INVESTIGATING THE WEAK FORM EFFICIENCY OF AN EMERGING MARKET USING PARAMETRIC TESTS: EVIDENCE FROM KARACHI STOCK MARKET OF PAKISTAN

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1 Elecronic Journal of Applied Saisical Analysis EJASA, Elecron. J. App. Sa. Anal. Vol. 3, Issue 1 (21), ISSN , DOI /i275948v3n1p52 28 Universià del Saleno SIBA hp://siba-ese.unile.i/index.php/ejasa/index INVESTIGATING THE WEAK FORM EFFICIENCY OF AN EMERGING MARKET USING PARAMETRIC TESTS: EVIDENCE FROM KARACHI STOCK MARKET OF PAKISTAN Muhammad Irfan 1*, Maria Irfan 1, Muhammad Awais 2 1 Deparmen of Saisics, GC Universiy, Faisalabad, Pakisan. 2 Deparmen of Compuer Science, NFC- IE&FR Faisalabad, Pakisan. Received 25 Sepember 29; Acceped 21 December 29 Available online 28 February 21 Absrac: This paper focuses on he exisence of weak from efficiency wheher he Karachi Sock Exchange (KSE) is efficien marke or no. The sample includes he daily and monhly closing prices of KSE- 1 indexes for he period of 1 s January1999 o 31 s Augus 29. Several differen parameric approaches: uni roo es, auocorrelaion ess and ARIMA model are used o es he cerainy of he KSE marke. All parameric mehods ell us ha boh reurn series do no follow he random walk model and he significance auocorrelaion rejec he hypohesis of weak from efficiency. Generally, resuls from he observed analysis srongly recommend ha he Karachi Sock Marke of Pakisan is no efficien in weak from. Keywords: KSE, Random Walk, Efficien marke, ARIMA. 1. Inroducion Marke inadequacy is he key negaive aspec for developing counries like Bangladesh, Pakisan and India. A grea deal of he work on weak from efficiency is based on he parameric approaches, on develop markes of Europe and Lain American, (for example Hudson e al. (1994) consider he UK sock marke; Nicolaas and Groenewold (1997) sudy he Ausralia and New Zealand markes while Ojah and Karemera (1999) examine he Lain American markes wih many researchers). There exiss enough lieraure on weak efficiency of emerging markes as well, such as, of Asia (for insance Mobarek and Keasey (2), Ahmad (22), Hossain (24) and Mousafa (24) * Corresponding Auhor. mirfanbal@yahoo.com 52

2 Irfan M., Irfan M., Awais M., Elecron. J. App. Sa. Anal., Vol 3, Issue 1 (21), checked for Bangladesh sock exchange, Hussain (1996) Pakisan Marke, Poshakwale (1996) consider he Indian sock marke). However, a few sudies have appeared in he lieraure focusing on he Karachi Sock Marke (KSE). The objecive of his research work is o es and invesigae wheher he Karachi Sock marke (KSE) is an efficien marke or no. A brief review of findings of some of earlier research work is presened as under: Abrosimova e al. (25) invesigaed he exisence of week from in he Russian sock marke for he period of 1995 o 21 by using daily, weekly and monhly Russian Trading Sysem (RTS) index. Numerous dissimilar approaches are used o check he weak from efficiency of he RTS. The resuls indicaed ha daily and weekly daa do no follow he normal hypohesis bu he resuls suppor he null hypohesis for he monhly daa only. Their research resuls provide some limied evidence of shor-erm marke predicabiliy on he RTS. Chakrabory (26) examined he weak from efficiency of he Pakisan sock marke using KSE -1 index. The auhor was applying he variance raio ess, runs ess and serial correlaion ess. Serial correlaion es and runs es rejec he random walk hypohesis which means ha KSE is no an efficien sock marke. Furhermore, he repored ha auocorrelaion and heeroscedasiciy is presen in he daa. I has been also found ha ARMA (3, ) was a suiable model for forecasing purpose o he Karachi Sock Marke. There are hree main sock exchanges in Pakisan. Karachi Sock Exchange (KSE) is he larges sock marke in Pakisan which was esablished on Sepember 18, Oher wo are Islamabad and Lahore which are inacive as compared o Karachi sock exchange. I was declared ha KSE is he bes performing sock marke in all over he World for he year of companies were lised a he end of 3 May, 28. KSE -1 is used as a benchmark Pakisani index. Some informaion is given in Table. 1 abou KSE. Table 1. Overview of KSE Karachi Sock Exchange (KSE) Type Sock Exchange Locaion Karachi, Pakisan Owner Karachi Sock Exchange Limied Key People Adnan Afridi, CEO Currency PKR No of lising companies 671 Marke Capial US$ 56 Billion Volume US$ 12 Billion Indexes KSE- 1 & KSE-3 Websie The objecives of his research paper are mainly having an idea abou wheher he Karachi sock marke of Pakisan is efficien marke or no, o do his we used parameric approaches o check his and conclude ha KSE is weak from efficiency marke in oher words do no follow he random walk model. The res of he aricle is prepared as follows. The second secion reviews he mehodology and daa; he hird secion presens he empirical resuls and discussion; and he fourh secion concludes he sudy. 53

