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The trading behavior of foreign, domestic institutional, and domestic individual investors: Evidence from the Taiwan stock market
Pacific-Basin Finance Journal 20 (2012) 745–754
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The trading behavior of foreign, domestic institutional, and domestic individual investors: Evidence from the Taiwan stock market☆ Sue-Jane Chiang a,⁎, Li-Ju Tsai b, Pei-Gi Shu a, Show-Lin Chen c a b c
Department of Business Administration, Fu Jen Catholic University, New Taipei City, Taiwan Department of Finance and International Business, Fu Jen Catholic University, New Taipei City, Taiwan Department of Economics, Fu Jen Catholic University, New Taipei City, Taiwan
a r t i c l e
i n f o
Article history: Received 11 July 2011 Accepted 2 March 2012 Available online 10 March 2012 JEL classification: G11 G15 Keywords: Trading behavior Threshold model Foreign investors Domestic institutions Domestic individual investors
a b s t r a c t In this paper, we apply the threshold cointegration model of Hansen and Seo (2002), incorporating differences in the nonlinear behavior of investors across regimes. An examination of the trading behavior of foreign, domestic institutional, and domestic individual investors in Taiwan revealed no predominance among the three types of investors. When the market was near equilibrium, the purchases of domestic individual investors positively impacted stock prices. This finding, which is consistent with Choe et al. (2005), suggests that domestic individual investors have an edge in investment performance over other types of investors. However, when the market departed substantially from equilibrium, the purchases of foreign and domestic institutional investors predicted a rise in stock prices. On the other hand, domestic individuals traded at worse stock prices; these prices tended to fall (rise) after the purchase (sale). © 2012 Elsevier B.V. All rights reserved.
1. Introduction The debate about whether domestic or foreign investors have an information advantage over the other is far from over. One argument is that foreign investors are better traders because of their presumed information advantage. Grinblatt and Keloharju (2000), Seasholes (2000), and Froot and Ramadorai (2008) interpreted the predictive power of information flow as providing foreign investors with an information ☆ The authors thank the anonymous reviewer and the Editor (S. Ghon Rhee) for valuable comments. Chiang would also like to thank the Fu Jen Catholic University and the National Science Council of R.O.C. for the research support. We accept responsibilities for all remaining errors. ⁎ Corresponding author at: Department of Business Administration, Fu Jen Catholic University, New Taipei City, Taiwan. Tel.: +886 2 29053935; fax: +886 2 2908 9219. E-mail address: [email protected] (S.-J. Chiang). 0927-538X/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.pacfin.2012.03.002
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advantage On the other hand, Brennan and Cao (1997), Hau (2001), Dvorak (2005), and Choe et al. (2005) reported the opposite. Brennan and Cao (1997) argued that an information disadvantage on the part of foreign investors can turn them into trend followers, buying when the market rises and selling when it falls. Dvorak (2005) attributed this inferior trading performance of foreign investors to an information disadvantage, whereas Choe et al. (2005) attributed it to poor timing of their trades. Recent studies further explore the possible factors that might reconcile the contradictory findings. For example, Choe et al. (2005) find that whether foreign investors have better information or not is strongly related to their trading size: they were at a disadvantage for medium and large trades but not for small trades. Agarwal et al. (2009), who classified executed orders as initiated and non-initiated, found that foreign investors underperformed domestic investors for non-initiated orders but outperformed them for initiated orders. Moreover, they attributed the overall underperformance of foreign investors to aggressiveness rather than to an information disadvantage or timing of trades. Taechapiroontong and Suecharoenkit (2011) found that foreign investors performed best when buying medium- and large-cap stocks during a bull market. Bae et al. (2011) attributed foreign investors' superior performance to their ability to discern whether a company's stock was good or bad. The evidence suggests that foreign investors prefer large-cap stocks with high dividends, individual investors prefer small-cap, high-leveraged, low-dividend-paying stocks, and local institutions tend to buy small-cap, low-leveraged stocks. Institutional investors, both foreign and domestic, behave like shortterm momentum traders by pursuing growth (value) stocks, whereas individual investors trade like contrarians. Nevertheless, the classification of stock prices or firm size is subject to arbitrarily chosen threshold values that can create bias. We therefore used the threshold cointegration model developed by Hansen and Seo (2002) to investigate threshold effects and non-linear dynamic behavior in the Taiwan stock market. We empirically examined the existence of threshold cointegration in the trading behavior of foreign, domestic institutional and individual investors. We then applied the threshold cointegration model to examine the causal relationships between the stock price index and the trading behavior for different types of investors. For our study, we selected a sample of stocks listed on the Taiwan stock market to contrast the trading behavior and performance of different types of investors. Our reasons for selecting the Taiwan stock market are as follows. First, whether to open their domestic market to foreign investors remains a topic of controversy for governments of countries with emerging markets. Some might argue that openness to foreign investors enhances the efficiency of domestic stock markets, whereas others have been concerned that the induction of sophisticated foreign investors sweeps all the profits away from domestic investors. Second, ever since the abolishment of the Qualified Foreign Institutional Investor (QFII) system, foreign investors have increased their ownership of firms listed on the Taiwan stock exchange, which has increased their influence on both individual stock prices and overall market momentum. 1 This makes it worthwhile to investigate the trading behavior and performance of different types of investors. Our main findings can be easily summarized as follows. First, neither foreign, domestic, nor individual investors were found to be predominant in the market. Second, when the market is around equilibrium, domestic individual investors' buy-in causes the stock prices to rise, consistent with the finding of Choe et al. (2005) and Taechapiroontong and Suecharoenkit (2011) that individual domestic investors had an edge over other types of investors with respect to trading performance. However, when the market departed markedly from equilibrium, purchases by foreign and domestic institutional investors had a positive impact on stock prices, but the trading of individual investors had a negative impact on them. An important difference between our study and prior ones can be briefly summarized as follows. First, Bae et al. (2011) noted that both foreign and local institutional investors behave like short-term momentum traders, whereas individual investors trade like contrarians. This conclusion is similar in spirit to our finding that when the market was not in equilibrium, institutional investors' purchases had a positive impact on stock prices, whereas individual investors' purchases had a negative impact on them. Second, like Brennan and Cao (1997) and Seasholes (2000), we examined foreign investors' trading to judge whether they have been trend followers and to determine from the predictability of their trading on subsequent stock prices whether they have an information advantage. Nevertheless, because we recognize that the buying and selling behavior of 1 The percentage of total trades on the Taiwan stock market made by foreign investors increased from 2.41% in 1999 to 18.40% in 2006 (see Table 1 for detailed statistics).
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Table 1 Trading ratio-breakdown by investor types and years. Year
Foreign investors %
Domestic institutions %
Domestic individual investors %
1999 2000 2001 2002 2003 2004 2005 2006
2.41 3.63 5.9 7.65 10.65 12.5 17.87 18.4
9.36 10.27 9.69 10.05 11.51 11.56 13.29 11.04
88.23 86.1 84.41 82.3 77.84 75.94 68.84 70.56
investors might be asymmetric, we chose to analyze the two types of behavior separately. Third, although we followed Seasholes (2000) in choosing the Taiwan stock market for our survey, we recognize that over time foreign institutional investors have become increasingly important as their trading in the market has increased compared to other investors. Finally, to the best of our knowledge, our study is the first to analyze the non-linear dynamic trading behavior of investors using the threshold cointegration model of Hansen and Seo (2002). The rest of the paper is organized as follows. Section 2 describes the data. Section 3 reports the method and results of the empirical investigation. Our conclusions are presented in Section 4. The details of the empirical models based on Hansen and Seo (2002) are given in the Appendix A. 2. The data The QFII system has been in effect in Taiwan since 1991. In 2003, the reviewing process was changed from a permit system to a registration system. This innovation simplified the application process for foreigners investing in Taiwan's stock market. Table 1 shows that the proportion of foreign investors' trades to total trades in the Taiwan market increased from 2.41% in 1999 to 18.4% in 2006. In contrast, the proportion of individual investors’ trades decreased from 88.23% in 1999 to 70.56% in 2006. Finally, domestic institutional investors' proportion of total trades remained at around 10% throughout the sampling period. Our sampling period for collecting data on stock transactions in the Taiwan Stock Exchange was from January 1999 through October 2006. The data, which were taken from the Taiwan Economic Journal (TEJ), contain the following variables for each trading day: (i) the stock-price index (S_P), and (ii) buy and sell trading volumes for domestic institutional investors, individual investors, and foreign investors (DI_B, DI_S, IND_B, IND_S, FI_B and FI_S). The statistics are summarized in Tables 2 and 3. All variables are transformed by natural logarithms. 3. Empirical investigation 3.1. Empirical results of the Johansen (1991) cointegration Before conducting the cointegration analysis, the stationarity of the variables had to be examined. We evaluated the unit-root hypothesis by the conventional ADF (Dickey and Fuller, 1979) test. The results Table 2 Summary statistics. Stock price index Mean Median S.D. Min. Max.
