Different from the data of Chow [29], who respectively used individual stocks of the Hang Seng Index, we try to build a general model by different kinds of industrial data for the first time. The data in our models can be divided by two parts. First, similar to the previous models, we focus on individual stock of the stock market index, which included TWSE Taiwan 50 Index, TWSE Taiwan Mid-Cap 100 Index, and TWSE Taiwan Dividend+ Index. Secondly, we try to consider the data of the eight major sectors, which included Cement & Ceramics, Foods, Plastics & Chemicals, Textiles, Electric & Machinery, Construction, Finance, and Paper sectors, into nonlinear model.
Table 1. The individual stock of the TWSE Taiwan 50 Index
Companies Companies
11 China Stell Corporation 36 China Development Financial Holding Corporation
12 Hotai Motor Co., Ltd 37 Yuanta Financial Holdings
13 Cheng Shin Rubber Ind., Co., Ltd. 38 Mega Financial Holding Co.,
14 LITE-ON Technology Corporation 39 Sinopac Financial Holding Company Limited 15 United Microelectronics Corporation 40 Chinatrust Financial Holding Company Ltd.
16 Delta Electronics, INC 41 First Financial Holding Co. Ltd.
17 Advanced Semiconductor Engineering Inc 42 President Chain Store Corporation 18 Hon Hai Precision Ind. Co., Ltd. 43 Largan Precision Co., Ltd
19 Compal Electronics, Inc. 44 Taiwan Mobile CO., LTD.
20 Siliconware Precision Industries Co.,Ltd 45 Wistron Corporation 21 Taiwan Semiconductor Manufacturing Co., Ltd. 46 CHIMEI Innolux Corporation 22 Synnex Technology International Corporation 47 TPK Holding Co., Ltd.
23 ACER Incorporated 48 Far EasTone Telecommunications Co., Ltd.
24 Foxconn Technology Co., Ltd 49 Taiwan Cooperative Bank 25 Asustek Computer Inc. 50 Formosa Petrochemical Corporation
According to TWSE Taiwan 50 Index, similar to the Dow Jones Index for industrial stocks of the New York Stock Exchange, which consists of the fifty blue-chip stocks in the Taiwan Stock Exchange. There are fifty representative stocks of TWSE Taiwan 50
Index listed in Table 1. The market value of TWSE Taiwan 50 Index accounted for 70%
of the market.
Table 2. The individual stock of the TWSE Taiwan Mid-Cap 100 Index
Companies Companies
12 Oriental Union Chemical Corp. 62 President Securities Corp.
13 Eternal Chemical Co., Ltd 63 E. Sun Financial Holding Company ,Ltd.
19 Hiwin Technologies Corp. 69 Ruentex Industries Limited 20 NanKang Rubber Tire Corp., Ltd 70 Novatek Microelectronics Corp.
21 Tsrc Corporation 71 Unimicron Technology Corp.
22 Kenda Rubber Industrial Co., Ltd 72 Tripod Technology Corporation 23 China Motor Corporation 73 Kinsus Interconnect Technology Corp.
24 Yageo Corporation 74 Genius Electronic Optical Co., Ltd.
25 Macronix International Co., Ltd 75 Inotera Memories, Inc.
26 Winbond Electronics Corp. 76 MStar Semiconductor, Inc.
27 Inventec Corporation 77 WPG Holdings Limited
28 Chroma Ate Inc. 78 Taiwan Prosperity Chemical Corporation
29 Clevo Co. 79 Pegatron Corporation
30 Tatung Co. 80 Zhen Ding Technology Holding Limited
31 Realtek Semiconductor Corp 81 Farglory Land Development Co., Ltd
32 Wintek Corporation 82 Chailease Holding Company Limited
33 Chicony Electronics Co., Ltd 83 Capital Securities Corp.
34 VIA Technologies, Inc. 84 Radiant Opto-Electronics Corp.
35 Cheng Uei Precision Industry Co., Ltd 85 Powertech Technology Inc.
36 Everlight Electronics Co., Ltd. 86 Flexium Interconnect Inc
37 Advantech Co., Ltd. 87 Wistron NeWeb Corporation
38 EPISTAR corporation 88 Richtek Technology Corp.
39 Senao International Co.,Ltd. 89 Lite-On IT Corporation
40 Transcend Information, Inc. 90 Nan Ya Printed Circuit Board Corporation 41 Cathay Real Estate Development Co., Ltd 91 Compal Communications Inc.