3 The weak form efficiency of sock marke using parameric ess 2. Mehodology Efficien marke hypoheses (EMH) claim ha sock price indices are basically random. The basic model for esimaing volailiy in sock reurns is he random walk model (RWM): Y u (1) Secondly, he simples ways o sae Auoregressive of order one AR (1) model may also be esimaed as: Y Y 1 u 1 1 (2) Where in boh above equaions 1 & 2 is he consan parameer, is he esimaed parameer 2 and u is an uncorrelaed random error erm wih zero mean and consan variance (i.e., i is whie noise). This model looks like he Markov firs order auoregressive model. If 1, Y becomes non saionary series which means a uni roo problem occurs in he reurns. The erm non saionary, random walk and uni roo can be reaed as idenical. If 1, Y be convered ino saionary series. 2.1 Auo Regressive (AR) Model The mos widely used model of serial correlaion is he firs-order auoregressive. The AR (1) model is specified as: Y Y 1 u 1 1 (3) Where is he vecor of consan erm, here he value of Y a ime depends on is value in he previous ime period and a random erm; he Y values are expressed as deviaions from heir mean value. The higher order auoregressive model or auoregressive model of order p denoed by AR (p) is given as: Y Y Y Y u (4) p p Then Y is said o follow a random walk model wih drif because he presence of is consan parameer, p are he parameers of Auoregressive coefficiens and u is an uncorrelaed random error erm. 2.2 Moving Average (MA) Model Moving average process of order q is creaed by a weighed average of random error erm and wrien is equaion as: Y u u u u (5) q q 54

4 Irfan M., Irfan M., Awais M., Elecron. J. App. Sa. Anal., Vol 3, Issue 1 (21), Where is he inercep erm, uncorrelaed random error erm u having zero mean and 2 variance u and q are unknown parameers. In shor we can say a moving average process is simply a linear combinaion of whie noise error erm. 2.3 Auo Regressive Moving Average (ARMA) Model If Y has characerisic of boh AR and MA componens as an ARMA (p, q) model, where p and q are he orders of he AR and MA componen, respecively. The algebraic represenaion of he ARMA model is: Y Y... Y u u... u (6) 1 1 p p 1 1 q q Where he inercep parameer is relaed o he mean of Y, he errors are assumed o be uncorrelaed random variable wih zero mean and consan variance, are he unknown parameers of auoregressive process and are he unknown parameers of moving average q process. A simples form of he auoregressive moving average model of order 1 of boh p and q orders ARMA (1, 1) can be wrien as: Y Y u u (7) p Where is an inercep erm and u is assumed o be uncorrelaed random variables, 1 is an unknown parameer of auoregressive model and is an unknown parameer of moving average process. 2.4 Forecasing Performance The common measures of forecasing performance are: MAE, RMSE and Theil- U (Abrosimova e al., 25). The repored forecas error saisics are: MAE T k T 1 RMSE Theil-U yˆ h T k T 1 y yˆ y 2 h T k T 1 yˆ y 2 h T k T k 2 2 yˆ y T 1 T 1 h h (8) (9) (1) 55