6191.41 6001.26 1292.7 3446 10202
Foreign investors (in million NT dollars)
Domestic institutions (in million NT dollars)
Domestic individual investors (in million NT dollars)
Buy
Sell
Net flow
Buy
Sell
Net flow
Buy
Sell
Net flow
9498.49 7661.50 7041.6 190 135109
8130.18 6732.50 5713.8 87 44000
1368.31 905.00 5301.6 − 23772 125288
5639.54 5178.50 2626.2 241 18674
5748.49 5406.00 2424.4 463 29878
− 108.95 − 108.00 1993.4 − 20053 10837
18680.69 15810.50 10164.4 1610 72703
21349.48 18427.00 10610.1 4727 77067
− 2668.78 − 2204.00 2839.3 − 21465 7062
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Table 3 Data description-breakdown by investor types, trading, and years. Year
Stock price index
1999 2000 2001 2002 2003 2004 2005 2006
7419.05 7837.69 4907.43 5225.61 5161.90 6033.78 6092.27 6754.26
Foreign investors (in million NT dollars)
Domestic institutions (in million NT dollars)
Domestic individual investors (in million NT dollars)
Buy
Sell
Net flow
Buy
Sell
Net flow
Buy
Sell
Net flow
3905.80 5392.84 5943.56 6826.86 9868.14 12658.78 15240.21 18873.86
2652.20 4857.10 4688.39 6714.40 7663.57 11522.94 12327.63 16988.12
1253.60 535.74 1255.16 112.46 2204.58 1135.85 2912.58 1885.74
5878.91 6314.36 4360.84 5293.20 5610.14 6202.27 5625.58 5791.18
5882.23 6635.94 4360.66 5255.20 5513.22 6316.09 5906.60 6030.94
− 3.32 − 321.59 0.18 38.00 96.91 − 113.82 − 281.01 − 239.76
27213.1 24229.0 16924.4 18731.1 15920.3 17249.2 12487.9 14843.9
30955.1 28323.1 19750.2 21701.6 17906.2 19315.3 14100.0 16453.5
− 3741.98 − 4094.09 − 2825.82 − 2970.46 − 1985.88 − 2066.09 − 1612.19 − 1609.61
from the ADF test (Table 4) indicate that the original data failed to reject the unit-root hypothesis at the 5% level. However, the first difference of data did reject the unit-root hypothesis, which implies that all of the seven processes are integrated of order one. Because the data were non-stationary, we applied Johansen's (1991) cointegration test, which was developed for linear models. The results are summarized in Table 5. Of interest are the pairings of stock prices from the stock price index (S_P) with the buy and sell volumes for foreign investors (FI_B, FI_S), domestic institutional investors (DI_B, DI_S), and domestic individual investors (IND_B, IND_S), respectively. We used the information criterion proposed by Schwarz (1978) to select the lag order. Based on the trace and maximum eigenvalues, the hypothesis of no cointegration was rejected for all these pairs, as shown in Table 5. However, the null hypothesis that the cointegration vector is less than or equal to 1 could not be rejected at the 5% level. It is therefore reasonable to conclude that there is one cointegration vector for all three VAR systems. According to Balke and Fomby (1997), the Johansen test can have low power if there is threshold cointegration. Therefore, to determine whether cointegration exists among the variables in the threshold nonlinear model, we performed Enders and Siklos (2001) F-test, which is reported in the last column of Table 5. The result indicates that the null hypothesis of no cointegration can be rejected in all three cases. Overall, the table indicates that the cointegration of the buy and sell trading volumes with stock prices holds for both the linear and threshold models. We next derived estimates from Johansen's (1991) linear error-correction models (Table 6). The lag order was found to be 1 for all three pairs. The error terms for all these pairs are significant at the 5% level. These results are consistent with those of the cointegration test reported in Table 5. For the foreign investors, the first panel in Table 6 shows that there was a two-direction causal relationship between their buy and sell volumes, but there was only one-direction causality from the stock
Table 4 ADF unit root test.
S_P(1) FI_B(5) FI_S(5) DI_B(4) DI_S(5) IND_B(4) IND_S(5)
Level data
First differenced data
− 1.731 − 0.049 − 0.098 − 0.439 − 0.241 − 0.346 − 0.328
− 49.499*** − 40.599*** − 40.254*** − 31.123*** − 33.725*** − 36.595*** − 36.358***
Notes: (1) FI_B and FI_S represent the buy-in and the sell-out of foreign investors, respectively. DI_B and DI_S represent the buy-in and sell-out of domestic institutional investors, respectively. IND_B and IND_S represent the buy-in and sell-out of domestic individual investors, respectively. The stock price index is denoted as S_P. (2) The numbers in parentheses are the appropriate lag order of the AR process chosen by Schwarz (1978) information criterion. (3) The numbers in the Table are the ADF, τμ, statistics. (4) The critical values of different significant levels, i.e., 1%, 5% and 10%, are − 3.458, -2.8733 and − 2.573, respectively. (5) ‘***’ indicates significant at the 1% level of significance.
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Table 5 Johansen Cointegration Test and Threshold Cointegration Test. λMax
TRACE
Enders and Siklo's F statistics
Null hypothesis
γ≤2
γ≤1
γ=0
γ=2
γ=1
γ=0
γ=0
(S_P, FI_B, FI_S) (S_P, DI_B, DI_S) (S_P, IND_B, IND_S)
3.411 (3.841) 1.065 (3.841) 2.953 (3.841)
15.452 (15.495) 14.810 (15.495) 14.968 (15.494)
105.77** (29.797) 38.009** (29.797) 74.281** (29.797)
3.411 (3.841) 1.065 (3.841) 2.953 (3.841)
12.049 (14.265) 13.745 (14.265) 12.015 (14.265)
90.309** (21.132) 23.200** (21.132) 59.313** (21.132)
277.032** 162.323** 151.021**
Notes : (1) γ is the number of cointegrated vector. Trace and λMax are Johansen's (1991) Trace and maximum eigenvalue test, respectively. (2) The numbers in parentheses are the 5% finite sample critical values which are constructed from the asymptotic critical values from MacKinnon et al. (1999). (3) The F statistics are Enders and Siklos' (2001) test the null of no threshold cointegration, and the 5% and 10% critical values for the F statistic are 5.87 and 4.92, respectively. (4) ‘**’ indicates significant at a 5% significance level.
price to both the buy and sell volumes. The two-way negative feedback effect between foreign investors' buy and sell volumes implies that they bought (sold) more if they sold (bought) less on the preceding day. This means that they did not overreact by adjusting their trading positions in the opposite direction. Moreover, they bought (sold) more if stock prices rose (fell) on the preceding day. This means that the foreign investors followed a momentum strategy, a conclusion that is also indicated by the findings from Bae et al.'s (2011) investigation of the Korean stock market. Finally, we conclude that the trading practices of foreign investors, whether buying or selling, had no leading effect on the Taiwan stock price index. For domestic institutional investors, the results shown in the second panel of Table 6 are similar to those for foreign investors. Again, there was a feedback relationship between these investors' buy and sell volumes, but there was only one-way causality from the stock price to the purchase volume. The meaning and implications of these findings are the same as those for foreign investors. However, the situation for domestic individual investors was somewhat different. As shown in the last panel of Table 6, stock prices influenced these investors' buy volumes, which in turn influenced their sell volumes. However, there was a positive feedback relationship between their sell volumes and the stock price index. In other words, both buy and sell volumes increase (decreased) if the stock price index rose (fell) on the previous day. One implication of this positive relation between these individual investors' sell volumes and the stock price index is that they received a lower return when they sold their stocks. 3.2. Empirical results of threshold cointegration Hansen and Seo (2002)'s supLM threshold test was employed to examine the necessity of using a threshold model. 2 The results in the first column of Table 7 indicate that the threshold effect is significant at the 5% level for both domestic institutional investors and domestic individual investors, and it is significant at the 10% level for foreign investors. These results imply that the conventional linear error-correction model is not appropriate. The results of Wald test revealed that the short-term dynamic coefficients are significantly different across the different regimes for each of the three cointegration systems. This evidence further illustrates the inappropriateness of using a linear error-correction model. Next, we estimated the threshold error-correction model to look for possible causal relationships. Table 8 summarizes the estimates from the threshold cointegration model for the foreign investors' buy and sell volumes and the stock price index. Regime I is defined as the values of the error-correction terms being less than or equal to the estimates of the threshold values (i.e. |ECMt − 1| ≤ 0.647). The other cases form Regime II. 3 Because, for foreign investors, the deviation from the long-term cointegration 2
The methodology is illustrated in the Appendix A. In the cointegation system for foreign institutional investors, ECMt− 1 = FI_Bt− 1 − 0.78FI_St− 1 − 0.22S_Pt− 1: And we modify Hansen and Seo (2002)'s model by adopting |ECMt-1| instead of ECMt-1 as the threshold variable in our empirical studies. 3
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Table 6 Johansen's (1991) Error-Correction Model.
