Asian Journal of Economics and Empirical Research Vol. 4, No. 2, 106-120, 2017 ISSN(E) 2409-2622 / ISSN(P) 2518-010X DOI: 10.20448/journal.501.2017.42.106.120 106 Why are the Performances of Business Groups Different? A Case Study of Formosa Plastics Group and Far Eastern Group Yu-Wei Lan1  Dan Lin2 Lu Lin3 ( Corresponding Author) 1,2Department of Banking and Finance, Takming University of Science and Technology, Taiwan 3Department of Public Finance and Taxation, Takming University of Science and Technology, Taiwan Abstract This study examines the difference in performances of two business groups, Formosa Plastics Group and Far Eastern Group, under the impact of financial tsunami (2007.10.29~2017.8.10). The aim of this study is to help investors understand the operating model of business groups and use the herding effect to enhance the trading performance in financial markets. The empirical evidence shows that for the Formosa Plastics Group, the news impact curve (based on EGARCH model) including the leading company is flatter when the news impact is less than zero (that is, negative news impact) than the news impact curve excluding the leading company. In contrast, the news impact curve of the Far Eastern Group is steeper when the leading company is included. Moreover, when the leading company is included as an endogeneous variable in the model as a filter for the program trading simulation, results show that investors can profit from the Formosa Plastics Group. Therefore, business groups that include the leading company have lower risks. It is beneficial to the stability of the market trading by incorporating the leverage effect of the leading company in business groups. On the contrary, the leading company of the Far Eastern Group does not have such an effect. The absolute profits and the increment of performance are both lower than that of the Formosa Plastics Group. The results suggest that the diversification strategy of Far Eastern Group is worse than the vertical integration strategy of the Formosa Plastics Group. The implication is that investors should carefully choose the business group for investment if they are to utilize the herding effect in investment. Keywords: Family business, EGARCH, Herd effect, Granger causality test, Symmetric trading. Citation | Yu-Wei Lan; Dan Lin; Lu Lin (2017). Why are the Performances of Business Groups Different? A Case Study of Formosa Plastics Group and Far Eastern Group. Asian Journal of Economics and Empirical Research, 4(2): 106-120. History: Received: 18 October 2017 Revised: 8 November 2017 Accepted: 13 November 2017 Published: 16 November 2017 Licensed: This work is licensed under a Creative Commons Attribution 3.0 License Publisher: Asian Online Journal Publishing Group Contribution/Acknowledgement: All authors contributed to the conception and design of the study. Funding: This study received no specific financial support. Competing Interests: The authors declare that they have no conflict of interests. Transparency: The authors confirm that the manuscript is an honest, accurate, and transparent account of the study was reported; that no vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained. Ethical: This study follows all ethical practices during writing. Contents 1. Introduction .................................................................................................................................................................................... 107 2. Literature Review .......................................................................................................................................................................... 107 3. Research Methods .......................................................................................................................................................................... 108 4. Data .................................................................................................................................................................................................. 110 5. Empirical Results of the Formosa Plastics Group .................................................................................................................. 110 6. Empirical Results of the Far Eastern Group ............................................................................................................................ 115 7. Conclusion and Discussion on Investment Strategies ............................................................................................................ 119 References ............................................................................................................................................................................................ 119 Appendixes .......................................................................................................................................................................................... 120 http://creativecommons.org/licenses/by/3.0/ http://creativecommons.org/licenses/by/3.0/ https://orcid.org/orcid-search/quick-search?searchQuery=Yu-Wei Lan https://orcid.org/orcid-search/quick-search?searchQuery=Dan Lin https://orcid.org/orcid-search/quick-search?searchQuery=Lu Lin https://orcid.org/orcid-search/quick-search?searchQuery=Yu-Wei Lan https://orcid.org/orcid-search/quick-search?searchQuery=Dan Lin https://orcid.org/orcid-search/quick-search?searchQuery=Lu Lin https://orcid.org/orcid-search/quick-search?searchQuery=Yu-Wei Lan https://orcid.org/orcid-search/quick-search?searchQuery=Dan Lin https://orcid.org/orcid-search/quick-search?searchQuery=Lu Lin https://orcid.org/orcid-search/quick-search?searchQuery=Yu-Wei Lan https://orcid.org/orcid-search/quick-search?searchQuery=Dan Lin https://orcid.org/orcid-search/quick-search?searchQuery=Lu Lin Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 107 1. Introduction All business groups around the world are formed based on independent companies. Businesses that have certain resources (such as entrepreneurial skills and technical skills) are likely to profit from other businesses. Alternatively, businesses can lower the risks through diversifications. When there is a lack of basic infrastructure or weak social economic and legal systems, the cost of transactions between buyers and sellers can be expensive. It may be cheaper and more efficient to trade within the business group. Some business groups may even use this method to monopolize the market. Therefore, some business groups attempt to diversify by connecting several unrelated businesses through formal stock holdings or informal family networks. Some other business groups operate by focusing on their industry through vertical integrations.1 Two issues arisen from this complex organizational style. The first treats business groups as a diversified entity and analyzed the relationship between this feature, industrial organization and financing problems. Business groups can control their related enterprises through internal trading and capital. Currently, 40% of the top 500 companies around the world are controlled by families. Families tend to use pyramid holdings to maintain their controls. Finkelstein (1992) finds that family members have higher commitments to their businesses and pay attention to the businesses‟ long-term developments. By extending their tenure to consolidate their power, the transaction costs in business management can be lowered. Johannisson and Huse (2000) also support the view that the cohesion of the founder to the enterprise can help increase the operating efficiency of the family business group. The second issue is raised by the corporate governance survey of Shleifer and Vishny (1997) and the following work by La Porta et al. (1997;1998). La Porta et al. (1999) examine the top 20 companies around 27 countries and find that the ultimate holders of business groups will expropriate small shareholders and hollowed out the companies through pyramid holdings. Jain and Kini (2000) argue that if there are too many family members on the board of directors, this is likely to limit the resource network of the companies. Baek and Kang (2004) also find that controlling shareholders