Which pairs of stocks should we trade? Selection of pairs for statistical arbitrage and pairs trading in Karachi Stock Exchange.

Qazi, Laila Taskeen ; Rahman, Atta Ur ; Gul, Saleem 等

Pairs Trading refers to a statistical arbitrage approach devised to take advantage from short term fluctuations simultaneously depicted by two stocks from long run equilibrium position. In this study a technique has been designed for the selection of pairs for pairs trading strategy. Engle-Granger 2-step Cointegration approach has been applied for identifying the trading pairs. The data employed in this study comprised of daily stock prices of Commercial Banks and Financial Services Sector. Restricted pairs have been formed out of highly liquid log share price series of 22 Commercial Banks and 19 Financial Services companies listed on Karachi Stock Exchange. Sample time period extended from November 2, 2009 to June 28, 2013 having total 911 observations for each share prices series incorporated in the study. Out of 231 pairs of commercial banks 25 were found cointegrated whereas 40 cointegrated pairs were identified among 156 pairs formed in Financial Services Sector. Furthermore a Cointegration relationship was estimated by regressing one stock price series on another, whereas the order of regression is accessed through Granger Causality Test. The mean reverting residual of Cointegration regression is modeled through the Vector Error Correction Model in order to assess the speed of adjustment coefficient for the statistical arbitrage opportunity. The findings of the study depict that the cointegrated stocks can be combined linearly in a long/short portfolio having stationary dynamics. Although for the given strategy profitability has not been assessed in this study yet the VECM results for residual series show significant deviations around the mean which identify the statistical arbitrage opportunity and ensure profitability of the pairs trading strategy.

JEL classifications: C32, C53, G17

Keywords: Pairs Trading, Statistical Arbitrage, Engle-Granger 2-step Cointegration Approach, VECM.

1. INTRODUCTION

The concept of statistical arbitrage emerged from the notion of predictability and long-term relationship in stock returns, which has been further support by the recent advent of the idea of mean reversion. The idea of mean reversion in stock prices supports predictability and works against the concept of efficient market hypothesis according to which stock prices exhibit a random walk and cannot be forecasted. A mean reverting time series, on the contrary can be forecasted using historical data [Charles and Darne (2009); Gupta and Basu (2007)]. Furthermore literature also reported the role of mean reversion for portfolio allocation and asset management. Over the past decade, the hedge funds and investment banks have capitalised on statistical arbitrage opportunities using mean reverting portfolios. Simplest of such portfolios is a two-asset portfolio in case of pairs trading [Pole (2007); Vidyamurthy (2004)].

Pairs trading strategy was initiated by Nunzio Tartaglias while working with Morgan and Stanley during the era of 1980s. It has been adopted by hedge funds as a statistical arbitrage technique. The idea emerged from the fact that certain securities depicted daily correlated returns over a long period of time. Therefore trading strategies were developed in order to capitalise upon these statistical arbitrage opportunities evolving due to the market inefficiencies [Lo and MacKinlay (1988); Khandani and Lo (2007); Lo and Mackinlay (1997); Gatev, et al. (2006); Guidolin, et al. (2009)]. In pairs trading, pairs are formed of those stocks, which had shown similar price movements historically. When the selected pair depicts divergence between the price movements, it is assumed to be temporary and is capitalised upon through opening long/short positions simultaneously. The strategy aspires that these short-term fluctuations will converge over the period of time under the effect of long run equilibrium relationship between the two stocks.

Traditionally stocks are allocated in a portfolio on the basis of correlation or other non-parametric techniques. In this study Cointegration based trading pairs have been developed. The existence of a cointegrating association provided a base for developing a certain linear combination between the cointegrated trading pairs and as a result the portfolio developed is a stationary process. Any deviation depicted by stock price series from the equilibrium is regarded as mispricing. Hence the stock price series are expected to return to zero from these short term mispricing deviations. The effect of mispricing makes one stock appear as undervalued and the other as overvalued and creates a statistical arbitrage opportunity for pair traders. Therefore in pair trading a two stock portfolio is developed through taking a long position in an undervalued stock and a short position in an overvalued stock. A portfolio maintaining a value below its equilibrium position creates a prospect for opening a long position however it is closed when the portfolio value returns back to its likely mean position. Whereas a short position is opened in the portfolio when its value is above its equilibrium value and is closed out when the portfolio value falls close to the estimated mean. Such short-term mis-pricing moments make the portfolio profitable under the pairs trading strategy.

Which pairs of stocks should we trade? This is a critical question, imperative for the traders to address, in order to avoid trading with the mismatched pairs which may make the pairs trading strategy unprofitable. Therefore the primary objective of this study is to select a trading pair based on the co-movement of two stock price series in the long run and the speed of adjustment of the disequilibrium term. Engle-Granger (EG) Test for Cointegration has been applied to identify the long run equilibrium relationship between two stocks. The EG approach to Cointegration will help in assessing whether the relationship between two stocks in a pair is spurious or not. A Cointegration relationship is estimated by regressing one stock price series on another, whereas the order of regression is accessed through Granger Causality Test. The stationary residual series of the cointegrating regression depicts the mean reverting behaviour of a trading pair. Consequently, the Vector Error Correction Model (VECM) has been employed to model the stationary residual series. The residual series contains significant information pertaining to co-movement between the trading pairs. For instance the 'speed of adjustment' coefficients in the VECM describe how quickly the system reverts to its mean after observing a short-term deviation and also identifies which stock in a pair performs the error correction function.

In order to achieve the above mentioned objectives the rest of the study has been organised into following sections. Section 2 postulates a brief overview of academic literature pertaining to pairs trading strategy. Section 3 explains the methodology adopted in the study for describing pairs trading strategy. Section 4 specifies the empirical results and Section 5 provides discussion and conclusion of the empirical study.

2. LITERATURE REVIEW

Since long the pairs trading strategy has fascinated the practitioners as well as the academicians. Kawasaki, et al. (2003) analysed the profitability of taking both long and short positions simultaneously in a pair of stocks that yields a stationary spread series. The long/short investment strategies proved to be profitable. Kawasaki, et al. (2003) did not present the idea of pairs trading formally however the underlying concept remained same. Nath (2003) proposed a simple yet profitable pairs trading strategy based on Cointegration analysis, in the large and highly liquid secondary market of US treasury securities while accounting for finance and transaction cost. Hong and Susmel (2003) further tested the pairs trading strategy based on Cointegration analysis for 64 Asian shares listed in their local markets as well as in the US markets as American Depository Receipt (ADR). The findings of the study revealed significant pairs trading profits in the US ARD market. Elliot, et al. (2005) extended the concept of pairs trading and asserted that the Pairs trading strategy works through making a market neutral portfolio with zero beta and is referred to as spread. This spread is further modelled as mean reverting process using the Gaussian Markov Chain model. On the basis of the simulated data, the findings of the study revealed that the methodology proposed by Elliot, et al. (2005) has the ability to generate profits from the financial time series data which is found out to be out of equilibrium. Andrade, et al. (2005) introduced the effect of uninformed demand shocks in the pairs trading strategy in the Taiwanese stock market revealing significant excess returns.

The literature pertaining to pairs trading is pioneered by Gatev, et al. (2006). Under the pairs trading strategy proposed by Gatev, et al. (2006) pairs were selected on the basis of the distance approach and using the identified pairs long and short positions were taken on the basis of preset criteria. The strategy yielded annualised returns of 11 percent and the findings of the study also suggested that the pair trading strategy is a profitable option for those investors who are exposed to smaller transaction costs and can execute short sale activities. Do, et al. (2006) followed the pairs trading strategy proposed by Gatev, et al. (2006) and introduced the stochastic spread approach for the formation of restricted pairs. The findings of Do, et al. (2006) reported stable performance results and also confirmed the mean reversion behaviour observed under the stochastic residual spread approach. Lin, et al. (2006) also extended the work of Gatev, et al. (2006) through replacing the distance approach with Cointegration analysis during the pair formation period. Papadakis and Wysocki (2007) attempted to test the impact of accounting information events (i.e. earnings announcements and analyst's earnings forecasts) on the profitability of the pairs trading strategy proposed by Gatev, et al. (2006) and inferred that the stock prices drift, due to the earnings announcements and the analyst's earnings forecasts, is a significant factor affecting the profitability of the pairs trading strategy. Later Bock and Mestel (2009) attempted to execute the traditional pairs trading strategy through apply the trading rules.

The idea of pairs trading further evolved with the work of Engelberg, et al. (2009) for whom the primary motivation was to understand and identify those factors that cause the pairs to diverge. Certain factors identified by Engelberg, et al. (2009), that might affect the convergence and divergence patterns in stock prices, included liquidity of the stocks in a pair, information diffusions, horizon risk and divergence risk. The results suggested that the profits from the pairs trading strategy are short lived and are directly related to the information pertaining to the constituent firms in a pair. Engelberg, et al. (2009), asserted that the identification of a lead lag relationship between stocks due to a common information event depicts a strong lacking in the unconditional pairs trading strategy proposed by Gatev, et al. (2006) which works without referring to the events leading to the changes in the prices of stocks in a pair.

Huck, et al. (2009) introduced combined forecast approach and Multi criteria decision methods for pair selection and depicted promising results and categorised the proposed methodology as a powerful tool for pair's selection. Perlin (2009) tested the pairs trading strategy in the Brazilian stock market with high frequency data and discovered that the pairs trading strategy is profitable and market neutral in the Brazilian market and generates best results for the high frequency daily data. The concept of high frequency pairs trading was further supported by Bowen, et al. (2010) confirming that higher profits from the strategy are generated during the first hour of the trading. Bianchi, et al. (2009) tested the pairs trading strategy in the commodity futures market and the findings of the study revealed statistically significant excess returns. Bolgun, et al. (2010) and Yuksel, et al. (2010) tested the pairs trading strategy proposed by Gatev, et al. (2006) in the Istanbul Stock Exchange and revealed that the profitability from pairs trading is highly sensitive to transaction restrictions and transaction commissions.

Do and Faff (2010) extended the pairs trading strategy proposed by Gatev, et al. (2006) and suggested that the pairs trading strategy performs well during the turbulent times in the market i.e. it is profitable in the bearish markets. Mori and Ziobrowski (2011) further asserted that only the market trends are not important for explaining divergence patterns and the profitability of pairs trading rather the market characteristics and dynamics also play a significant role. Do and Faff (2012) once again tested the pairs trading strategy proposed by Gatev, et al. (2006) while assessing the impact of transaction cost on the profitability of pairs trading strategy. The empirical results exhibited that the pairs trading strategy remains profitable even after controlling for the trading costs however the level of profit decreases. These findings were further supported by Pizzutilo (2013) while testing the effectiveness of the pairs trading strategy for the individual investors under the existence of the relevant constraints in the form of restriction to short selling and trading costs. Furthermore Huck (2013) also tested the sensitivity of the pairs trading strategy to the length of the formation period and signified that the large abnormal positive returns are generated when long formation periods are employed.

Hong, et al. (2012) revealed a positive performance of the pairs trading strategy in the Korean stock market whereas Broussard and Vaihekoski (2012) described excess positive returns from the pairs trading strategy in the Finish market. Mashele, et al. (2013) also affirmed that the investment strategy based on pairs trading is successful in the Johannesburg stock exchange. Caldeira and Moura (2013) claimed that the pairs trading strategy based on Cointegration remains profitable in the Brazilian market even during the times of financial crisis and thus generate consistent profits.

Several techniques have been reported in the literature for the implementation of pairs trading strategy. The four most commonly reported techniques include the nonparametric distance approach [Gatev, et al. (1999); Nath (2003)], the stochastic spread method [Elliot, et al. (2005)], the stochastic residual spread method [Do, et al. (2006)] and the Cointegration method [Vidyamurthy (2004)].

The significance and power of the Cointegration technique can be inferred from the fact that it allows for the application of estimation models like Ordinary Least Square and Maximum Likelihood to non-stationary time series. Regardless of its vast applicability, the use of Cointegration technique in the field of investment analysis and portfolio management is still limited. This limited use of Cointegration in investment strategies is attributable to massive use of a standardised correlation analysis for asset returns. Correlation analysis technique works for stationary variables, which in turn entails prior de-trending of stock prices and financial time series data which is normally integrated of order one or higher. As a result all inferences are based on returns [Damghani, et al. (2012)]. Due to the de-trending procedure valuable information is lost from the differenced time series [Johansen (2011)]. Likewise if time series included in a system are integrated of different orders then different orders of differencing are needed to make the variables stationary. Therefore inferences made on the basis of correlation analysis fail to incorporate important information pertaining to the time series understudy.

The Cointegration approach for pairs trading is significantly adopted and favoured in the literature due to its simplicity and ability to avoid the problem of model misspecification and to identify mean reversion in price series [Broussard and Vaihekoski (2012); Gutierrez and Tse (2011); Puspaningrum, Lin, and Gulati (2010); Chiu and Wong (2012)]. In order to benefit from the positive features of Cointegration approach this study also strives to adopt the Cointegration approach in order to form and select pairs for pairs trading strategy in Karachi Stock Exchange while using Engle Granger Cointegration methodology. Literature concludes pairs trading as an efficient arbitrage opportunity emerged through statistical transformations however this arbitrage opportunity can only be materialised through the correct selection of pairs possessing long term equilibrium. The next section elaborates the methodology adopted to assess the long run equilibrium relationship between stocks included in a pair and their mean reversion behaviour imperative for a successful pairs trading strategy.