5 The weak form efficiency of sock marke using parameric ess Daa and saisical feaures of daily & monhly marke reurns We used he daily and monhly closing prices of KSE- 1 indexes for he period of 1s January1999 o 31s Augus 29 ( 261 and 128 observaions respecively) covering a sufficien period of en and half years afer removing he holidays, which is easily available on yahoo finance. Boh daily and monhly close prices are calculaed by aking he logarihm ransformaion (e.g. Mobarek and Keasey, 2; Mousafa, 24 and Abrosimova e al., 25 ;). We esimaed he models using boh EViews 5.1 and Miniab 15 programs Descripive saisics The essenial assumpion of random walk model is ha he disribuion of he reurn series mus be normal. To assess he disribuional propery various descripive saisics are repored in Table 2. From Table 2. I can be seen ha he disribuion of he reurn series are no normal. The reurn series of boh daily and monhly are lepokuric because of is large Kurosis value which means non normal according o he Jarque and Bera es (198), which rejecs he normaliy a he 1% level. Table 2. Descripive Saisics of daily & monhly reurns Variables KSE Daily Reurn KSE Monhly Reurn Mean Median Maximum Minimum Sandard deviaion Skewness Kurosis Jarque and Bera Probabiliy The evidence of posiive skewness in boh reurns is similar o he findings of Poshokwale (1996) in Indian sock marke bu heir posiive skewness coefficien (.98) is much larger and Mobarek and Keasey (2) in Dhaka sock marke of Bangladesh who find he posiive skeweness (1.23) is a larger amoun. In oher words, Jarque and Bera es, Skewness and Kurosis values for boh series of sock reurn series on he KSE indicaes ha he disribuion is no normal Hypoheses The sudy looks for evidence wheher he Karachi Sock Marke follows random walk mode or no and second marke is efficien or no i,e. H : The Karachi Sock Marke follows a random walk model H o 1 : The Karachi Sock Marke do no follow random walk model H : The Karachi Sock Marke is efficien in weak from o H : 1 The Karachi Sock Marke is no efficien in weak from. 56

6 Closing prices Closing prices Irfan M., Irfan M., Awais M., Elecron. J. App. Sa. Anal., Vol 3, Issue 1 (21), Empirical Analysis and Resuls Figure 1 and 2 illusrae firsly daily and monhly ime series plos which indicaes clearly ha daa is non-saionary and coninuous rend and secondly afer aking he logarihm ransformaion, he daily and monhly reurn series confirm ha he mean of he series are now abou consan which indicae clearly saionary, even hough he variance becomes unusually high which clearly exhibi volailiy clusering (Nourrendine (1998), Mousafa (24) and Irfan e al. (21)). 16 Daily closing prices of KSE 1 index Daily Reurn series of KSE 1 index RT Figure 1. Time series plo of daily closing prices & Reurn series of KSE 1 indexes Monhly closing prices of KSE 1 index Monhly Reurn series of KSE 1 index RT Figure 2. Time series plo of monhly closing prices & Reurn series of KSE 1 index. 3.1 Uni Roo Tes The KSE indexes are esed for he occurrence of uni roos using he Augmened Dickey Fuller (ADF) (see in Table. 3) and Phillips Perron (PP) ess (no repored). Augmened Dickey Fuller (ADF) es is he mos powerful es raher han oher uni roo ess. The ADF es examines he uni roo of he observed daa by aking he uni roo (non saionariy) as aking he null hypohesis. The rejecion of H o implies ha he reurn series R is saionary. Table. 3 repors he resuls of he ADF es for boh indexes of KSE. We will employ he criical values offered by Mckinnon (1991) o esimae he null hypohesis. As a second sep, anoher mehod o calculae uni roo ess is applied (no repored). Therefore, daily and monhly reurns series are saionary. The significance of all he coefficiens and he value of Durbin-Wason Saisic 57