of business groups often use internal trading and asset restructuring to transfer the companies‟ resources to become their property. Therefore, understanding this complex operating model is a great challenge to investors. The aim of this research is to directly examine the stock performance of business groups in order to search for better investment opportunities. The prime job is then to understand the relationship between the operating strategy of business groups and their stock performance. The Formosa Plastics Group was first established in 1954 as a plastics company. After more than 50 years of hard work, the Formosa Plastics Group now have more than hundreds of related enterprises including Formosa Plastics, Nan Ya, Formosa Chemicals & Fibre, Formosa Petrochemicals, Formosa Ha Tinh Steel and etc. These companies are spread out in Taiwan, USA, China, Vietnam, Philippine, and Indonesia. The Group is also committed to education and medical care by establishing a hospital and universities. The Formosa Plastics Group is the largest private company in Taiwan. To follow the spirit of a separation of ownership and control, the founders of Formosa Plastics Group established an Administration Centre which is for the Group‟s family members and an Executive Centre which is led by a professional manager. This structure was executed in June 2017.2 The second business group examined in this study is the Far Eastern Group, which was first established in 1937 in China. The company started its textile business in 1953 in Taiwan. It then diversified to other businesses such as petrochemical energy, cement building materials, department store retailing, financial services, land & sea transportation, communication networks, and tourism hotels. The business group has more than 200 related companies. Of which, eight companies are listed in Taiwan, and one company, Asia Cement, is listed in Hong Kong. Far Eastern Group is the third largest business group in Taiwan and is a model of diversified companies in Taiwan.3 In 2014, the total market values of Formosa Plastics Group and Far Eastern Group were $2680.8 billion and $679 billion, respectively. However, in July 2017, the market value of Formosa Plastics Group increased to $3032.6 billion while the market value of Far Eastern Group decreased to $572.3 billion. One common feature of the business group is the cross holdings between related businesses. Therefore, if the performance of related companies changes, the investment profits of the whole business group will be affected. When the benefit of vertical integration gradually reveals, the after tax net profits of Formosa Plastics group increased by 43.11% in 2016. In contrast, as the economy becomes more volatile, diversified operations will encounter greater challenges. Hence, the after tax net profits of Far Eastern Group reduced by 19.44% in 2016.4 Therefore, this study proposes a program trading investment strategy based on behavioral finance theory to help individual investors trade the stocks of family businesses. The organization of the paper is as follows. Section 2 is the literature review. Section 3 discusses the Granger causality, EGARCH model and the estimation method for program trading. Section 4 describes that data source. Section 5 and 6 presents that empirical results and analyses for the Formosa Plastics Group and the Far Eastern Group, respectively. Finally, the conclusion is presented in the last section. 2. Literature Review Both researches by Bachelier (1900) and Samulson (1965) argue that the stock prices are unpredictable. Fama (1965) also suggests that the trend in stock price is random. Fama (1970) then proposes an efficient market 1According to Khanna and Yishay (2015). diversification is measured by two-digit ISIC industry classifications. The degree of vertical integration of a business group (x, y) is measured by the degree of investment in each other‟s businesses. The petrochemical system of Formosa Plastics Group basically mimicked Japan‟s regional petrochemical industry connection model of Isard (1951). in Taiwan Tsai (1997). Based on the investment input, the correlation coefficients of petrochemical industry businesses are 7.72 for Formosa Plastics Group and 6.71 for Far Eastern Group (see Appendix 1). As for the degree of diversification, as this study does not use individual company‟s data, there is no need to calculate the weighted entropy index of Palepu (1985). The Formosa Plastics Group has nine companies across four industries (0.44) and the Far Eastern Group has eight companies across seven industries (0.87). Therefore, comparing the two business groups, this study defines the former as having a vertical integration and the later as having a diversification. 2 Refer to United Daily News (2017-05-18), “Family Members of Formosa Plastics Group Withdraw from Executive Centre from June.” https://udn.com/news/story/11142/2471011. Unique Business Weekly (Issue 1011) (2017-10-23), “Profits Tracing by Formosa Plastics Group”. 3Refer to http://www.feg.com.tw/tw/business/important.aspx and https://zh.wikipedia.org/ 4Refer to Wealth Magazine (2017-07-27), “Why does the difference in market values of the two biggest business groups grow larger? Vertical integration of Formosa Plastics Group versus the diversification of Far Eastern Group.” http://www.wealth.com.tw https://udn.com/news/story/11142/2471011 http://www.feg.com.tw/tw/business/important.aspx http://www.wealth.com.tw/ Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 108 hypothesis (EMH) by suggesting that all participating investors in the market are rational, are aimed to maximize their utility and are able to make unbiased estimates based on all available information. As the stock prices follow random walks and investors arbitrage, no abnormal profits exist in the market. More and more evidence reveal market anomalies after 1980s, showing “limited rational behavior” as suggested by behavioral finance. Shiller (1981) finds that the results of NYSE listed companies are completely differently from Sharp‟s asset pricing model. The return of higher risk stocks is lower than the theoretical prediction. The volatility of stock prices cannot be predicted by the discounted present value of premium. Banz (1981) finds that the monthly returns of 50 smallest market cap companies are 1% higher than the returns of 50 largest market cap companies. Lakonishok and Smidt (1988) also find season effect in US stock markets and Cadsby (1989) reports calendar effect in Canadian stock market. As for the herding behavior, Shiller (1979) finds over reaction in speculative asset prices. Investors often trade based on noise trading and have positive feedback behavior. Economists propose reasons from the perspectives of information asymmetry, reputation, return and limited rational behavior. From the information cascade point of view, Bikhchandani et al. (1992) argue that when investors omit private information and simply mimic others, this has great impacts on the markets and is likely to cause a domino effect. Scharfstein and Stein (1990) from the reputation viewpoint suggest that by mimicking other managers‟ investment portfolio, managers can save the cost of information search. They can also shirk responsibility and have less regrets if making investment losses. Maug and Naik (2013) from the return viewpoint argue that due to moral hazard and inverse selection, having optimal contracts between managers and the owner that link remuneration with performance is the best solution. Managers are encouraged to collect information and therefore avoid moral hazard. Also, we can separate good and bad fund managers and avoid inverse selections. Therefore, fund managers tend to have herd behavior. The empirical evidence by Lakonishok et al. (1992) shows herding behavior among fund managers when they trade small companies‟ stocks. Froot et al. (1993) also find herding behavior among financial analysts as they use similar information sources, economic models, investment portfolios and hedging strategies. Christie and Huang (1995) examine the measures for herding effect, stock market returns and dispersion in investment portfolio returns. They find that the smaller