3. DATA COLLECTION AND METHODOLOGY

This study utilised daily stock prices of 22 Commercial banks and 19 Financial Services companies listed on the Karachi Stock Exchange (KSE). The daily data of stock prices has been retrieved from Business Recorder. Since it is imperative for pairs trading that the stocks remain actively traded and liquid, therefore only those stocks were included in the study, which depicted high turnover and active trading. Out of the 23 listed commercial banks and 40 listed financial services companies, 22 banks and 19 financial services companies were included in the study solely on the basis of high turnover and active trading [Do and Faff (2010)]. The issue of stale prices and restricted trading became a reason for stocks exclusion from the study. See Appendix I for the list of companies included in the study.

The sample time period consists of daily stock returns collected over a period extending from November 2, 2009 to June 28, 2013 having total 911 observations for each time series incorporated in the study. This study is based upon restricted trading pairs, which refers to pair formation of stocks from the same industry or sector [Kawasaki, et al. (2003)]. There are several reasons attributable to opting for restricted pairs trading. Pairs trading, by virtue of its construction is largely perceived as a market neutral strategy in which portfolios are deliberately constructed to hold zero beta and inhibit the systematic risk. In such neutralised portfolios profits are generated by the long and short positions solely due to the convergence of residual spread in the form of mean reversion. Therefore stocks in a pair have been selected from the same sector with an assumption that they would be affected by similar systematic risk factors and resultantly the portfolios developed would have a zero beta. In this study 231 restricted pairs have been developed using 22 sampled Commercial Banks (see Table 3 in Appendix III) and 171 pairs have been developed using 19 financial services companies however 15 pairs were dropped due to the Stationarity issues and for the rest of the analysis 156 pairs have been considered (see Table 4 in Appendix III). The formula employed for developing stock pairs is given below,

No. of Stock Pairs = [N.sup.2] - N/2, N is the number of sample Companies.

Another reason supporting the formation of restricted pairs is the theoretical justification for a cointegrating relationship existing between the two stocks of the same sector. Although Cointegration alone provides fundamental basis for the formation of a trading strategy yet in case of restricted pairs this statistical relationship is also justified by the fact that the two stocks are affected by similar fundamental factors in the long run. Therefore a cointegrating relationship found in-sample would be expected to prevail in the long run out-of-sample as well. However a cointegrating relationship between two randomly selected stocks would possess no economic and theoretical justification along with any surety to prevail in the long run. Consequently the study worked with two sectors being commercial banks and financial services sector as described above. Trading pairs made in each sector are handled separately.

As mentioned earlier, the objective of the study is to identify trading pairs on the basis of a long run equilibrium relationship between two stocks in a pair and the speed of adjustment of the disequilibrium term. On the basis of the set objective, the methodology has been divided in to four subsections. For testing long run equilibrium relationship Engle-Granger (EG) approach to Cointegration has been discussed in subsection 3.1. Later in subsection 3.2., Granger Causality test has been discussed in detail due to its ability to provide an insight into the dynamics of a cointegrating relationship for cointegrated pair of stocks. A uni-directional Granger Causality test describes which stock informationally leads another stock in a trading pair. In subsection 3.3., a cointegrating equation and a residual spread has been established on the basis of uni-directional Granger Causality output. In subsection 3.4., for estimating the short run relationship between the cointegrated share prices series, Vector Error Correction Model has been discussed in detail.

3.1. Engle Granger (EG) 2-step Approach to Cointegration

A simple approach to Cointegration has been proposed by Engle and Granger (1987) in order to estimate a long run equilibrium relationship between two non-stationary time series. If a linear combination of two non-stationary time series is stationary then the two series exhibit a long run equilibrium relationship. For two series to be cointegrated it is imperative that they must be integrated of same order. Alexander (2008) asserted that although the OLS estimators are normally employed for stationary time series yet it can also be applied to non-stationary time series in case the cointegrating regression residual is a stationary process [Greene (2002)]. EG approach to Cointegration is a two step process illustrated below.

Step 1: Cointegrating Regression

For testing Cointegration, it is imperative for the two series to be non-stationary and integrated of same order. Hence the Augmented Dickey-Fuller test (ADF) applied to the log price series as a test of Stationarity in which appropriate lag length is determined using Aikaike's Information Criterion (AIC). If any of the log prices series is reported to be stationary i.e. 1(0) by the ADF test, such a series is excluded from the analysis. This exclusion is attributable to the fact that Cointegration of a stationary and a non-stationary series results in a spurious regression with non-stationary residual series [Greene (2002)]. Hence if [x.sub.t] and [y.sub.t] are 1(1) processes, then a long run relationship is estimated between log of [x.sub.t] and log of [y.sub.t] using the OLS estimator.

[y.sub.t] = [[beta].sub.0] + [[beta].sub.1] [x.sub.t] + [e.sub.t] (3.1)

In the Equation 1, [[beta].sub.0] is a constant and [[beta].sub.1] is the Cointegration coefficient. The residual series of the cointegrating regression is tested for Stationarity in step 2.

Step 2: Testing Stationarity of Residual Series

In this step ADF test is employed to verify the Stationarity of the estimated residual series [[??].sub.t] retrieved from Equation 1 in step 1 of the EG approach, described through the Equation 2 below.

[[??].sub.t] = [y.sub.t] - [[beta].sub.0] - [[beta].sub.1][x.sub.t] (3.2)

According to the EG approach, the estimated residual series has to be stationary for the [x.sub.t] and [y.sub.t] to be cointegrated.

The Equation 3.2 depicts a portfolio consisting of 1 Long unit of stock [y.sub.t] for every [[beta].sub.1] short units of stock [x.sub.t] and the portfolio has an equilibrium value of [e.sub.t]. The deviations from the equilibrium value are represented by [[??].sub.t], which is a stationary process ensuring mean reversion in portfolio value. In case the two variables are not cointegrated then the resulting regression provides spurious results and [[??].sub.t] is not a stationary process.

3.2. Granger Causality Test

In the EG approach ordering of variables can emerge as an issue. For instance if log prices of [y.sub.t] are regressed on log prices of [x.sub.t], then a different residual series is generated which is further tested for stationarity. In case of pairs trading strategy the ordering issue can be resolved through the Granger Causality test. Moreover the use of Granger Causality test also allows for assessing the lead-lag relationship between two stocks [Greene (2002)].

Granger causality test under bivariate (x, y) setting can be expressed as under,

[y.sub.t] = [[beta].sub.0] + [[beta].sub.1][y.sub.t-1] + ... + [[beta].sub.i][y.sub.t-i] + [[alpha].sub.1][x.sub.t-1] + ... + [[alpha].sub.i][x.sub.t-i] + [e.sub.t] (3.3)

[x.sub.t] = [[beta].sub.0] + [[beta].sub.1][x.sub.t-1] + ... + [[beta].sub.i][x.sub.t-i] + [[alpha].sub.1][y.sub.t-1] + ... + [[alpha].sub.i][y.sub.t-i] + [e.sub.t] (3.4)

This analysis provides two tests; first test examines a null hypothesis that the x does not granger causes y and the second tests examines that y does not granger causes x. If the first null hypothesis is rejected and the second is accepted, it can be inferred that x granger causes y indicating uni-directional causality from x to y. This also depicts that x informationally leads y [Greene (2002)]. However in case if both the hypotheses are rejected then there is a bi-directional causality between x and y but if both the hypotheses are accepted there are no evidence of causality between x and y.

3.3. Cointegrating Directional Regression and Testing Residual Spread for Stationarity

After assessing the direction of causality through the Uni-directional Granger Causality test, the issue pertaining to ordering of variables in cointegrating regression is resolved and allows the researchers to estimate a cointegrating directional regression as given in Equation 3.1 if null hypothesis of Equation 3.3 is rejected in Granger Causality test [Greene (2002)]. As mentioned under the EG approach to Cointegration, estimated residual spread series is tested for Stationarity using ADF test.

3.4. Vector Error Correction Model (VECM)

According to the Granger Representation Theorem, when the two time series are cointegrated, the Vector Autoregressive model (VAR) is mis-specified [Greene (2002)]. The mis-specification problem can be treated through incorporating the previous disequilibrium term in the VAR model as an explanatory variable and thus the model becomes well-specified and is termed as Vector Error Correction model (VECM). VECM allows for modelling the dynamics of one time series as a function of its own lags, lags of its cointegrated pair and the error correction component. The error correction component determines the speed of adjustment of time series from a short run deviation to its equilibrium position [Gujarati (2003)]. After obtaining the disequilibrium term from Equation 3.1, the VECM is applied to the two cointegrated log return series [DELTA][y.sub.t] and [DELTA][x.sub.t].

[DELTA][y.sub.t] = [[alpha].sub.1] + [[gamma].sub.1][e.sub.t-1] + [[epsilon].sub.it] (3.5)

[DELTA][x.sub.t] = [[alpha].sub.2] + [[gamma].sub.2][e.sub.t-1] + [[epsilon].sub.it] (3.6)

In the Equation 3.5 and Equation 3.6, [e.sub.t-1] is the lag of disequilibrium term obtained from Equation 3.2 above. [[alpha].sub.1] and [[alpha].sub.2] are constant terms whereas [[gamma].sub.1] and [[gamma].sub.2] are the speed of adjustment coefficients.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3.7)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3.8)

Both the Equations 3.7 and 3.8 have been estimated through OLS while including the lags of the dependent and independent variables in order to avoid autocorrelation problem. From the Equations 3.7 and 3.8, the values of [[gamma].sub.1] and [[gamma].sub.2] can be retrieved which can be termed as speed of adjustment coefficients [Gujarati (2003)]. The size and sign of the speed of adjustment coefficients are the two critical characteristics. In VECM, it is imperative that either one of the two or both coefficients must be statistically different from zero. When both the statistically significant speed of adjustment coefficients depict opposite sign, it can be inferred that the two cointegrated time series will move in opposite direction to resume equilibrium [Gujarati (2003)]. However if the two depict same sign, then both series will exhibit convergence in the same direction, with one moving faster than the other one.

The size of the speed of adjustment coefficient indicates that the larger the size of the speed of adjustment coefficient the faster will be the response of the dependent variable towards the deviation from the long run equilibrium. Large values of speed of adjustment coefficients also indicate highly stationary disequilibrium term. However in case these coefficients have small values it can be concluded that the dependent variable either does not responds or responds very slowly to the short term deviations [Gujarati (2003)].

Here the size and sign of the speed of adjustment coefficients depict the mean reversion and convergence characteristics of two cointegrated time series in a pair. Therefore for pairs trading profitability it is imperative that the speed of adjustment coefficients must be significant having the right sign and a large size.

On the basis of the methodology devised above, empirical results of the study have been illustrated in the next section.

4. EMPIRICAL RESULTS

This section pertains to the empirical testing of the trading pairs selection idea presented in the preceding sections and the interpretation of results. Table 1 (Appendix I) contains a List of companies included in the study pertaining to Commercial Banks and the Financial Services sector. For each company given in Table 1, a symbol is also given as quoted in Karachi Stock Exchange. Later in the analysis, these companies will be referred to using these symbols. Subsequent subsections depict application of the methodology devised in Section 3.

4.1. Cointegration Results

Cointegration analysis strives to work with non-stationary time series data in order to assess long run equilibrium relationship. Therefore for Cointegration analysis, the sample time series have to be non-stationary. Table 2 in Appendix II, provides the summary of ADF test for the entire log share price series incorporated in the study related to commercial banks and financial services sector. Table 2 provides the tau-statistic for the ADF test in levels along with the relevant p-values given in parenthesis. According to the ADF test results for all the understudy log share price series, all the series are non-stationary being 1(1) except for two series in Financial Services Sector. Hence overall the null hypothesis of unit root cannot be rejected, on the basis of the ADF test results all the series qualify for Cointegration analysis under the EG two step approach.

In this study, Long run relationship has been assessed through EG Cointegration approach for all the potential trading pairs in Commercial Banks and Financial Service Sector listed on the Karachi Stock Exchange. In the EG two step approach, the Stationarity of the residual series, estimated through the OLS regression, when applied to two non-stationary log share price series, has been tested. Table 5 and Table 6 in Appendix IV contains the result of EG Cointegration tests for Commercial Banks and Financial Services Sector respectively. For each trading pair EG Cointegrating regression estimated residual series has been tested for Stationarity using the ADF test and the p-values have been reported. In Commercial Banks Sector out of the 231 potential trading pairs 60 pairs were found out to be cointegrated as reported in Table 5. P-values reported in Table 5 indicate the rejection of unit root null hypothesis. Similarly Table 6 reports the EG Cointegration rest results for Financial Services Sector indicating that out of 156 potential trading pairs 77 were found out to be cointegrated as the p-values reported in Table 6 rejected the unit root null hypothesis at the significance level of 1 percent, 5 percent and 10 percent.

For all the cointegrated pairs, revealed in both Commercial Banks and Financial Services Sector, a long run equilibrium relationship can be inferred as meaningful and statistically significant. In order to assess the direction of causality or the order of cointegrating regression for all the cointegrated pairs in Commercial Banks and Financial Services Sector granger causality results have been reported in the next sub section.

4.2. Results of Granger Causality Test

For 60 cointegrated pairs in Commercial Banks sector and 77 cointegrated pairs in Financial Services Sector granger causality has been tested in this sub section. This will provide an insight into the dynamics of the cointegrated pairs through describing which share price series in a cointegrated pairs informationally leads the other series. Table 7 and Table 8 in Appendix V provide pair-wise granger causality test results for each cointegrated pairs in Commercial Banks and Financial Services Sector respectively. For every trading pair two null hypotheses have been tested and reported along with the p-values in Table 7 and Table 8. The acceptance or rejection of the null hypothesis determines the direction of causality in each trading pair.

