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MFC-210 NArasimhanPradhan.doc


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MFC-210 NArasimhanPradhan.doc

  1. 1. Time Varying Market Integration as a regime switching process Lakshmi Narasimhan S Fellow of XLRI XLRI, Jamshedpur, India Email: Phone: 0657-225506 Extn (254) Dr H.K. Pradhan Professor of Finance & Economics XLRI, Jamshedpur, India Email: Phone: 0657-225506 Extn (401)
  2. 2. Time Varying Market Integration as a regime switching process Abstract We attempt to estimate the likelihood of the integration of Indian stocks with the world market using Markov regime switching model. Bekaert and Harvey (1995)’s empirical model has been suitably extended to accommodate GARCH-M effect to estimate the level of integration. Given the small sample size, the maximum likelihood estimates have been estimated using an innovative grid approach. The level of integration clearly varies with the size of the stocks: larger stocks are more integrated than smaller stocks. Time varying integration plots are used to identify the change in the level of integration with important events that took place in Indian/International capital markets. 1.1. Market Integration and Asset Pricing Asset-pricing models assume a priori whether the capital markets are perfectly integrated or segmented. Or in other words, asset-pricing models can be broadly classified into (1) models that assume that the markets are integrated and (2) models that assume that the markets are segmented. This assumption is very crucial as it affects the optimal portfolio choice of investors in mean-variance framework. Stulz (1981a) defines market integration as the condition where “ two assets which belong to different countries but have the same risk with respect to some model of international asset pricing without barriers to international investment should have same expected returns”. Otherwise it would result in arbitrage situation. However the term "without barriers to international investment" is note worthy because existence of barriers in any form could prevent capital markets from being perfectly integrated even when foreign portfolio investments are allowed. These barriers can take the form of quantitative or qualitative restrictions. Differential tax rates, restrictions on the ownership, different classes of assets are the very popular form of restrictions used by the local governments to restrict foreign portfolio investments. The qualitative
  3. 3. restrictions arise because of asymmetric information between the domestic and foreign investors, unfamiliarity with the domestic market functioning. Asset pricing under perfect market integration: Studies that assume that markets are perfectly integrated, in fact, assume that such barriers do not exist and test their asset pricing models. The departures found from their hypotheses are considered evidence of the existence of barriers. Harvey (1991), Dumas and Solnik (1995), Wheatley (1988), Solnik (1983), Cho, Eun and Senbet (1986), Ferson and Harvey (1993, 1994a, 1994b), Campbell and Hamao (1992), Bekaert and Hodrick (1992) and Harvey, Solnik and Zhou (1994) are some of the very important under this category1. Transaction barriers and Market Segmentation The second group of studies that assumes that markets are segmented considers various types of barriers explicitly in their models and test for their presence. Some of the barriers that are considered are: Differential tax rates, Existence of different classes of assets, quantitative restrictions on the ownership. In the presence of differential taxes for domestic investors and foreign investors, global investors would have to optimize their investments based on the after tax returns instead of pre tax returns. This idea was incorporated by Black (1972). Many countries used to have different classes of securities for foreign portfolio investors to differentiate them from the domestic investors and fungibility was not allowed between these two classes of securities. This results in the assets on which foreign investors trade being traded at a premium compared to the shares traded by the domestic investors. Domowitz, Glenn and Madhavan (1997) estimate the cost of ownership restrictions for Mexican market where multiple classes of equity shares exist. Huge premiums that existed between the GDR/ADR issued by Indian companies and the price of the corresponding underlying shares listed in Indian stock market when two-way fungibility2 was not allowed is evidence to this phenomenon. 1 For detailed references on this please refer Harvey (1991). 2 Two-way fungibility allows the conversion of ADR/GDRs into underlying shares and reconversion of the same into depository receipts. Before June'2002, only one way fungibility was allowed, i.e. ADR/GDRs can be converted into underlying shares and the reverse was not allowed. This barred the process of arbitrage and resulted in ADR/GDRs being traded at a huge premium compared to the price of underlying
  4. 4. Besides, local Governments can enforce restrictions on the maximum foreign ownership allowed in any domestic firms thus preventing the foreign investors to hold their optimal portfolio choices. For example, in India, no single foreign institutional investor can hold more than 10% in any of the Indian companies and FIIs as a group cannot hold more than 25%. This can be increased up to 40% with the permission of the shareholders3. These ownership restrictions are explicitly modelled in Eun and Janakiraman (1986) and Alford (1990). Given these barriers to foreign investments, Errunza and Losq (1985, 1989) take asset pricing a step close to the reality where the capital markets are neither fully integrated nor fully segmented. In their model of partial integration/segmentation, there are two types of securities; eligible securities where the foreign investors can participate and the rest are ineligible securities in which only domestic investors can invest. In this situation, the eligible securities shall be priced as if the markets are perfectly integrated and the ineligible securities are priced in the segmented market framework. However, an important assumption in their model is that that the extent of integration/segmentation of the capital market remains constant. The qualitative barriers arise because the foreign investors would be unfamiliar with the local market functioning and there could be asymmetric information between the local and foreign investors or the cost of obtaining information is significant enough to give different returns for foreign and domestic investors. This result in a situation termed as ‘home bias’ in the literature, where in portfolio of foreign investors is dominated by assets from their respective domestic markets in spite of superior returns that can be achieved through international diversification. In the section that follows we focus on the studies that look into the integration of emerging markets. 1.2. Emerging markets and Time varying Market Integration share listed in Indian stock market. 3 Even there are differences in voting rights also thus making the foreign investment funds to be just an investment agencies without any interest for ownership control.