42 Golddsun Development & Construction Co., Ltd 92 Cleanaway Company Limited 43 Prince Housing & Development Corp. 93 Pou Chen Corporation
50 Evergreen International Storage & Transport 100 Ruentex Development Co., Ltd.
Simultaneously, we also use individual stock of the other stock market index. There are one hundred representative stocks of TWSE Taiwan Mid-Cap 100 Index listed in Table 2. TWSE Taiwan Mid-Cap 100 Index is made up of the 100 large, publicly owned companies in Taiwan, which except for individual stock of the TWSE Taiwan 50 Index.
In other words, the individual stock of TWSE Taiwan Mid-Cap 100 Index are ranked from 51th to 150th in the Taiwan Stock Exchange. In comparison with the market value of TWSE Taiwan 50 Index, TWSE Taiwan Mid-Cap 100 Index accounted for 20% of the market. The individual stock of TWSE Taiwan Dividend+ Index are listed in Table 3.
TWSE Taiwan Dividend+ Index is composed of the 30 listed companies in individual stock of the TWSE Taiwan 50 Index and the TWSE Taiwan Mid-Cap 100 Index, which predicts the cash dividend yield will be higher in the next year. In other words, the individual stock in the TWSE Taiwan Dividend+ Index are selected from 150 large, outstanding stocks which ranked in the Taiwan Stock Exchange.
Table 3. The individual stock of the TWSE Taiwan Dividend+ Index
Companies Companies
1 Taiwan Cement Corporation 16 Quanta Computer Inc.
2 Formosa Plastics Corporation 17 Chicony Electronics Co., Ltd 3 Nan Ya Plastics Corporation 18 Chunghwa Telecom Co., Ltd 4 Formosa Chemicals & Fibre Corporation 19 Transcend Information, Inc.
5 Oriental Union Chemical Corp. 20 MediaTek Inc.
6 Eternal Chemical Co., Ltd 21 Highwealth Construction Corp.
7 Tung Ho Steel Enterprise Corp. 22 Huaku Development Co., Ltd
8 Tsrc Corporation 23 U-Ming Marine Transport Corp.
9 LITE-ON Technology Corporation 24 Mega Financial Holding Co., 10 United Microelectronics Corporation 25 Novatek Microelectronics Corp.
11 Compal Electronics, Inc. 26 Taiwan Mobile CO., LTD.
12 Siliconware Precision Industries Co.,Ltd 27 Wistron Corporation
13 Yageo Corporation 28 Far EasTone Telecommunications Co., Ltd.
14 Macronix International Co., Ltd 29 Farglory Land Development Co., Ltd 15 Realtek Semiconductor Corp 30 Lite-On IT Corporation
Furthermore, the individual stock of the eight major sectors are reported in the Appendix D. Since different companies have different time to be a listed company and did not issue dividends in cash every year, the total information of the data is listed in Table 4. To fulfill the purpose of researches, which investigate how dividends, growth
rate of dividends, nominal risk-free rates and risk premiums affect individual stock prices, we build the unbalanced panel data. For the stock market index, the date covers a period from 1991 to 2010 and total number of observations respectively are 496, 817 and 326. In the second section, we consider individual stock of the eight major sectors in Taiwan. The eight major sectors we selected in Taiwan Stock Exchange are respectively Cement & Ceramics sector, Foods sector , Plastics & Chemicals sector, Textiles sector, Electric & Machinery sector, Construction sector, Finance sector, and Paper sector. We discover that the samples of individual stock in Paper sector has minimum amount in eight sectors and different sample period.