Foreigners' trading and stock price index
ECMt − 1 Constant ΔFI_Bt-1 ΔFI_St-1 ΔS_Pt-1
Domestic institutions' trading and stock price index
ECMt − 1 Constant ΔDI_Bt-1 ΔDI_St-1 ΔS_Pt-1
Domestic individuals' trading and stock price index
ECMt − 1 Constant ΔIND_Bt-1 ΔIND_St-1 ΔS_Pt-1
ΔFI_Bt
ΔFI_St
ΔS_Pt
− 0.293 (0.028)** 0.0003 (0.010) − 0.205 (0.029)** − 0.107 (0.026)** 1.967 (0.681)**
0.212 (0.029)** 0.0003 (0.011) − 0.096 (0.030)** − 0.293 (0.027)** − 2.246 (0.712)**
0.005 (0.001)** 0.0001(0.0004) 0.0002 (0.001) − 0.0002(0.001) 0.018 (0.024)
ΔDI_Bt
ΔDI_St
ΔS_Pt
− 0.540 (0.035)** − 0.0002 (0.008) − 0.009 (0.028) − 0.265 (0.032)** 2.774 (0.635)**
0.227 (0.027)** − 0.0002 (0.006) − 0.109 (0.022)** − 0.272 (0.025)** 0.346 (0.505)
0.008 (0.002)** 0.0002(0.0004) 0.002 (0.001) 0.002 (0.001) − 0.044 (0.028)
ΔIND_Bt
ΔIND_St
ΔS_Pt
− 0.085 (0.043)** − 0.0002 (0.005) − 0.337 (0.035)** 0.072 (0.045) 3.688 (0.347)**
− 0.137 (0.041)** − 0.0003 (0.005) − 0.166 (0.033)** − 0.164 (0.043)** 1.739 (0.334)**
− 0.040 (0.003)** 0.0001 (0.0003) 0.002 (0.002) 0.009 (0.003)** 0.137 (0.023)**
Note: (1) FI_B and FI_S represent the buy-in and the sell-out of foreign investors, respectively. DI_B and DI_S represent the buy-in and sell-out of domestic institutional investors, respectively. IND_B and IND_S represent the buy-in and sell-out of domestic individual investors, respectively. ECM is the error-correction term and the stock price index is denoted as S_P. (2) The numbers in parentheses are the standard errors of the estimated coefficients. (3) ** means significant at a 5% significance level.
relationship is small for the buy and sell volumes as well as the stock price index, Regime I was assumed to be in a state of near equilibrium. On the other hand, for Regime II the market was assumed to be far from equilibrium. The findings shown in Table 8 illustrate that there was a two-way, short-term dynamic causal relationship between foreign investors’ buy and sell volumes in both regimes. In Regime I (II), the stock prices led foreign investors to buy (sell). However, their purchases increased the stock prices, leading to decreased selling in Regime II. Because there was a two-way negative feedback relation between foreign investors' buying and selling in both Regimes I and II, they bought (sold) more if they had sold (bought) less on the previous day. That is, they followed a consistent trading strategy, regardless of whether their position was short or long; they rarely adjusted their position. In addition, in Regime I, they bought more (less) if the stock price index rose (fell) on the previous day. Their purchasing reflected a momentum strategy, as did their selling in Regime II. Finally, their transactions did not affect domestic stock prices in Regime I. In contrast, their purchases did have a positive effect on stock price index in Regime II. These results imply that foreign investors paid less when they purchased Taiwan stocks. Table 9 reports the estimates from the threshold cointegration model for domestic institutional investors' buy and sell volumes and the stock price index. The results indicate a two-way causal relationship between
Table 7 Test for threshold effect.
Foreigners' trading and stock price index Domestic institutions' trading and stock price index Domestic individuals' trading and stock price index
SupLM test for threshold effect
Wald test for the equality of the short-run dynamic coefficients at different regimes.
Statistics
P-value
Statistics
P-value
31.206* 49.861** 46.647**
0.060 0.000 0.000
156.484** 48.424** 27.185**
0.000 0.000 0.0001
Note: ** and * means significant at 5% and 10% significance levels.
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Table 8 Threshold Error-Correction Model (foreign investors). REGIME I : |ECMt − 1| ≤ 0.647
ECMt − 1 Constant ΔFI_Bt−1 ΔFI_St−1 ΔS_Pt−1
REGIME II: |ECMt − 1| > 0.647
ΔFI_Bt
ΔFI_St
ΔS_Pt
ΔFI_Bt
ΔFI_St
ΔS_Pt
− 0.323** (0.031) − 0.004 (0.011) − 0.207** (0.030) − 0.097** (0.027) 2.384** (0.706)
0.142** (0.032) − 0.009 (0.011) − 0.098** (0.030) − 0.286** (0.028) − 1.160 (0.728)
− 0.005** (0.001) 0.0001 (0.0004) − 0.0003 (0.001) − 0.0004 (0.001) 0.009 (0.025)
0.052 (0.035) − 0.200** (0.012) − 0.260** (0.033) − 0.112** (0.031) − 0.752 (0.792)
1.215** (0.037) − 0.614** (0.012) − 0.266** (0.035) − 0.149** (0.032) − 10.013** (0.835)
− 0.003** (0.001) 0.004** (0.0003) 0.007** (0.001) − 0.001 (0.001) 0.067** (0.024)
Note: (1) FI_B and FI_S represent the buy-in and the sell-out of foreign investors, respectively. ECM is the error-correction term, ECMt− 1 = FI_Bt− 1 − 0.78FI_St− 1 − 0.22S_Pt− 1. The stock price index is denoted as S_P. (2) The numbers in parentheses are the standard errors of the estimated coefficients. (3) The numbers in parentheses are the standard errors of the estimated coefficients, and ** means significant at a 5% significance level.
buy and sell volumes in Regime I (|ECMt − 1| ≤ 0.049)4 However, there were only one-way causal relationships from stock prices to purchases in Regime I and from selling to buying in Regime II. Moreover, there was a feedback effect between domestic institutional investors' purchases and stock prices in Regime II. The two-way negative feedback effect between buying and selling in Regime I means that domestic institutional investors purchased (sold) more if they sold (purchased) less on the previous day, provided that the market was near equilibrium. It also indicates that these investors pursued a consistent trading strategy at such times, regardless of whether their position was short or long. In both regimes, domestic institutions purchased more (less) when the stock price index rose (fell) on the previous day, representing a consistent momentum strategy. Finally, in Regime I, domestic institutions’ trading behavior had no effect on domestic stock prices, but their purchases had a positive effect on stock prices in Regime II, meaning that they paid less when they bought stocks; they could also make money when the market was not in equilibrium, because of the effect of their behavior on domestic stock prices in Regime II. The estimates from the threshold cointegration model for domestic individual investors are shown in Table 10. There was bi-directional causality between these investors' purchases and stock prices in both regimes, and between buy and sell volumes in Regime I (|ECMt − 1| ≤ 0.039). 5 In contrast, there were only one-way causal relationships from stock prices to sales volume in Regime I and from sales volume to stock prices in Regime II. As the stock price index had a positive effect on individual investors' buy and sell volumes in Regime I, both the purchases and sales of these investors increased (decreased) when the stock price index rose (fell) on the previous day. Note that the investors' transactions had opposite effects on stock prices in the two regimes. In Regime I, the purchases had a positive effect on stock prices, implying that the investors paid less when they purchased stocks and thus made money by affecting stock prices when the market was near equilibrium. In Regime II, the investors' purchases (sales) had a negative (positive) effect on stock prices, meaning that they paid more when purchasing, and they received less when selling in Regime II. Individual investors could not make money by affecting stock prices when the market was far from equilibrium. In general, the trading patterns of foreign investors and domestic institutions were similar when the market was near equilibrium: they both followed a consistent trading strategy and they did not overreact in trading. They can be characterized as momentum traders, and their trading had no effect on domestic stock prices. On the other hand, the purchases of domestic individual investors had a positive effect on stock prices in Regime I, which resulted in their making money when the market was near equilibrium. The trading patterns and performance of the three types of investors were quite different when the market was not in equilibrium. Purchases by the foreign and domestic institutional investors had a positive effect on stock prices, meaning that these investors paid less when they purchased stocks. In contrast, 4 5
In the cointegation system for domestic institutional investors, ECMt− 1 = DI_Bt− 1 − 0.81DI_St− 1 − 0.13S_Pt− 1. In the cointegation system for domestic individual investors, ECMt− 1 = IND_Bt− 1 − 1.11IND_St− 1 − 0.01S_Pt− 1.
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Table 9 Threshold Error-Correction Model (domestic institutional investors). REGIME I : |ECMt − 1| ≤ 0.049
ECMt − 1 Constant ΔDI_Bt−1 ΔDI_St−1 ΔS_Pt−1
REGIME II : |ECMt − 1| > 0.049
ΔDI_Bt
ΔDI_St
ΔS_Pt
ΔDI_Bt
ΔDI_St
ΔS_Pt
− 0.636** (0.074) − 0.056** (0.023) − 0.117** (0.043) − 0.201** (0.049) 2.204** (1.044)
0.034 (0.061) − 0.087** (0.019) − 0.196** (0.036) − 0.181** (0.040) 0.769 (0.859)
0.005 (0.003) − 0.001 (0.001) − 0.002 (0.002) 0.001 (0.002) − 0.026 (0.046)
− 0.487** (0.072) − 0.022 (0.022) 0.072** (0.042) − 0.323** (0.047) 3.094** (1.008)
0.230** (0.055) 0.002 (0.017) − 0.050 (0.032) − 0.358** (0.036) 0.356 (0.771)
0.008** (0.003) − 0.0002 (0.0010) 0.005** (0.002) 0.002 (0.002) − 0.068 (0.044)
Note: (1) DI_B and DI_S represent the buy-in and sell-out of domestic institutional investors, respectively. ECM is the error-correction term, ECMt− 1 = DI_Bt− 1 − 0.81DI_St− 1 − 0.13S_Pt− 1. The stock price index is denoted as S_P. (2) The numbers in parentheses are the standard errors of the estimated coefficients. (3) The numbers in parentheses are the standard errors of the estimated coefficients and ** means significant at 5% significance level.
the purchases (sales) of domestic individual investors had a negative (positive) effect on stock prices, meaning that these investors paid more when they purchased stocks and received less money when they sold stocks. When the market was not in equilibrium, however, the foreign and domestic institutional investors could make money through their trading behavior, but the domestic individual investors risked losing money.