7 The weak form efficiency of sock marke using parameric ess (DWS) which is approximaely 2 in boh indexes (see in Table. 4 & Table. 5) indicae he correc specificaion of he es equaion. So he Karachi Sock Marke is no efficien in weak from. Table 3. Tes of Uni Roo Augmened Dickey Fuller (ADF) Tes saisic Indexes ADF Tes Saisic Criical value a 1% P- Value Daily KSE Monhly KSE (MacKinnon criical values for rejecion of hypohesis of a uni roo) Table 4. Augmened Dickey Fuller (ADF) Tes Equaion for Daily closing prices Variable Coefficien Sd. Error T- Saisic P- Value RETURN (-1) Consan R-squared Mean dependen var.147 Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared residuals Schwarz crierion Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic). Table 5. Augmened Dickey Fuller (ADF) Tes Equaion for Monhly closing prices Variable Coefficien Sd. Error T- Saisic P- Value RETURN (-1) Consan R-squared Mean dependen var Adjused R-squared S.D. dependen var S.E. of regression Akaike info crierion Sum squared residuals Schwarz crierion Log likelihood F-saisic Durbin-Wason sa Prob(F-saisic). 3.2 Auocorrelaion and Parial Auocorrelaion Tess Auocorrelaion and Parial Auocorrelaion are performed for 36 lags of daily reurn series (See Table. 6 for only 1 lags). I was found ha only 1 s lag of daily daa is significan differen from zero a he 95 % confidence level. Box- Pierce Q saisic and Ljung- Box (LB) saisic give similar resuls. Auocorrelaion (ACF) and Parial Auocorrelaion (PACF) up o 1 lags due o insufficien sample of size for he KSE monhly reurn index ha covers he period of 1999 o 29 is performed in Table. 7, he coefficien for only on 1 s lag is significan for weekly daa. On he basis of boh Auocorrelaion ess we can rejec he hypohesis of he random walk i,e. 58

8 Irfan M., Irfan M., Awais M., Elecron. J. App. Sa. Anal., Vol 3, Issue 1 (21), he Karachi Sock Marke do no follow he random walk model in boh daily and weekly cases. A similar observaion was made in he sudy of Abrosimova e al. (25) and Irfan e al. (21). Table 6. Auocorrelaion and Parial Auocorrelaion Funcions of he daily reurns of he KSE index Auocorrelaion Parial Correlaion lags AC PAC Q-Sa Prob **** **** *** ** ** * * * * * * Table 7. Auocorrelaion and Parial Auocorrelaion Funcions of he monhly reurns of he KSE index Auocorrelaion Parial Correlaion lags AC PAC Q-Sa Prob ***. *** ** *. ** ** * * *. ** * * * ARIMA Model Building ADF es saisic for boh indexes is highly significan means rejec he null hypohesis ha KSE reurns for boh daily and monhly have a uni roo; herefore he order of inegraion is se as zero. The resuls are in accordance wih he findings of Mousafa (24) and Abrosimova e al. (25). ARIMA (1,, 1) appear o be fied he bes model for daily reurn series according o he differen crierion like Akaike crierion and Schwarz crierion (see Table. 8). The correlogram of ARIMA (1,, 1) residuals shows no auocorrelaion and parial Auocorrelaion is lef (see Table. 9), herefore, here is no need o search ou anoher ARIMA model. Similarly, for monhly reurn series ARIMA (, 1) is a suiable model according o he boh crierion (see Table. 1). The correlogram of ARIMA (,, 1) residuals shows no auocorrelaion and parial Auocorrelaion is presen (see Table. 11). A graphical analysis for boh daily and monhly reurn series also indicaes ha he fied and he acual values are very close o each oher (see Figure. 3). Therefore, here is no need o look for anoher ARIMA model. 59