  5. 5. Emerging markets provide a very good case for the testing of capital market integration and its effects. Most of the emerging markets started liberalizing their capital markets (including allowing foreign portfolio investment) from late eighties through early nineties. However, the two main hurdles in empirical testing these propositions are (1) dating the liberalization and (2) time varying integration of capital markets. Authors who have studied the impact of liberalization on emerging markets have handled this issue by using various mile stone events as a proxy for starting date of liberalization viz., listing of first depository receipts, launching of first country fund, starting of foreign portfolio investments etc (Henry, 2000a and 2000b, Bekaert and Harvey, 2000). Alternatively, testing for structural breaks in the return generating process to see their coincidence with any of the milestone events is done (Bekaert, Harvey and Lumsdaine, 2002) The second hurdle arises because the capital market integration due to liberalization measures is very smooth. Even after the domestic markets are opened up, foreign investors would take some time to get acclimatized with the local market conditions. In the case of Indian market, FIIs were allowed officially from Sept 1992 but the investments started flowing in only after several months (Shah and Sivsankar, 2000). Also reversion of liberalization policies by the respective Governments can also hamper integration of markets. After the South East Asian crisis, the Thailand Government have imposed new restrictions on foreign investments to strengthen their financial system. Another pointer towards time varying market integration is the empirical finding that capital markets become more integrated during highly volatile periods (or contagion effect). The big market crash of 1987 in USA and its repercussion on various markets in Europe and Asia is the best indication of the integration of capital markets. Bekaert and Harvey (1995) address these empirical issues in their model for time varying world market integration based on Hamilton's regime switching model. They show that
  6. 6. emerging markets4 indeed become more integrated with the world market over time. The measure of integration/segmentation in their study is the probability/likelihood of the capital market being in the integrated/segmented state. The ‘time varying integration’ issue is answered by allowing the likelihood of integration to vary over time. Since the integration of the market is determined from the behavior of the ex post data, the issue of dating of liberalization also do not arise. Our study, take Bekaert and Harvey (1995) forward to test the integration at portfolio level. The following section discuss about the empirical studies on Indian securities market where inferences can be drawn about the market integration. 1.3. Indian Studies on market integration Indian studies related to capital market integration can be classified into two types. The first group of studies examines the stocks that are listed in multiple stock exchanges and compare their returns. Under the perfectly integrated market condition the returns from the stocks on these exchanges should mimic each other. Listing of depository receipts on American and European stock exchanges provide an ideal opportunity to test this. The second group of studies focuses on testing whether the factors that determine stock market returns are the same. Or in other words, they test whether there are causal linkages between the markets. Kiran and Mukhopadhyay (2002) finds that there is significant one way causal effect from Nasdaq to NSE-Nifty. Similarly, Pradhan and Narasimhan (2003) finds evidence for causal linkages between various emerging and developed markets in the Asia-Pacific region suggesting that market in Asia-Pacific Basin become more integrated. However, these studies are silent about the time varying nature of the market integration. Our study would fill this gap, by giving how the market integration of five size-based portfolios have changed over the time. This study is organized as follows. The section that follow details the empirical specification of our asset-pricing model along with the assumptions made. The third 4 Beakert and Harvey (1995) considers two emerging markets: Chile, Columbia, Greece, India, Jordan, Korea, Malaysia, Mexico, Nigeria, Taiwan, Thailand and Zimbabwe.