4. Conclusion Foreign investors have comprised more and more of the total market trading in Taiwan ever since the abolishment of the Qualified Foreign Institutional Investors (QFII) system in 2003. There is no consensus on its role being able to enhance market efficiency or to siphon profit from their local counterparts. In this paper, we apply the threshold cointegration model of Hansen and Seo (2002), incorporating differences in the nonlinear behavior of investors across regimes. Our results are easily summarized as follows. First, neither foreign, domestic institutional, nor domestic individual investors were found to be predominant in the market. Second, when the market was near equilibrium, domestic individual investors' purchases caused the stock prices to rise. However, when the market departed markedly from equilibrium, purchases by foreign and domestic institutional Table 10 Threshold Error-Correction Model (domestic individual investors). REGIME I : |ECMt − 1| ≤ 0.039
ECMt − 1 Constant ΔIND_Bt−1 ΔIND_St−1 ΔS_Pt−1
REGIME II : |ECMt − 1| > 0.039
ΔIND_Bt
ΔIND_St
ΔS_Pt
ΔIND_Bt
ΔIND_St
ΔS_Pt
− 0.826** (0.079) 0.009 (0.014) − 0.511** (0.053) 0.128** (0.069) 5.218** (0.533)
− 0.131** (0.074) − 0.006 (0.014) − 0.356** (0.050) − 0.002 (0.065) 3.400** (0.501)
− 0.036** (0.006) 0.003** (0.001) 0.012** (0.004) − 0.001 (0.005) 0.108** (0.039)
− 0.676** (0.075) − 0.023** (0.014) − 0.217** (0.051) 0.043 (0.065) 2.494** (0.505)
0.036 (0.073) − 0.026** (0.013) − 0.032 (0.050) − 0.263** (0.064) 0.631 (0.494)
− 0.034** (0.005) − 0.003 (0.001) − 0.006** (0.003) 0.016** (0.004) 0.145** (0.031)
Note: (1) IND_B and IND_S represent the buy-in and sell-out of domestic individual investors, respectively. ECM is the errorcorrection term, ECMt− 1 = IND_Bt− 1 − 1.11IND_St− 1 − 0.01S_Pt− 1. The stock price index is denoted as S_P. (2) The numbers in parentheses are the standard errors of the estimated coefficients. (3) The numbers in parentheses are the standard errors of the estimated coefficients and ** means significant at a 5% significance level.
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investors had a positive impact on stock prices, but the trading of individual investors had a negative impact on them. We have shown that segregating two trading regimes can help reconcile the controversy about how foreign investors perform. We did not bet for or against foreign investors; rather, we found that foreign (as well as domestic) institutional investors performed quite well when the market deviated markedly from equilibrium. In contrast, the domestic individual investors outperformed their foreign and domestic institutional counterparts when the market was near equilibrium. Further studies could profitably explore the reasons why institutional investors are better able than other investors to affect the market when it is not in equilibrium. Appendix A. Methodology A.1. Threshold Cointegration Balke and Fomby (1997) demonstrated that the two-step version of the cointegration test developed by Engle and Granger (1987) has good power when applied to a non-linear threshold model. Using the two-step cointegration method, Enders and Siklos (2001) modified the second step of the conventional AR model by adopting a threshold autoregressive (TAR) model, in which an asymmetric adjustment of the first-order autoregressive coefficient under different regimes is allowed. The TAR model is as follows: x1t ¼ β1 þ β2 x2t þ β3 x3t þ ωt ; Δωt ¼ It ρ1 ωt−1 þ ð1−I t Þρ2 ωt−1 þ
ðA:1Þ p−1 X
βi Δωt−i þ εt ;
ðA:2Þ
i¼1
and
It ¼
1 if ωt1 ≥τ ; 0 if ωt1 bτ
ðA:3Þ
where x1t represents the stock prices; x2t is the trading purchase volume, x3t is the trading sales volume, and ωt is the equilibrium error in the cointegration model. The model is the same as that of Engle and Granger (1987) if there is no threshold effect in Eq. (A.2). The null hypothesis of no threshold cointegration implies ρ1 = ρ2 = 0. To examine the null hypothesis, Enders and Siklos (2001) proposed two statistics: t-Max and F. Their simulation results demonstrate that F has higher power than t-Max. We therefore employed F to test our hypothesis of no threshold cointegration. A.2. Estimation and Testing for Threshold ECM As there was a threshold effect in the cointegration model, we proceeded to derive estimates from the threshold error-correction model (ECM). Hansen and Seo (2002) proposed a method for obtaining the maximum likelihood estimate (MLE) for the threshold ECM. Let xt = {x1t, x2t, x3t} be a 3-dimensional I (1) process cointegrated with a 3 × 1 cointegrating vector β, and let ωt − 1(β) = β′xt− 1 denote the error-correction term. The two-regime threshold ECM can then be written as: ( Δxt ¼
A′ 1 X t−1 ðβÞ þ ut ; if ωt1 ðβÞ ≤τ ; A′ 2 X t−1 ðβÞ þ ut ; if ωt1 ðβÞ > τ
ðA:4Þ
Hansen and Seo (2002) performed an evenly-spaced grid search of the two-dimensional space (β, τ) over the regions [τL, τU] and [βL, βU], conditional onπ0 ≤ Pr(ωt − 1 ≤ τ) ≤ 1 − π0, where π0 > 0 is the selected trimming parameter. 6 In our empirical analysis, we set π0 = 0.05 and then constructed the interval [τL, τU] ~ 6σ~ β , where β ~ is from the previous inequality. Following Hansen and Seo (2002), we set ½β ; β ¼ β L
6
Our empirical studies used 200 gridpoints over the regions [τL, τU] and [βL, βU], respectively.
U
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~ We let the estimates of β Johansen's estimated cointegrating vector and σ~ β is the standard deviation of β. ^ and τ^ respectively) be the values of (β, τ) in this grid search over ([βL, βU] and [τL, τU]) respectively, and τ (β which yielded the maximum value of the concentrated likelihood function.7 We then obtained the estimated ^ 2 β; ^ 1 β; ^ τ^ and A ^ τ^ , using the OLS regression of Eq. (A.4) for the subsamples, where coefficient vectors, A ^ ≤τ^ and ωt−1 β ^ > τ^ . ωt−1 β The hypothesis of no threshold cointegration is rejected if the hypothesis A1' = A2' is rejected. It is worth noting that the threshold parameter is not identified under the null hypothesis of no threshold cointegration. To solve this problem, Hansen and Seo (2002) introduced a SupLM statistic to test for a threshold effect in the model.8 The SupLM statistic for testing the hypothesis of A1' = A2' is defined as: SupLM ¼
~ τ ; sup LM β;
τ L ≤τ≤τU
~ τ is the heteroskedasticity-robust LM-like statistic as defined by Hansen and Seo (2002). The where LM β; critical values of SupLM can be calculated by the “fixed regressor bootstrap” or “parametric residual bootstrap” methods. For our empirical study, we only reported the critical value of the “parametric residual bootstrap,” as the two critical values approximate each other. References Andrews, D.W.K., Ploberger, W., 1994. Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383–1414. Agarwal, S., Faricloth, S., Rhee, S.G., 2009. Why do foreign investors underperform domestic investors in trading activities? Evidence from Indonesia. Journal of Finance Market 12, 32–53. Bae, S., Min, J.H., Jung, S., 2011. Trading behavior, performance, and stock preference of foreigners, local institutions, and individual investors: evidence from the Korean stock market. Asia-Pacific Journal of Financial Studies 40, 199–239. Balke, N.S., Fomby, T.B., 1997. Threshold cointegration. International Economic Review 38, 627–645. Brennan, M.J., Cao, H., 1997. International portfolio flows. Journal of Finance 52, 1851–1880. Choe, H., Kho, B.C., Stulz, R.M., 2005. Do domestic investors have an edge? The trading experience of foreign investors in Korean. Review of Financial Studies 18 (3), 795–829. Dickey, D.A., Fuller, W.A., 1979. Distribution of the estimates for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–431. Dvorak, T., 2005. Do domestic investors have an informational advantage? Evidence from Indonesia. Journal of Finance 60 (2), 817–839. Enders, W., Siklos, P.L., 2001. Cointegration and threshold adjustment. Journal of Business & Economic Statistics 19, 166–176. Engle, R.F., Granger, C.W.J., 1987. Co-integration and error correction: representation, estimation, and testing. Econometrica 55, 251–276. Froot, K.A., Ramadorai, T., 2008. Institutional portfolio flows and international investments. Review of Financial Studies 21 (2), 937–971. Grinblatt, M., Keloharju, M., 2000. The investment behavior and performance of various investor types: a study of Finland's unique data set. Journal of Financial Economics 55, 43–67. Hansen, B.E., Seo, B., 2002. Testing for two-regime threshold cointegration in vector error-correction models. Journal of Econometrics 110, 293–318. Hau, H., 2001. Location matters: an examination of trading profits. Journal of Finance 56, 1959–1983. Johansen, S., 1991. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580. MacKinnon, J.G., Haug, A., Michelis, L., 1999. Numerical distribution functions of likelihood ratio tests for cointegration. Journal of Applied Econometrics 14 (5), 563–577. Schwarz, G., 1978. Estimating the dimension of a model. The Annals of Statistics 6, 461–464. Seasholes, M., 2000. Smart foreign traders in emerging markets. Working paper. Harvard Business School. Taechapiroontong, N., Suecharoenkit, P., 2011. Trading performance of individual, institutional, and foreign investors: evidence from the stock market of Thailand. International Research Journal of Finance and Economics 75, 157–174.
7 8
^ is more accurate than β ~. Hansen and Seo (2002) demonstrated that β See Andrews and Ploberger (1994) for the rationale and justification of this testing strategy.