For instance, in Commercial Bank Sector pair-wise granger causality test results for BAFL/BOK depict bi-directional causality as both the null hypotheses have been rejected. Same is found out to be true for ABL/UBL pair. However in case of HBL/HMB pair, both the null hypotheses have been accepted indicating no causal relationship between the two return series.

Analysing the granger causality results (see Table 7) for ABL/BOK pair, it can be inferred that BOK granger causes ABL whereas ABL does not granger causes BOK. Such inferences are based on the p-values of both the null hypotheses. This is an evidence of unidirectional causality exhibiting that BOK leads ABL. Similarly in Financial Services Sector unidirectional causality has been reported in FDIBL/FCSC pair for which the null hypothesis stating that FD1BL does not granger causes FCSC is accepted as its p-value > 0.05. However null hypothesis stating FCSC does not granger causes FDIBL is rejected with the p-value < 0.05. This is again an evidence of unidirectional causality.

Out of the 60 cointegrated pairs in Commercial Bank Sector 25 pairs reported unidirectional causality. Similarly in Financial Services Sector 40 pairs reported unidirectional causality. Since in this study, the idea is to form a long/short two asset portfolio with one asset leading the other, therefore only the pairs demonstrating unidirectional causality have been considered for further analysis. 35 pairs from Commercial Bank Sector and 37 pairs from Financial Services Sector have been excluded from the analysis either due to no causality or bi-directional causality.

4.3. Estimation of Directional Regression and Residual Spread Stationarity

After identifying the direction of causality, in this section cointegrating direction regression equation has been estimated and the estimated residual series is tested for stationarity. This step of the methodology strives to confirm the long term equilibrium relationship between the trading pairs depicting unidirectional causality. Since it is a cointegrating regression, OLS estimator has been applied on two non-stationary log share price series for which the stationarity of the estimated residual series has been ensured through the ADF test. Table 9 and Table 10 contain cointegrating directional regression results for commercial banks and financial services sector respectively.

Continuing the BAHL/FABL pair from the Commercial Banks Sector, the cointegrating coefficient estimated through the cointegrating regression is 0.5812 (see Table 9 in Appendix VI). The cointegrating coefficient is significant and can be interpreted as the number of units of FABL held short for every one unit of ABL held long so that the resulting portfolio is mean reverting. The value of the portfolio is given by [C+[e.sub.t]] exhibiting an equilibrium value of 23.61016 (see Table 9 in Appendix VI). Fluctuations in the portfolio value around its equilibrium value are governed by the deviations in et. Here it can be inferred that the behaviour of et dictates the behaviour of the total portfolio value. For a meaningfully cointegrated pair of share price series, it is critical for [e.sub.t] to be stationary as only then the dynamic behaviour of [e.sub.t] will depict strong levels of mean reversion. Stationarity of [e.sub.l] ensuring mean reversion is a necessary condition for a successful pairs trading strategy. Table 9 also provides the ADF test statistics along with its p-value for residual series estimated through the cointegrating regression of BAHL/FABL pair. For BAHL/FABL pair residual series, the unit root null hypothesis has been rejected at the significance level of 5 percent hence confirming the existence of a long run equilibrium relationship between BAHL/FABL. Similarly in the Financial Services Sector, the cointegrating regression for FDIBL/FCSC pair exhibits a cointegrating coefficient of 0.1910 indicating the number of FCSC units to be held short for every one unit of FDIBL held long. The portfolio has an equilibrium value of 0.9069 and any deviations in the equilibrium value are governed by deviations in [e.sub.t] as the estimated residual series is reported to be stationary and mean reverting on the basis of the ADF test results.

The strong evidences of long term equilibrium relationship and mean reversion revealed by the results of the cointegrating directional regression lead the discussion towards estimating error correction model in order to understand the short term dynamics of the cointegrated variables.

4.4. Validation Short Term Deviations through VECM

In this subsection, the error component has been modelled using Vector Error Correction Model (VECM) for which the results are given in Table 11 and Table 12 for Commercial Banks and Financial Services sector respectively. For VECM, log differences of stock prices have been employed. Table 11 and Table 12 also include Long run [beta] Coefficient and its [t-statistic] for each cointegrated pair. Speed of Adjustment Coefficients [gamma]1 and [gamma]2 are also given along with their [t-statistic].

The VECM results for Commercial Banks Sector indicate that at least one of the speed of adjustment coefficients is statistically significant confirming the existence of cointegrating relationship as reported in the previous subsection. VECM results for BAHL/FABL pair, of Commercial Banks, depict a significant long run [beta] coefficient confirming the granger causality results and indicating that FABL granger causes BAHL. Furthermore for BAHL/FABL pair, both the speed of adjustment coefficients is statistically significant having opposite signs. This indicates that both the stocks in the pair respond towards the exogenous shocks to restore the equilibrium position of the portfolio however their response is opposite to each other. Similarly for ABL/BOK, both the speed of adjustment coefficients is significant having same signs (see Table 11 in Appendix VII). According to the reported results [gamma]1 (-0.0599) and [gamma]2 (-0.0025) is significant at 5 percent. For ABL/BOK pair speed of adjustment coefficients depict same sign which indicates that in response to a shock, ABL and BOK move in the same direction however ABL moves faster than BOK on the basis of larger size of its [gamma]1 coefficient in order to restore the equilibrium. Considering the case of NBP/BAHL pair, there is a significant long run [beta] coefficient confirming the granger causality results and indicating that BAHL leads NBP and confirms the long term equilibrium relationship. For NBP/BAHL pair, one speed of adjustment coefficient is found out to be significant ([gamma]1=-6.13575) indicating that in case of disequilibrium and short term shocks NBP responds to restore the equilibrium.

Considering KASBSL/JSIL pair from the Financial Services Sector, the VECM results in Table 12 report a significant long term [beta] coefficient confirming the cointegrating relationship however none of the speed of adjustment coefficients are statistically different from zero. In this case it can be inferred that although KASBSL and JSIL report a long run equilibrium relationship yet there is no term in the model that responds to restore the model to some equilibrium level after experiencing short term deviations. For such pairs in pairs trading mean reversion is not possible.

Therefore on the basis of the VECM results it can be recommended that only those cointegrated pairs must be traded for which either one or both speed of adjustment coefficients are significant having correct signs and are large enough to generate faster response for restoring equilibrium after short term shocks.

5. CONCLUSION

In this study an attempt has been made to answer a primary question in pairs trading strategy being; which pairs of stocks should we trade? In order to answer this question, the study has focused on cointegration analysis for ensuring mean reversion in the selected pairs. For a successful pairs trading strategy it is imperative that a trading pair must depict long run equilibrium relationship as well as short run relationship ensuring mean reversion. Here mean reversion is imperative due to the fact that if any divergence from equilibrium position creates an arbitrage opportunity and a trade is opened, then there must be convergence in order to restore the equilibrium and close the trade to earn arbitrage profits. This can only be achieved with pairs that depict a long run equilibrium relationship as well as also respond to the short term deviations due to exogenous shocks.

The focus of the study remained Commercial Banks and Financial Services Sector in Karachi Stock Exchange and formed 231 restricted pairs in Commercial Banks sector and 156 restricted pairs were formed in Financial Services sector. The alternate hypothesis of long run equilibrium relationship between stocks in pair is found out to be true for 60 pairs in Commercial Banks sector and for 77 pairs in Financial Services sector under the EG 2 step Cointegration approach. In order to further confirm the cointegration relationship, direction of causality has also been assessed through Granger Causality test revealing 25 trading pairs in Commercial Banks demonstrating unidirectional causality whereas 40 pairs depicted unidirectional causality in Financial Services sector. For all the cointegrating pairs, a long run directional regression has been estimated and the regression residuals have been tested for stationarity in order confirm the long run equilibrium relationship. Later for all the cointegrating pairs, the residual is modeled through employing the VECM in order to ensure that at least one of the two speed of adjustment coefficients is significant so that mean reversion can be expected in a pair. The methodology for pairs selection proposed in this study works through forming restricted pairs of highly liquid stocks and ensures the existence of long term as well as short term equilibrium relationship between stocks in a pair. In doing so this methodology responds to a major risk factor in pairs trading being absence of co movement or long run relationship between stocks in a pair. The pairs formed under this methodology depict long run relationship as well as short term corrections to the random shocks experienced and are capable of executing a profitable pairs trading strategy.

The scope of this study has remained limited to proposing and empirically testing the pairs selection technique within the context of Karachi Stock Exchange. The scope of the study did not include assessing the profitability of pairs trading in Karachi Stock Exchange which should be the next research endeavour. Future research attempts can be made through expanding the scope to other sectors of Karachi Stock Exchange. Further the proposed pair's selection technique should be employed for pairs trading in Karachi Stock Exchange.

6. PRACTICAL IMPLICATION OF THE STUDY

This study focuses upon a comprehensive application of pairs trading strategy within the context of Pakistan. The pairs trading strategy as a hedge fund strategy is new to the emerging equity market of Pakistan. Through this research the application of pairs trading investment strategy in Pakistan will help in broadening the investment horizon of the local investors. Although short selling is not allowed in Pakistan which is the primary assumption of the pairs trading strategy yet it can be based on the assumption that the stocks can be sold short. Therefore this study tends to challenge the restricted short selling policy in the equity market of Pakistan.

APPENDIX I

Table 1
List of Companies

Table 1 contains a List of companies included in the study
pertaining to Commercial Banks and the Financial Services sector.
For each company given in the Table 1, a symbol is also given as
quoted in Karachi Stock Exchange. Later in the analysis, these
companies will be referred to using these symbols

         Commercial Banks

Symbol   Company Name

ABL      Allied Bank Limited
AKBL     Askari Bank Limited
BAFL     Bank Al-Falah Limited
BAHL     Bank Al-Habib Limited
BOK      Bank Of Khyber Limited
BOP      Bank Of Punjab Limited
BIPL     Bankislami Pakistan Limited
FABL     Faysal Bank Limited
HBL      Habib Bank Limited
HMB      Habib Metropolitan Bank Limited
JSBL     JS Bank Limited
KASBB    KASB Bank Limited
MCB      MCB Bank Limited
MEBL     Meezan Bank Limited
NIB      NIB Bank Limited
NBP      National Bank of Pakistan
SBL      Samba Bank Limited
SILK     Silkbank Limited
SNBL     Soneri Bank Limited
SCBPL    Standard Chartered Bank Limited
SMBL     Summit Bank Limited
UBL      United Bank Limited

         Financial Services Sector

Symbol   Company Name

AHL      Arif Habib Limited
DEL      Dawood Equities Limited
ESBL     Escorts Investment Bank Limited
FCSC     First Capital Securities Corporation Limited
FDIBL    First Dawood Investment Bank Limited
FNEL     First National Equities Limited
GRYL     Grays Leasing Limited
IGIBL    IGI Investment Bank Limited
JSGCL    JS Global Capital Limited
JSIL     JS Investments Limited
JSCL     Jahangir Siddiqui Company Limited
KASBSL   KASB Securities Limited
MCBAH    MCB-ARIF Habib Savings & Investments Ltd
OLPL     Orix Leasing Pakistan Limited
PASL     Pervez Ahmed Securities Limited
SPLC     Saudi Pak Leasing Company Limited
SIBL     Security Investment Bank Limited
SCLL     Standard Chartered Leasing Limited
TRIBL    Trust Investment Bank Limited

APPENDIX II

Table 2
Augmented Dickey Fuller (ADF) Test Results for Log Price Series

Table 2 contains ADF test results of log prices in order to ensure
that the price series qualifies the condition of non-Stationarity
for the Cointegration analysis. Table 2 provides the tau-statistic
for the ADF test along with the relevant p-values given in
parenthesis

           Commercial Banks

Symbol    tau-Statistic (p-value)

ABL         -0.12981 (0.22445)
AKBL         -2.07698 (0.2542)
BAFL         -1.11167 (0.7136)
BAHL        -1.41394 (0.51052)
BOK          -1.4434 (0.5624)
BOP          -1.79736 (0.3823)
BIPL         -1.09327 (0.7208)
FABL         -1.68157 (0.4407)
HBL         -1.01707 (0.33335)
HMB          -2.44617 (0.129!)
JSBL         -1.50221 (0.5327)
KASBB        -2.22589 (0.1971)
MCB          -2.29299 (0.1743)
MEBL         -1.36619 (0.6005)
NIB           -1.5681 (0.499)
NBP          -2.04519(0.2675)
SBL          -2.03015 (0.2739)
SILK         -2.27314 (0.1808)
SNBL         -2.5003 (0.1153)
SCBPL       -0.0529857 (0.9526)
SMBL         -1.92746 (0.3198)
UBL         -0.512045 (0.8866)

      Financial Services Sector

Symbol    tau-Statistic (p-value)

AHL          -1.79456 (0.3837)
DEL          -1.97609 (0.2977)
ESBL         -1.81009 (0.376)
FCSC         -2.38769 (0.1452)
FDIBL        -2.23861 (0.1926)
FNEL          -1.7598 (0.401)
GRYL         -1.92371 (0.3216)
IGIBL        -2.36111 (0.153)
JSGCL        -2.33763 (0.1601)
JSIL         -2.36966 (0.1505)
JSCL         -2.14956 (0.2253)
KASBSL       -2.38842 (0.145)
MCBAH     -2.72558 (0.06965 ***)
OLPL         0.170826 (0.9708)
PASL         -1.72358 (0.4193)
SPLC        -0.928116 (0.7799)
SIBL        -0.750174 (0.8322)
SCLL         -2.25135 (0.1882)
TRIBL      -2.72648 (0.0695 ***)

* Significant at 1 percent,
** Significant at 5 percent,
*** Significant at 10 percent.