the dispersion, the more prominent the herding effect. Wermers (1999) studies the herding behavior of mutual funds between 1975 and 1994 and finds that herding behavior of mutual funds is rational as it can fasten the absorption of information in stock prices and help stabilize the market. However, Kim and Wei (2002) examine the herding behavior of QFIIs in Korea and find that it can increase volatilities in the emerging markets. Moreover, Alanyali et al. (2013) find a positive relationship between the numbers of issues mentioned in Financial Times and daily trading volume. This shows a close relation between changes in financial markets and financial news. Cipriani and Guarino (2014) builds a herding information model and shows that the herding behavior is rational when there is information uncertainty. Herding behavior also typically happens on certain days. On average, there is a 2% of herding buyers and 4% of herding sellers. Balcilar and Demirer (2015) examine Turkish investors and find that apart from industrial departments, US and market related factors cause a transformation in the market, causing herding behavior in all market departments. Furthermore, since the financial tsunami in 2007, Exchange Traded Funds (ETFs) become a popular passive investment tool among retail and professional investors due to its low transaction costs. However, Ben-David et al. (2017) find that although ETFs can help with price discovery, they can inject non-fundamental volatility to market prices and affect the correlation structure of returns. During the events of market stress, ETFs will affect the liquidity of the underlying portfolios and are likely to cause a herding effect of a sudden drop in markets. Taiwan 50 ETF (0050), issued in 2005, is currently the largest ETF in terms of size ($58.6 billion) in Taiwan. Taiwan Mid 100 (0051) was issued in 2007. The fund size is $380 million. This study uses 0050 and 0051 as filters in the experiments to examine the herding behavior of following large business groups. This research studies the herding behavior from the business group viewpoint. Past studies typically measure the degree of dispersion. In contrast, this study proposes a new testing method by utilizing quantitative models and optimal program trading to test the following two hypotheses. The first hypothesis is that including the price information of leading company should lower the impact of selling news on investors. The first hypothesis is tested in two steps with an attempt to find a stabilized investment strategy for trading family business groups‟ stocks. The second hypothesis tests if the trading performance can be enhanced using technical analyzes by including the leading company of the family business group. The second hypothesis can also indirectly prove the existence of herding behavior in business groups. 3. Research Methods 3.1. Theoretical Models and Estimation Methods of VAR and Granger Causality The traditional test of herding effect measures the degree of dispersion. However, this method requires internal trading data. Due the data collection problem, this study uses econometric methods to examine herding effect, the testing methods are as follows: (1) examining if unit roots exist; (2) testing if the model has co-integration; (3) testing the causal relationship between variables in the model; (4) using the variable that has the strongest causal relationship as the leading company and using program trading experiments to test if the herding effect exists. Engle and Granger (1987) suggest that one important function of VAR model is to use co-integration relationship as a restriction in VAR model to examine long-term dynamic relationships between variables in the model. Later, Johansen and Juselius (1988) and Johansen (1991) propose a co-integration test for multi-variables, VAR(P), which is outlined below: tptpttt UYYYCY   ...2211 ………… (1) where ' 1 )...( nttt yyY  and hypothesize )1(~ IYt . After transformation, VAR(P) in Equation (1) can be represented as the following: UYYYYCY ptptpttt   112211 ... ……………. (2) Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 109 where ,...1,...1 piI ii  and pI  ...1 In Equation (2), apart from ptY  , all other variables are stationary. Therefore, similar to VAR(1), the compressed matrix  before vector ptY  can be used to test the co-integration relationship between variables. If the rank of coefficient matrix  is nrrk  , then there exists an adjacency matrix ( rn )  and  . As their ranks are both r, this means ' and ptT  ' is stationary with )0(~' IT pt .  is a co-integrated parameter matrix that reflects the long-term relationship between variables.  is an adjusted coefficient matrix that reflects the short- term imbalance adjustment of this period‟s variable from last period. One method of co-integration test proposed by Johansen is the trace test, which can be calculated as follows: )1(* 1    n ri ir LnTLR  ..............................(3) where i is the eigenvalue of a certain matrix arisen from the testing process. The second method is to use the maximum eigenvalue test, which can is calculated as follows: )1(*max rLnTLR  ................................(4) where i is the maximum eigenvalue. Based on the feature of time series (with or without trend and linearity or secondary type) and the form of co- integration equation (CE) and VAR, Johansen co-integration test can be checked one by one.5 3.2. Theoretical Model and Estimation Method of EGARCH Past research often uses GARCH models to test stock market volatility. However, as many time series data in the financial market do not have normal distribution or do not meet the traditional requirement of homoscedasticity and have fat tails and volatility cluster, Bollerslev (1986) builds a GARCH model based on ARCH. It has become a common method of testing the volatility in stock market returns. The econometrists continue to modify the GARCH model. Nelson (1991) then proposes an EGARCH model. Compared to GARCH models which have restrictions on coefficients, EGARCH (1, 1) can give more appropriate conditional variance and better reflect the volatility in market returns. The EGARCH model is provided below: Mean equation: yt = xt + ut ................................(5) Conditional variance: ................................(6) Moreover, to test the effect on investors when the leading company‟s stock price is or is not included, this paper adopts the method used in Lan et al. (2014;2017) and tests for the difference in  coefficients. The t statistics can be calculated as follows: 2 2 2 1 2 1 12 ˆˆ /)( nn t    ................................(7) where 21, are the  coefficient for including (or excluding) the leading company‟s stock prices. ̂ 2 1 and ̂ 2 2 are the covariance of . n1 and n2 represent the sample size. If the latter is greater than the former and there is a significant difference in coefficients, this suggests that excluding the leading company‟s stock price information in investors‟ investment decisions, investors worry more about their future cash flow risks. Therefore, the results provide support for hypothesis 1. That is, including the stock price information of the leading company can lower the leverage effect and reduce the impact of selling news on investors. 