Contents lists available at SciVerse ScienceDirect
Pacific-Basin Finance Journal journal homepage: www.elsevier.com/locate/pacfin
The trading behavior of foreign, domestic institutional, and domestic individual investors: Evidence from the Taiwan stock market☆ Sue-Jane Chiang a,⁎, Li-Ju Tsai b, Pei-Gi Shu a, Show-Lin Chen c a b c
Department of Business Administration, Fu Jen Catholic University, New Taipei City, Taiwan Department of Finance and International Business, Fu Jen Catholic University, New Taipei City, Taiwan Department of Economics, Fu Jen Catholic University, New Taipei City, Taiwan
a r t i c l e
i n f o
Article history: Received 11 July 2011 Accepted 2 March 2012 Available online 10 March 2012 JEL classification: G11 G15 Keywords: Trading behavior Threshold model Foreign investors Domestic institutions Domestic individual investors
a b s t r a c t In this paper, we apply the threshold cointegration model of Hansen and Seo (2002), incorporating differences in the nonlinear behavior of investors across regimes. An examination of the trading behavior of foreign, domestic institutional, and domestic individual investors in Taiwan revealed no predominance among the three types of investors. When the market was near equilibrium, the purchases of domestic individual investors positively impacted stock prices. This finding, which is consistent with Choe et al. (2005), suggests that domestic individual investors have an edge in investment performance over other types of investors. However, when the market departed substantially from equilibrium, the purchases of foreign and domestic institutional investors predicted a rise in stock prices. On the other hand, domestic individuals traded at worse stock prices; these prices tended to fall (rise) after the purchase (sale). © 2012 Elsevier B.V. All rights reserved.
1. Introduction The debate about whether domestic or foreign investors have an information advantage over the other is far from over. One argument is that foreign investors are better traders because of their presumed information advantage. Grinblatt and Keloharju (2000), Seasholes (2000), and Froot and Ramadorai (2008) interpreted the predictive power of information flow as providing foreign investors with an information ☆ The authors thank the anonymous reviewer and the Editor (S. Ghon Rhee) for valuable comments. Chiang would also like to thank the Fu Jen Catholic University and the National Science Council of R.O.C. for the research support. We accept responsibilities for all remaining errors. ⁎ Corresponding author at: Department of Business Administration, Fu Jen Catholic University, New Taipei City, Taiwan. Tel.: +886 2 29053935; fax: +886 2 2908 9219. E-mail address: [email protected] (S.-J. Chiang). 0927-538X/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.pacfin.2012.03.002
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advantage On the other hand, Brennan and Cao (1997), Hau (2001), Dvorak (2005), and Choe et al. (2005) reported the opposite. Brennan and Cao (1997) argued that an information disadvantage on the part of foreign investors can turn them into trend followers, buying when the market rises and selling when it falls. Dvorak (2005) attributed this inferior trading performance of foreign investors to an information disadvantage, whereas Choe et al. (2005) attributed it to poor timing of their trades. Recent studies further explore the possible factors that might reconcile the contradictory findings. For example, Choe et al. (2005) find that whether foreign investors have better information or not is strongly related to their trading size: they were at a disadvantage for medium and large trades but not for small trades. Agarwal et al. (2009), who classified executed orders as initiated and non-initiated, found that foreign investors underperformed domestic investors for non-initiated orders but outperformed them for initiated orders. Moreover, they attributed the overall underperformance of foreign investors to aggressiveness rather than to an information disadvantage or timing of trades. Taechapiroontong and Suecharoenkit (2011) found that foreign investors performed best when buying medium- and large-cap stocks during a bull market. Bae et al. (2011) attributed foreign investors' superior performance to their ability to discern whether a company's stock was good or bad. The evidence suggests that foreign investors prefer large-cap stocks with high dividends, individual investors prefer small-cap, high-leveraged, low-dividend-paying stocks, and local institutions tend to buy small-cap, low-leveraged stocks. Institutional investors, both foreign and domestic, behave like shortterm momentum traders by pursuing growth (value) stocks, whereas individual investors trade like contrarians. Nevertheless, the classification of stock prices or firm size is subject to arbitrarily chosen threshold values that can create bias. We therefore used the threshold cointegration model developed by Hansen and Seo (2002) to investigate threshold effects and non-linear dynamic behavior in the Taiwan stock market. We empirically examined the existence of threshold cointegration in the trading behavior of foreign, domestic institutional and individual investors. We then applied the threshold cointegration model to examine the causal relationships between the stock price index and the trading behavior for different types of investors. For our study, we selected a sample of stocks listed on the Taiwan stock market to contrast the trading behavior and performance of different types of investors. Our reasons for selecting the Taiwan stock market are as follows. First, whether to open their domestic market to foreign investors remains a topic of controversy for governments of countries with emerging markets. Some might argue that openness to foreign investors enhances the efficiency of domestic stock markets, whereas others have been concerned that the induction of sophisticated foreign investors sweeps all the profits away from domestic investors. Second, ever since the abolishment of the Qualified Foreign Institutional Investor (QFII) system, foreign investors have increased their ownership of firms listed on the Taiwan stock exchange, which has increased their influence on both individual stock prices and overall market momentum. 1 This makes it worthwhile to investigate the trading behavior and performance of different types of investors. Our main findings can be easily summarized as follows. First, neither foreign, domestic, nor individual investors were found to be predominant in the market. Second, when the market is around equilibrium, domestic individual investors' buy-in causes the stock prices to rise, consistent with the finding of Choe et al. (2005) and Taechapiroontong and Suecharoenkit (2011) that individual domestic investors had an edge over other types of investors with respect to trading performance. However, when the market departed markedly from equilibrium, purchases by foreign and domestic institutional investors had a positive impact on stock prices, but the trading of individual investors had a negative impact on them. An important difference between our study and prior ones can be briefly summarized as follows. First, Bae et al. (2011) noted that both foreign and local institutional investors behave like short-term momentum traders, whereas individual investors trade like contrarians. This conclusion is similar in spirit to our finding that when the market was not in equilibrium, institutional investors' purchases had a positive impact on stock prices, whereas individual investors' purchases had a negative impact on them. Second, like Brennan and Cao (1997) and Seasholes (2000), we examined foreign investors' trading to judge whether they have been trend followers and to determine from the predictability of their trading on subsequent stock prices whether they have an information advantage. Nevertheless, because we recognize that the buying and selling behavior of 1 The percentage of total trades on the Taiwan stock market made by foreign investors increased from 2.41% in 1999 to 18.40% in 2006 (see Table 1 for detailed statistics).
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Table 1 Trading ratio-breakdown by investor types and years. Year
Foreign investors %
Domestic institutions %
Domestic individual investors %
1999 2000 2001 2002 2003 2004 2005 2006
2.41 3.63 5.9 7.65 10.65 12.5 17.87 18.4
9.36 10.27 9.69 10.05 11.51 11.56 13.29 11.04
88.23 86.1 84.41 82.3 77.84 75.94 68.84 70.56
investors might be asymmetric, we chose to analyze the two types of behavior separately. Third, although we followed Seasholes (2000) in choosing the Taiwan stock market for our survey, we recognize that over time foreign institutional investors have become increasingly important as their trading in the market has increased compared to other investors. Finally, to the best of our knowledge, our study is the first to analyze the non-linear dynamic trading behavior of investors using the threshold cointegration model of Hansen and Seo (2002). The rest of the paper is organized as follows. Section 2 describes the data. Section 3 reports the method and results of the empirical investigation. Our conclusions are presented in Section 4. The details of the empirical models based on Hansen and Seo (2002) are given in the Appendix A. 2. The data The QFII system has been in effect in Taiwan since 1991. In 2003, the reviewing process was changed from a permit system to a registration system. This innovation simplified the application process for foreigners investing in Taiwan's stock market. Table 1 shows that the proportion of foreign investors' trades to total trades in the Taiwan market increased from 2.41% in 1999 to 18.4% in 2006. In contrast, the proportion of individual investors’ trades decreased from 88.23% in 1999 to 70.56% in 2006. Finally, domestic institutional investors' proportion of total trades remained at around 10% throughout the sampling period. Our sampling period for collecting data on stock transactions in the Taiwan Stock Exchange was from January 1999 through October 2006. The data, which were taken from the Taiwan Economic Journal (TEJ), contain the following variables for each trading day: (i) the stock-price index (S_P), and (ii) buy and sell trading volumes for domestic institutional investors, individual investors, and foreign investors (DI_B, DI_S, IND_B, IND_S, FI_B and FI_S). The statistics are summarized in Tables 2 and 3. All variables are transformed by natural logarithms. 3. Empirical investigation 3.1. Empirical results of the Johansen (1991) cointegration Before conducting the cointegration analysis, the stationarity of the variables had to be examined. We evaluated the unit-root hypothesis by the conventional ADF (Dickey and Fuller, 1979) test. The results Table 2 Summary statistics. Stock price index Mean Median S.D. Min. Max.