  7. 7. section would describe the data used for the study and provide some descriptive statistics. The empirical findings are discussed in section 4 followed by concluding remarks. Empirical Model Specification Under perfectly integrated market condition, returns can be written in the following form under conditional CAPM framework: Et-1 [ ri,t ] = λi, t-1 Covt-1 [ ri,t , rw,t ] (1) Where Et-1 [ ri,t ] is the expected excess return on asset i and rw,t is the return on world market portfolio. Covt-1 is the conditional covariance of the portfolio returns with the world market portfolio and λt-1 is the conditionally expected world price of covariance risk at time t-1 and can be written as the ratio of the excess return on the world market E[rw,t ] portfolio to the variance of the returns of the world market portfolio ( ). In case Var[rw,t ] of segmented market, the world market portfolio would be replaced by domestic market portfolio and the return on any asset i can be written as: Et-1 [ ri,t ] = λi, t-1 Covt-1 [ ri,t , rd,t ] (2) Bekaert and Harvey (1995) parameterize the returns in the follow to estimate the time varying market integration as follows: Et-1 [ ri,t ] = φi, t-1 λi, t-1 Covt-1 [ ri,t , rw,t ] + (1- φi, t-1) λi, t-1 Covt-1 [ rd,t ] (3) Where φi, t-1 is the econometrician's estimation of time varying likelihood of the market being integrated and takes the value between 0 and 1. An unobserved state variable S it takes the value of 1 in case of market being integrated and 2 in case of market being segmented. By defining Sit as a two state markov process, the likelihood of market
  8. 8. integration can be estimated. Now the conditional probability of market integration, transition probabilities can be written as: φi, t-1 = Prob [Sit = 1/ Zt-1 ] (4) In the end analysis, φi, t-1 gives an estimation for the measure of the extent of integration if Sit = 1 stands for integration. In addition, the transition probabilities i.e. the probability of being in State 1 at time t conditional to being in State 1 at time t-1. Or in other words, these probabilities tell us how ‘sticky’ these states are. P = Prob [St=1/ St-1 =1] (5) Q = Prob [St=2/ St-1 =2] (6) In general, the value of P and Q would be typical high (close to 1), because market cannot fluctuate between integrated and segmented states frequently. Bekaert and Harvey (1995) tests their model in two different ways: (1) by allowing the transition probabilities to remain the same over the time (2) Allowing changes in transition probabilities over the time by parameterizing them as a logistic function on certain information variables. In our study, we would be using the constant transition probability because of two reasons (1) With a smaller sample size, the increase in the number of parameters by allowing P&Q to change would deteriorate the finite sample properties (2) Even when the transition probabilities are kept constant over the time, the likelihood of integration would change over time. We use the recursive representation for the estimation of φi, t-1 given by Gray (1995): φi, t-1 = (1-Q) + (P-Q-1) [ f1, t-1 φi, t-2 / (f1, t-1 φi, t-2 + f2, t-1 (1-φi, t-2)] (7) where fj,t is the likelihood at time t conditional on being in regime j and time t-1 information, Zt-1. The second moments of the returns need to be parameterized for the
  9. 9. estimation of the model. The discussion in the next section would make clear the presence of heterskedasticity in the data being used. Considering path dependent heterskedasticity models could render the model intractable. To tackle this problem, Bekaert and Harvey (1995) uses ARCH (k) for the second moments and prespecify the weights attached to them. Fortunately, Gray (1997) later offers a solution to make the conditional second moments path independent and this is used in our GARCH specification.5 Now our empirical specification can be written as: Ri, t = [ri,t , rw,t]’ where ri ,t = φ i, t -1λt −1Cov[ ri .t , rw,t ] + (1 - φ i, t -1 )λi ,t −1Vart −1 [ri ,t ] + e i, t (8) rw,t = λ t -1Vart −1 [rw,t ] + e w,t (9) Define et = [ei,t,ew,t]’ which can be written as: φ i ,t −1 = φ i, t -1eti + (1 - φ i, t -1 )ets (10) The variance and covariance equations are defined in the BEKK format (Baba, Engle, Kraft and Kroner, 1989) as given below: ∑ it = C i + (B i ) ' ∑ it −1 ( B i ) + (C i ) ' et (C i ) (11) ∑ ts = C s + (B s ) ' ∑ it −1 ( B s ) + (C s ) ' et (C s ) (12) To reduce the proliferation of number of parameters, we assume that the A,B and C arrays defined above are symmetric. This reduces the number of parameters to be estimated to reasonable level. Moreover, the testing is done for individual portfolios thus optimizing on the number of parameters. This follows from our earlier finding that the 5 For detailed discussion about this problem please refer to page no 34-36 of Gray (1997).