3.3. Experimental Design and Estimation Method Two main research methods in behavioral finance are Structural Equation Modeling (SEM) and experimental methods. As the former requires a carefully designed questionnaire and a large scale of survey to find a suitable theoretical model, this study adopts the experimental method and uses a simulation program in MultiCharts to develop a model for following the leading company‟s stock prices. Specifically, for the Formosa Plastics Group, the leading company of model 1 is Formosa Advanced Technologies and the leading company of model 2 is Nan Ya Printed Circuit Board. Data1 is the price of individual stocks; Data2 is the price of 0050; Data 3 is the stock price of leading company (i.e., Formosa Advanced Technologies for model 1 and Nan Ya Printed Circuit Board for model 2).6 As for the Far Eastern Group, the leading company of model 1 is U-Ming Marine and the leading company of model 2 is Far Eastern Department Stores. Similarly, Data1 is the price of individual stocks; Data2 is the price of 0050; Data 3 is the stock price of leading company (i.e., U-Ming Marine for model 1 and Far Eastern Department Stores for model 2). Then, this study follows the method in Williams (1999) adds in filters and adopts the RSI technical trading strategy in Lan et al. (2014;2017) which is based on the closing price and the breakthrough by the 20-day moving average. Specifically, a “system buy” requires the following three conditions to be met and they are: (1) today‟s closing price of Data2 is higher than 20-day moving average price of Data2; (2) today‟s closing price of Data1 is higher than the 20-day moving average price of Data1; and (3) the RSI of today‟s stock prices is higher than the best buying point‟s RSI. On the contrary, a “system sell” requires three conditions to be met and they are: (1) today‟s closing price of Data2 is lower than 20-day moving average price of Data2; (2) today‟s closing price of 5Due to page limit, the detail discussions are not provided here. 6The choice of leading company is based on Granger causality test results. Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 110 Data1 is lower than the 20-day moving average price of Data1; and (3) the RSI of today‟s stock prices is lower than the best selling point‟s RSI. This study uses the optimized trading program to find the optimal number of days in moving average. The position is closed out if the profit is greater than 500 points or the loss is greater than 100 points. Based on the results from simulated experiments, we can test for hypothesis 2; that is, incorporating the leading company of the business group in the technical analysis can enhance the trading performance in the stock market. This, at the same time, indirectly proves the existence of herding behavior. 4. Data Based on the classifications provided in TEJ database, nine publicly listed companies of the Formosa Plastics Group (including Formosa Plastics (1301), Na Ya Plastics (1303), Formosa Petrochemical (6505), Formosa Chemicals & Fibre (1326), Formosa Taffeta (1434), Nanya Technology (2408), Nan Ya Printed Circuit Board (8046) and Formosa Advanced Technologies (8131) and Formosa Sumco Technology (3532)) and Taiwan 50 ETF (0050) are included as filters. That is, this study has 10 sample set of time series data. The sample period covers from 10 December 2007 to 10 August 2017; that is, a total of 2393 daily sample data.7 As for the Far Eastern Group, eight publicly listed companies (including Asia Cement (1102), Far Eastern New Century (1402), Everest Textile (1460), Oriental Union Chemical (1710), U-Ming Marine (2606), Far Eastern International Bank (2845), Far Eastern Department Stores (2903), Far EsTone Telecommunications (4904)) and Taiwan 50 ETF (0050) are included as filters. That is, nine sample sets of time series data are investigated. The sample period covers from 29 October 2007, the peak before financial tsunami, to 10 August 2017; that is, a total of 2423 daily sample data. All the data mentioned above are obtained from TEJ database and MultiCharts daily stock price database. To ensure that integrity of the model, the experiments are carried out in two stages. For the Formosa Plastics Group, the first stage covers the period from 2007.12.10~2014.12.29 (which is the end of QE). The second stage covers the period from 2007.12.10~2017.8.10. As for the Far Eastern Group, only the starting date differs, where the sample period starts on 29 October 2007. The method of testing the Far Eastern Group is the same as the Formosa Plastics Group. The parameters used in the second stage of simulation are based on the optimal parameters from the first stage. The trading cost in simulated models is assumed to be about 1% of the 200-day moving average of the underlying company‟s stock prices. Transaction fees and slippage are not considered in the experiments. 5. Empirical Results of the Formosa Plastics Group 5.1. Granger Causality Test of Formosa Plastics Group 5.1.1. Unit Root Test of Model Variables To ensure the validity of empirical results, we need to ensure the stationarity of the series by testing the VAR model and choosing the minimal AIC value. The results of Formosa Plastics Group are as follows. Including the intercept and trend (2.7044(0)) does not reject the null hypothesis. That is, the variables are not stationary, have fat tails that are often observed in financial data, and have autocorrelations. Therefore, I(0) is not stationary. After taking a difference (.46.4714(0)), the null hypothesis is rejected and I(1) is stationary (Table 1). Therefore, we can proceed with VAR and Johansen co-integration test. Table-1. Unit root test of VAR model variables of Formosa Plastics Group Original Value First Order Difference Variables / Model Intercept and Trend Intercept and Trend A1301 -2.7044(0) -3.4905(1)** -2.5880(1) -3.6787(0)** -2.3178(0) -3.2634(1)*** -3.3609(0)*** -4.2184(0) ** -2.8096(1) -2.8347(0) -46.4714(0)* -44.9050(0)* -45.5030(0)* -50.9778(0)* -47.7780(0)* -44.5537(0)* -50.3610(0)* -47.3754(0)* -47.5000(0)* -48.7114(0)* A1303 A1326 A1434 A2408 A3532 A6505 A8046 A8131 A50 Note: *，**，*** shows significance level at 1%, 5% and 10%. The number inside the bracket represents the number of lagging periods. (0) shows that when the lag period is 0, it has the minimal AIC. Sample code is as provided in Section 4. 5.1.2. Lag Period Test of the Model In order to proceed with the VAR model estimation, lagging periods must be tested first. The results show that the AIC and FPE of the Formosa Plastics Group are at their minimum when the data are lagged 8 periods (Table 2). This study also tests the maximum likelihood proposed by Johansen and Juselius (1990) to examine the co- integration relationships between multi-variables. The model has five co-integration equations (Table 3). Therefore, we can conduct the Granger causality test. 7As Formosa Sumco Technology (3532) was listed on 10 December 2007, the sample period for Formosa Plastics Group started on that day. Quang Viet Enterprise (4438) was excluded from the Formosa Plastics Group‟s sample as the data of Quang Viet Enterprise was available after 10 December 2007. Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 111 Table-2. Lag period estimation of Formosa Plastics Group‟s VAR model Lag LogL LR FPE AIC SC HQ 0 -61799.68 NA 1.29E+10 51.65874 51.68289 51.66753 1 -34712.05 53926.22 2.063684 29.10326 29.36897* 29.19994 7 -33026.5 2440.603 0.833097 28.19599 29.911 28.82000* 8 -32926.22 193.7792 0.832969* 28.19575* 30.15231 28.90766 11 -32689.69 126.8364* 0.878709 28.2488 30.93001 29.22437 12 -32640.19 94.00331 0.916767 28.29101 31.21377 29.35447 Table-3. Co-integration estimation results of Johansen model for Formosa Plastics Group Trace Max-Eigen No. of CE(s) Eigenvalue Statistic Critical Value(0.05) Prob. Statistic Critical Value(0.05) Prob. None * 0.1982 1955.79 219.40 0 528.53 61.03 0.0001 At most 1* 0.1573 1427.26 179.51 0 409.64 54.97 0.0001 At most 2* 0.1373 1017.62 143.67 0.0001 353.32 48.88 0.0001 At most 3* 0.1278 664.30 111.78 0.0001 327.14 42.77 0.0001 At most 4* 0.1125 337.16 83.94 0 285.54 36.63 0.0001 At most 5 0.0096 51.62 60.06 0.2101 23.00 30.44 0.315 5.1.3. Granger Causality Test As the relationships between variables are not clear based on economic theories, in this case we can use the VAR model to examine the dynamic relationships between variables. Specifically, we assume that the variables are related to each other and regress the variables in the current period with their lag periods. To investigate the investment behavior of Formosa Plastics Group, we include the trading information of nine companies and Taiwan 50 ETF in the VAR model and conduct Granger causality test. The results show that when lagging eight periods, Formosa Advanced Technologies (8 times), Nan Ya Printed Circuit Board (5 times) and Taiwan 50 ETF (4 times) are the top three that have the highest number of Granger cause of other companies. In other words, the investment behavior of the other eight companies of the Formosa Plastics Group all refuse to reject the data of Taiwan 50 ETF and Formosa Advanced Technologies. Therefore, the