6191.41 6001.26 1292.7 3446 10202
Foreign investors (in million NT dollars)
Domestic institutions (in million NT dollars)
Domestic individual investors (in million NT dollars)
Buy
Sell
Net flow
Buy
Sell
Net flow
Buy
Sell
Net flow
9498.49 7661.50 7041.6 190 135109
8130.18 6732.50 5713.8 87 44000
1368.31 905.00 5301.6 − 23772 125288
5639.54 5178.50 2626.2 241 18674
5748.49 5406.00 2424.4 463 29878
− 108.95 − 108.00 1993.4 − 20053 10837
18680.69 15810.50 10164.4 1610 72703
21349.48 18427.00 10610.1 4727 77067
− 2668.78 − 2204.00 2839.3 − 21465 7062
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Table 3 Data description-breakdown by investor types, trading, and years. Year
Stock price index
1999 2000 2001 2002 2003 2004 2005 2006
7419.05 7837.69 4907.43 5225.61 5161.90 6033.78 6092.27 6754.26
Foreign investors (in million NT dollars)
Domestic institutions (in million NT dollars)
Domestic individual investors (in million NT dollars)
Buy
Sell
Net flow
Buy
Sell
Net flow
Buy
Sell
Net flow
3905.80 5392.84 5943.56 6826.86 9868.14 12658.78 15240.21 18873.86
2652.20 4857.10 4688.39 6714.40 7663.57 11522.94 12327.63 16988.12
1253.60 535.74 1255.16 112.46 2204.58 1135.85 2912.58 1885.74
5878.91 6314.36 4360.84 5293.20 5610.14 6202.27 5625.58 5791.18
5882.23 6635.94 4360.66 5255.20 5513.22 6316.09 5906.60 6030.94
− 3.32 − 321.59 0.18 38.00 96.91 − 113.82 − 281.01 − 239.76
27213.1 24229.0 16924.4 18731.1 15920.3 17249.2 12487.9 14843.9
30955.1 28323.1 19750.2 21701.6 17906.2 19315.3 14100.0 16453.5
− 3741.98 − 4094.09 − 2825.82 − 2970.46 − 1985.88 − 2066.09 − 1612.19 − 1609.61
from the ADF test (Table 4) indicate that the original data failed to reject the unit-root hypothesis at the 5% level. However, the first difference of data did reject the unit-root hypothesis, which implies that all of the seven processes are integrated of order one. Because the data were non-stationary, we applied Johansen's (1991) cointegration test, which was developed for linear models. The results are summarized in Table 5. Of interest are the pairings of stock prices from the stock price index (S_P) with the buy and sell volumes for foreign investors (FI_B, FI_S), domestic institutional investors (DI_B, DI_S), and domestic individual investors (IND_B, IND_S), respectively. We used the information criterion proposed by Schwarz (1978) to select the lag order. Based on the trace and maximum eigenvalues, the hypothesis of no cointegration was rejected for all these pairs, as shown in Table 5. However, the null hypothesis that the cointegration vector is less than or equal to 1 could not be rejected at the 5% level. It is therefore reasonable to conclude that there is one cointegration vector for all three VAR systems. According to Balke and Fomby (1997), the Johansen test can have low power if there is threshold cointegration. Therefore, to determine whether cointegration exists among the variables in the threshold nonlinear model, we performed Enders and Siklos (2001) F-test, which is reported in the last column of Table 5. The result indicates that the null hypothesis of no cointegration can be rejected in all three cases. Overall, the table indicates that the cointegration of the buy and sell trading volumes with stock prices holds for both the linear and threshold models. We next derived estimates from Johansen's (1991) linear error-correction models (Table 6). The lag order was found to be 1 for all three pairs. The error terms for all these pairs are significant at the 5% level. These results are consistent with those of the cointegration test reported in Table 5. For the foreign investors, the first panel in Table 6 shows that there was a two-direction causal relationship between their buy and sell volumes, but there was only one-direction causality from the stock
Table 4 ADF unit root test.
S_P(1) FI_B(5) FI_S(5) DI_B(4) DI_S(5) IND_B(4) IND_S(5)
Level data
First differenced data
− 1.731 − 0.049 − 0.098 − 0.439 − 0.241 − 0.346 − 0.328
− 49.499*** − 40.599*** − 40.254*** − 31.123*** − 33.725*** − 36.595*** − 36.358***
Notes: (1) FI_B and FI_S represent the buy-in and the sell-out of foreign investors, respectively. DI_B and DI_S represent the buy-in and sell-out of domestic institutional investors, respectively. IND_B and IND_S represent the buy-in and sell-out of domestic individual investors, respectively. The stock price index is denoted as S_P. (2) The numbers in parentheses are the appropriate lag order of the AR process chosen by Schwarz (1978) information criterion. (3) The numbers in the Table are the ADF, τμ, statistics. (4) The critical values of different significant levels, i.e., 1%, 5% and 10%, are − 3.458, -2.8733 and − 2.573, respectively. (5) ‘***’ indicates significant at the 1% level of significance.
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Table 5 Johansen Cointegration Test and Threshold Cointegration Test. λMax
TRACE
Enders and Siklo's F statistics
Null hypothesis
γ≤2
γ≤1
γ=0
γ=2
γ=1
γ=0
γ=0
(S_P, FI_B, FI_S) (S_P, DI_B, DI_S) (S_P, IND_B, IND_S)
3.411 (3.841) 1.065 (3.841) 2.953 (3.841)
15.452 (15.495) 14.810 (15.495) 14.968 (15.494)
105.77** (29.797) 38.009** (29.797) 74.281** (29.797)
3.411 (3.841) 1.065 (3.841) 2.953 (3.841)
12.049 (14.265) 13.745 (14.265) 12.015 (14.265)
90.309** (21.132) 23.200** (21.132) 59.313** (21.132)
277.032** 162.323** 151.021**
Notes : (1) γ is the number of cointegrated vector. Trace and λMax are Johansen's (1991) Trace and maximum eigenvalue test, respectively. (2) The numbers in parentheses are the 5% finite sample critical values which are constructed from the asymptotic critical values from MacKinnon et al. (1999). (3) The F statistics are Enders and Siklos' (2001) test the null of no threshold cointegration, and the 5% and 10% critical values for the F statistic are 5.87 and 4.92, respectively. (4) ‘**’ indicates significant at a 5% significance level.
price to both the buy and sell volumes. The two-way negative feedback effect between foreign investors' buy and sell volumes implies that they bought (sold) more if they sold (bought) less on the preceding day. This means that they did not overreact by adjusting their trading positions in the opposite direction. Moreover, they bought (sold) more if stock prices rose (fell) on the preceding day. This means that the foreign investors followed a momentum strategy, a conclusion that is also indicated by the findings from Bae et al.'s (2011) investigation of the Korean stock market. Finally, we conclude that the trading practices of foreign investors, whether buying or selling, had no leading effect on the Taiwan stock price index. For domestic institutional investors, the results shown in the second panel of Table 6 are similar to those for foreign investors. Again, there was a feedback relationship between these investors' buy and sell volumes, but there was only one-way causality from the stock price to the purchase volume. The meaning and implications of these findings are the same as those for foreign investors. However, the situation for domestic individual investors was somewhat different. As shown in the last panel of Table 6, stock prices influenced these investors' buy volumes, which in turn influenced their sell volumes. However, there was a positive feedback relationship between their sell volumes and the stock price index. In other words, both buy and sell volumes increase (decreased) if the stock price index rose (fell) on the previous day. One implication of this positive relation between these individual investors' sell volumes and the stock price index is that they received a lower return when they sold their stocks. 3.2. Empirical results of threshold cointegration Hansen and Seo (2002)'s supLM threshold test was employed to examine the necessity of using a threshold model. 2 The results in the first column of Table 7 indicate that the threshold effect is significant at the 5% level for both domestic institutional investors and domestic individual investors, and it is significant at the 10% level for foreign investors. These results imply that the conventional linear error-correction model is not appropriate. The results of Wald test revealed that the short-term dynamic coefficients are significantly different across the different regimes for each of the three cointegration systems. This evidence further illustrates the inappropriateness of using a linear error-correction model. Next, we estimated the threshold error-correction model to look for possible causal relationships. Table 8 summarizes the estimates from the threshold cointegration model for the foreign investors' buy and sell volumes and the stock price index. Regime I is defined as the values of the error-correction terms being less than or equal to the estimates of the threshold values (i.e. |ECMt − 1| ≤ 0.647). The other cases form Regime II. 3 Because, for foreign investors, the deviation from the long-term cointegration 2
The methodology is illustrated in the Appendix A. In the cointegation system for foreign institutional investors, ECMt− 1 = FI_Bt− 1 − 0.78FI_St− 1 − 0.22S_Pt− 1: And we modify Hansen and Seo (2002)'s model by adopting |ECMt-1| instead of ECMt-1 as the threshold variable in our empirical studies. 3
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Table 6 Johansen's (1991) Error-Correction Model.