Table 4. Data Information
Stock Market Index Period firms observations
TWSE Taiwan 50 Index 1991~2010 48 496
TWSE Taiwan Mid-Cap 100 Index 1991~2010 93 817
TWSE Taiwan Dividend+ Index 1991~2010 29 326
Eight Major Sectors period firms observations
Cement & Ceramics 1991~2010 11 133
Foods 1991~2010 18 160
Plastics & Chemicals 1991~2010 52 473
Textiles 1991~2010 32 199
Electric & Machinery 1991~2010 35 295
Construction 1991~2010 35 189
Finance 1991~2010 31 221
Paper 1994~2010 5 35
In this research we will use four models, built upon the assumption of adaptive expectation, to explain the prices of stocks in Taiwan. Following the model of Chow [2], our model only implies that the logarithm stock price is a linear function of expected log dividends, expected log rate of growth in model 1. In regards to data for stock prices, the price of stock was reflected by the market value of the listed company; when a listed company issues cash dividends, the market value of the stock prices will reduce.
For market value of post-dividend stocks, we use the ex-dividend stock prices to build the unbalanced panel data. Consequently, since the data ranges across a time span of 20 years, we will also take the effect of inflation into account. To solve the issue with inflation, we use the GDP deflator (2006 = 100), which is a measurement of the level of prices of all new, domestically produced, final goods and services in an economy, to process the data. To calculate the real stock prices, we will divide the ex-dividend stock prices by the GDP deflator. For dividends data, the GDP deflator is also used to process the data. After the calculations, we build the data called real cash dividends.
Besides, different from Chow [2], we add two discount factors, nominal risk-free rates and risk premiums into our model. The beta for TWSE Taiwan 50 Index is shown in Table 5. We discover that the average beta for individual stocks of the TWSE Taiwan 50 Index is higher in the Global Financial Crisis in 2009. Furthermore, we also note that the average of individual betas is highest than each years, when Asian Financial crisis happened in 1997.
Table 5. The beta for TWSE Taiwan 50 Index, 1991-2010
Table 6 shows descriptive statistics of beta for individual stock of the eight major sectors. The mean beta of Electric & Machinery sector is at the summit in 20 years, which suggests that the individual stock may have higher systematic risk. We also
Year Mean Std. Dev. Year Mean Std. Dev.
1991 0.9391 0.0742 2001 1.0139 0.3039
1992 0.8525 0.2606 2002 0.9499 0.3679
1993 0.8660 0.1467 2003 0.9818 0.2975
1994 0.9523 0.2190 2004 0.9865 0.2707
1995 0.8996 0.1980 2005 0.9825 0.4186
1996 0.9203 0.2055 2006 1.0099 0.3851
1997 1.1597 0.3523 2007 1.0223 0.2591
1998 1.1302 0.3008 2008 1.0454 0.2593
1999 0.9915 0.1899 2009 1.0699 0.2979
2000 0.9425 0.2040 2010 1.0067 0.2837
discover that Construction sector have the highest standard deviation in eight major sectors. This result indicates that the beta of Construction sector may have higher volatility than others.
Table 6. The beta for eight major sectors, 1991-2010
Sector Mean Median Maximum Minimum Std. Dev.
Cement & Ceramics 0.8380 0.8124 2.6195 0.665 0.3139
Foods 0.8461 0.8466 2.1119 0.2327 0.2802
Plastics & Chemicals 0.8888 0.9045 1.7285 0.1787 0.2294
Textiles 0.9812 0.9981 1.8853 0.1025 0.2489
Electric & Machinery 1.0597 1.0437 1.9658 0.2737 0.1904
Construction 0.9471 0.9325 2.7373 0.2665 0.3366
Finance 1.0488 1.0363 1.9239 0.2477 0.2419
Paper 0.9278 0.9471 2.7135 0.2605 0.3209
Figure 1 gives plots of the variance of market return from 1991 to 2010 in Taiwan.
Similar to the average beta in TWSE Taiwan 50 Index, the variance of market return is higher in the Global Financial Crisis in 2009. Based on the results of Robert Merton [8], we consider that risk premium is the sector’s beta times the variance of market return in our models. Hence, the higher variance of market return may cause higher risk premiums in this year.