9 The weak form efficiency of sock marke using parameric ess Table 8. ARMA (p, q) Order Selecion p/q Akaike info crierion Schwarz crierion Akaike info crierion Schwarz crierion Akaike info crierion Schwarz crierion Table 9. Correlogram of ARIMA (1,, 1) residuals Auocorrelaion Parial Correlaion lags AC PAC Q-Sa Prob Table 1. ARMA (p, q) Order Selecion p/q 1 2 Akaike info crierion Schwarz crierion Akaike info crierion Schwarz crierion Akaike info crierion Schwarz crierion

10 Irfan M., Irfan M., Awais M., Elecron. J. App. Sa. Anal., Vol 3, Issue 1 (21), Table 11. Correlogram of ARIMA (,, 1) residuals Auocorrelaion Parial Correlaion lags AC PAC Q-Sa Prob. *. * *. * *. * *. * Residual Acual Fied Residual Acual Fied Figure 3. Residual, Acual and Fied graph for he ARIMA (1,, 1) & ARIMA (,, 1) Resuls of he ARIMA sudy for boh reurn series (see Table 12 & 13) sugges ha boh ARIMA Models (1,, 1) and (,, 1) do no suppor he random walk model. The coefficiens of AR (1) and MA (1) for daily reurn series ( & ) wih sandard errors of ( &.1683) and probabiliies of (. &.) rejec he null hypohesis of random walk which indicaes also ha KSE daily reurn series do no follow he random walk hypohesis. Similarly, same resuls have found for monhly reurn series of KSE. Our resuls are similar wih he findings of Sharma e al. (1977) on he Bombay, London and New York Sock Exchanges, Nourredine (1998) on he Saudi Arabian marke, Mousafa (24) Bangladesh sock Exchange, Abrosimova e al. (25) Russian sock marke and Poshakwale (1996) Indian sock marke who find he evidence of weak-form efficien. Table 12. ARIMA (1,, 1) model esimaion Variable Coefficien Sd. Error T- Saisic P- Value Consan -7.32E AR(1) MA(1)

11 The weak form efficiency of sock marke using parameric ess Table 13. ARMA (,, 1) model esimaion Variable Coefficien Sd. Error T- Saisic P- Value Consan MA(1) Forecas Analysis We menioned in he previous discussion ha ARIMA (1,, 1) and ARIMA (,, 1) are he bes fied model for boh daily and monhly reurn series on he basis Akaike crierion, Schwarz crierion and residuals correlogram also ell us he same saus. By using hese fied models, he forecasing performance is done on he basis of differen error crieria. Theil inequaliy in daily reurn series ( ) and in monhly reurn series ( ) is no close o zero hus we conclude ha model is no an ideal fi in boh cases. We also noed ha bias proporion in daily and monhly reurns is approximaely zero bu he variance proporion in daily reurn 19 % and in monhly reurn 13 % (see in Figure 4 & 5). Hence in he end we can say ha boh models are no good for forecasing purpose Forecas: RETURNF Acual: RETURN Forecas sample: Adjused sample: Included observaions: 269 Roo Mean Squared Error Mean Absolue Error Mean Abs. Percen Error Theil Inequaliy Coefficien Bias Proporion.1 Variance Proporion Covariance Proporion Figure 4. Saic forecas for 1999 o 29 of daily reurn series Forecas: RETURNF Acual: RETURN Forecas sample: Included observaions: 126 Roo Mean Squared Error Mean Absolue Error Mean Abs. Percen Error Theil Inequaliy Coefficien Bias Proporion.1243 Variance Proporion Covariance Proporion Figure 5. Saic forecas for 1999 o 29 of monhly reurn series 62