  10. 10. price of risk varies across portfolios. By testing for individual portfolios, we are not constraining them to be the same for all the portfolios. The model is estimated using maximum likelihood method and the log likelihood function can be written as: log L( Ri ,T ) = ∑ T=1 log{φ i ,t −1 g1,t + (1 - φ i, t -1 ) g 2,t } where t (13) −1 / 2  1  g1,t = (2π ) -1 ∑ it exp − (eti (∑ it ) −1 eti  (14)  2  −1 / 2  1  g 2,t = (2π ) -1 ∑ ts exp − (ets (∑ ts ) −1 ets  (15)  2  The initial values for the parameters can be defined as the unconditional probability values or it can be specified as 0.5 (equal probability for integration as well as segmentation). However, it should be noted that the final distribution is a mixture of two normal distribution. Hence depending on the mean/variance of the two distributions, it can have more than one peaks. The typical hill climbing techniques that are used for maximum likelihood estimation might give us wrong results. Therefore Bekaert and Harvey (1995) use different sets of initial values to see whether the results obtained are global optimum. In additional to doing that, we find out the log likelihood values are behaving for combinations of initial values. Then these values are plotted as grids and this will show us the combination of initial values for which the log likelihood values are global optimum. In our case, we found that the log likelihood values are more sensitive to the initial values of the transitional probabilities and hence different combination of transition probabilities are used to find the global optimum. Specification Tests and Diagnostics
  11. 11. To test the performance of the model, we regress the disturbance vector et on the information available at time T-1. In our case, we can consider the returns at time T-1 as the information variable. For the model to be performing well, the disturbance vector should be orthogonal to the lagged returns. The diagnostic tests consider the R2 obtained from the regression and the Wald statistic for the joint testing of all the coefficients obtained from the regression. Data Description and Summary Statistics We use monthly data from 1990:01 - 2001:12 for 100 stocks listed in Bombay Stock Exchange during the period 1990-2001. These 100 stocks are selected based on the following criteria: (1) The stocks selected should have been listed in Bombay Stock Exchange for the entire period 1990:01 - 2001:12. (2) There should be at least one trading in every month during the time period. (3) The final 100 stocks were selected based on the number of trading days. Five value-weighted portfolios were constructed by value ranking of the companies on the basis of market capitalization at the end of every year and splitting these companies into value-ranked quintiles, and then forming five portfolios based on value weights within a quintile. The monthly adjusted closing price data for the stocks were collected from the data published by the 'Centre for Monitoring Indian Economy' (CMIE). The call money rate published by the Reserve Bank of India (2001) was used as the short term risk free rate 6. For the market return, we have used the monthly return on the value-weighted index, BSE-National Index of the Bombay Stock Exchange. BSE-National Index comprising 100 stocks is less volatile and broader and hence would serve better as market proxy compared to BSE-30 or NSE-507. 6 Three-month treasury bill rates are generally used for this purpose. Since it is not available for the whole period call money rates have been used. 7 NSE-50 has been back worked till 1990 and is provided by the National Stock Exchange.
  12. 12. Table2 gives the basic summary statistics such as mean, standard deviation, skewness and Kurtosis apart from the average market capitalization for the size based portfolios. For the portfolio with the largest stocks (Portfolio I), the average Mcap is 758 billion and the portfolio with smallest stocks (Portfolio V) has an average Mcap of 21 billion. The range of the average market capitalization obtained justifies one of the purpose of this study: to infer size effect. The mean return and the standard deviation are typical of an emerging market return: very high. The mean return is highest for Portfolio 5 (5.55%) and Portfolio 1 has the highest standard deviation of the returns (32.45%) and even the market proxy has a standard deviation of 9.6%. Table 2: Summary Statistics for the Portfolio Returns The statistics are based on monthly data from 1995:02 to 2001:12 (143 observations). The country returns are in excess of the risk free short-term interest rate. Portfolio 1 is the portfolio of largest stocks and Portfolio 5 is the portfolio of smallest stocks. The average value of the Market capitalization is given in Indian Rupee Billion. The test statistic is the Kolmogrov-Smirnov test statistic for normality of the return series for a significance level of 10%. Average Mean Std. Test Variable Skewness Kurtosis Market cap Return Dev. Statistic Portfolio 1 757.7988 0.0342 0.3245 6.16696 59.9114 0.256 Portfolio 2 153.7983 0.0257 0.1424 2.3441 10.6222 0.155 Portfolio 3 77.7109 0.0306 0.1292 1.0769 3.6458 0.079 Portfolio 4 51.1562 0.0367 0.1382 1.8344 10.8454 0.126 Portfolio 5 21.2809 0.0555 0.1360 0.9184 1.8240 0.095 Domestic 0.0016 0.0962 0.4110 0.9568 0.063 Market World 0.0052 0.042 -0.4353 0.4571 Market Note: The test statistic more than 0.10 depicts rejection of normality