Figure 1. The variance of market return in Taiwan, 1991-2010
0
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
th e v ar ia n ce o f m ar ke t re tur n
We directly use the one-year deposit rates to represent nominal risk-free rates. Figure 2 gives plots of the one-year deposit rates series from 1991 to 2010 in Taiwan.
Figure 2. One-year deposit rates series in Taiwan, 1991-2010 Sources: Central Bank of Republic of China (Taiwan)
We can discover that the trend of one-year deposit rates are gradually reduced from 1991 to 2010. Since the Internet bubble and the September 11th event were in early 2000’s, America’s economy suffered the recession. Governments in other countries adopt the easy money policy which has the great effect of reducing deposits rates to encourage their domestic economies. From 2000 to 2001, Government in Taiwan rapidly cut down the one-year deposit rates from 5% to 2.41%, which means a 51.8%
reduction. We note that one-year deposit rates are maintained around 2% after the year of 2001. Furthermore, when Financial crisis happened in 2009, the one-year deposit rates was reduced under 1%.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
o n e- y ea r de po si t ra te s
Table 7 contains the results of applying unit root tests to log stock price series. We discover that the unit root hypothesis are rejected in log stock price series of TWSE Taiwan Mid-Cap 100 Index and Electric & Machinery sector. The result indicates that the log stock price series of TWSE Taiwan Mid-Cap 100 Index and Electric &
Machinery sector are stationary series. And we note that the stock price series of TWSE Taiwan 50 Index and TWSE Taiwan Dividend+ Index are stationary when the log stock price series are first differenced. Furthermore, the log stock prices series in Cement &
Ceramics, Foods, Plastics & Chemicals, Textiles, Construction, Finance and Paper sector are stationary when the series are first differenced.
Table 7. Unit root tests in stock price series
Stock Market Index ADF – Intercept
s △s
TWSE Taiwan 50 Index 76.0678 (0.2895) *240.330 (0.0000)
TWSE Taiwan Mid-Cap 100 Index *119.299 (0.0914)
TWSE Taiwan Dividend+ Index 55.9100 (0.2021) *176.464 (0.0000)
Eight Major Sector ADF - Intercept
s △s
Cement & Ceramics 25.2871 (0.1907) *65.3129 (0.0000)
Foods 10.2091 (0.9936) *43.1105 (0.0020)
Plastics & Chemicals 70.6650 (0.4553) *164.124 (0.0000)
Textiles 35.7078 (0.3881) *97.5862 (0.0000)
Electric & Machinery *71.9905 (0.0225)
Construction 42.3539 (0.2158) *61.3339 (0.0001)
Finance 44.0598 (0.4691) *79.4822 (0.0002)
Paper 8.6578 (0.3720) *17.2769 (0.0083)
NOTE. The null hypothesis is that the series in question contains a unit root in its univariate autoregressive representation. ADF is the regression t-ratio for the autoregressive coefficients to sum to unity-the augmented Dickey-Fuller statistic; * p < 0.1. ; (．):
p-value; s: log stock prices; △s: difference of log stock prices
Table 8 contains the results of applying unit root tests to log dividends series. Our conjecture that the log dividends series are stationary in the TWSE Taiwan 50 Index, TWSE Taiwan Mid-Cap 100 Index, Foods, Plastics & Chemicals, Textiles, Electric &
Machinery, Construction, and Finance sector. Furthermore, the log dividends series in TWSE Taiwan Dividend+ Index, Cement & Ceramics Sector and Paper Sector are stationary when the series are first differenced.
Table 8. Unit root tests in dividends series
Stock Market Index ADF – Intercept
dvd △dvd
TWSE Taiwan 50 Index *113.086 (0.0009)
TWSE Taiwan Mid-Cap 100 Index *123.570 (0.0551)
TWSE Taiwan Dividend+ Index 49.6398 (0.4077) *134.740 (0.0000)
Eight Major Sector ADF - Intercept
dvd △dvd
Cement & Ceramics 22.9366 (0.2919) *92.9127 (0.0000)
Foods *45.1695 (0.0056)
NOTE. The null hypothesis is that the series in question contains a unit root in its univariate autoregressive representation. ADF is the regression t-ratio for the autoregressive coefficients to sum to unity-the augmented Dickey-Fuller statistic; * p < 0.1. ; (．):
p-value; dvd: log dividends; △dvd: difference of log dividends
Table 9 lists the results of tests for unit roots in risk premiums and nominal risk-free rates series. Since the beta value, which measured the total market risk, is a constant figure of one in stock market index, the value of risk premiums will be the variance of market return. Hence, the risk premiums series are equal in TWSE Taiwan 50 Index, TWSE Taiwan Mid-Cap 100 Index and TWSE Taiwan Dividend+ Index. We discover that the unit root hypothesis are rejected at the 10% level in log risk premiums series of the Stock Market Index. The result suggests that the log risk premiums series in stock market index are stationary.