APPENDIX III

Table 3
List of Trading Pairs for Commercial Banks

Table 3 provides a list of pairs for Commercial Banks Sector. Using
22 sampled Commercial Banks, 231 pairs have been formed employing
the following formula No. of Stock Pairs = ([N.sup.2] /N)/2, N is
the number of sampled Commercial Banks. Relevant symbols have been
used to represent a specific Commercial Bank in a pair.

1     BAFL/BAHL
2     BAFL/ABL
3     BAFL/AKBL
4     BAFL/BOK
5     BAFL/BOP
6     BAFL/BIPL
7     BAFL/FAJBL
8     BAFL/HBL
9     BAFL/HMB
10    BAFL/JSBL
11    BAFL/KASBB
12    BAFL/MCB
13    BAFL/MEBL
14    BAFL/NBP
15    BAFL/NIB
16    BAFL/SBL
17    BAFL/UBL
18    BAFL/SMBL
19    BAFL/SCBPL
20    BAFL/SILK
21    BAFL/SNBL
22    BAHL/ABL
23    BAHL/AKBL
24    BAHL/BOK
25    BAHL/BOP
26    BAHL/BIPL
27    BAHL/FABL
28    BAHL/HBL
29    BAHL/HMB
30    BAHL/JSBL
31    BAHL/KASBB
32    BAHL/MCB
33    BAHL/MEBL
34    BAHL/NBP
35    BAHL/N1B
36    BAHL/SBL
37    BAHL/UBL
38    BAHL/SMBL
39    BAHL/SCBPL
40    BAHL/SILK
41    BAHL/SNBL
42    ABL/AKBL
43    ABL/BOK
44    ABL/BOP
45    ABL/BIPL
46    ABL/FABL
47    ABL/HBL
48    ABL/HMB
49    ABL/JSBL
50    ABL/KASBB
51    ABL/MCB
52    ABL/MEBL
53    ABL/NBP
54    ABL/NIB
55    ABL/SBL
56    ABL/UBL
57    ABL/SMBL
58    ABL/SCBPL
59    ABL/SILK
60    ABL/SNBL
61    AKBL/BOK
62    AKBL/BOP
63    AKBL/BIPL
64    AKBL/FABL
65    AKBL/HBL
66    AKBL/HMB
67    AKBL/JSBL
68    AKBL/KASBB
69    AKBL/MCB
70    AKBL/MEBL
71    AKBL/NBP
72    AKBL/NIB
73    AKBL/SBL
74    AKBL/UBL
75    AKBL/SMBL
76    AKBL/SCBPL
77    AKBL/SILK
78    AKBL/SNBL
79    BOK/BOP
80    BOK/BIPL
81    BOK/FABL
82    BOK/HBL
83    BOK/HMB
84    BOK/JSBL
85    BOK/KASBB
86    BOK/MCB
87    BOK/MEBL
88    BOK/NBP
89    BOK/NIB
90    BOK/SBL
91    BOK/UBL
92    BOK/SMBL
93    BOK/SCBPL
94    BOK/SILK
95    BOK/SNBL
96    BOP/BIPL
97    BOP/FAB L
98    BOP/HBL
99    BOP/HMB
100   BOP/JSBL
101   BOP/KASBB
102   BOP/MCB
103   BOP/MEBL
104   BOP/NBP
105   BOP/NIB
106   BOP/SBL
107   BOP/UBL
108   BOP/SMBL
109   BOP/SCBPL
110   BOP/SILK
111   BOP/SNBL
112   BIPL/FABL
113   BIPL/HBL
114   B1PL/HMB
115   BIPL/JSBL
116   BIPL/KASBB
117   BIPL/MCB
118   BIPL/MEBL
119   BIPL/NBP
120   BIPL/NIB
121   BIPL/SBL
122   B1PL/UBL
123   BIPL/SMBL
124   BIPL/SCBPL
125   BIPL/SILK
126   BIPL/SNBL
127   FABL/HBL
128   FABL/HMB
129   FABL/JSBL
130   FABL/KASBB
131   FABL/MCB
132   FABL/MEBL
133   FABL/NBP
134   FABL/NIB
135   FABL/SBL
136   FABL/UBL
137   FABL/SMBL
138   FABL/SCBPL
139   FABL/SILK
140   FABL/SNBL
141   HBL/HMB
142   HBL/JSBL
143   HBL/KASBB
144   HBL/MCB
145   HBL/MEBL
146   HBL/NBP
147   HBL/NIB
148   HBL/SBL
149   HBL/UBL
150   HBL/SMBL
151   HBL/SCBPL
152   HBL/SILK
153   HBL/SNBL
154   HMB/JSBL
155   HMB/KASBB
156   HMB/MCB
157   HMB/MEBL
158   HMB/NBP
159   HMB/NIB
160   HMB/SBL
161   HMB/UBL
162   HMB/SMBL
163   HMB/SCBPL
164   HMB/SILK
165   HMB/SNBL
166   JSBL/KASBB
167   JSBL/MCB
168   JSBL/MEBL
169   JSBL/NBP
170   JSBL/NIB
171   JSBL/SBL
172   JSBL/UBL
173   JSBL/SMBL
174   JSBL/SCBPL
175   JSBL/SILK
176   JSBL/SNBL
177   KASBB/MCB
178   KASBB/MEBL
179   KASBB/NBP
180   KASBB/N1B
181   KASBB/SBL
182   KASBB/UBL
183   KASBB/SMBL
184   KASBB/SCBPL
185   KASBB/SILK
186   KASBB/SNBL
187   MCB/MEBL
188   MCB/NBP
189   MCB/NIB
190   MCB/SBL
191   MCB/UBL
192   MCB/SMBL
193   MCB/SCBPL
194   MCB/SILK
195   MCB/SNBL
196   MEBL/NBP
197   MEBL/NIB
198   MEBL/SBL
199   MF.BL/UBL
200   MEBL/SMBL
201   MEBL/SCBPL
202   MEBL/SILK
203   MEBL/SNBL
204   NBP/NIB
205   NBP/SBL
206   NBP/UBL
207   NBP/SMBL
208   NBP/SCBPL
209   NBP/SILK
210   NBP/SNBL
211   NIB/SBL
212   NIB/UBL
213   N1B/SMBL
214   NIB/SCBPL
215   NIB/SILK
216   NIB/SNBL
217   SBL/UBL
218   SBL/SMBL
219   SBL/SCBPL
220   SBL/SILK
221   SBL/SNBL
222   UBL/SMBL
223   UBL/SCBPL
224   UBL/SILK
225   UBL/SNBL
226   SMBL/SCBPL
227   SMBL/SILK
228   SMBL/SNBL
229   SCBPL/SILK
230   SCBPL/SNBL
231   SILK/SNBL

Table 4
List of Trading Pairs for Financial Services Sector

Table 4 provides a list of pairs for Financial Sector. Using 19
sampled Financial Services companies, 156 pairs have been formed
employing the following formula,

No. of Stock Pairs = [N.sup.2]/N/2, is the number of sampled
Financial Services Companies. Relevant symbols have been used to
represent a specific Financial Services Company in a pair.

1      FDIBL/AHL
2      FDIBL/DEL
3      FDIBL/IG1BL
4      FDIBL/JSCL
5      FDIBL/FNEL
6      FDIBL/FCSC
7      FD1BL/JSIL
8      FDIBL/JSGCL
9      FDIBL/KASBSL
10     FDIBL/OLPL
11     FDIBL/PASL
12     FDIBLVSCLL
13     FDIBL/SPLC
14     AHL/DEL
15     AHL/ESBL
16     AHL/GRYL
17     AHL/IG1BL
18     AHIVJSCL
19     AHL/FNEL
20     AHL/FCSC
21     AHL/JSIL
22     AHL/JSGCL
23     AHL/KASBSL
24     AHL/MCBAH
25     AHL/OLPL
26     AHL/PASL
27     AHUSCLL
28     AHL/SPLC
29     AHL/SIBL
30     AHL/TRIBL
31     DEL/ESBL
32     DEL/GRYL
33     DEL/IGIBL
34     DEL/JSCL
35     DEL/FNEL
36     DEL/FCSC
37     DEL/JSIL
38     DEL/JSGCL
39     DEL/KASBSL
40     DEL/MCBAH
41     DEL/OLPL
42     DEL/PASL
43     DEL/SCLL
44     DEL/SPLC
45     DEL/SIBL
46     DEL/TRIBL
47     ESBL/IGIBL
48     ESBL/JSCL
49     ESBL/FNEL
50     ESBL/FCSC
51     ESBL/JSIL
52     ESBL/JSGCL
53     ESBL/KASBSL
54     ESBL/OLPL
55     ESBL/PASL
56     ESBL/SCLL
57     ESBL/SPLC
58     GRYL/IGIBL
59     GRYL/JSCL
60     GRYL/FNEL
61     GRYL7FCSC
62     GRYL/JS1L
63     GRYL/JSGCL
64     GRYL/KASBSL
65     GRYL/OLPL
66     GRYL/PASL
67     GRYL/SCLL
68     GRYL/SPLC
69     IGIBL/JSCL
70     IGIBL/FNEL
71     1GIBL/FCSC
72     IGIBL/JSIL
73     IGIBL/JSGCL
74     IGIBL/KASBSL
75     IGIBL/MCBAH
76     IGIBL/OLPL
77     IGIBL/PASL
78     IGIBL/SCLL
79     1GIBL/SPLC
80     IGIBL/SIBL
81     IGIBL/TRIBL
82     JSCL/FNEL
83     JSCL/FCSC
84     JSCL/JSIL
85     JSCL/JSGCL
86     JSCL/KASBSL
87     JSCL/MCBAH
88     JSCL/OLPL
89     JSCL/PASL
90     JSCL/SCLL
91     JSCL/SPLC
92     JSCL/SIBL
93     JSCL/TRIBL
94     FNEL/FCSC
95     FNEL/JS1L
96     FNEUJSGCL
97     FNEL/KASBSL
98     FNEL/MCBAH
99     FNEL/OLPL
100    FNEL/PASL
101    FNEL/SCLL
102    FNEL/SPLC
103    FNEL/SIBL
104    FNEL/TRIBL
105    FCSC/JSIL
106    FCSC/JSGCL
107    FCSC/KASBSL
108    FCSC/MCBAH
109    FCSC/OLPL
110    FCSC/PASL
111    FCSC/SCLL
112    FCSC/SPLC
113    FCSC/SIBL
114    FCSC/TRIBL
115    JSIL/JSGCL
116    JSIL/KASBSL
117    JSIL/MCBAH
118    JSIL/OLPL
119    JSIL/PASL
120    JSIL/SCLL
121    JSIUSPLC
122    JSIL/SIBL
123    JSIL/TRIBL
124    JSGCL/KASBSL
125    JSGCL/MCBAH
126    JSGCL/OLPL
127    JSGCL/PASL
128    JSGCIVSCLL
129    JSGCL/SPLC
130    JSGCL/SIBL
131    JSGCL/TRIBL
132    KASBSL/MCBAH
133    KASBSL/OLPL
134    KASBSL/PASL
135    KASBSL/SCLL
136    KASBSL/SPLC
137    KASBSL/SIBL
138    KASBSL/TR1BL
139    MCBAH/OLPL
140    MCBAH/PASL
141    MCBAH/SCLL
142    MCBAH/SPLC
143    OLPL/PASL
144    OLPL/SCLL
145    OLPL/SPLC
146    OLPL/SIBL
147    OLPL/TRIBL
148    PASL/SCLL
149    PASL/SPLC
150    PASL/SIBL
151    PASL/TRIBL
152    SCLL/SPLC
153    SCLL/SIBL
154    SCLL/TRIBL
155    SPLC/SIBL
156    SPLC/TRIBL

APPENDIX IV

Table 5
Cointegration Results for Commercial Banks

Table 5 contains the Engle-Granger (EG) Cointegration test results
for Commercial Banks. For each trading pairs, Engle-Granger
Cointegrating Regression error has been tested for Stationarity
using the ADF test and the p-values have been reported in the table
below

     Trading Pairs   EG (p-value)

1    BAFL/BOK        0.008789 *
2    BAFL/MEBL       0.02299 **
3    BAHL/AKBL       0.04425 **
4    BAHL/BOP        0.06455 ***
5    BAHL/BIPL       0.0918 ***
6    BAHL/FABL       0.002668 *
7    BAHL/HMB        0.0003476 *
8    BAHL/KASBB      0.0411 **
9    BAHL/MEBL       0.0358 **
10   BAHL/NBP        0.001183 *
11   BAHL/NIB        0.02914 **
12   BAHL/SMBL       0.04305 **
13   BAHL/SCBPL      0.04955 **
14   BAHL/SILK       0.02161 **
15   BAHL/SNBL       0.0681 ***
16   ABL/BOK         0.02138 **
17   ABL/B1PL        0.0274 **
18   ABL/JSBL        0.03491 **
19   ABL/MEBL        0.02807 **
20   ABL/SBL         0.9959 ***
21   ABL/UBL         0.08923 ***
22   ABL/SCBPL       0.04085 **
23   AKBL/KASBB      0.08669 ***
24   AKBL/NIB        0.02887 **
25   AKBL/SBL        0.05104 ***
26   AKBL/SNBL       0.08551 ***
27   BOK/BIPL        0.02936 **
28   BOK/MEBL        0.001175 *
29   BOK/SCBPL       0.01992 *
30   BOP/KASBB       0.004174 *
31   BOP/NIB         0.009164 *
32   BOP/SBL         0.02544 **
33   BOP/SNBL        0.07581 ***
34   BIPL/JSBL       0.01882 *
35   B1PL/MEBL       0.05611 **
36   FABL/HMB        0.00924 *
37   FABL/NBP        0.0007933 *
38   FABL/NIB        0.04268 **
39   FABL/SMBL       0.09897 ***
40   FABL/SILK       0.01807 *
41   HBL/HMB         0.05596 **
42   HBL/JSBL        0.06623 ***
43   HBL/KASBB       0.06546 ***
44   HBL/MCB         0.09504 ***
45   HBL/MEBL        0.06476 ***
46   HBL/NBP         0.08939 ***
47   HBL/NIB         0.06438 ***
48   HBL/SMBL        0.07491 ***
49   HMB/NBP         0.01724 **
50   HMB/SILK        0.05437 ***
51   K.ASBB/NIB      0.001719 *
52   KASBB/SBL       0.0724 ***
53   KASBB/SILK      0.08409 ***
54   KASBB/SNBL      0.04456 **
57   MEBL/UBL        0.0918 ***
56   NBP/SILK        0.09046 ***
57   NIB/SNBL        0.0697 ***
58   SBL/SNBL        0.01072 **
59   UBL/SCBPL       0.000009841 *
60   SMBL/SILK       0.003712 *

* Significant at 1 percent, ** Significant at 5 percent,
*** Significant at 10 percent.