  13. 13. Another regular feature that is observed on emerging market return data is non-normality. The statistics provided on the skewness and kurtosis justifies that. Besides, we have conducted Kolmogorov-Smirnov test for the normality on the data and the results are reported for 10% significance level in the last column of Table 1. The normality is rejected for Portfolio1, 2 and 4 at conventional levels and for Portfolio 3, 5 and the market return they are rejected at 5% significance level. This justifies our use of Generalized Method of Moments (GMM) procedure to estimate the model. Table 3 and Table 4 reports the auto correlation properties of the returns, as well as the correlation between the portfolio returns and the instrumental variables respectively. The autocorrelation coefficients and the Ljung-Box Q statistics provide evidence that the Indian stock returns are highly persistent. The correlation between portfolio returns and the market in Table 4 reveals high correlation but counter intuitive. Portfolio 1 has the lower correlation coefficient (0.50) with the market compared to smaller stock portfolios. One would expect larger stock to move more closely with the market. This could be because our Portfolio 1 is more volatile compared to the market proxy, which is a value- weighted index of 100 stocks. The cross correlation between the portfolios are also very high (Table 3). It also reveals another interesting detail. The strength of correlation with other portfolios decreases with the decrease in size. To understand this more we find the cross correlation coefficients with lags because it is quite possible that the larger stocks reflect market information quickly and smaller stocks take more time to reflect market information due to poor liquidity. The results obtained confirm our doubts. Table 3: Autocorrelation and Ljung-Box Q statistics This table presents the Autocorrelation coefficients at various lags and the Ljung-Box Q statistics are presented in parentheses. The statistics that are significant at 10% level are marked with *. Variable ρ1 ρ2 ρ3 ρ4 ρ 12 ρ 24
  14. 14. 0.0661 -0.1644 -0.1330 0.0138 -0.0117 -0.0081 Portfolio 1 [0.4238] [0.0994]* [0.0646]* [0.1224] [0.0434]* [0.2762] 0.2245 -0.0353 -0.1057 -0.0996 -0.0527 0.0487 Portfolio 2 [0.0066]* [0.0230]* [0.0267]* [0.0303]* [0.0019]* [0.0001]* 0.1567 -0.0009 0.0124 -0.1498 -0.0557 -0.0201 Portfolio 3 [0.0582]* [0.1663] [0.3066]* [0.1378] [0.1137] [0.1664] 0.1232 -0.0382 -0.0086 -0.0614 -0.0839 0.0449 Portfolio 4 [0.1365] [0.2964] [0.4856] [0.5568] [0.1342] [0.3383] 0.1755 0.0609 -0.0138 -0.1006 -0.0544 -0.0055 Portfolio 5 [0.0338]* [0.0801]* [0.1663] [0.1593] [0.6788] [0.6218] Domestic 0.1404 0.0311 -0.1350 -0.1652 0.0258 0.0519 Market [0.0896]* [0.2206] [0.1259] [0.0440]* [0.0076]* [0.0002]* World -0.0509 -0.1080 -0.0116 -0.0478 0.0423 0.1085 Market [0.5377] [0.3504] [0.5483] [0.6519] [0.5426] [0.6420] Table 4 Autocorrelation and Ljung-Box Q statistics for squared returns This table presents the Autocorrelation coefficients at various lags for the squared returns and the Ljung-Box Q statistics are presented in parentheses. The statistics that are significant at 10% level are marked with *. Variable ρ1 ρ2 ρ3 ρ4 ρ 12 ρ 24 Portfolio 1 -0.0069 0.1059 0.0018 0.0043 -0.0160 -0.0095 Portfolio 2 0.22578 0.1192 -0.0348 -0.0284 -0.0356 0.0750 Portfolio 3 0.0361 0.0357 -0.0255 -0.0511 -0.0312 -0.0256 Portfolio 4 0.0007 0.0091 -0.0080 -0.0058 -0.0094 0.0057 Portfolio 5 -0.0022 -0.0023 -0.0030 -0.0038 -0.0036 -0.0037 Domestic 0.2558 0.2189 -0.0312 -0.0276 0.1685 0.0622 Market World 0.0979 0.1120 -0.0058 0.0888 0.0028 -0.1088 Market Table 5: Correlation between portfolio returns Variable P1 P2 P3 P4 P5 P1 - 0.7195 0.5558 0.3578 0.3566
  15. 15. P2 - 0.8742 0.7628 0.7127 P3 - 0.8363 0.8146 P4 - 0.8488 P5 - Market Proxy 0.5040 0.7847 0.8265 0.8092 0.7679 Empirical Results This section discusses the empirical estimation of the likelihood of integration of the size based portfolio. As mentioned above, the parameters are estimated using the grid approach. Appendix 1 gives the changes in the P, Q and φ for various combinations of initial parameters. We have varied P & Q systematically over the range 0.9 to 0.99 with small increments (0.3) to estimate value of the likelihood function. The range of 0.9 to 0.99 is used because the transition probabilities are expected to be in the higher range because the markets cannot switch between integrated and segmented states quite frequently. The initial value for φ is given as 0.5, which means that there, is equal chance for being in integrated state as well as segmented state (Please also see foot note 8). The maximum value of likelihood function obtained through the step described above is given in the tables given below8. Table 6 presents