Table 9. Unit root tests in risk premiums and nominal risk-free rates series
Stock Market Index ADF – Intercept
m △m
TWSE Taiwan 50 Index *104.592 (0.0000)
TWSE Taiwan Mid-Cap 100 Index *104.592 (0.0000)
TWSE Taiwan Dividend+ Index *104.592 (0.0000)
NOTE. The null hypothesis is that the series in question contains a unit root in its univariate autoregressive representation. ADF is the regression t-ratio for the autoregressive coefficients to sum to unity-the augmented Dickey-Fuller statistic; * p < 0.1. ; (．):
p-value; m: log risk premiums; △m: difference of log risk premiums; r: log nominal risk-free rates; △r: difference of log nominal risk-free rates
In the eight major sectors, we discover that the log risk premiums series of Cement &
Ceramics, Foods, Plastics & Chemical, Textiles, Electric & Machinery and Finance sectors are stationary. And the unit root hypothesis of log risk premiums series in Construction sector can be rejected at the 10% level when the series are first differenced.
Table 9 also presents the result of unit root test in the log nominal risk-free rates series.
The result shows that the unit root hypothesis can be rejected at the 10% level. In other words, the log nominal risk-free rates series are stationary in all data.
Table 10 summarizes the results from individual stock of the TWSE Taiwan 50 Index, in which assumes all parameters follows the adaptive expectation hypothesis.
Table 10. Results in the TWSE Taiwan 50 Index
TWSE Taiwan 50 Index
Under the assumption of adaptive expectation, the adjustment coefficients c, b, e, and
h in the adaptive formation of expected level of log dividends, expected log rate of
growth, expected log risk-free rates and expected level of log risk premiums, respectively, must between zero and one. If the adjustment coefficients are over than one, which means the assumption of the adaptive expectation would be violated. The standard errors of the parameter estimates are given in parentheses. The point estimates of the βi coefficients are unconstrained least squares estimates provided for reference.From the first column of Table 10, the adjustment coefficients c and b in the formation of expected dividends and expected rate of growth are respectively 0.0547 and 1.1722. Different from the previous models of Chow, the adjustment coefficients b for the formation of expected rate of growth would violate the assumption of adaptive expectation. Column 2 of Table 10 shows the results of model 2, we also find that the adjustment coefficients h for the formation of expected level of log risk premiums is over than one. In model 3, the adjustment coefficients c in the adaptive formation of expected level of dividends is not significant. Similar to the previous models, the adjustment coefficients c for the formation of expected level of log dividends is 1.4224 in model 4, which means the data is inconsistent with the adaptive expectation hypothesis. In spite of the adjustment coefficients c is inconsistent with the adaptive expectations in model 4, the coefficients δ, α for Etdt and Etgt in the equation for log stock price are 0.1824 and
. The positive results suggest that expected level of
log dividends and expected level rate of growth may contribute to the current pricing in individual stock of the TWSE Taiwan 50 Index.Table 11 shows the result from individual stock of the TWSE Taiwan Mid-Cap 100 Index. Similar to the results of TWSE Taiwan 50 Index, we also discover that the adjustment coefficients b for the formation of expected rate of growth are inconsistent with the adaptive expectations in model 1 and 3. Besides, the adjustment coefficients c
in model 2 and the adjustment coefficients h in model 4 are both inconsistent with the adaptive expectations. However, we still discover that the coefficients δ, ω for Etdt and Etmt in the equation for log stock price are significant in model 4.