data of Taiwan 50 ETF and Formosa Advanced Technologies can be treated as endogeneous variables (Table 4). The data of Taiwan 50 ETF and Formosa Advanced Technologies are the Granger cause of other companies and cause herding trading behavior in other companies. Table-4. Granger causality test of Formosa Plastics Group Dependent variable: D(A1301) Dependent variable: A1434 Dependent variable: A6505 Dependent variable: D(P50) Excluded Chi-sq Prob. Excluded Chi-sq Prob. Excluded Chi-sq Prob. Excluded Chi-sq Prob. A1303 19.34 0.01 D(A1301) 10.68 0.22 D(A1301) 6.79 0.56 D(A1301) 14.23 0.08 D(A1326) 26.43 0.00 A1303 20.98 0.01 A1303 12.62 0.13 A1303 11.35 0.18 A1434 14.14 0.08 D(A1326) 5.44 0.71 D(A1326) 8.41 0.39 D(A1326) 5.19 0.74 D(A2408) 2.65 0.95 D(A2408) 7.11 0.52 A1434 7.93 0.44 A1434 16.39 0.04 A3532 18.61 0.02 A3532 11.01 0.20 D(A2408) 4.28 0.83 D(A2408) 1.71 0.99 A6505 13.05 0.11 A6505 10.31 0.24 A3532 9.44 0.31 A3532 38.55 0.00 A8046 21.89 0.01 A8046 11.13 0.19 A8046 5.20 0.74 A6505 4.54 0.81 D(A8131) 20.93 0.01 D(A8131) 14.87 0.06 D(A8131) 20.16 0.01 A8046 12.45 0.13 D(P50) 14.04 0.08 D(P50) 22.66 0.00 D(P50) 7.79 0.45 D(A8131) 22.96 0.00 All 140.86 0.00 All 118.33 0.00 All 102.73 0.01 All 130.16 0.00 Dependent variable: A1303 Dependent variable: D(A2408) Dependent variable: A8046 Dependent variable: D(A8131) Excluded Chi-sq Prob. Excluded Chi-sq Prob. Excluded Chi-sq Prob. Excluded Chi-sq Prob. D(A1301) 10.49 0.23 D(A1301) 4.20 0.84 D(A1301) 17.84 0.02 D(A1301) 19.14 0.01 D(A1326) 9.95 0.27 A1303 6.96 0.54 A1303 12.15 0.14 A1303 6.57 0.58 A1434 9.78 0.28 D(A1326) 1.36 0.99 D(A1326) 9.45 0.31 D(A1326) 5.87 0.66 D(A2408) 2.78 0.95 A1434 8.81 0.36 A1434 8.28 0.41 A1434 10.08 0.26 A3532 13.20 0.11 A3532 1.48 0.99 D(A2408) 2.44 0.96 D(A2408) 1.10 1.00 A6505 11.30 0.19 A6505 1.13 1.00 A3532 82.27 0.00 A3532 33.59 0.00 A8046 14.31 0.07 A8046 7.05 0.53 A6505 7.48 0.49 A6505 4.31 0.83 D(A8131) 23.09 0.00 D(A8131) 4.97 0.76 D(A8131) 25.88 0.00 A8046 19.40 0.01 D(P50) 18.24 0.02 D(P50) 4.03 0.85 D(P50) 15.02 0.06 D(P50) 21.89 0.01 All 124.28 0.00 All 38.79 1.00 All 185.72 0.00 All 137.11 0.00 Dependent variable: D(A1326) Dependent variable: A3532 Excluded Chi-sq Prob. Excluded Chi-sq Prob. D(A1301) 6.67 0.57 D(A1301) 9.15 0.33 A1303 12.98 0.11 A1303 11.62 0.17 A1434 12.34 0.14 D(A1326) 4.47 0.81 D(A2408) 7.09 0.53 A1434 11.87 0.16 A3532 9.66 0.29 D(A2408) 5.08 0.75 A6505 16.45 0.04 A6505 9.96 0.27 A8046 16.10 0.04 A8046 54.20 0.00 D(A8131) 18.33 0.02 D(A8131) 3841.38 0.00 D(P50) 10.24 0.25 D(P50) 70.84 0.00 All 112.94 0.00 All 4186.39 0.00 Note: Prob. means probability. Chi-sq is the χ2 statistics. Sample code is the same as Table 1. D means taking the first difference. Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 112 5.2. Granger Causality Test of Na Ya Plastic, Taiwan 50 ETF and Formosa Advanced Technologies 5.2.1. Lag Period Test In this section, we use Na Ya Plastic, Taiwan 50 ETF and Formosa Advanced Technologies as examples and carry out the VAR model estimation. We need to first test the lagging period and the results show that the AIC and FPE of Na Ya Plastic, Taiwan 50 ETF and Formosa Advanced Technologies are at their minimum when lagging two periods (Table 5). Therefore, this model is estimated using a lag period of two. Also, based on the maximum likelihood estimation proposed by Johansen and Juselius (1990) we test the co-integration relationship between multi-variables. The model has two co-integrated equations (Table 6). Table-5. Lag period estimation of VAR model of Na Ya Plastic, Taiwan 50 ETF and Formosa Advanced Technologies Lag LogL LR FPE AIC SC HQ 0 -13756.69 NA 19.81256 11.49995 11.50719 11.50258 1 -7645.846 12201.25 0.120823 6.400206 6.429192* 6.410753 2 -7622.395 46.76492 0.119373* 6.388128* 6.438854 6.406585* 6 -7592.430 18.20995* 0.119977 6.393171 6.530855 6.443268 Table-6. Co-integration estimation results of Johansen model for Na Ya Plastic, Taiwan 50 ETF and Formosa Advanced Technologies Trace Max-Eigen No. of CE(s) Eigenvalue Statistic Critical Value(0.05) Prob. Statistic Critical Value(0.05) Prob. None * 0.4051 2252.31 24.28 1 1242.90 17.80 1 At most 1 * 0.3440 1009.41 12.32 0.0001 1008.88 11.22 0.0001 At most 2 0.0002 0.54 4.13 0.5261 0.54 4.13 0.5261 5.2.2. Granger Causality Test Three variables, Na Ya Plastic, Taiwan 50 ETF and Formosa Advanced Technologies, are included in the VAR model and conducted the Granger causality test. Results show that when lagging two periods, apart from Taiwan 50 ETF which is not the Granger cause of Na Ya Plastic, Na Ya Plastic, Taiwan 50 ETF and Formosa Advanced Technologies are Granger cause of each other and can be treated as endogenous variables (Table 7). In other words, the three variables refuse to reject the data of each other and we can proceed with the investment simulation in the next stage. Table-7. Granger causality relationships between Na Ya Plastic, Taiwan 50 ETF and Formosa Advanced Technologies A1303 P50 A8131 A1303 - 2.1692 (0.338) 8.8867 (0.0118) P50 11.6966 (0.0029) - 13.1406 (0.0014) A8131 4.4544 (0.0178) 26.7587 (0.0000) - Note: Sample codes are the same as provided in Table 1. 5.3. Estimation of EGARCH Model’s Coefficient and News Impact Response 5.3.1. Estimation Results of EGARCH model (excluding Formosa Advanced Technologies) The values of  (0.0679),  (0.9941),  (0.0452) of the model (excluding Formosa Advanced Technologies) are all significant at the 1% level and are all positive. This suggests the existence of asymmetric volatility. The volatility caused by good news (0.1131) is greater than the impact of bad news on the logarithm of conditional variance (0.022 times) (Table 8). Table-8. Estimation Results of EGARCH model (excluding Formosa Advanced Technologies) Variable Coefficient Std. Error z-Statistic Prob. A1303 0.000142 0.001566 0.090982 0.9275 D(A1326) 0.503892 0.010579 47.63353 0 A1434 -0.00074 0.003351 -0.2206 0.8254 D(A2408) -0.01361 0.014484 -0.93948 0.3475 A3532 -0.00103 0.000507 -2.03818 0.0415 A6505 0.00073 0.000785 0.929408 0.3527 A8046 0.000188 0.000287 0.655265 0.5123 D(P50) 0.47616 0.023113 20.60105 0 Variance Equation C(9) -0.05348 0.006881 -7.77239 0 C(10) 0.067979 0.008613 7.892741 0 C(11) 0.045297 0.0076 5.959912 0 C(12) 0.994168 0.001492 666.2372 0 R-squared 0.526442 Akaike info criterion 2.325313 Log likelihood -2770.24 Schwarz criterion 2.354299 Then, this study draws the news impact curve based on the EGARCH model (excluding Formosa Advanced Technologies) (Figure 1). In order to see the difference between Figure 1 and Figure 2 more easily, the figure includes kernel density at the frame of the figures. The kernel density is a non-parametric way to estimate the Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 113 probability density function of a random variable and can be presented by a non-continuous bar graph. The kernel density of series X at point x can be estimated by: )( 1 )( 1     N i i h Xx K Nh xf ……………………………… (8) where N is the sample size, h is the width based on Silverman (1986) and k is the kernel function. The Epanechnikov density form is given by: )1()1( 4 3 2   I where I is the index function; when 1 , 1 is chosen, or otherwise 0. Figure 1 shows that when the news impact is less than 0 (i.e., when encountering negative news), the curve is flatter. In contrast, the news impact curve is steeper when having positive news. This is likely due to the integration strategy and company policy within the Formosa Plastics Group, which strengthen the function of the business group‟s headquarter.8 Therefore, the effect of negative news on stock prices is weakened. Figure-1. News impact curve of Formosa Plastics Group (excluding Formosa Advanced Technologies) 5.3.2. Estimation Results of EGARCH Model (including Formosa Advanced Technologies) The coefficients of this model (including Formosa Advanced Technologies) are all significant at the 1% level without adding any restrictions. The values of α (0.0661), β (0.9943) and γ (0.0460) are all positive. The value of α + γ is proportional to its sensitivity. When having good news, the impact on the logarithm of conditional variance can be presented as: 0.0661 + 0.0460 = 0.1121 times; when having bad news, the impact on the