the estimation of the transition probability (P & Q) along with the estimation of the likelihood of integration. P in our case is the transition probability for being in State 1 (i.e. integration) and Q is the respective probability for being in State 2 (i.e. segmentation). The last column gives the average value of φ for the whole time period. The figures obtained reveal a very interesting pattern. The transition probability P reduces consistently with the reduction in the size of the portfolio. This can be explained intuitively. The bigger size portfolios consists of stocks that are actively traded by the 8 As a further refinement, for this combination of P & Q, we then change the initial estimate of φ and see whether there is change in the likelihood function. Change of φ do not have much impact on increasing the value of the likelihood function.
  16. 16. domestic investors as well as the foreign investors. Because of this, these stocks have higher probability of being integrated. Hence the bigger portfolios have higher value of P compared to smaller portfolios. The transition probability Q is very high for all the portfolios which shows that segmented states are very sticky for all the portfolios. The estimation of ex post likelihood of integration also tells us that the level of integration goes down when the size of the portfolio decreases. Bigger stocks are more integrated with the world market compared to smaller stocks. This is also very intuitive. Table 6: Estimation of the Model with Constant Transition Probabilities Portfolio Transition Probabilities φ P Q Portfolio 1 0.9064 0.9842 0.0997 Portfolio 2 0.6886 0.9592 0.1236 Portfolio 3 0.6501 0.9674 0.0784 Portfolio 4 0.7236 0.9727 0.0724 Portfolio 5 0.0612 0.9833 0.0235 Table 7: Model Diagnostics statistics: Portfolio R2 Wald Statistic Portfolio 1 0.0017 1.2015 [0.3131] Portfolio 2 0.0123 2.7635 [0.0301]* Portfolio 3 0.0058 1.9112 [0.1121] Portfolio 4 -0.0162 0.9810 [0.4201] Portfolio 5 -0.0989 1.6898 [0.1559] Table 7 presents the diagnostic statistics for the performance of the model for all the portfolios. The R 2 of the regression of the model errors on the past information is very negligible. We have used lagged returns of the portfolios as the past information because as per the assumptions of our model, the model errors should be orthogonal to the past returns. The last column provides wald statistic for the joint hypothesis that coefficients obtained from the above regression is zero. The wald statistics also confirm that the regression coefficients obtained are not significantly different from zero.
  17. 17. Figure 1: Plot of likelihood of market integration Portfolio 1 1.00 0.75 0.50 0.25 0.00 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Portfolio 2 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
  18. 18. Portfolio 3 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Portfolio 4 0.75 0.50 0.25 0.00 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 Portfolio 5 0.016696 0.016688 0.016680 0.016672 0.016664 0.016656 0.016648 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001
  19. 19. Figure 1 gives a plot on how the level of integration changes over time. The plots for Portfolio 1 and Portfolio 2 looks similar to the plot obtained by Bekaert and Harvey (1995) for the period up to 1995. For Portfolio 1,2 and 3 (larger stock portfolios) show that they are integrated with the world market during the year 1994. It may be noted that that active participation of foreign portfolio investments in India started during this period only. Also Portfolio 1 and Portfolio 2 shows a spike during the 1992. This period coincides with the securities market scam in India and the stocks comprising Portfolio 1 and 2 showed witnessed extreme volatility. Another important event that did not have any significant impact conspicuously on the level of integration is the South East Asian Crisis during 1997. Though the quantum of foreign portfolio investments to Indian capital market have increased multifold post South Asian crisis that does not seem to have impact on the level of integration. Conclusion We have attempted to estimate the likelihood of integration of size-based portfolios of Indian stocks with the world market using markov regime switching model. Given smaller sample size and lesser likelihood of integration, we use a grid approach to estimate the maximum likelihood estimates. We find that that there is a clear pattern on the integration of size based portfolios. The transition probability of being in integrated state and the average level of integration decrease with the reduction in the size of the portfolios. Also the segmented state seems to be a very sticky stage. Plot of time varying integration of these portfolios were drawn and it was checked whether the periods of higher integration coincide with any of major mile stone event in the Indian /International capital market. References Alexander, G J., Eun, C. S. and Janakiraman, S., 1988, "International listings and stock returns: some empirical evidence", Journal of financial and Quantitative analysis, 23, 135-51.