Table 6
Cointegration Results for Financial Services Sector

Table 6 contains the Engle-Granger (EG) Cointegration test results
for Financial Services Sector. For each trading pairs, Engle-
Granger Cointegrating Regression error has been tested for
Stationarity using the ADF test and the p-values have been
reported in the table below.

                     EG
Trading Pairs        p-value

 1 FDIBL/AHL         0.0056 *
 2 FDIBL/DEL         0.0000 *
 3 FDIBL/IGIBL       9.147e-05 *
 4 FDIBL/JSCL        0.001359 *
 5 FDIBL/FNEL        0.02285 **
 6 FDIBL/FCSC        0.0001264 *
 7 FDIBL/JSIL        0.001275 *
 8 FDIBL/JSGCL       0.001362 *
 9 FDIBL/KASBSL      0.00007 *
10 FDIBL/PASL        0.00011 *
11 FDIBL/SCLL        0.06495 ***
12 FDIBL/SPLC        0.00976 *
13 AHL/DEL           0.00074 *
14 AHL/ESBL          0.05041 ***
15 AHL/FCSC          0.05804 ***
16 AHL/KASBSL        0.08265 *
17 DEL/ESBL          0.00002 *
18 DEL/IGIBL         0.00005 *
19 DEL/JSCL          0.00001903 *
20 DEL/FNEL          0.03626 **
21 DEL/FCSC          0.00000 *
22 DEL/JSIL          0.0001 *
23 DEL/JSGCL         0.00000 *
24 DEL/KASBSL        0.00000 *
25 DEL/PAS L         0.00000 *
26 DEL/SIBL          0.02753 **
27 DEL/TRIBL         0.0009031 *
28 ESBL/JSCL         0.00248 *
29 ESBL/FNEL         0.03565 **
30 ESBI./FCSC        0.0001 *
31 ESBL/JSGCL        0.00053 *
32 ESBL/KASBSL       0.00006 *
33 ESBL/OLPL         0.07936 ***
34 ESBL/PASL         0.00001 *
35 GRYL/IG1BL        0.00064 *
36 GRYL/JSCL         0.00080 *
37 GRYL/FNEL         0.0001 *
38 GRYL/FCSC         0.00066 *
39 GRYL/JSIL         0.00076 *
40 GRYL/JSGCL        0.00082 *
41 GRYL/KASBSL       0.00044 *
42 GRYL/OLPL         0.00038 *
43 GRYL/PASL         0.00048 *
44 GRYL/SCLL         0.00064 *
45 GRYL/SPLC         0.00000 *
46 IGIBL/JSCL        0.00163 *
47 1GIBL/FNEL        0.08451 ***
48 IGIBL/FCSC        0.02687 **
49 IGIBL/JSIL        0.0005128 *
50 IGIBL/JSGCL       0.02714 **
51 IGIBL/KASBSL      0.009774 *
52 IGIBL/SIBL        0.05003 ***
53 IGIBLATRIBL       0.09656 ***
54 JSCL/JSIL         0.0026 *
55 JSCL/JSGCL        0.0384 **
56 JSCL/KASBSL       0.03866 **
57 FCSC/JSGCL        0.006474 *
58 FCSC/KASBSL       0.01155 *
59 FCSC/PASL         0.06795 ***
60 FCSC/SIBL         0.09751 ***
61 FCSC/TRIBL        0.0001118 *
62 JS1L/JSGCL        0.04554 **
63 JSIL/KASBSL       0.02953 **
64 JSGCL/KASBSL      0.03947 **
65 JSGCL/PASL        0.07957 ***
66 JSGCL/TRIBL       0.03619 **
67 KASBSL/SPLC       0.04196 **
68 KASBSL/SIBL       0.03391 **
69 KASBSL/TRIBL      0.007249 *
70 MCBAH/SCLL        0.04695 **
71 MCBAH/SPLC        0.08559 ***
72 OLPL/SCLL         0.00000 *
73 PASL/SPLC         0.03601 **
74 PASL/SIBL         0.02605 **
75 PASL/TRIBL        0.0587 ***
76 SCLL/SIBL         0.07853 ***
77 SPLC/SIBL         0.00051 *

* Significant at 1 percent, ** Significant at 5 percent.
*** Significant at 10 percent.

Appendix V

Table 7
Pair-wise Granger Causality Test Results for Commercial Banks

Table 7 provides pair-wise Granger Causality Test Results, for each
cointegrated trading pair of Commercial Banks identified in Table 5.
For every trading pair two null hypotheses have been given along
with their p-values. The acceptance or rejection of the null
hypothesis determines the direction of causality in each trading
pair.

                           Direction of Causality
     Trading Pairs           (Null Hypothesis)             p-value

1    BAFL/BOK        BAFL does not Granger Cause BOK      0.045 **
2    BAFL/MEBL       MEBL does not Granger Cause BAFL      0.007 *
3    BAHL/AKBL       AKBL does not Granger Cause BAHL       0.392
4    BAHL/BOP        BOP does not Granger Cause BAHL        0.159
5    BAHL/BIPL       B1PL does not Granger Cause BAHL       0.738
6    BAHL/FABL       FABL does not Granger Cause BAHL      0.005 *
7    BAHL/HMB        BAHL does not Granger Cause HMB        0.369
8    BAHL/KASBB      KASBB does not Granger Cause BAHL    0.017 **
9    BAHL/MEBL       MEBL does not Granger Cause BAHL       0.118
10   BAHL/NBP        BAHL does not Granger Cause NBP       0.000 *
11   BAHL/NIB        NIB does not Granger Cause BAHL      0.033 **
12   BAHL/SMBL       SMBL does not Granger Cause BAHL     0.026 **
13   BAHL/SCBPL      SCBPL does not Granger Cause BAHL      0.266
14   BAHL/SILK       BAHL does not Granger Cause SILK       0.355
15   BAHL/SNBL       BAHL does not Granger Cause SNBL       0.191
16   ABL/BOK         ABL does not Granger Cause BOK         0.475
17   ABL/BIPL        ABL does not Granger Cause BIPL        0.892
IS   ABL/JSBL        JSBL does not Granger Cause ABL       0.003 *
19   ABL/MEBL        MEBL does not Granger Cause ABL      0.010 **
20   ABL/SBL         SBL does not Granger Cause ABL         0.883
21   ABL/UBL         ABL does not Granger Cause UBL       0.020 **
22   ABL/SCBPL       ABL does not Granger Cause SCBPL     0.061 ***
23   AKBL/KASBB      KASBB does not Granger Cause AKBL    0.012 **
24   AKBL/NIB        NIB does not Granger Cause AKBL        0.252
25   AKBL/SBL        SBL does not Granger Cause AKBL        0.647
26   AKBL/SNBL       SNBL does not Granger Cause AKBL       0.106
27   BOK/BIPL        BOK does not Granger Cause BIPL       0.000 *
28   BOK/MEBL        MEBL does not Granger Cause BOK      0.038 **
29   BOK/SCBPL       SCBPL does not Granger Cause BOK     0.055 ***
30   BOP/KASBB       KASBB does not Granger Cause BOP      0.000 *
31   BOP/NIB         NIB does not Granger Cause BOP       0.019 **
32   BOP/SBL         SBL does not Granger Cause BOP       0.049 **
33   BOP/SNBL        SNBL does not Granger Cause BOP      0.020 **
34   BIPL/JSBL       JSBL does not Granger Cause BIPL      0.008 *
35   B1PL/MEBL       MEBL does not Granger Cause BIPL     0.016 **
36   FABL/HMB        HMB does not Granger Cause FABL       0.002 *
37   FABL/NBP        FABL does not Granger Cause NBP      0.033 **
38   FABL/NIB        NIB does not Granger Cause FABL       0.000 *
39   FABL/SMBL       SMBL does not Granger Cause FABL      0.002 *
40   FABL/SILK       SILK does not Granger Cause FABL      0.006 *
41   HBL/HMB         HMB does not Granger Cause HBL         0.56
42   HBL/JSBL        JSBL does not Granger Cause HBL        0.263
43   HBL/KASBB       KASBB does not Granger Cause HBL       0.816
44   HBL/MCB         MCB does not Granger Cause HBL        0.004 *
45   HBL/MEBL        MEBL does not Granger Cause HBL        0.571
46   HBL/NBP         NBP does not Granger Cause HBL         0.375
47   HBL/NIB         NIB does not Granger Cause HBL          0.9
48   HBL/SMBL        SMBL does not Granger Cause HBL        0.981
49   HMB/NBP         NBP does not Granger Cause HMB        0.000 *
50   HMB/SILK        HMB does not Granger Cause SILK      0.087 ***
51   KASBB/NIB       NIB does not Granger Cause KASBB      0.000 *
52   KASBB/SBL       SBL does not Granger Cause KASBB      0.001 *
53   KASBB/SILK      SILK does not Granger Cause KASBB     0.004 *
54   KASBB/SNBL      SNBL does not Granger Cause KASBB      0.195
55   MEBL/UBL        UBL does not Granger Cause MEBL      0.029 **
56   NBP/SILK        SILK does not Granger Cause NBP      0.034 **
57   NIB/SNBL        SNBL does not Granger Cause NIB        0.293
58   SBL/SNBL        SNBL does not Granger Cause SBL       0.000 *
59   UBUSCBPL        SCBPL does not Granger Cause UBL      0.000 *
60   SMBL/SILK       SILK does not Granger Cause SMBL      0.001 *

                           Direction of Causality
     Trading Pairs           (Null Hypothesis)             p-value

1    BAFL/BOK        BOK does not Granger Cause BAFL       0.005 *
2    BAFL/MEBL       BAFL does not Granger Cause MEBL     0.049 **
3    BAHL/AKBL       BAHL does not Granger Cause AKBL       0.643
4    BAHL/BOP        BAHL does not Granger Cause BOP        0.509
5    BAHL/BIPL       BAHL does not Granger Cause BIPL       0.551
6    BAHL/FABL       BAHL does not Granger Cause FABL       0.933
7    BAHL/HMB        HMB does not Granger Cause BAHL       0.001 *
8    BAHL/KASBB      BAHL does not Granger Cause KASBB      0.259
9    BAHL/MEBL       BAHL does not Granger Cause MEBL       0.218
10   BAHL/NBP        NBP does not Granger Cause BAHL        0.562
11   BAHL/NIB        BAHL does not Granger Cause NIB        0.957
12   BAHL/SMBL       BAHL does not Granger Cause SMBL       0.692
13   BAHL/SCBPL      BAHL does not Granger Cause SCBPL      0.18
14   BAHL/SILK       SILK does not Granger Cause BAHL     0.076 ***
15   BAHL/SNBL       SNBL does not Granger Cause BAHL     0.037 **
16   ABL/BOK         BOK does not Granger Cause ABL        0.001 *
17   ABL/BIPL        BIPL does not Granger Cause ABL      0.027 **
IS   ABL/JSBL        ABL does not Granger Cause JSBL        0.757
19   ABL/MEBL        ABL does not Granger Cause MEBL        0.735
20   ABL/SBL         ABL does not Granger Cause SBL         0.522
21   ABL/UBL         UBL does not Granger Cause ABL       0.010 **
22   ABL/SCBPL       SCBPL does not Granger Cause ABL     0.038 **
23   AKBL/KASBB      AKBL does not Granger Cause KASBB    0.031 **
24   AKBL/NIB        AKBL does not Granger Cause NIB      0.033 **
25   AKBL/SBL        AKBL does not Granger Cause SBL      0.018 **
26   AKBL/SNBL       AKBL does not Granger Cause SNBL       0.359
27   BOK/BIPL        BIPL does not Granger Cause BOK        0.213
28   BOK/MEBL        BOK does not Granger Cause MEBL       0.004 *
29   BOK/SCBPL       BOK does not Granger Cause SCBPL      0.068 *
30   BOP/KASBB       BOP does not Granger Cause KASBB     0.037 **
31   BOP/NIB         BOP does not Granger Cause NIB       0.017 **
32   BOP/SBL         BOP does not Granger Cause SBL        0.005 *
33   BOP/SNBL        BOP does not Granger Cause SNBL        0.12
34   BIPL/JSBL       BIPL does not Granger Cause JSBL     0.028 **
35   B1PL/MEBL       BIPL does not Granger Cause MEBL       0.131
36   FABL/HMB        FABL does not Granger Cause HMB        0.226
37   FABL/NBP        NBP does not Granger Cause FABL       0.002 *
38   FABL/NIB        FABL does not Granger Cause NIB        0.390
39   FABL/SMBL       FABL does not Granger Cause SMBL       0.773
40   FABL/SILK       FABL does not Granger Cause SILK       0.291
41   HBL/HMB         HBL does not Granger Cause HMB         0.31
42   HBL/JSBL        HBL does not Granger Cause JSBL        0.351
43   HBL/KASBB       HBL does not Granger Cause KASBB     0.039 **
44   HBL/MCB         HBL does not Granger Cause MCB        0.000 *
45   HBL/MEBL        HBL does not Granger Cause MEBL        0.467
46   HBL/NBP         HBL does not Granger Cause NBP         0.349
47   HBL/NIB         HBL does not Granger Cause NIB         0.397
48   HBL/SMBL        HBL does not Granger Cause SMBL        0.384
49   HMB/NBP         HMB does not Granger Cause NBP        0.000 *
50   HMB/SILK        SILK does not Granger Cause HMB       0.007 *
51   KASBB/NIB       KASBB does not Granger Cause NIB      0.001 *
52   KASBB/SBL       KASBB does not Granger Cause SBL      0.000 *
53   KASBB/SILK      KASBB does not Granger Cause SILK     0.001 *
54   KASBB/SNBL      KASBB does not Granger Cause SNBL     0.000 *
55   MEBL/UBL        MEBL does not Granger Cause UBL      0.057 **
56   NBP/SILK        NBP does not Granger Cause SILK        0.591
57   NIB/SNBL        NIB does not Granger Cause SNBL        0.221
58   SBL/SNBL        SBL does not Granger Cause SNBL        0.196
59   UBUSCBPL        UBL does not Granger Cause SCBPL      0.000 *
60   SMBL/SILK       SMBL does not Granger Cause SILK     0.081 **

* Significant al 1 percent, ** Significant at 5 percent,
*** Significant at 10 percent.