logarithm of conditional variance can be presented as: 0.0661 + 0.0460*(-1) = 0.0201 times. This suggests that investors do not have greater psychological reactions to bad news (Table 9). Table-9. Estimation results of EGARCH model (including Formosa Advanced Technologies) Variable Coefficient Std. Error z-Statistic Prob. A1303 4.47E-05 0.001562 0.028636 0.9772 D(A1326) 0.504051 0.010627 47.42908 0 A1434 -0.00063 0.0033 -0.18953 0.8497 D(A2408) -0.01376 0.014311 -0.96156 0.3363 A3532 -0.00104 0.000495 -2.09259 0.0364 A6505 0.000754 0.000763 0.987339 0.3235 A8046 0.000203 0.00028 0.723959 0.4691 D(A8131) 0.018598 0.022756 0.817257 0.4138 D(P50) 0.465813 0.025222 18.46823 0 Variance Equation C(10) -0.05208 0.00679 -7.67018 0 C(11) 0.066172 0.008509 7.7765 0 C(12) 0.046068 0.007513 6.131406 0 C(13) 0.994309 0.00147 676.2493 0 R-squared 0.526034 Akaike info criterion 2.325885 Log likelihood -2769.92 Schwarz criterion 2.357287 Based on the EGARCH model results, including Formosa Advanced Technologies, the news impact curve is drawn and shown in Figure 2. The Figure also shows that when the news impact is less than 0 (i.e., when encountering negative news), the curve is flatter. In contrast, the news impact curve is steeper when having positive news. However, compared with Figure 1 (which excludes Formosa Advanced Technologies), the curve is even flatter when Formosa Advanced Technologies is included. This suggests that including Formosa Advanced Technologies can lower the risks and the β of the model (0.99) is close to 1; that is, it is slowly stabilize. Therefore, the effect of negative news on stock prices is weakened. 8Refer to Wealth Magazine (Issue 531, 2017.06.15), “Things that the headquarter of the business groups do.” https://www.wealth.com.tw https://www.wealth.com.tw/ Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 114 Figure-2. News impact curve of Formosa Plastics Group (including Formosa Advanced Technologies) As the γ coefficients are positive no matter the leading company‟s stock prices are included or not, very little difference in figures can be observed in figures. Therefore, this study further test for the difference in γ coefficients. The t statistic is 3.52 (Appendix 2), suggesting a significant difference in γ coefficients of Formosa Advanced Technologies. Investor sentiment is calmer when Formosa Advanced Technologies is included. 5.4. Comparison of Formosa Plastics Group’s Investment Performance The model adopts the stock prices of leading company, Taiwan 50 ETF and other stocks. That is, Data1 is the price of individual stocks; Data2 is the price of 0050 ETF; Data3 is the price of leading company, where Formosa Advanced Technologies is used in model 1 and Nan Ya Printed Circuit Board is used in model 2. The results show that in model 1, the returns increase in the second stage for six companies (Table 10-1). If the investment portfolio includes the eight companies in the Formosa Plastics Group, the investment is profitable. The profits increase from $353.66 in the first stage to $357.86 in the second stage, showing an increase of 12.49%. The results show that this program trading is profitable. However, the performance of Formosa Plastics Group is worse than the whole market by 16.01%. This is probably because the peak in Taiwan‟s stock market is mainly caused by iphone‟s supply chain companies. Table-10.1. Investment returns of model 1, including Formosa Advanced Technologies as the leading company (Unit: $, times, %) Company Code 2007.12.10-2014.12.29 2007.12.10-2017.8.10 Changes in Profits Total Profits Net Profit No. of Transactions Winning Probability Net Profit No. of Transactions Winning Probability A1301 26.56 1 -100 35.88 3 100 9.32 44.2 A1303 25 1 100 25 1 100 0 A6505 14.1 5 80 27.64 9 64 13.54 A1326 48.36 4 75 48.36 4 75 0 A1434 14.34 1 100 14.68 2 100 0.34 A2408 44.6 4 100 59.7 6 100 15.1 A8406 128.7 5 80 132.07 6 83 3.37 A3532 52.0 6 83 54.53 8 75 2.53 Note: The first stage covers the period 2007.12.10~2014.12.29. The second stage covers the period 2007.12.10~2017.8.10. Changes in profits cover the period 2014.10.29~2017.8.10. The results of model 2 show that four companies in model 2 increase the returns in the second stage. The portfolio formed by eight companies in the Formosa Plastics Group is also profitable (Table 10-2). The profit in the first stage is $192.76 and increases by $28.35 (14.7%) in the second stage. The results are better than that in model 1. However, when the profit of $353.66 in model 1 is used as the denominator, the increase is only 8.01%, which is worse than the 12.49% in model 1. Therefore, the model with Formosa Advanced Technologies as the leading company is better than the model with Nan Ya Printed Circuit Board as the leading company. The results of Formosa Plastics Group also provide support for hypothesis 1 and 2. That is, including the stock price data of the leading company can lower the impact of negative news. In addition, after choosing the leading company of the business group, we can use technical analysis to enhance the trading performance in the stock market and we indirectly prove the existence of herding behavior. Table-10.2. Investment returns of model 2, including Nan Ya Printed Circuit Board as the leading company (Unit: $, times, %) Company Code 2007.12.10-2014.10.29 2007.12.10-2017.8.10 Changes in Profits Total Profits Net Profit No. of Transactions Winning Probability Net Profit No. of Transactions Winning Probability A1301 26.81 1 100 48.67 2 100 21.86 28.35 A1303 27.46 1 100 27.46 1 100 0 A6505 11.9 1 100 11.9 1 100 0 A1326 34.54 6 83 40.92 8 75 6.38 A1434 12.23 1 100 12.23 1 100 0 A2408 27.98 2 100 28.68 3 100 0.7 A8131 24.79 4 75 26.55 5 80 1.76 A3532 27.05 6 83 24.7 11 63 -2.35 Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 115 6. Empirical Results of the Far Eastern Group 6.1. Granger Causality Test of the Far Eastern Group 6.1.1. Unit Root Test of Model Variables of Far Eastern Group To ensure the validity of empirical results, we check the stationarity of the series by testing the VAR model and choosing the minimal AIC value. Taking Asia Cement as an example, the results reject the null hypothesis when the intercept and trend (2.9108(0)) are included. That is, the variable is stationary. Therefore, we can proceed with VAR and Granger causality test. Other variables are found to have fat tails and autocorrelation. That is, I(1) is not stationary. After taking a difference, the null hypotheses are rejected (Table 11) and I(0) is stationary. Table-11. Unit root test of VAR model variables of Far Eastern Group Original Value First Order Difference Variables / Model Intercept and Trend Intercept and Trend A1102 -2.9108(0)** -2.9712(0) -3.2906(0)** -2.3558(0) -3.3800(1)** -2.2999(0) -2.3971(1) -2.7583(0) -2.8347(0) -30.8949(2)* -37.5003(0)* -46.5832(0)* -47.3465(0)* -43.2681(0)* -47.5449(0)* -40.2399(0)* -36.7305(1)* -48.7114(0)* A1402 A1460 A1710 A2606 A2845 A2903 A4904 A50 Note: *，**，*** shows significance level at 1%, 5% and 10%. The number inside the bracket represents the number of lagging periods. (0) shows that when the lag period is 0, it has the minimal AIC. Sample code is as provided in Section 4. 6.1.2. Lag-Period Co-integration Test of Far Eastern Group’s VAR Model Before proceeding with the VAR model estimation, lag periods need be tested. The results show that the AIC and FPE of the Far Eastern Group are at their minimum when the data are lagged two periods (Table 12). Therefore, the model is tested with two lagging periods. This study also tests the maximum likelihood proposed by Johansen and Juselius (1990) to examine the co-integration relationships between multi-variables. The model has five co-integration equations (Table 13). Therefore, we can conduct the Granger causality test. Table-12. Lag period estimation of Far Eastern Group‟s VAR model Lag LogL LR FPE AIC SC HQ 0 -40212.81 NA 2399.206 33.32379 33.34537 33.33164 1 -16202.17 47822.35 5.89E-06 13.49807 13.71390* 13.57657* 2 -16048.74 304.4466 5.54e-06* 13.43806* 13.84814 13.5872 8 -15648.49 141.4467* 5.95E-06 13.50911 15.08466 14.08213 Table-13. Johansen co-integration test results Trace Max-Eigen No. of CE(s) Eigenvalue Statistic Critical Value(0.05) Prob. Statistic Critical Value(0.05) Prob. None * 0.4489 5824.35 179.51 0 1442.06 54.97 1.00 At most 1 * 0.3966 4382.29 143.67 0 1222.33 48.88 1.00 At most 2 * 0.3769 3159.96 111.78 1 1144.92 42.77 1.00 At most 3 * 0.3561 2015.04 83.94 1 1065.23 36.63 1.00 At most 4 * 0.3151 949.81 60.06 0.0001 915.82 30.44 0.00 At most 5 0.0087 33.98 40.17 0.1826 21.20 24.16 0.12 Note: * means below the 5% level and rejects H0. 