  20. 20. Baba, Yoshihisa, Robert F. Engle, Dennis F. Kraft and Kenneth F. Kroner, 1989, “Multivariate simultaneous generalized ARCH”, working paper, University of California, San Diego, California. Bekaert, Geert, and Robert Hodrick, 1992, “Characterizing predictable components in excess returns on equity and foreign exchange markets”, Journal of Finance, 47, 467-509 Bekaert, G. and Harvey, Campbell R, 1995, "Time-Varying World Market Integration", Journal of Finance, 50, 2, 403-445. Bekaert, G, and Harvey, Campbell R, 2000, "Foreign speculators and emerging equity markets", Journal of Finance, 55, 2, 565-614. Bekaert, Geert, Harvey, Campbell, R., and Robin Lumsdaine, 2002, “ Dating the integration of world capital markets”, Journal of Financial Economics, 65:2, 2002, 203-249 Black, F., 1972, "Capital Market Equilibrium with Restricted Borrowing", Journal of Business, 45, July, 444-454. Campbell, John Y., and Yasushi Hamao,1989, “Predictable bond and stock returns in the United States and Japan: A study of long-term capital market integration”, working paper, Princeton University. Campbell, J.Y., and J.H.Hentschel, 1992, "No News is Good News: An Asymmetric Model of Changing Volatility in Stock Returns", Journal of Financial Economics, 31, 281-318. Cho, Chinhyung D., Cheol S. Eun and Lemma W. Senbet, 1986, “International arbitrage pricing theory: An empirical investigation”, Journal of Finance, 41, 313-330 Choe, Hyuk, Kho, Bong-Chan and Stulz, R.M., 1998, "Do foreign investors destabilize stock markets - The Korean experience in 1997", NBER working paper. Domowitz, I, Glen J and Madhavan, A., 1997, "Market Segmentation and Stock Prices: Evidence from an Emerging Market", Journal of Finance, 52, 1059-1085. Dumas, Bernard and Bruno, Solnik, 1995, “The world price of foreign price risk”, Journal of Finance, 50, 445-479. Errunza, V. and Losq, E., 1985, "International asset pricing under mile segmentation: theory and test", Journal of Finance, 40, 105-24.
  21. 21. Errunza, V. and Losq, E., 1989, "Capital flow controls, international asset pricing, and investors’ welfare: a multi country framework", Journal of Finance, 44, 1025-38. Eun, C.S. and Janakiraman, S., 1986, "A model of international asset pricing with a constraint on the foreign equity ownership", Journal of Finance, 41, 897-914. Ferson, Wayne E., and Harvey, Campbell, Harvey, R., 1993, “The risk and predictability of international equity returns, Review of Financial Studies, 6, 527-566. Ferson, Wayne E., and Harvey, Campbell, Harvey, R., 1994a, “Sources of risk and expected returns in global equity markets”, Journal of Banking and Finance, 18, 775-803. Ferson, Wayne E., and Harvey, Campbell, Harvey, R., 1994b, “An exploratory investigation of the fundamental determinants of national equity market returns, in Jeffrey Frankel Ed.: The Internationalization of Equity Markets, University of Chicago Press, Chicago, IL, 59-138 Gray, Stephen F., 1995, “An analysis of conditional regime switching models”, working paper, Duke University. Gray, Stephen F., 1997, “Modeling the conditional distribution of interest rates as a regime-switching process”, Journal of Financial Economics, 42, 27-62. Harvey, Campbell R., 1991, “The world price of covariance risk”, The Journal of Finance 46, 111-157. Henry, Peter B., 2000a, Stock Market Liberalization, Economic Reform and Emerging Equity Prices, Journal of Finance, 55,2, 529-564. Henry, Peter B., 2000b, "Do Stock Market Liberalizations Cause Investment Booms?", Journal of Financial Economics, 58, 301-334. Kim, E. Han and Singhal, Vijay, 2000, Stock Market Openings: Experience of Emerging Economies, Journal of Business, 73, 1, 25-66. .Harvey, Campbell R., Bruno, H., Solnik and Guofu Zhou, 1994, “What determines expected international asset returns?”, Working paper, Duke University, Durham, N.C. Kiran, K.K. and Mukhopadyay C., 2002, " Equity Market Interlinkages: Transmission of volatility a case study of US and India", NSE research initiative, Paper No. 16. Pradhan, H.K., and Narasimhan, S.L, 2003, Stock Price Behavior in India since liberalization, Asia-Pacific Development Journal, 9, 83-106.