Table 8
Pair-wise Granger Causality Test Results for Financial Services Sector

Table 8 provides pair-wise Granger Causality Test Results, for each
reintegrated trading pair of Financial Services Sector identified in
Table 6. For every trading pair two null hypotheses have been given
along with their p-values. The acceptance or rejection of the null
hypothesis determines the direction of causality in each trading
pair.

   Trading Pairs  Direction of Causality               p-value

1  FDIBL/AHL      FDIBL does not Granger Cause AHL     0.624
2  FDIBL/DEL      FD1BL does not Granger Cause DEL     0.245
3  FDIBL/IGIBL    FDIBL does not Granger Cause IGIBL   0.023 **
4  FDIBL/JSCL     FDIBL does not Granger Cause JSCL    0.319
5  FDIBL/FNEL     FDIBL does not Granger Cause FNEL    0.576
6  FD1BL/FCSC     FDIBL does not Granger Cause FCSC    0.393
7  FDIBL/JSIL     FDIBL does not Granger Cause JSIL    0.591
8  FDIBL/JSGCL    FDIBL does not Granger Cause JSGCL   0.091 ***
9  FDIBL/KASBSL   FDIBL does not Granger Cause KASBSL  0.053 ***
10 FDIBL/PASL     FDIBL does not Granger Cause PASL    0.001 *
11 FDIBL/SCLL     FDIBL does not Granger Cause SCLL    0.723
12 FDIBL/SPLC     FDIBL does not Granger Cause SPLC    0.183
13 AHL/DEL        AHL does not Granger Cause DEL       0.001 *
14 AHL/ESBL       AHL does not Granger Cause ESBL      0.016 **
15 AHL/FCSC       AHL does not Granger Cause FCSC      0.081 ***
16 AHL/KASBSL     AHL does not Granger Cause KASBSL    0.202
17 DEL/ESBL       ESBL does not Granger Cause DEL      0.647
18 DEL/IGIBL      DEL does not Granger Cause IGIBL     0.012 **
19 DEL/JSCL       DEL does not Granger Cause JSCL      0.186
20 DEIVFNEL       DEL does not Granger Cause FNEL      0.107
21 DEL/FCSC       DEL does not Granger Cause FCSC      0.088 ***
22 DEL/JSIL       DEL does not Granger Cause JSIL      0.072 ***
23 DEL/JSGCL      DEL does not Granger Cause JSGCL     0.000 *
24 DEL/KASBSL     DEL does not Granger Cause KASBSL    0.074 ***
25 DEL/PASL       DEL does not Granger Cause PASL      0.000 *
26 DEL/SIBL       DEL does not Granger Cause SIBL      0.005 *
27 DEL/TRIBL      DEL does not Granger Cause TRIBL     0.001 *
28 ESBL/JSCL      ESBL does not Granger Cause JSCL     0.464
29 ESBL/FNEL      ESBL does not Granger Cause FNEL     0.363
30 ESBL/FCSC      ESBL does not Granger Cause FCSC     0.405
31 ESBUJSGCL      ESBL does not Granger Cause JSGCL    0.953
32 ESBL/KASBSL    ESBL does not Granger Cause KASBSL   0.359
32 ESBL/OLPL      ESBL does not Granger Cause OLPL     0.333
34 ESBL/PASL      ESBL does not Granger Cause PASL     0.292
35 GRYL/IG1BL     GRYL does not Granger Cause IGIBL    0.76877
36 GRYL/JSCL      GRYL does not Granger Cause JSCL     0.17222
37 GRYL/FNEL      GRYL does not Granger Cause FNEL     0.96619
38 GRYL/FCSC      GRYL does not Granger Cause FCSC     0.53427
39 GRYL/JSIL      GRYL does not Granger Cause JSIL     0.10984
40 GRYL/JSGCL     GRYL does not Granger Cause JSGCL    0.98607
41 GRYL/KASBSL    GRYL does not Granger Cause KASBSL   0.33830
42 GRYL/OLPL      GRYL does not Granger Cause OLPL     0.12011
43 GRYL/PASL      GRYL does not Granger Cause PASL     0.3759
44 GRYL/SCLL      GRYL does not Granger Cause SCLL     0.25314
45 GRYL/SPLC      GRYL does not Granger Cause SPLC     0.05378 ***
46 IGIBL/JSCL     1GIBL does not Granger Cause JSCL    0.57933
47 IGIBL/FNEL     IGIBL does not Granger Cause FNEL    0.81196
48 IGIBL/FCSC     1GIBL does not Granger Cause FCSC    0.79704
49 IGIBL/JSIL     IGIBL does not Granger Cause JSIL    0.64385
50 IGIBL/JSGCL    IGIBL does not Granger Cause JSGCL   0.22881
51 IGIBL/KASBSL   IGIBL does not Granger Cause KASBSL  0.42880
52 IGIBL/SIBL     IGIBL does not Granger Cause SIBL    0.31957
53 IGIBL/TRIBL    IGIBL does not Granger Cause TRIBL   0.07367 ***
54 JSCL/JSIL      JSCL does not Granger Cause JSIL     0.02360 **
55 JSCL/JSGCL     JSCL does not Granger Cause JSGCL    0.00013 *
56 JSCL/KASBSL    JSCL does not Granger Cause KASBSL   0.00023 *
57 FCSC/JSGCL     FCSC does not Granger Cause JSGCL    0.000034 *
58 FCSC/KASBSL    FCSC does not Granger Cause KASBSL   0.24617
59 FCSC/PASL      FCSC does not Granger Cause PASL     0.00055 *
60 FCSC/SIBL      FCSC does not Granger Cause SIBL     0.76366
61 FCSC/TRIBL     FCSC does not Granger Cause TRIBL    0.00012 *
62 JSU7JSGCL      JSIL does not Granger Cause JSGCL    0.00116 *
63 JSHVKASBSL     JSIL does not Granger Cause KASBSL   0.00027 *
64 JSGCL/KASBSL   JSGCL does not Granger Cause KASBSL  0.03094 **
65 JSGCIVPASL     JSGCL does not Granger Cause PASL    008093 **
66 JSGCL/TRIBL    JSGCL does not Granger Cause TRIBL   0.01116 **
67 KASBSIVSPLC    KASBSL does not Granger Cause SPLC   0.87545
68 KASBSL/SIBL    KASBSL does not Granger Cause SIBL   0.51602
69 KASBSL/TRIBL   KASBSL does not Granger Cause TRIBL  0.000068 *
70 MCBAH/SCLL     MCBAH does not Granger Cause SCLL    0.21970
71 MCBAH/SPLC     MCBAH does not Granger Cause SPLC    0.73239
72 OLPL/5CLL      OLPL does not Granger Cause SCLL     0.00039 *
73 PASL/SPLC      PASL does not Granger Cause SPLC     0.6873
74 PASUSIBL       PASL does not Granger Cause SIBL     0.00974 *
75 PASl/TRIBL     PASL does not Granger Cause TRIBL    0.00312 *
76 SCL1VSIBL      SCLL does not Granger Cause SIBL     0.0073 *
77 SPLC/SIBL      SPLC does not Granger Cause SIBL     0.00442 *

   Trading Pairs  Direction of Causality               p-value

1  FDIBL/AHL      AHL does not Granger Cause FDIBL     0.00954 *
2  FDIBL/DEL      DEL does not Granger Cause FDIBL     0.00000043 *
3  FDIBL/IGIBL    IGIBL does not Granger Cause FDIBL   0.01046 **
4  FDIBL/JSCL     JSCL does not Granger Cause FDIBL    1.6E-05 *
5  FDIBL/FNEL     FNEL does not Granger Cause FDIBL    0.02073 **
6  FD1BL/FCSC     FCSC does not Granger Cause FDIBL    6.5E-06 *
7  FDIBL/JSIL     JSIL does not Granger Cause FDIBL    0.0000014 *
8  FDIBL/JSGCL    JSGCL does not Granger Cause FDIBL   0.00045 *
9  FDIBL/KASBSL   KASBSL does not Granger Cause FDIBL  4.7E-10 *
10 FDIBL/PASL     PASL does not Granger Cause FDIBL    1.0E-05 *
11 FDIBL/SCLL     SCLL does not Granger Cause FDIBL    0.50789
12 FDIBL/SPLC     SPLC does not Granger Cause FDIBL    0.11682
13 AHL/DEL        DEL does not Granger Cause AHL       0.04378 **
14 AHL/ESBL       ESBL does not Granger Cause AHL      0.31485
15 AHL/FCSC       FCSC does not Granger Cause AHL      0.21266
16 AHL/KASBSL     KASBSL does not Granger Cause AHL    0.00017 *
17 DEL/ESBL       DEL does not Granger Cause ESBL      0.00229 *
18 DEL/IGIBL      IGIBL does not Granger Cause DEL     0.18355
19 DEL/JSCL       JSCL does not Granger Cause DEL      0.00000077 *
20 DEIVFNEL       FNEL does not Granger Cause DEL      0.18414
21 DEL/FCSC       FCSC does not Granger Cause DEL      2.2E-06 *
22 DEL/JSIL       JSIL does not Granger Cause DEL      0.00418 *
23 DEL/JSGCL      JSGCL does not Granger Cause DEL     0.0000001 *
24 DEL/KASBSL     KASBSL does not Granger Cause DEL    0.00000000014 *
25 DEL/PASL       PASL does not Granger Cause DEL      0.00049 *
26 DEL/SIBL       SIBL does not Granger Cause DEL      0.10931
27 DEL/TRIBL      TRIBL does not Granger Cause DEL     0.00491 *
28 ESBL/JSCL      JSCL does not Granger Cause ESBL     0.00611 *
29 ESBL/FNEL      FNEL does not Granger Cause ESBL     0.47728
30 ESBL/FCSC      FCSC does not Granger Cause ESBL     0.01547 **
31 ESBUJSGCL      JSGCL does not Granger Cause ESBL    0.01357 **
32 ESBL/KASBSL    KASBSL does not Granger Cause ESBL   0.00093 *
32 ESBL/OLPL      OLPL does not Granger Cause ESBL     0.18549
34 ESBL/PASL      PASL does not Granger Cause ESBL     6.4E-05 *
35 GRYL/IG1BL     IGIBL does not Granger Cause GRYL    0.86253
36 GRYL/JSCL      JSCL does not Granger Cause GRYL     0.05647 ***
37 GRYL/FNEL      FNEL does not Granger Cause GRYL     0.50531
38 GRYL/FCSC      FCSC does not Granger Cause GRYL     0.32847
39 GRYL/JSIL      JSIL does not Granger Cause GRYL     0.64746
40 GRYL/JSGCL     JSGCL does not Granger Cause GRYL    0.23617
41 GRYL/KASBSL    KASBSL does not Granger Cause GRYL   0.31856
42 GRYL/OLPL      OLPL does not Granger Cause GRYL     0.04313 **
43 GRYL/PASL      PASL does not Granger Cause GRYL     0.29695
44 GRYL/SCLL      SCLL does not Granger Cause GRYL     0.3681
45 GRYL/SPLC      SPLC does not Granger Cause GRYL     0.00405 *
46 IGIBL/JSCL     JSCL does not Granger Cause IGIBL    0.000000056 *
47 IGIBL/FNEL     FNEL does not Granger Cause IGIBL    0.02041 *
48 IGIBL/FCSC     FCSC does not Granger Cause IGIBL    0.00338 *
49 IGIBL/JSIL     JSIL does not Granger Cause IGIBL    0.00000000019 *
50 IGIBL/JSGCL    JSGCL does not Granger Cause IGIBL   0.000093 *
51 IGIBL/KASBSL   KASBSL does not Granger Cause IGIBL  0.00000066 *
52 IGIBL/SIBL     SIBL does not Granger Cause IGIBL    0.58752
53 IGIBL/TRIBL    TRIBL does not Granger Cause IGIBL   0.13207
54 JSCL/JSIL      JSIL does not Granger Cause JSCL     0.18699
55 JSCL/JSGCL     JSGCL does not Granger Cause JSCL    0.2979
56 JSCL/KASBSL    KASBSL does not Granger Cause JSCL   0.55267
57 FCSC/JSGCL     JSGCL does not Granger Cause FCSC    0.00191 *
58 FCSC/KASBSL    KASBSL does not Granger Cause FCSC   0.00012 *
59 FCSC/PASL      PASL does not Granger Cause FCSC     0.70983
60 FCSC/SIBL      SIBL does not Granger Cause FCSC     0.48351
61 FCSC/TRIBL     TRIBL does not Granger Cause FCSC    0.08037 ***
62 JSU7JSGCL      JSGCL does not Granger Cause JSIL    0.16529
63 JSHVKASBSL     KASBSL does not Granger Cause JSIL   0.25675
64 JSGCL/KASBSL   KASBSL does not Granger Cause JSGCL  0.06883 ***
65 JSGCIVPASL     PASL does not Granger Cause JSGCL    0.00157 *
66 JSGCL/TRIBL    TRIBL does not Granger Cause JSGCL   0.07006 ***
67 KASBSIVSPLC    SPLC does not Granger Cause KASBSL   0.05085 ***
68 KASBSL/SIBL    SIBL does not Granger Cause KASBSL   0.14843
69 KASBSL/TRIBL   TRIBL does not Granger Cause KASBSL  0.59387
70 MCBAH/SCLL     SCLL does not Granger Cause MCBAH    0.06382 ***
71 MCBAH/SPLC     SPLC does not Granger Cause MCBAH    0.75992
72 OLPL/5CLL      SCLL does not Granger Cause OLPL     0.00421 *
73 PASL/SPLC      SPLC does not Granger Cause PASL     0.1347
74 PASUSIBL       SIBL does not Granger Cause PASL     0.77292
75 PASl/TRIBL     TRIBL does not Granger Cause PASL    0.20855
76 SCL1VSIBL      SIBL does not Granger Cause SCLL     0.19709
77 SPLC/SIBL      SIBL does not Granger Cause SPLC     0.03593 **