6.1.3. Granger Causality Test of the Far Eastern Group In order to examine the investment behavior of Far Eastern Group, we include the trading information of eight companies and Taiwan 50 ETF in the VAR model and conduct Granger causality test. The results show that when lagging two periods, U-Ming Marine (2606) (5times), Taiwan 50 ETF and Far Eastern Department Stores (2903) (4times) have the highest and second highest number of Granger causes. In other words, the investment behavior of the other eight companies of the Far Eastern Group all refuse to reject the data of Taiwan 50 ETF and U-Ming Marine. That is, they are treated as endogeneous variables (Table 14). Therefore, the data of Taiwan 50 ETF and U-Ming Marine are the Granger cause of other companies and cause herding trading behavior in other companies. 6.2. Granger Causality Test of Asia Cement, Taiwan 50 ETF, and U-Ming Marine 6.2.1. Lag Period Test In this section, we use Asia Cement, Taiwan 50 ETF and U-Ming Marine as examples to carry out the VAR model estimation. We need to first test the lagging periods. The results show that the AIC, FPE and LR of Asia Cement, Taiwan 50 ETF and U-Ming Marine are at their minimum when lagging 10 periods (Table 15). Therefore, this model is estimated using a lag period of 10. Also, based the maximum likelihood estimation proposed by Johansen and Juselius (1990) we test the co-integration relationship between multi-variables. The model has one co-integrated equations (Table 16). Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 116 Table-14. Granger causality test of Far Eastern Group Dependent variable: P2606 Dependent variable: D(P1402) Dependent variable: D(P2903) Excluded Chi-sq Prob. Excluded Chi-sq Prob. Excluded Chi-sq Prob. P1102 4.55 0.10 P2606 4.77 0.09 P2606 17.28 0.00 P1460 2.22 0.33 P1102 0.76 0.68 P1102 13.08 0.00 P50 7.59 0.02 P1460 2.85 0.24 P1460 0.76 0.69 D(P1402) 4.10 0.13 P50 9.67 0.01 P50 3.41 0.18 D(P1710) 0.67 0.71 D(P1710) 2.94 0.23 D(P1402) 34.79 0.00 D(P2845) 8.11 0.02 D(P2845) 2.42 0.30 D(P1710) 0.17 0.92 D(P2903) 3.11 0.21 D(P2903) 28.97 0.00 D(P2845) 1.82 0.40 D(P4904) 1.36 0.51 D(P4904) 6.50 0.04 D(P4904) 3.35 0.19 All 32.28 0.01 All 64.06 0.00 All 206.51 0.00 Dependent variable: P1102 Dependent variable: D(P1710) Dependent variable: D(P4904) Excluded Chi-sq Prob. Excluded Chi-sq Prob. Excluded Chi-sq Prob. P2606 37.31 0.00 P2606 15.54 0.00 P2606 0.30 0.86 P1460 1.20 0.55 P1102 2.08 0.35 P1102 1.30 0.52 P50 1.79 0.41 P1460 1.27 0.53 P1460 1.24 0.54 D(P1402) 27.23 0.00 P50 3.83 0.15 P50 3.98 0.14 D(P1710) 5.45 0.07 D(P1402) 0.14 0.93 D(P1402) 0.49 0.78 D(P2845) 1.37 0.50 D(P2845) 1.72 0.42 D(P1710) 0.14 0.93 D(P2903) 18.80 0.00 D(P2903) 2.64 0.27 D(P2845) 4.64 0.10 D(P4904) 2.07 0.36 D(P4904) 0.41 0.81 D(P2903) 0.32 0.85 All 107.58 0.00 All 45.11 0.00 All 20.74 0.19 Dependent variable: P1460 Dependent variable: D(P2845) Dependent variable: P50 Excluded Chi-sq Prob. Excluded Chi-sq Prob. Excluded Chi-sq Prob. P2606 5.12 0.08 P2606 2.30 0.32 P2606 0.59 0.74 P1102 3.76 0.15 P1102 1.55 0.46 P1102 1.46 0.48 P50 5.51 0.06 P1460 0.31 0.86 P1460 1.49 0.47 D(P1402) 0.97 0.61 P50 6.43 0.04 D(P1402) 10.79 0.00 D(P1710) 1.50 0.47 D(P1402) 0.18 0.91 D(P1710) 5.87 0.05 D(P2845) 3.04 0.22 D(P1710) 4.14 0.13 D(P2845) 4.33 0.12 D(P2903) 2.06 0.36 D(P2903) 11.73 0.00 D(P2903) 7.91 0.02 D(P4904) 0.94 0.62 D(P4904) 0.80 0.67 D(P4904) 1.26 0.53 All 26.89 0.04 All 46.19 0.00 All 40.04 0.00 Note: Prob. means probability. Chi-sq is the χ2 statistics. Sample code is the same as Table 1. D means taking the first difference. Table-15. Lag period estimation of VAR model of Asia Cement, Taiwan 50 ETF (P50), and U-Ming Marine Lag LogL LR FPE AIC SC HQ 1 -7737.154 24911.57 0.181921 6.809450 6.839662 6.820471 2 -7683.505 106.9673 0.174922 6.770216 6.823086* 6.789502 3 -7656.867 53.04309 0.172232 6.754716 6.830246 6.782268* 10 -7587.266 21.63717* 0.171236* 6.748916* 6.983057 6.834326 12 -7575.269 14.37891 0.172143 6.754191 7.033650 6.856132 Table-16. Johansen co-integration test results Trace Max-Eigen No. of CE(s) Eigenvalue Statistic Critical Value(0.05) Prob. Statistic Critical Value(0.05) Prob. None * 0.4489 5824.35 179.51 0 1442.06 54.97 1.00 At most 1 0.3966 4382.29 143.67 0 1222.33 48.88 1.00 6.2.2. Granger Causality Test We include three variables, Asia Cement, Taiwan 50 ETF and U-Ming Marine, in the VAR model and conduct the Granger causality test. The results show that when lagging 10 periods, except that U-Ming Marine is not the Granger cause of Taiwan 50 ETF, all other variables are Granger cause of each other and can be treated as endogenous variables (Table 17). In other words, the three variables refuse to reject the data of each other and we can proceed with the investment simulation in the next stage. Table-17. Granger Causality Relationships between Asia Cement, Taiwan 50 ETF, and U-Ming Marine P1102 P50 P2606 P1102 - 22.3095 (0.0136) 52.0642 (0.0000) P50 23.1639 (0.0102) - 12.7971 (0.2352) P2606 43.1905 (0.0000) 36.1488 (0.0001) - Note: Sample codes are the same as that presented in Table 14. 6.3. Coefficients Estimation of EGARCH Model 6.3.1. Estimation Results of EGARCH Model (Excluding U-Ming Marine) Using log(VAR), the values of  (1.2459) and  (0.9363) of the model (excluding U-Ming Marine) are both significant at the 1% level. As for γ (0.0822), it is positive and significant at the 10% level. This shows the existence of asymmetric volatility. The volatility caused by good news (1.3282) is greater than the volatility caused by bad news (1.1637) (Table 18). The news impact curve of Far Eastern Group excluding U-Ming Marine is presented in Figure 3. Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 117 Table-18. Estimation results of EGARCH model (excluding U-Ming Marine) Variable Coefficient Std. Error z-Statistic Prob. LOG(GARCH) 0.253939 0.013727 18.49924 0 P1460 -1.37272 0.003421 -401.274 0 P50 0.855594 0.000819 1044.124 0 D(P1402) -0.01974 0.029651 -0.66584 0.5055 D(P1710) -0.07774 0.017068 -4.55488 0 D(P2845) 0.012349 0.037818 0.326538 0.744 D(P2903) 0.123528 0.024697 5.001772 0 D(P4904) -0.01338 0.013625 -0.98203 0.3261 Variance Equation C(9) -1.0055 0.039416 -25.51 0 C(10) 1.245943 0.06153 20.24945 0 C(11) 0.082286 0.045586 1.805092 0.0711 C(12) 0.934208 0.016346 57.15351 0 R-squared -0.11256 Akaike info criterion 5.347462 Log likelihood -6463.78 Schwarz criterion 5.376161 Figure-3. News impact curve of Far Eastern Group (excluding U-Ming Marine) 6.3.2. Estimation Results of EGARCH Model (Including U-Ming Marine) Using the log(VAR) method,  (=1.0893),  (=0.5299), and  (=-0.1797) of this model (including U-Ming Marine) are all significant at the 1% level. The results shows that due to leverage effect negative news have greater impacts on investors‟ psychological reactions. The leverage effect of positive news can be presented as: 0.9090=(1.0893-0.1797). The leverage effect of negative news can be presented as: 1.2690=1.0893-0.1797*(-1) (Table 19). The  of the model including U-Ming Marine is smaller than that of the model excluding U-Ming Marine. This suggests that the model stabilizes more quickly. The news impact curve of the Far Eastern Group, including U-Ming Marine, is presented in Figure 4. Table-19. Estimation results of EGARCH model (including U-Ming Marine) Variable Coefficient Std. Error z-Statistic Prob. LOG(GARCH) -1.99369 0.000332 -6010.5 0 P1102 1.408301 4.92E-05 28652.68 0 P1460 -3.35942 0.000292 -11514.9 0 P50 0.746751 8.08E-05 9237.694 0 D(P1402) -0.40108 0.002449 -163.802 0 D(P1710) 0.296476 0.002707 109.5347 0 D(P2845) -0.15351 0.003334 -46.0395 0 D(P2903) -0.38407 0.000308 -1247.76 0 D(P4904) 0.100932 0.003646 27.68309 0 Variance Equation C(10) 0.076418 0.000226 337.6941 0 C(11) 1.089367 0.000739 1473.486 0 C(12) -0.17974 0.000256 -701.306 0 C(13) 0.529939 0.000348 1521.322 0 R-squared 0.75463 Akaike info criterion 6.527433 Log likelihood -7891.72 Schwarz criterion 6.558523 Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 118 Figure-4. News impact curve of Far Eastern Group (including U-Ming Marine) Figure 3 and 4 shows that returns and risks are significantly different depending on weather U-Ming Marine is included. This study also tests for the differences in γ coefficients. The t statistic is 105.16, suggesting significant differences in γ. The results show investor sentiment is calmer when excluding U-Ming Marine. 