12 Irfan M., Irfan M., Awais M., Elecron. J. App. Sa. Anal., Vol 3, Issue 1 (21), Conclusion In his paper, we esed for weak from efficiency using he daily and monhly closing prices of Karachi Sock Exchange (KSE) 1 indexes for he period of 1 s January1999 o 31 s Augus 29. Several differen parameric approaches: uni roo es, auocorrelaion ess and ARIMA model are used o es he sureness of he KSE marke. The parameers of AR (p) and MA (q) were compared according o he differen crierion like Akaike crierion and Schwarz crierion o selec he bes fiing model in boh reurns. Correlogram of ARIMA residuals show no auocorrelaion and parial Auocorrelaion is lef in boh series, herefore, here is no need o search ou anoher ARIMA model. ARIMA (1,, 1) for daily reurn series and ARIMA (,, 1) for monhly reurn series are seleced. All parameric mehods srongly recommended ha boh reurn series do no follow he random walk model and also rejec he hypohesis of weak from efficiency. Overall resuls from he empirical analysis powerfully proposed ha he Karachi Sock Marke of Pakisan is no efficien in weak from. References [1]. Ahmad, F. (22). Marke Efficiency in Emerging Sock Markes: The Case of Dhaka Sock Exchange. [2]. Abrosimova, N., Dissanaike, G., Linowski, D. (25). Tesing he weak from Efficiency of he Russian Sock Marke. hps://papers.ssrn.com/sol3/papers.cfm?absrac_id= [3]. Chakrabory, M. (26). Marke Efficiency for he Pakisan Sock Marke: Evidence from he Karachi Sock Exchange. Souh Asia Economic Journal, 7 (1), [4]. Gujarai, D.N. (23). Basic Economerics, 4h ed.. New York: McGraw Hill. [5]. Hossain, F. (24). Days of he Week Effec in Dhaka Sock Exchange: Evidence from small Porfolios of Banking Secor. Jahangirnagar Review, Par II: Social Science, XXVIII, [6]. Hudson, R., Dempsey, M., Keasey, K. (1994). A noe on he weak from efficiency of capial markes: The applicaion of simple echnical rading rules o UK Sock prices o Journal of Banking & Finance, 2, [7]. Hussain, F. (1996). Sock price Behaviour in an Emerging Marke: A case sudy of Pakisan. Ph. D hesis, The Caholic Universiy of America. [8]. Irfan, M., Irfan, M., Awais, M. (21). Modeling Condiional Heeroscedasiciy and Forecasing in shor erm ineres rae of KIBOR. Inernaional Journal of Economics Perspecives, 4 (3), Forhcoming. [9]. Jarque, C. M., Bera, A.K. (198). Efficien ess for normaliy, homoscedasiciy and serial independence of regression residuals. Economics Leers, 6 (3), [1]. Nourrendine, K. (1998). Behavior of sock prices in he Saudi Arabian Financial Marke: Empirical research findings. Journal of Finance Managemen & Analysis, 11(1), [11]. Mackinnon, J.G. (1991). Criical values for coinegraion ess, in Long Run Economic Relaionships, eds. R.F. Engle and C.W.J. Granger, Oxford Universiy Press, Oxford,

13 The weak form efficiency of sock marke using parameric ess [12]. Mobarek, A., & Keasey, K. (2). Weak-Form Marke Efficiency of an Emerging Marke: Evidence from Dhaka Sock Marke of Bangladesh, in ENBS Conference held on Oslo, May 2, 1-3. [13]. Mousafa, M. A. (24). Tesing he weak from Efficiency of he Unied Arab Emiraes Sock Marke. Inernaional Journal of Business, 9 (3), [14]. Nicolaas, & Groenwold. (1997). Share marke efficiency: Tess using daily daa for Ausralia and New Zealand. Applied Financial Economics, 7, [15]. Ojah, K., & Karemera. (1999). Random walks and Marke efficiency Tess of Lain Amaeracean Emerging Equiy Markes: A Revisi. The Financial Review, 34, [16]. Poshakwale, S. (1996). Evidence on he Weak form efficiency and he day of he week effec in he Indian Sock Marke. Finance India, 1 (3), [17]. Sharma, J.L., Kennedy., Rober, E. (1977). A Comparaive analysis of sock price behavior on he Bombay, London and New York Sock Exchanges. Journal of Financial and Quaniaive Analysis,