Foreigners' trading and stock price index
ECMt − 1 Constant ΔFI_Bt-1 ΔFI_St-1 ΔS_Pt-1
Domestic institutions' trading and stock price index
ECMt − 1 Constant ΔDI_Bt-1 ΔDI_St-1 ΔS_Pt-1
Domestic individuals' trading and stock price index
ECMt − 1 Constant ΔIND_Bt-1 ΔIND_St-1 ΔS_Pt-1
ΔFI_Bt
ΔFI_St
ΔS_Pt
− 0.293 (0.028)** 0.0003 (0.010) − 0.205 (0.029)** − 0.107 (0.026)** 1.967 (0.681)**
0.212 (0.029)** 0.0003 (0.011) − 0.096 (0.030)** − 0.293 (0.027)** − 2.246 (0.712)**
0.005 (0.001)** 0.0001(0.0004) 0.0002 (0.001) − 0.0002(0.001) 0.018 (0.024)
ΔDI_Bt
ΔDI_St
ΔS_Pt
− 0.540 (0.035)** − 0.0002 (0.008) − 0.009 (0.028) − 0.265 (0.032)** 2.774 (0.635)**
0.227 (0.027)** − 0.0002 (0.006) − 0.109 (0.022)** − 0.272 (0.025)** 0.346 (0.505)
0.008 (0.002)** 0.0002(0.0004) 0.002 (0.001) 0.002 (0.001) − 0.044 (0.028)
ΔIND_Bt
ΔIND_St
ΔS_Pt
− 0.085 (0.043)** − 0.0002 (0.005) − 0.337 (0.035)** 0.072 (0.045) 3.688 (0.347)**
− 0.137 (0.041)** − 0.0003 (0.005) − 0.166 (0.033)** − 0.164 (0.043)** 1.739 (0.334)**
− 0.040 (0.003)** 0.0001 (0.0003) 0.002 (0.002) 0.009 (0.003)** 0.137 (0.023)**
Note: (1) FI_B and FI_S represent the buy-in and the sell-out of foreign investors, respectively. DI_B and DI_S represent the buy-in and sell-out of domestic institutional investors, respectively. IND_B and IND_S represent the buy-in and sell-out of domestic individual investors, respectively. ECM is the error-correction term and the stock price index is denoted as S_P. (2) The numbers in parentheses are the standard errors of the estimated coefficients. (3) ** means significant at a 5% significance level.
relationship is small for the buy and sell volumes as well as the stock price index, Regime I was assumed to be in a state of near equilibrium. On the other hand, for Regime II the market was assumed to be far from equilibrium. The findings shown in Table 8 illustrate that there was a two-way, short-term dynamic causal relationship between foreign investors’ buy and sell volumes in both regimes. In Regime I (II), the stock prices led foreign investors to buy (sell). However, their purchases increased the stock prices, leading to decreased selling in Regime II. Because there was a two-way negative feedback relation between foreign investors' buying and selling in both Regimes I and II, they bought (sold) more if they had sold (bought) less on the previous day. That is, they followed a consistent trading strategy, regardless of whether their position was short or long; they rarely adjusted their position. In addition, in Regime I, they bought more (less) if the stock price index rose (fell) on the previous day. Their purchasing reflected a momentum strategy, as did their selling in Regime II. Finally, their transactions did not affect domestic stock prices in Regime I. In contrast, their purchases did have a positive effect on stock price index in Regime II. These results imply that foreign investors paid less when they purchased Taiwan stocks. Table 9 reports the estimates from the threshold cointegration model for domestic institutional investors' buy and sell volumes and the stock price index. The results indicate a two-way causal relationship between
Table 7 Test for threshold effect.
Foreigners' trading and stock price index Domestic institutions' trading and stock price index Domestic individuals' trading and stock price index
SupLM test for threshold effect
Wald test for the equality of the short-run dynamic coefficients at different regimes.
Statistics
P-value
Statistics
P-value
31.206* 49.861** 46.647**
0.060 0.000 0.000
156.484** 48.424** 27.185**
0.000 0.000 0.0001
Note: ** and * means significant at 5% and 10% significance levels.
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Table 8 Threshold Error-Correction Model (foreign investors). REGIME I : |ECMt − 1| ≤ 0.647
ECMt − 1 Constant ΔFI_Bt−1 ΔFI_St−1 ΔS_Pt−1
REGIME II: |ECMt − 1| > 0.647
ΔFI_Bt
ΔFI_St
ΔS_Pt
ΔFI_Bt
ΔFI_St
ΔS_Pt
− 0.323** (0.031) − 0.004 (0.011) − 0.207** (0.030) − 0.097** (0.027) 2.384** (0.706)
0.142** (0.032) − 0.009 (0.011) − 0.098** (0.030) − 0.286** (0.028) − 1.160 (0.728)
− 0.005** (0.001) 0.0001 (0.0004) − 0.0003 (0.001) − 0.0004 (0.001) 0.009 (0.025)
0.052 (0.035) − 0.200** (0.012) − 0.260** (0.033) − 0.112** (0.031) − 0.752 (0.792)
1.215** (0.037) − 0.614** (0.012) − 0.266** (0.035) − 0.149** (0.032) − 10.013** (0.835)
− 0.003** (0.001) 0.004** (0.0003) 0.007** (0.001) − 0.001 (0.001) 0.067** (0.024)
Note: (1) FI_B and FI_S represent the buy-in and the sell-out of foreign investors, respectively. ECM is the error-correction term, ECMt− 1 = FI_Bt− 1 − 0.78FI_St− 1 − 0.22S_Pt− 1. The stock price index is denoted as S_P. (2) The numbers in parentheses are the standard errors of the estimated coefficients. (3) The numbers in parentheses are the standard errors of the estimated coefficients, and ** means significant at a 5% significance level.
buy and sell volumes in Regime I (|ECMt − 1| ≤ 0.049)4 However, there were only one-way causal relationships from stock prices to purchases in Regime I and from selling to buying in Regime II. Moreover, there was a feedback effect between domestic institutional investors' purchases and stock prices in Regime II. The two-way negative feedback effect between buying and selling in Regime I means that domestic institutional investors purchased (sold) more if they sold (purchased) less on the previous day, provided that the market was near equilibrium. It also indicates that these investors pursued a consistent trading strategy at such times, regardless of whether their position was short or long. In both regimes, domestic institutions purchased more (less) when the stock price index rose (fell) on the previous day, representing a consistent momentum strategy. Finally, in Regime I, domestic institutions’ trading behavior had no effect on domestic stock prices, but their purchases had a positive effect on stock prices in Regime II, meaning that they paid less when they bought stocks; they could also make money when the market was not in equilibrium, because of the effect of their behavior on domestic stock prices in Regime II. The estimates from the threshold cointegration model for domestic individual investors are shown in Table 10. There was bi-directional causality between these investors' purchases and stock prices in both regimes, and between buy and sell volumes in Regime I (|ECMt − 1| ≤ 0.039). 5 In contrast, there were only one-way causal relationships from stock prices to sales volume in Regime I and from sales volume to stock prices in Regime II. As the stock price index had a positive effect on individual investors' buy and sell volumes in Regime I, both the purchases and sales of these investors increased (decreased) when the stock price index rose (fell) on the previous day. Note that the investors' transactions had opposite effects on stock prices in the two regimes. In Regime I, the purchases had a positive effect on stock prices, implying that the investors paid less when they purchased stocks and thus made money by affecting stock prices when the market was near equilibrium. In Regime II, the investors' purchases (sales) had a negative (positive) effect on stock prices, meaning that they paid more when purchasing, and they received less when selling in Regime II. Individual investors could not make money by affecting stock prices when the market was far from equilibrium. In general, the trading patterns of foreign investors and domestic institutions were similar when the market was near equilibrium: they both followed a consistent trading strategy and they did not overreact in trading. They can be characterized as momentum traders, and their trading had no effect on domestic stock prices. On the other hand, the purchases of domestic individual investors had a positive effect on stock prices in Regime I, which resulted in their making money when the market was near equilibrium. The trading patterns and performance of the three types of investors were quite different when the market was not in equilibrium. Purchases by the foreign and domestic institutional investors had a positive effect on stock prices, meaning that these investors paid less when they purchased stocks. In contrast, 4 5
In the cointegation system for domestic institutional investors, ECMt− 1 = DI_Bt− 1 − 0.81DI_St− 1 − 0.13S_Pt− 1. In the cointegation system for domestic individual investors, ECMt− 1 = IND_Bt− 1 − 1.11IND_St− 1 − 0.01S_Pt− 1.
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Table 9 Threshold Error-Correction Model (domestic institutional investors). REGIME I : |ECMt − 1| ≤ 0.049
ECMt − 1 Constant ΔDI_Bt−1 ΔDI_St−1 ΔS_Pt−1
REGIME II : |ECMt − 1| > 0.049
ΔDI_Bt
ΔDI_St
ΔS_Pt
ΔDI_Bt
ΔDI_St
ΔS_Pt
− 0.636** (0.074) − 0.056** (0.023) − 0.117** (0.043) − 0.201** (0.049) 2.204** (1.044)
0.034 (0.061) − 0.087** (0.019) − 0.196** (0.036) − 0.181** (0.040) 0.769 (0.859)
0.005 (0.003) − 0.001 (0.001) − 0.002 (0.002) 0.001 (0.002) − 0.026 (0.046)
− 0.487** (0.072) − 0.022 (0.022) 0.072** (0.042) − 0.323** (0.047) 3.094** (1.008)
0.230** (0.055) 0.002 (0.017) − 0.050 (0.032) − 0.358** (0.036) 0.356 (0.771)
0.008** (0.003) − 0.0002 (0.0010) 0.005** (0.002) 0.002 (0.002) − 0.068 (0.044)
Note: (1) DI_B and DI_S represent the buy-in and sell-out of domestic institutional investors, respectively. ECM is the error-correction term, ECMt− 1 = DI_Bt− 1 − 0.81DI_St− 1 − 0.13S_Pt− 1. The stock price index is denoted as S_P. (2) The numbers in parentheses are the standard errors of the estimated coefficients. (3) The numbers in parentheses are the standard errors of the estimated coefficients and ** means significant at 5% significance level.
the purchases (sales) of domestic individual investors had a negative (positive) effect on stock prices, meaning that these investors paid more when they purchased stocks and received less money when they sold stocks. When the market was not in equilibrium, however, the foreign and domestic institutional investors could make money through their trading behavior, but the domestic individual investors risked losing money.