  22. 22. Shah, Ajay and Sivkumar, Sivaprakasam, 2000, “Changing Liquidity in the Indian equity market”, Emerging Markets Quarterly, 4(2), Summer 2000, 62-71. Solnik, Bruno, 1983, “The relationship between stock prices and inflationary expectations: The international evidence”, Journal of Finance, 38, 35-48. Stulz, Rene, 1981, “A model of international asset pricing”, Journal of Financial Economics, 9, 383-406. Wheatley, Simon, 1988, “Some tests of international equity integration”, Journal of Financial Economics, 21, 177-212. Annexure 1 – Grid Approach for finding Maximum Likelihood Estimators Description of Portfolio Initial Values Estimated Values
  23. 23. P Q P Q Likelihood Function 0.90 0.813 0.974 799.619 0.93 0.808 0.974 765.305 0.90 0.96 0.840 0.974 795.882 0.99 0.796 0.974 798.316 0.90 0.9064 0.984 800.120 0.93 0.8252 0.974 796.027 0.93 0.96 0.8343 0.974 797.938 0.99 0.8150 0.975 796.856 0.90 0.832 0.975 796.817 0.93 0.820 0.974 797.650 0.96 0.799 0.975 799.336 0.96 0.99 0.805 0.974 797.491 Portfolio 1 0.90 0.823 0.974 797.661 0.93 0.824 0.974 796.911 0.96 0.797 0.974 797.123 0.99 0.99 0.816 0.975 795.371 Description of Portfolio Initial Values Estimated Values P Q P Q Likelihood Function 0.90 0.720 0.963 738.059 0.93 0.704 0.964 740.179 0.90 0.96 0.703 0.961 741.540 0.99 0.708 0.960 738.833 0.90 0.726 0.963 737.284 0.93 0.718 0.960 742.193 0.93 0.96 0.688 0.959 742.252 0.99 0.493 0.933 736.385 0.90 0.713 0.956 741.510 0.93 0.715 0.957 741.868 0.96 0.718 0.962 737.806 0.96 0.99 0.681 0.960 740.268 Portfolio 2 0.90 0.717 0.801 739.973 0.93 0.717 0.860 740.876 0.96 0.699 0.950 739.521 0.99 0.99 0.728 0.956 739.398 Description of Portfolio Initial Values Estimated Values
  24. 24. P Q P Q Likelihood Function 0.90 0.525 0.979 698.688 0.93 0.334 0.971 698.114 0.90 0.96 0.547 0.972 698.379 0.99 0.623 0.965 702.890 0.90 0.602 0.965 699.494 0.93 0.389 0.866 698.897 0.93 0.96 0.243 0.930 690.450 0.99 0.565 0.978 699.441 0.90 0.549 0.967 698.885 0.93 0.535 0.960 700.681 0.96 0.547 0.959 700.309 0.96 0.99 0.650 0.967 703.559 Portfolio 3 0.90 0.535 0.968 699.176 0.93 0.574 0.974 699.669 0.96 0.403 0.973 701.150 0.99 0.99 0.376 0.972 699.741 Description of Portfolio Initial Values Estimated Values P Q P Q Likelihood Function 0.80 0.680 0.979 691.488 0.83 0.178 0.898 688.607 0.80 0.86 0.517 0.978 688.677 0.89 0.695 0.982 687.081 0.80 0.608 0.978 687.715 0.83 0.83 0.86 0.622 0.973 684.198 0.89 0.401 0.967 685.740 0.80 0.63 0.988 690.496 0.83 0.168 0.989 691.495 0.86 0.723 0.972 698.830 0.8 0.89 0.624 0.979 690.444 Portfolio 4 0.80 0.80 0.367 0.996 665.755 0.80 0.86 0.050 0.984 682.494 0.70 0.70 0.0313 0.988 681.005 Portfolio 5 0.70 0.95 0.0612 0.9833 683.982