* Significant at 1 percent, ** Significant at 5 percent,
*** Significant at 10 percent.

APPENDIX VI

Table 9
Cointegration (Directional) Regression Results for Commercial Banks

On the basis of the direction of causality (Uni-directional
Causality) identified in Table 7 for trading pairs of Commercial
Banks, Table 9 presents the results of Cointegration directional
regression. Results presented in Table 9 include indentified
dependent variable and an independent variable in a pair,
coefficient of the independent variable along with a p-value given
in (), regression constant. Table 9 also contains the ADF Test
results for testing Stationarity of the Cointegration regression
residual along with the p-value given in ().

   Dependent   Independent        Coeff.
     Vari.        Vari.          (p-value)         cont

1    BAHL         FABL        0.5812(0.000) *    23.61016
2    BAHL          HMB       0.4781 (0.000) *    20.9131
3    BAHL         KASBB       1.0195(0.000) *    28.18701
4     NBP         BAHL       3.3711 (0.000) *    -47.1737
5    BAHL          NIB        1.6054(0.000) *    26.55518
6    BAHL         SMBL       1.2250 (0.000) *    26.52914
7    BAHL         SILK       1.7729 (0.000) *    26.15899
8    BAHL         SNBL       0.6498 (0.000) *    26.20657
9     ABL          BOK       2.3337 (0.000) *    50.81223
10    ABL         BIPL       1.5024 (0.000) *    54.87699
11    ABL         JSBL       2.0844 (0.000) *    55.34554
12    ABL         MEBL       0.6842 (0.000) *    48.75288
13    NIB         AKBL       0.1922 (0.000) *    -0.44271
14    SBL         AKBL        0.1002(0.000) *    0.688091
15   BIPL          BOK       1.3391 (0.000) *    -1.56108
16    BOP         SNBL       1.8304 (0.000) *    -3.24987
17   BIPL         MEBL       0.3592 (0.000) *    -2.03251
18   FABL          HMB       0.5624 (0 000) *    0 717819
19   FABL          NIB       2.6246 (0.000) *    5.427415
20   FABL         SMBL       2.0361 (0.000) *    5.26936
21   FABL         SILK       3.2383 (0.000) *    3.897978
22   KASBB         HBL       0.0206 (0.000) *    0.198711
23   SNBL         KASBB      1.2111 (0.000) *    3.949449
24    NBP         SILK       13.4228 (0.000) *   21.7032
25    SBL         SNBL       0.2733 (0.000) *    0.370128

   Dependent   Residual ADF
     Vari.     (t-statistic)    p-value

1    BAHL         -3.8999      0.0124 **
2    BAHL         -4.7210      0.0007 *
3    BAHL         -3.7632      0.0189 **
4     NBP         -5.0585      0.0002 *
5    BAHL         -3.8510      0.0145 **
6    BAHL         -3.7731      0.0183 **
7    BAHL         -3.7202      0.0215 **
8    BAHL         -3.8015      0.0168 **
9     ABL         -3.8655      0.0138 **
10    ABL         -3.7509      0.0196 **
11    ABL         -3.8163      0.0161 **
12    ABL         -3.9042      0.0123 **
13    NIB         -3.5417      0.0072 *
14    SBL         -4.1347      0.0009 *
15   BIPL         -4.0016      0.0015 *
16    BOP         -3.1873      0.0211 **
17   BIPL         -3.3139      0.0146 **
18   FABL         -4 0477      0.0012 *
19   FABL         -4 1568      0.0008 *
20   FABL         -3.3659      0.0125 **
21   FABL         -3.9692      0.0017 *
22   KASBB        -2.8660      0.0498 **
23   SNBL         -3.2217      0.0191 **
24    NBP         -3.0897      0.0277 **
25    SBL         -3.9730      0.0016 *

* Significant at 1 percent, ** Significant at 5 percent,
*** Significant at 10 percent.

Table 10
Cointegration (Directional) Regression Results for Financial
Services Sector

On the basis of the direction of causality (Uni-directional
Causality) identified in Table 8 for trading pairs of Financial
Services Sector, Table 10 presents the results of Cointegration
directional regression. Results presented in Table 10 include
indentified dependent variable and an independent variable in a
pair, coefficient of the independent variable along with a p-value
given in (), regression constant. Table 10 also contains the ADF
Test results for testing Stationarity of the Cointegration
regression residual along with the p-value given in ().

                            Coeff.                   Residual ADF
    Vari.    Vari.        (p-value)        cont     (t-statistic)

1   FDIBL     AHL      0.022 (0.000) *    0.9391       -3.6719
2   FDIBL     DEL     0.4413 (0.000) *    0.7483       -5.3018
3   FDIBL     JSCL    0.0593 (0.000) *    0.8801       -3.9091
4   FDIBL     FNEL    0.0882 (0.000) *    1.1233       -3.3445
5   FDIBL     FCSC     0.1910(0.000) *    0.9069       -4.0146
6   FDIBL     JSIL    0.1276 (0.000) *    0.7231       -3.6734
7    ESBL     AHL     0.0353 (0.000) *    1.4183       -2.7528
8    FCSC     AHL     0.1197 (0.000) *    0.0303       -4.3509
9    AHL     KASBSL   7.3470 (0.000) *    -1.9622      -2.7436
10   ESBL     DEL     0.6531 (0.000) *    1.2258       -3.0762
11  IGIBL     DEL     0.5484 (0.000) *    0.9852       -3.2389
12   DEL      JSCL    0.1343 (0.000) *    0.3012       -4.3547
13   SIBL     DEL     0.2696 (0.000) *    1.9144       -3.1713
14   ESBL     JSCL    0.0853 (0.000) *    1.4554       -2.7354
15   ESBL     FCSC    0.2678 (0.000) *    1.5210       -3.3724
16   ESBL    JSGCL    0.0384 (0.000) *    1.2938       -2.8211
17   ESBL    KASBSL   0.3271 (0.000) *    1.0211       -3.0346
18   ESBL     PASL    0.5847 (0.000) *    1.1869       -4.3860
19   GRYL     JSCL    0.0459 (0.000) *    2.1951       -4.8257
20   GRYL     OLPL    0.0925 (0.000) *    2.0081       -5.2584
21  IGIBL     JSCL    0.0803 (0.000) *    1.0600       -4.0200
22  IGIBL     FNEL    0.1260 (0.000) *    1.3466       -3.4668
23  IGIBL     FCSC    0.2292 (0.000) *    1.2156       -3.6535
24  IGIBL     JSIL    0.1836 (0.000) *    0.7650       -4.4445
25  IGIBL    JSGCL    0.0336 (0.000) *    0.9958       -3.7915
26  IGIBL    KASBSL   0.2804 (0.000) *    0.7851       -3.8290
27  TRIBL    IGIBL    1.4681 (0.000) *    -1.1119      -4.1332
28   JSIL     JSCL    0.4202 (0.000) *    1.8400       -3.7587
29  JSGCL     JSCL    2.1842 (0.000) *    4.6630       -3.4752
30  KASBSL    JSCL    0.2498 (0.000) *    1.4770       -3.5062
31   FCSC    KASBSL   1.0593 (0.000) *    -1.0784      -3.5066
32   PASL     FCSC    0.4627 (0.000) *    0.5522       -3.0213
33  JSGCL     JSIL    4.7029 (0.000) *    -1.1674      -2.7882
34  KASBSL    JSIL     0.5513(0.000) *    0.7092       -3.2210
35  KASBSL    SPLC    0.9838 (0.000) *    3.7645       -3.5790
36  TRIBL    KASBSL   0.6692 (0.000) *    -1.2134      -4.0567
37  MCBAH     SCLL    -1.2208 (0.000) *   22.6492      -4.0032
38   SIBL     PASL    0.2894 (0.000) *    1.7810       -3.3519
39  TRIBL     PASL    0.9436 (0.000) *    -0.2571      -3.7394
40   SIBL     SCLL     0.2410(0.000) *    1.6021       -3.3991

     Vari.     p-value

1    FDIBL    0.0047 *
2    FDIBL    0.0000 *
3    FDIBL    0.0021 *
4    FDIBL    0.0133 *
5    FDIBL    0.0014 *
6    FDIBL    0.0047 *
7     ESBL    0.0657 ***
8     FCSC    0.0004 *
9     AHL     0.0671 ***
10    ESBL    0.0287 **
11   IGIBL    0.0182 **
12    DEL     0.0004 *
13    SIBL    0.0221 **
14    ESBL    0.0685 ***
15    ESBL    0.0122 **
16    ESBL    0.0557 ***
17    ESBL    0.0322 **
18    ESBL    0.0003 *
19    GRYL    0.0001 *
20    GRYL    0.0000 *
21   IGIBL    0.0014 *
22   IGIBL    0.0091 *
23   IGIBL    0.0050 *
24   IGIBL    0.0003 *
25   IGIBL    0.0031 *
26   IGIBL    0.0027 *
27   TRIBL    0.0009 *
28    JSIL    0.0035 *
29   JSGCL    0.0089 *
30   KASBSL   0.0081 *
31    FCSC    0.0080 *
32    PASL    0.0333 **
33   JSGCL    0.0603 ***
34   KASBSL   0.0191 **
35   KASBSL   0.0064 *
36   TRIBL    0.0012 *
37   MCBAH    0.0015 *
38    SIBL    0.0130 **
39   TRIBL    0.0037 *
40    SIBL    0.0113 **

* Significant at 1 percent, ** Significant at 5 percent,
*** Significant at 10 percent.

Appendix VII

Table 11
Vector Error Correction Model for Commercial Banks

For all the cointegrated trading pairs in Table 9 depicting
stationary residual series, the error component has been modeled
using Vectoi Error Correction Model (VECM) for which the results
are given in Table 11. For VECM, log differences of stock prices
have been employed. Table 11 includes Long run [beta] Coefficient and
its [t-statistic] for each cointegrated pair. Speed of Adjustment
Coefficients [gamma]1 and [gamma]2 are also given along with their
[t-statistic].