4. Conclusion Foreign investors have comprised more and more of the total market trading in Taiwan ever since the abolishment of the Qualified Foreign Institutional Investors (QFII) system in 2003. There is no consensus on its role being able to enhance market efficiency or to siphon profit from their local counterparts. In this paper, we apply the threshold cointegration model of Hansen and Seo (2002), incorporating differences in the nonlinear behavior of investors across regimes. Our results are easily summarized as follows. First, neither foreign, domestic institutional, nor domestic individual investors were found to be predominant in the market. Second, when the market was near equilibrium, domestic individual investors' purchases caused the stock prices to rise. However, when the market departed markedly from equilibrium, purchases by foreign and domestic institutional Table 10 Threshold Error-Correction Model (domestic individual investors). REGIME I : |ECMt − 1| ≤ 0.039
ECMt − 1 Constant ΔIND_Bt−1 ΔIND_St−1 ΔS_Pt−1
REGIME II : |ECMt − 1| > 0.039
ΔIND_Bt
ΔIND_St
ΔS_Pt
ΔIND_Bt
ΔIND_St
ΔS_Pt
− 0.826** (0.079) 0.009 (0.014) − 0.511** (0.053) 0.128** (0.069) 5.218** (0.533)
− 0.131** (0.074) − 0.006 (0.014) − 0.356** (0.050) − 0.002 (0.065) 3.400** (0.501)
− 0.036** (0.006) 0.003** (0.001) 0.012** (0.004) − 0.001 (0.005) 0.108** (0.039)
− 0.676** (0.075) − 0.023** (0.014) − 0.217** (0.051) 0.043 (0.065) 2.494** (0.505)
0.036 (0.073) − 0.026** (0.013) − 0.032 (0.050) − 0.263** (0.064) 0.631 (0.494)
− 0.034** (0.005) − 0.003 (0.001) − 0.006** (0.003) 0.016** (0.004) 0.145** (0.031)
Note: (1) IND_B and IND_S represent the buy-in and sell-out of domestic individual investors, respectively. ECM is the errorcorrection term, ECMt− 1 = IND_Bt− 1 − 1.11IND_St− 1 − 0.01S_Pt− 1. The stock price index is denoted as S_P. (2) The numbers in parentheses are the standard errors of the estimated coefficients. (3) The numbers in parentheses are the standard errors of the estimated coefficients and ** means significant at a 5% significance level.
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investors had a positive impact on stock prices, but the trading of individual investors had a negative impact on them. We have shown that segregating two trading regimes can help reconcile the controversy about how foreign investors perform. We did not bet for or against foreign investors; rather, we found that foreign (as well as domestic) institutional investors performed quite well when the market deviated markedly from equilibrium. In contrast, the domestic individual investors outperformed their foreign and domestic institutional counterparts when the market was near equilibrium. Further studies could profitably explore the reasons why institutional investors are better able than other investors to affect the market when it is not in equilibrium. Appendix A. Methodology A.1. Threshold Cointegration Balke and Fomby (1997) demonstrated that the two-step version of the cointegration test developed by Engle and Granger (1987) has good power when applied to a non-linear threshold model. Using the two-step cointegration method, Enders and Siklos (2001) modified the second step of the conventional AR model by adopting a threshold autoregressive (TAR) model, in which an asymmetric adjustment of the first-order autoregressive coefficient under different regimes is allowed. The TAR model is as follows: x1t ¼ β1 þ β2 x2t þ β3 x3t þ ωt ; Δωt ¼ It ρ1 ωt−1 þ ð1−I t Þρ2 ωt−1 þ
ðA:1Þ p−1 X
βi Δωt−i þ εt ;
ðA:2Þ
i¼1
and
It ¼
1 if ωt1 ≥τ ; 0 if ωt1 bτ
ðA:3Þ
where x1t represents the stock prices; x2t is the trading purchase volume, x3t is the trading sales volume, and ωt is the equilibrium error in the cointegration model. The model is the same as that of Engle and Granger (1987) if there is no threshold effect in Eq. (A.2). The null hypothesis of no threshold cointegration implies ρ1 = ρ2 = 0. To examine the null hypothesis, Enders and Siklos (2001) proposed two statistics: t-Max and F. Their simulation results demonstrate that F has higher power than t-Max. We therefore employed F to test our hypothesis of no threshold cointegration. A.2. Estimation and Testing for Threshold ECM As there was a threshold effect in the cointegration model, we proceeded to derive estimates from the threshold error-correction model (ECM). Hansen and Seo (2002) proposed a method for obtaining the maximum likelihood estimate (MLE) for the threshold ECM. Let xt = {x1t, x2t, x3t} be a 3-dimensional I (1) process cointegrated with a 3 × 1 cointegrating vector β, and let ωt − 1(β) = β′xt− 1 denote the error-correction term. The two-regime threshold ECM can then be written as: ( Δxt ¼
A′ 1 X t−1 ðβÞ þ ut ; if ωt1 ðβÞ ≤τ ; A′ 2 X t−1 ðβÞ þ ut ; if ωt1 ðβÞ > τ
ðA:4Þ
Hansen and Seo (2002) performed an evenly-spaced grid search of the two-dimensional space (β, τ) over the regions [τL, τU] and [βL, βU], conditional onπ0 ≤ Pr(ωt − 1 ≤ τ) ≤ 1 − π0, where π0 > 0 is the selected trimming parameter. 6 In our empirical analysis, we set π0 = 0.05 and then constructed the interval [τL, τU] ~ 6σ~ β , where β ~ is from the previous inequality. Following Hansen and Seo (2002), we set ½β ; β ¼ β L
6
Our empirical studies used 200 gridpoints over the regions [τL, τU] and [βL, βU], respectively.
U
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~ We let the estimates of β Johansen's estimated cointegrating vector and σ~ β is the standard deviation of β. ^ and τ^ respectively) be the values of (β, τ) in this grid search over ([βL, βU] and [τL, τU]) respectively, and τ (β which yielded the maximum value of the concentrated likelihood function.7 We then obtained the estimated ^ 2 β; ^ 1 β; ^ τ^ and A ^ τ^ , using the OLS regression of Eq. (A.4) for the subsamples, where coefficient vectors, A ^ ≤τ^ and ωt−1 β ^ > τ^ . ωt−1 β The hypothesis of no threshold cointegration is rejected if the hypothesis A1' = A2' is rejected. It is worth noting that the threshold parameter is not identified under the null hypothesis of no threshold cointegration. To solve this problem, Hansen and Seo (2002) introduced a SupLM statistic to test for a threshold effect in the model.8 The SupLM statistic for testing the hypothesis of A1' = A2' is defined as: SupLM ¼
~ τ ; sup LM β;
τ L ≤τ≤τU
~ τ is the heteroskedasticity-robust LM-like statistic as defined by Hansen and Seo (2002). The where LM β; critical values of SupLM can be calculated by the “fixed regressor bootstrap” or “parametric residual bootstrap” methods. For our empirical study, we only reported the critical value of the “parametric residual bootstrap,” as the two critical values approximate each other. References Andrews, D.W.K., Ploberger, W., 1994. Optimal tests when a nuisance parameter is present only under the alternative. Econometrica 62, 1383–1414. Agarwal, S., Faricloth, S., Rhee, S.G., 2009. Why do foreign investors underperform domestic investors in trading activities? Evidence from Indonesia. Journal of Finance Market 12, 32–53. Bae, S., Min, J.H., Jung, S., 2011. Trading behavior, performance, and stock preference of foreigners, local institutions, and individual investors: evidence from the Korean stock market. Asia-Pacific Journal of Financial Studies 40, 199–239. Balke, N.S., Fomby, T.B., 1997. Threshold cointegration. International Economic Review 38, 627–645. Brennan, M.J., Cao, H., 1997. International portfolio flows. Journal of Finance 52, 1851–1880. Choe, H., Kho, B.C., Stulz, R.M., 2005. Do domestic investors have an edge? The trading experience of foreign investors in Korean. Review of Financial Studies 18 (3), 795–829. Dickey, D.A., Fuller, W.A., 1979. Distribution of the estimates for autoregressive time series with a unit root. Journal of the American Statistical Association 74, 427–431. Dvorak, T., 2005. Do domestic investors have an informational advantage? Evidence from Indonesia. Journal of Finance 60 (2), 817–839. Enders, W., Siklos, P.L., 2001. Cointegration and threshold adjustment. Journal of Business & Economic Statistics 19, 166–176. Engle, R.F., Granger, C.W.J., 1987. Co-integration and error correction: representation, estimation, and testing. Econometrica 55, 251–276. Froot, K.A., Ramadorai, T., 2008. Institutional portfolio flows and international investments. Review of Financial Studies 21 (2), 937–971. Grinblatt, M., Keloharju, M., 2000. The investment behavior and performance of various investor types: a study of Finland's unique data set. Journal of Financial Economics 55, 43–67. Hansen, B.E., Seo, B., 2002. Testing for two-regime threshold cointegration in vector error-correction models. Journal of Econometrics 110, 293–318. Hau, H., 2001. Location matters: an examination of trading profits. Journal of Finance 56, 1959–1983. Johansen, S., 1991. Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica 59, 1551–1580. MacKinnon, J.G., Haug, A., Michelis, L., 1999. Numerical distribution functions of likelihood ratio tests for cointegration. Journal of Applied Econometrics 14 (5), 563–577. Schwarz, G., 1978. Estimating the dimension of a model. The Annals of Statistics 6, 461–464. Seasholes, M., 2000. Smart foreign traders in emerging markets. Working paper. Harvard Business School. Taechapiroontong, N., Suecharoenkit, P., 2011. Trading performance of individual, institutional, and foreign investors: evidence from the stock market of Thailand. International Research Journal of Finance and Economics 75, 157–174.
7 8
^ is more accurate than β ~. Hansen and Seo (2002) demonstrated that β See Andrews and Ploberger (1994) for the rationale and justification of this testing strategy.