Table 11. Results in the TWSE Taiwan Mid-Cap 100 Index
TWSE Taiwan Mid-Cap 100 Index
α 0.5091 (.7030) 0.0795 (.0598) 0.0636 (.0550) 0.0142 (.0185)
ω - 0.5336 (.2738) - 0.1977 (.0627)*
Table 12 summarizes the result from individual stock of the TWSE Taiwan Dividend+ Index. The results are similar to those achieved by Chow [35]; the adjustment coefficients c and b are respectively 0.2079 and 1.0977 in model 1. The relative weights of expected level of dividends and expected rate of growth in the determination of log stock price are as given by δ and α. The coefficients δ、α for Etdt
and Etgt in the equation for log stock price are 0.3182 and
0.0587. The result of
significantly positive expected level of log dividends indicates that more cash dividends issued may cause the stock price upswing. Column 2 of Table 12 shows the results of model 2, we find that the adjustment coefficients b for the formation of expected rate of growth is 1.2202, which violates the assumption of adaptive expectation. In model 3, the adjustment coefficient c for the formation of expected level of dividends is inconsistent with the adaptive expectation hypothesis.From the Column 4 of Table 12, the adjustment coefficients c, b, e, and h are respectively 0.9858, 0.2095, 0.9844 and 1.1289, which suggests the data is consistent with the adaptive expectation hypothesis in model 4. The coefficients δ、α for Etdt and Etgt in the equation for log stock price are 0.4696 and
1.9384. The result of
significantly negative expected level of growth rate indicates that investors in individual stocks of the TWSE Taiwan Dividends+ Index who does not believe that recent growth of dividend rate can let stock price upswing. In spite of the adjustment coefficients e andh are consistent with the adaptive expectation hypothesis, the coefficients γ and ω for
Etrt and Etmt in the equation for log stock price are both not significant. The results suggest that expected log free-risk rates and expected level of log risk premiums may not contribute to the current pricing in individual stocks of the TWSE Taiwan Dividends+ Index. To summarize the results from individual stock of the stock market index, we discover that only the data of TWSE Taiwan Dividend+ Index are consistent with the assumption of adaptive expectation in model 1 and 4.Table 12. Results in the TWSE Taiwan Dividend+ Index
α 0.0587(.0259)* 0.0290(.0225) 0.0381 (.0214) 1.9384(.7425)*
ω - 0.1789 (.1140) - 0.0632 (.2122)
The result of models from individual stock of the Cement and Ceramics sector is listed in Table 13.
Table 13. Results in the Cement and Ceramics sector
Cement and Ceramics sector
α 0.0373(.4137) 0.3888(1.1744) 0.4133 (2.0994) 0.3714 (1.1836)
ω - 0.1176 (0.1079) - 0.0449 (.1417)
From the first column of Table 13, we discover that the adjustment coefficients c and
b are respectively 0.3245 and 0.9205 in model 1. However, the coefficients δ, α for E
tdt and Etgt in the equation for log stock price are not significant. This result suggests that expected level of log dividends and expected rate of growth as projected by adaptive expectations does not contribute to the current pricing of Cement & Ceramics sector.Furthermore, the data of Cement and Ceramics sector are inconsistent with the adaptive expectation hypothesis in model 2, 3 and 4.
Table 14 summarizes the result from individual stock of the Foods sector. In spite of the adjustment coefficients c and b in the adaptive formation of expected level of log dividends, expected rate of growth are respectively 0.4210, and 0.7208, the coefficients
δ, α for E
tdt and Etgt in the equation for log stock price are not significant in model 1.These results suggest that the expected level of log dividends and expected rate of growth as projected by adaptive expectations does not contribute to the current pricing of Food sector. In model 2, the adjustment coefficients b and h in the adaptive formation of expected rate of growth and expected risk premiums are not significant. Hence, the
These results suggest that the expected level of log dividends and expected rate of growth as projected by adaptive expectations does not contribute to the current pricing of Food sector. In model 2, the adjustment coefficients b and h in the adaptive formation of expected rate of growth and expected risk premiums are not significant. Hence, the