                                                     Speed of
                                                     Adjustment
                                   Long run [beta]   Coefficient
                                   Coefficient       [t-statistic]
    Cointegrated                   and
    Pairs          Stock Returns   [t-statistic]     [gamma]1

                                                     -0.0586
1   BAHL/FABL      D(BAHL(-1))     2.1968            [-6.69236]
                   D(FABL(-1))     [14.4977]
                                                     -0.0831
2   BAHL/HMB       D(BAHL(-1))     -5.1874           [-7.36522]
                   D(HMB(-1))      [-18.6267]        -0.0513
3   BAHL/KASBB     D(BAHL(-1))     109.2040          [-6.10595]
                   D(KASBB(-1))    [18.9841]         -0.0362
4   NBP/BAHL       D(NBP(-1))      6.2869            [-6.13575]
                   D(BAHL(-1))     [14.3942]         -0.0525
5   BAHL/NIB       D(BAHL(-1))     -26.608           [-5.86007]
                   D(NIB(-1))      [-21.3260]        -0.0476
6   BAHL/SMBL      D(BAHL(-1))     -12.255           [-5.57379]
                   D(SMBL(-1))     [-18.8430]        -0.0481
7   BAHL/SNBL      D(BAHL(-1))     123.4980          [-5.85832]
                   D(SNBL(-1))     [18.2288]
                                                     -0.051
8   BAHL/SILK      D(BAHL(-1))     16.0746           [-6.26651]
                   D(SILK(-1))     [18.2065]
                                                     -0.0599
9   ABL/BOK        D(ABL(-1))      -53.3772          [-6.47245]
                   D(BOK(-l))      [-20.6643]
                                                     -0.0563
10  ABL/BIPL       D(ABL(-1))      -16.0092          [-6.19890]
                   D(BIPL(-1))     [-20.4628]
                                                     -0.0486
11  ABL/JSBL       D(ABL(-1))                        [-5.79719]
                                   -19.0039
                   D(JSBL(-1))     [-19.8613]
                                                     -0.0591
12  ABL/MEBL       D(ABL(-1))      -6.4267           [-6.20863]
                   D(MEBL(-1))     [-20.1588]
                                                     -0.0108
13  NIB/AKBL       D(NIB(-1))                        [-1.61586]
                                   -0.07675
                   D(AKBL(-1))     [-8.21175]
                                                     -0.029508
14  SBL/AKBL       D(SBL(-1))      0.008576          [-3.18985]
                   D(AKBL(-1))     [0.83123]
                                                     -0.021053
15  BIPL/BOK       D(BIPL(-1))     -2.804577         [-2.83659]
                   D(BOK(-l))      [-18.2003]        -0.015118
16  BOP/SNBL       D(BOP(-l))      -3.184867         [-2.41349]
                   D(SNBL(-1))     [-18.8377]        -0.015176
17  BIPL/MEBL      D(BIPL(-1))     -0.484138         [-2.39326]
                   D(MEBL (-1))    [-15.0934]        -0.043057
18  FABL/HMB       D(FABL (-1))    3.041034          [-5.73502]
                   D(HMB (-1))     [16.2935]         -0.041225
19  FABL/NIB       D(FABL (-1))    -23.49303         [-5.10291]
                   D(NIB(-1))      [-20.9658]        -0.029402
20  FABL/SMBL      D(FABL(-1))     -19.06986         [-4.34719]
                   D(SMBL(-1))     [-19.09061
                                                     -0.03419
21  FABL/SILK      D(FABL(-1))     146.8413          [-5.02514]
                   D(SILK(-1))     [18.9168]
                                                     -0.008937
22  KASBB/HBL      D(KASBB(-1))    -0.014373         [-2.77087]
                   D(HBL(-1))      [-4.96063]
                                                     -0.025673
23  SNBL/KASBB     D(SNBL(-1))     -2.350703         [-3.06487]
                   D(KASBB(-1))    [-18.8064]
                                                     -0.027807
24  NBP/SILK       D(NBP(-1))                        [-4.79866]
                                   190.4803
                   D(SILK(-1))     [18.7952]
                                                     -0.033859
25  SBL/SNBL       D(SBL(-1))      -0.325853         [-3.12691]
                   D(SNBL(-1))     [-14.1252]

    Cointegrated
    Pairs          [gamma]2

1   BAHL/FABL      0.0112
                   [2.24338]
2   BAHL/HMB       -0.0005
                   [-0.07867]
3   BAHL/KASBB     -0.0020
                   [-1.35322]
4   NBP/BAHL       0.0023
                   [1.08320]
5   BAHL/NIB       -0.0014
                   [-1.23619]
6   BAHL/SMBL      -0.0008
                   [-0.49040]
7   BAHL/SNBL      -0.0033
                   [-1.452291
8   BAHL/SILK      0.0011
                   [0.79015]
9   ABL/BOK        -0.0025
                   [-1.98667]
10  ABL/BIPL       -0.0018
                   [-1.12564]
11  ABL/JSBL
                   -0.0006
                   [-0.62591]
12  ABL/MEBL       -0.0078
                   [-2.36566]
13  NIB/AKBL
                   0.0955
                   [2.95370]
14  SBL/AKBL       0.114769
                   [2.55400]
15  BIPL/BOK       0.002953
                   [0.54793]
16  BOP/SNBL       0.001631
                   [0.48197]
17  BIPL/MEBL      0.008355
                   [0.66998]
18  FABL/HMB       0.018313
                   [2.06832]
19  FABL/NIB       -0.002011
                   [-1.08006]
20  FABL/SMBL      0.000169
                   [0.072751
21  FABL/SILK      0.002288
                   [1.16274]
22  KASBB/HBL      0.009231
                   [0.16207]
23  SNBL/KASBB     0.001515
                   [0.29131]
24  NBP/SILK
                   0.000358
                   [0.91714]
25  SBL/SNBL       0.011061
                   [0.44216]

Table 12
Vector Error Correction Model for Financial Services Sector

For all the cointegrated trading pairs in Table 10 depicting
stationary residual series, the error component has been modeled
using Vector Error Correction Model (VECM) for which the results
are given in Table 12. For VECM, log differences of stock prices
have been employed. Table 12 includes Long run [beta] Coefficient
and its [t-statistic] for each cointegrated pair. Speed of
Adjustment Coefficients [gamma]1 and [gamma]2 are also given along
with their [t-statistic].

                                    Long run [beta]
    Cointegrated                      Coefficient
       Pairs       Stock Returns   and [t-statistic]

1    FDIBL/AHL     D(FDIBL(-1))        -0.019315
                    D(AHL(-1))        [-5.24008]
2    FDIBL/DEL     D(FDIBL(-1))        -2.588218
                     D(DEM-1))        [-22.7248]
3    FDIBL/JSCL    D(FDIBL(-1))        -0.038733
                    D(JSCL(-1))       [-5 68741]
4    FDIBL/FNEL    D(FDIBL(-1))        0.370759
                    D(FNEL(-1))       [16.6720]
5    FDIBL/FCSC    D(FDIBL(-1))        -0.083461
                    D(FCSC(-1))       [-4.29110]
6    FDIBL/JSIL    D(FDIBL(-1))        -0.099844
                    D(JSIU-I))        [-9.15115]
7     ESBL/AHL      D(ESBL(-1))        -0030834
                     D(AHU-1))        [-4.63482]
8     FCSC/AHL      D(FCSC(-1))        -0.173071
                     D(AHU-U)         [-16.2000]
9    AHL/KASBSL     D(AHL(-1))         -6 970244
                   D(KASBSL(-1))      [-18.5089]
10    ESBL/DEL      D(ESBL(-1))        0.876937
                    D(DEL(-1))        [10.9883]
11   IGIBL/DEL     D(IGIBL(-1))        2.414926
                     D(DEU-l))        [18.5549]
12    DEL/JSCL       D(DEU-I))         -0.034454
                    D(JSCL(-l))       [-3.43876]
13    SIBL/DEL      D(SIBL(-1))        0.267976
                    D(DEL(-1))        [3.45499]
14   ESBL/JSCL      D(ESBL(-1))        -0.051042
                    D(JSCL(-1))       [-4.00034]
15   ESBL/FCSC      D(ESBL(-1))        -0.035455
                    D(FCSC(-1))       [-0.97287]
16   ESBL/JSGCL     D(ESBL(-1))        -0.031231
                   D(JSGCL(-1))       [-4.81474]
17  ESBL/KASBSL     D(ESBL(-1))        -0.201769
                   D(KASBSL(-1))      [-5.52764]
18   ESBL/PASL      D(ESBL(-1))        0.517249
                    D(PASL(-1))       [9.29244]
19   GRYIVJSCL      D(GRYL(-1))        0.165826
                    D(JSCL(-l))       [5.13007]
20   GRYL/OLPL      D(GRYL(-1))        2.177157
                    D(OLPL(-l))       [16.5884]
21   IGIBL/JSCL    D(IGIBL(-1))        -0.023225
                    D(JSCL(-1))       [-3.157141
22   IGIBL/FNEL    D(IGIBL(-1))        0.231905
                    D(FNEL(-1))       [14 6064]
23   IGIBL/FCSC    D(IGIBL(-1))        -0 068855
                    D(FCSC(-1))       [-3.27266]
24   IGIBL/JSIL    D(IGIBL(-1))        -0 021308
                     DIISIUl))        [-1.76307]
25  IGffiL/JSGCL   D(IGIBL(-1))        -0.014201
                   D(JSGCL(-1))       [-3.74714]
26  IGIBL/KASBSL   D(IGIBL(-1))        -0032959
                   D(KASBSL(-1))      [-1.53782]
27  TRIBL/IGIBL    D(TRIBL(-1))        -2.049311
                   D<IGIBL(-l))       [-16.0130]
28   JSIL/JSCL      D(JSIL(-1))        -0 219192
                    D(JSCL(-1))       [-8.70638]
29   JSGCL/JSCL    D(JSGCL(-1))        -2.31639
                    D(JSCL(-1))       [-23.7371]
30  KASBSL/JSCL    D(KASBSL(-1))       -0.177445
                    D(JSCL(-1))       [-11.2157]
31  FCSC/KASBSL     D(FCSC(-1))        -1.303408
                   D(KASBSL(-1))      [-19.5045]
32   PASL/FCSC      D(PASL(-1))        -0.234482
                    D(FCSC(-1))        [-662978]
33   JSGCL/JSIL    D(JSGCL(-1))        -5.941587
                     D(JSIU-O)        [-23.9589]
34  KASBSL/JSIL    D(KASBSL(-1))       -0.511235
                    D(JSIL(-1))       [-18.7492]
35  KASBSL/SPLC    D(KASBSL(-1))       -4.155565
                    D(SPLC(-1))       [-21.5997]
36  TR1BL/KASBSL   D(TR1BL(-1))        -0 143323
                   D(KASBSL(-1))      [-2.80295]
37  MACBAH/SCLL    D(MCBAH(-1))        36 49555
                    D(SCLU-l))        [21 7511]
38   SIBL/PASL      D(SIBL(-1))        -0 508298
                    D(PASL(-1))       [-8.98474]
39   TRIBL/PASL    D(TRIBL(-1))        -0 043496
                    D(PASL( 1))       [-0.70553]
40   SIBL/SCLL      D(SIBL(-1))        0.369581
                    D(SCLL(-1))       [6.63143]

                       Speed of Adjustment
                   Coefficient [t-statistic]

    Cointegrated
       Pairs        [gamma]1     [gamma]2

                   -0.031812
1    FDIBL/AHL     [-3.30189]    0.054080
                   -0.137529     [0.47173]
2    FDIBL/DEL     [-7.98745]    -0.002591
                   -0.043342    [-0.11908]
3    FDIBL/JSCL    [-3.64555]    0.082940
                   -0.059747    [1.15780]
4    FDIBL/FNEL    [-5.94349]    0.059412
                   -0.045059    [1.62395]
5    FDIBL/FCSC    [-3.68319]     0054825
                    -0032884    [1.83737]
6    FDIBL/JSIL    [-3.09409]    0.056210
                   -0.027807    [1.32916]
7     ESBL/AHL     [-2.64295]    0.025670
                   -0.024423    [0.42555]
8     FCSC/AHL     [-3.21811]     0028153
                                [0.75230]
                   -0.003615
9    AHL/KASBSL    [-0.86544]    0.001527
                   -0.069215    [1.78128]
10    ESBL/DEL     [-5.52993]    0.034502
                   -0.079991     [3.71409]
11   IGIBL/DEL     [-6.58810]    0.034104
                    -0.05546    [2.45157]
12    DEL/JSCL     [-4.12513]    0.174838
                    -0.03771    [3.18455]
13    SIBL/DEL     [-3.24110]    0.011506
                   -0.029934    [1.49624]
14   ESBL/JSCL     [-2.77626]    0.021119
                   -0.029534    [0.67898]
15   ESBL/FCSC     [-2.76647]    0.021081
                   -0.030514    [1.68788]
16   ESBL/JSGCL    [-2.74668]    0.028929
                   -0.033806    [0.46042]
17  ESBL/KASBSL    [-3.01345]    0.017342
                   -0.080183    [1.24966]
18   ESBL/PASL     [-6.07900]    0 049464
                   -0.049979    [4 30419]
19   GRYIVJSCL     [-4.55651]    0.022418
                   -0.095607    [1.32287]
20   GRYL/OLPL     [-7.96700]     0003701
                   -0.047519    [0.41263]
21   IGIBL/JSCL    [-4.34022]    0.118659
                                [2.00433]
                    -0.04956
22   IGIBL/FNEL    [-5.50098]    0.087592
                   -0.024715    [2.74258]
23   IGIBL/FCSC    [-2.80272]    0.035045
                   -0.054083    [1.82772]
24   IGIBL/JSIL    [-5.01955]    0.135760
                    -0.03288     [3.51931]
25  IGffiL/JSGCL   [-3.36403]    0.153874
                   -0.033948    [1.48559]
26  IGIBL/KASBSL   [-3.55983]    0.058937
                    -0.03069     [2.67901]
27  TRIBL/IGIBL    [-3.58503]    0.003966
                    -0.0243     [1.09014]
28   JSIL/JSCL     [-1 84488]    0.012750
                   -0.010112    [0.58442]
29   JSGCL/JSCL    [-1.21334]    0.005645
                                [1.37420]
                    -0.02026
30  KASBSL/JSCL    [-2.03111]    0.047565
                   -0.014724    [1.76590]
31  FCSC/KASBSL    [-1.76841]    0.010302
                   -0.012411    [1.20194]
32   PASL/FCSC     [-1.35292]    0.022040
                   -0.003932    [1.67156]
33   JSGCL/JSIL    [-0 71101]     0002702
                   -0.013585     [1.61516]
34  KASBSL/JSIL    [-1,48783]    0.022783
                    -0.01167    [1.55469]
35  KASBSL/SPLC    [-2.48194]    0.001923
                   -0.045089    [0.73082]
36  TR1BL/KASBSL   [-3.93622]    0.036783
                   -0.030546    [3 40445]
37  MACBAH/SCLL    [-4.60142]    -0 002715
                   -0 043652    [-1.13404]
38   SIBL/PASL     [-3.53746]    -0.004458
                   -0.037536    [-0.49363]
39   TRIBL/PASL    [-4.17065]    0.023109
                    -005772     [3 .46128]
40   SIBL/SCLL     [-4.64782]    0.033901
                                [2.75978]

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