6.4. Comparison of Far Eastern Group’s Investment Performance The model adopts the stock prices of leading company, Taiwan 50 ETF and other stocks. That is, Data1 is the price of individual stocks; Data2 is the price of 0050 ETF; Data3 is the price of leading company, where U-Ming Marine is used in model 1 and Far Eastern Department Stores is used in model 2. The results show that in model 1, only two companies have an increase in investment returns in the second stage. If the investment portfolio includes the eight companies in Far Eastern Group, the investment is profitable (Table 20-1). The profit in the first stage is $132.18 but it decreases to $129.41 in the second stage, showing a fall of 0.0209%. Therefore, this program trading is not profitable. Table-20.1. Investment returns of model 1, including U-Ming Marine as the leading company (Unit: $, times, %) Company Code 2007.10.29-2014.10.29 2007.10.29-2017.8.10 Changes in Profits Total Profits Net Profit No. of Transactions Winning Probability Net Profit No. of Transactions Winning Probability A1102 17.7 7 100 13.99 7 85 -3.71 -2.77 A1402 18.12 4 100 19.7 5 100 1.58 A1460 12.24 3 100 13.13 4 100 0.89 A1710 21.35 15 66 20.2 20 55 -1.15 A2606 - - - - - - 0 A2845 4.18 11 72 3.8 13 61 -0.38 A2903 28.56 4 100 28.56 4 100 0 A4904 30.03 2 100 30.03 2 100 0 Note: The first stage covers the period 2007.10.29~2014.10.29. The second stage covers the period 2007.10.29~2017.8.10. Changes in profits cover the period 2014.10.29~2017.8.10. The results of model 2 show that only one company (U-Ming Marine) has an increase in investment returns in the second stage. The portfolio formed by eight companies in the Far Eastern Group as a whole is profitable (Table 20-2). The profit of the investment portfolio in the first stage is $141.29 and increases by $12.07 (8.54%) in the second stage. The findings suggest that model 2 with Far Eastern Department Stores as the leading company is better than model 1 with U-Ming Marine as the leading company. However, when U-Ming Marine is excluded from model 2, it becomes unprofitable. Therefore, the results from Far Eastern Group do not support hypothesis 1 or 2. Specifically, the leading company of the Far Eastern Group is not useful for enhancing the profits. The program trading simulation results also suggest that the diversification strategy of the Far Eastern Group is not as good as the vertical integration strategy of the Formosa Plastics Group. Therefore, when investors are choosing a business group for investing based on herding effect, they should choose carefully.9 Table-20.2. Investment returns of model 2, including Far Eastern Department Stores as the leading company (Unit: $, times, %) Company Code 2007.10.29-2014.10.29 2007.10.29-2017.8.10 Changes in Profits Total Profits Net Profit No. of Transactions Winning Probability Net Profit No. of Transactions Winning Probability A1102 26.89 2 100 26.89 2 30 0 12.07 A1402 18.52 9 66 15.83 11 63 -2.69 A1460 11.11 1 100 11.11 1 100 0 A1710 17.36 3 100 17.36 3 100 0 A2606 56.83 3 100 72.77 4 100 15.94 A2845 4.04 6 50 4.04 6 50 0 A2903 0 - - 0 - - 0 A4904 6.54 2 100 5.36 3 66 -1.18 9This study has tried using Taiwan Mid 100 in the model instead of Taiwan 50. However, the sum of α (1.4335) and γ (0.4867) is greater than 1, suggesting that this model is not stationary. The program trading simulation also leads to similar conclusion. Therefore, due to page limit, the test results are not provided here. Asian Journal of Economics and Empirical Research, 2017, 4(2): 106-120 119 7. Conclusion and Discussion on Investment Strategies The aim of this study is to examine the difference in operating performance for two family business groups, Formosa Plastics Group and Far Eastern Group, after the impact of financial tsunami (2007.10.29~2017.08.10). This research helps investors understand the operating model of business groups and learn how to use the herding effect of business groups to enhance their trading performance in financial markets. The results show that for the Formosa Plastics Group, the news impact curve (based on EGARCH model) including the leading company is flatter than when the news impact curve excludes the leading company. In contrast, the news impact curve of the Far Eastern Group is steeper when the leading company is included. Moreover, when the leading company is include as an endogeneous variable in the model as a filter for the program trading simulation, the net profits for the first stage (2007.10.29~2014.12.29) and the second stage (2007.10.29~2017.08.10) are 12.49% and -0.02%, respectively. Therefore, this program trading of the Formosa Plastics Group can lead to trading profits. In sum, business groups that include the leading company have lower risks. It is also beneficial to the stability of the market trading by incorporating the leverage effect of the leading company in business groups. The results show that the Far Eastern Group does not support hypothesis 1 or hypothesis 2. In other words, the leading company of the Far Eastern Group does not have such an effect. The absolute profits and the increment of performance are both lower than that of the Formosa Plastics Group. 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The basic information of Formosa Plastics Group and Far Eastern Group Unit: $, %, „000 million Business Group Code Company Name Year Establish Industry Classification (correlation coefficient*) Stock Price (2017.8.10) Net Profits (2016) EPS (2016) Market Value (7.21) Stock holdings (%) Board Chairman Formosa Plastics Group 1301 Formosa Plastics 1954 Plastics (6.78) 92.6 394 6.19 5825 36 LIN JIAN NAN 1303 Na Ya Plastics 1958 Plastics (6.78) 75.4 484 6.16 5932 43 WU JIA ZHAO 1326 Formosa Chemicals & Fibre 1965 Plastics (6.78) 91.5 438 7.5 5322 47 WANG WEN YUAN 1434 Formosa Taffeta 1973 Textile (6.76) 29.7 35 2.07 535 37 WANG WEN YUAN 2408 Nanya Technology 1995 Electronic (7.32) 60.5 237 8.67 1740 33 WU JIA ZHAO 3532 Formosa Sumco Technology 1995 Electronic (7.32) 88.5 7 0.94 691 29 LIN JIAN NAN 6505 Formosa Petrochemical 1992 Oil and electricity (13.16) 103.5 758 7.95 10002 76 CHEN BAO LANG 8046 Nan Ya Printed Circuit Board 1997 Electronic (7.32) 23.35 -7 -1.07 158 67 WU JIA ZHAO 8131 Formosa Advanced Technologies 1990 Electronic (7.32) 27.2 10 2.31 121 66 WANG WEN YUAN Far Eastern Group 1102 Asia Cement 1957 Cement (14.8) 26.55 39 1.26 889 22 XU XU DONG 1402 Far Eastern New Century 1954 Textile (6.76) 24.35 63 1.26 1314 24 XU XU DONG 1460 Everest Textile 1988 Textile (6.76) 26.1 5 1.2 77 25 XI JIA YI 1710 Oriental Union Chemical 1975 Chemical (7.61) 26.1 -6 -0.63 255 43 XU XU DONG 2606 U-Ming Marine 1968 Shipping (6.13) 32.8 -8 -1.04 270 39 XU XU DONG 2845 Far Eastern International Bank 1992 Finance (4.64) 9.93 32 1.04 309 42 HOU JIN YING 2903 Far Eastern Department Stores 1967 Department store (3.43) 15.1 11 0.81 215 40 XU XU DONG 4904 Far EsTone Telecommunications 1997 Telecommunication (3.62) 73.3 114 3.5 2395 38 XU XU DONG Note: *including forward and backward correlation coefficient (http://www.dgbas.gov.tw/lp.asp?CtNode=2340&CtUnit=1088&BaseDSD=7&mp=1) Appendix-2. Test for difference in  coefficients of EGARCH model Formosa Plastics Group Far Eastern Group γ coefficient Std Dev. T γ coefficient Std Dev. T Including leading company 0.046068 0.0075 3.52 -0.1797 0.0003 105.16 Excluding leading company 0.045297 0.0076 0.0823 0.0456 Asian Online Journal Publishing Group is not responsible or answerable for any loss, damage or liability, etc. caused in relation to/arising out of the use of the content. 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