical Analysis and Fracal Geomery - Evidence from he Dow Jones Indusrial Average Componens, (9), [Online] Available: hp://ssrn.com/absrac=6365 Lipka, J., & Los,C. (). Persisence characerisics of European sock indexes. Working Paper (Ken Sae Universiy, Ken, OH). Lo, A.W. (99). Long Term Memory in Sock Marke Prices, Economerica, 59, Los, C. A., & Bing, Yu. (8). Persisence characerisics of he Chinese sock markes. Inernaional Review of Financial Analysis, 7, Mandelbro, B.B., & Van Ness, J. (968). Fracional Brownian moions, fracional noises and applicaions. SIAM Review,, Nah, G.C. (). Long Memory and Indian Sock Marke An Empirical Evidence, UTIICM Conference Paper. Peers, E. (99). Chaos and Order in he Capial Markes: A new view of cycles, prices, and marke volailiy, John Wiley & Sons: New York. Peers, E. (994). Fracal Marke Analysis: Applying Chaos Theory o Invesmen and Economics, John Wiley & Sons: New York. Qian, B., & Rasheed, K. (4). Hurs Exponen and Financial Marke Predicabiliy, Proceeds of he Financial Engineering and Applicaions, MIT, Cambridge, USA Razdan, A. (). Scaling in he Bombay sock exchange index. PRAMANA- Journal of Physics, 58, Singh, J.P., & Prabakaran, S. (8). On he Disribuion of Reurns & Memory Effecs in Indian Capial Markes, Inernaional Research Journal of Finance and Economics, 4, Table. Descripive Saisics of he Daa Series Index Values Series Mean Median Maximum Minimum Nify Junior Nify Defy CNX CNX IT BANK Index Published by Canadian Cener of Science and Educaion 9

8 Inernaional Journal of Business and Managemen Vol. 6, No. ; January Table. Descripive Saisics of he Daily Reurn Series Daily Reurn Values Series Mean Median Sd. Dev. Skewness Kurosis Nify.47%.43%.75% -.3. Junior Nify.37%.4%.53% Defy.46%.49%.883% CNX 5.48%.88%.775% CNX IT.%.66%.77% BANK Index.86%.84%.89% Table 3. Saionariy es of daa series (p-values of ADF and PP es) ADF es resuls Phillips-Perron es resuls Firs Firs Series Level Daa Difference Level Daa Difference Nify Junior Nify Defy CNX CNX IT BANK Index ISSN E-ISSN

9 Inernaional Journal of Business and Managemen Vol. 6, No. ; January Table 4. R/S Raio and Average 3-period Reurn* S&P CNX Nify CNX Nify Junior S&P CNX Defy Average Average Average R/S raio No. of Periods 3-period reurn No. of Periods 3-period reurn No. of Periods 3-period reurn % 3.7% -7.5% % -4.7% 3 3.7% % % 4.8% % % % % 6 9.% % % % 7.9% % 4.95% % S&P CNX 5 CNX IT Index CNX Bank Index Average Average Average R/S raio No. of Periods 3-period reurn No. of Periods 3-period reurn No. of Periods 3-period reurn % -9.4% -8.46% % % % % 8.3% 35.95% % 3.48% % % 6.33%.46% % 6.45% 7.99% % % 8.8% *The enire daa series is broken ino small window size conaining reurns of 3 consecuive rading days. The reurns are classified based on he R/S raio of he respecive windows. For example, while analyzing R/S raios of S&P CNX Nify, we found ha in 3 windows he R/S value were wihin 6-8 and he average 3-period reurns (following a moving average based rading rule) of hose 3 windows were 5.%. Table 5. Coefficien, Sandard Error and p-value of rend line parameers Series Slope Consan Sd. Sd. Value Error p-value Value Error p-value Nify Junior Nify Defy CNX CNX IT Bank Index Published by Canadian Cener of Science and Educaion 3

10 Inernaional Journal of Business and Managemen Vol. 6, No. ; January S&P CNX Nify CNX Nify Junior Index Value Index Value Jan- Jan- Jan-4 Jan-6 Jan-8 Jan- Jan- Jan- Jan-4 Jan-6 Jan-8 Jan- S&P CNX Defy S&P CNX Index Value 4 3 Index Value 4 3 Jan- Jan- Jan-4 Jan-6 Jan-8 Jan- Jan- Jan- Jan-4 Jan-6 Jan-8 Jan- CNX IT Index CNX Bank Index Index Value Index Value Jan- Jan- Jan-4 Jan-6 Jan-8 Jan- Jan- Jan- Jan-4 Jan-6 Jan-8 Jan- * Plo depic daily closing value of respecive index from January o April Char. Time Series Plos of he Index* 3 ISSN E-ISSN

11 Inernaional Journal of Business and Managemen Vol. 6, No. ; January S&P CNX Nify CNX Nify Junior.5 y =.546x y =.4853x +.48 log(r/s).5 log(r/s) log(n) log(n) S&P CNX Defy S&P CNX 5.5 y =.5478x y =.4397x +.54 log(r/s).5 log(r/s) log(n) log(n) CNX IT Index CNX Bank Index.5 y =.43x y =.4974x log(r/s).5 log(r/s) log(n) log(n) * A rend line is fied amongs he log(n) versus log(r/s) plos of each series and he equaion of he rend line is included. The slope coefficien of he equaion is he Hurs exponen value of he corresponding ime series. Char II. Log R/S versus Log (n) Plos* Published by Canadian Cener of Science and Educaion 33

12 Inernaional Journal of Business and Managemen Vol. 6, No. ; January S&P CNX Nify CNX Nify Junior 3 period reurn y =.95x R/S Value 3 period reurn y =.75x R/S Value S&P CNX Defy S&P CNX 5.3 y =.x y =.45x period reurn.. 3 period reurn R/S Value R/S Value CNX IT Index CNX Bank Index 3 period reurn y =.43x R/S Value 3 period reurn y =.43x R/S Value * All index series are spli ino a number of smaller series; each conains daily reurns of 3 consecuive rading days. For each 3-period series, we esimaed he R/S raio and rading reurn using a moving average rule. A fied rend-line and regression equaion for he same are also added. Char III. R/S raio versus Average 3-period Reurn* 34 ISSN E-ISSN