Effect of Transaction Tax on the Relationship between Volatility and Trading Activities of Taiwan Stock Index Futures

Chiao Da Management Re叫ew Vol. 30 No. 2, 2010

pp. 61-105

交易稅對台灣股價指數期貨波動與交

易活動關餘的影響

Effect of Transaction Tax on the Relationship Between

Volatility and Trading Activities of Taiwan Stock Index

Futures

I來家彬 Chia-Pin Chen

國立中興大學企業管理學系

Department of Business Administration, National Chung-Hsing University 劉映興 1 Ying-Sing Liu

仁德醫護管理專科學校通識教育中心

Jen-The Junior College ofMedicine, Nursing and Management Center for General Education

楊 E是為 Jen-Wei Yang

國立雲林科技大學財務金融系

Department of Finance, National Yunlin University of Science and Technology

摘要:本文主要探討調降期貨交易稅(台灣股價指數期貨在 2006 年 l 月 1 日

峙，交易稅由現行的千分之 0.25 調降成為千分之 0.1) 對於台灣期貨市場的 台指期、小指期、電子期與金融期等四種股價指數近月契約之報酬波動和交

易活動之間關餘的影響 。 我們考量時間趨勢及季節因素對於期貨波動和交易

活動的效應，使用 Luu and Martens (2003) 的彈性傅立業形式 (Flexible

Fourier Forrn, FFF) 進行個別檢定，同時並將 FFF 加入到日內總報酬波動與

交易量(投機性交易活動)所組成的兩結構方程式中以檢定交易稅、時間趨

勢及季節效應 。 研究期間從 2004 年 7 月 l 日起至 2007 年 6 月 31 日止 ， 使用

1 Corresponding author: Jen-The Junior College of Medici間，Nursing and Management, Center

62 Effect of transaction t，缸 on the relationship between volatili吵 and trading actiνities ofTaiwan stock indexfutures

每日與日內 5 分鍾的交易資料進行實證分析 。 主要結果顯示四種期貨的降稅 效果有所差異，台指期、小指朔和電子期的交易量在降稅後會顯著地增加， 但金融期則是顯著的減少，可能原因與投機性交易活動有關 。 另外也發現在 降稅後 ， 這四種期貨的投機性交易活動均會明顯地增加;同時，有部分的研 究結果指出調降交易稅會造成期貨的報酬波動增加 。 最後，我們也發現四種 期貨的交易活動均存在時間趨勢及季節效應 。 關鍵詞:指數期貨;交易稅;彈性傅立業形式 ; 波動性;投機性交易活動

Abstract: This paper examines the impact of the reduction of futures transaction taxes on the correlation between return volatility and trading activities of nearby contracts of the four stock index futures, i.e. TX fu仙res ， MTX futures, TE futures and TF futures on the Taiwan Futures Market. (The Taiwan futures 甘ansaction tax was lowered from 0.025% to 0.01 % on January 1,2006.) This paper considers the effects of time trends and seasonal factors on retum volatility and trading activities by performing individual tests with Flexible Fourier Form (FFF) developed by Luu and Martens (2003). Meanwhile, this paper incorporates FFF into the two-equation structural model, which consists of the sum of intraday retum volati\ity and trading volume (speculative trading activities) in order to test transaction taxes, time trends and seasonal effects. The research covers the period starting on July 1, 2004 through June 31, 2007. It performs an empirical analysis with daily and 5-minute intraday time series data. The result shows that there are

variances in the e缸ects of transaction taxes on the four futures. The trading volumes of TX futures, MTX futures and TE futures increased significantly after tax reductions; whereas the trading volume of TF futures fell markedly. This may be due to speculative trading activities. This paper also finds that after tax reductions, the speculative trading activities of these four fuωres dramatically picked up after tax cuts. Meanwhile, some studies indicate that the reduction of transaction taxes results in an increase in futures retum volatility. Finally, we find that the trading activities of the four futures show time trends and seasonal effects. Keywords: Index Futures; Transaction Tax; Flexible Fourier Form; Volatility;

Chiao Da Management Review 則. 30 No. 2, 2010 63

1.

Introduction

Stock index futures were first introduced in the US futures market in 1982 Similar index futures were introduced in Europe and Asia 1ater. In Taiwan, Taiwan Futures Exchange (TAIFEX) was estab!ished in September 1997. In Ju1y 21, 1998, the first futures product, Taiwan Stock Exchange Capita1ization Weighted Stock Index futures (TX futures) was 1aunched. As a response to market demand, on Ju1y 21, 1999, two stock index futures were introduced, i.e. Taiwan Stock Exchange E1ectronic Sector Index futures (TE futures) and Taiwan Stock Exchange Finance Sector Index futures (TF futures). On Apri1 9, 2001 and December 24, 2001, two more new products, i.e. MTX futures (Mini-TAIEX futures) and TAIEX options were created. To meet the demand of intemationa1 markets and investors, three USD-denominated futures, i.e. MSCI Taiwan Index Futures, MSCI Taiwan Index Options and Go1d Futures, and SGX-DT's MSCI Taiwan Index Futures were introduced on December 27, 2006. According to statistics from Futures Industry Association (FIA), the trading vo1ume of the Taiwan futures market ranked the 5ih around the wor1d in 1998. The ranking went up to the 18th in 2006. The trading vo1ume ofTaiwan index options was the 3rd 1argest in the wor1d, next on1y to that of KOSPI 200 options in Korea and that of Dow Jones Euro Stoxx 50 in the US. These numbers demonstrate the rapid growth of the Taiwan futures market over the recent years.

There have been no consistent views or conc1usions regarding the influence of transaction taxes on securities markets or futures markets. The scho1ars for the 1evy of transaction taxes suggest that it can increase tax revenues (Kiefer, 1990) and reduce specu1ative trading activities. Stig1itz (1989) argues that the 1evy of transaction taxes downsizes short-term specu1ative trading activities, and encourages investors to cornmit to 10ng-term investrnents by reducing short-term trades. Some scho1ars suggest that the 1evy of 甘ansaction taxes shrinks noise trading and futures retum vo1ati1ity (Summer and Summers, 1989).

Meanwhi1e, transaction taxes reduce excess price vo1ati1ity (Grundfest and Shoven,1991) and issuing volumes of securities (Amihud and Mendelson,1993).

64 足食ct of transaction tax on the relationshψ between volatility

and trading activities ofTaiwan stock indexfutures

transaction taxes increases asset-holding costs (Amihud and Mendelson, 1 993) and reduces the value of assets. It also lowers the trading volume and expands the bid-ask spreads, and sometimes even drive investors to seek altemative markets overseas (Campbell and Froot, 1994). Lo et al. (2004) indicate that the levy of transaction taxes mitigates market Iiquidity and results in obvious liquidity premmm m asset pncmg.

Seasonal effects refer to regular phenomena of returns or volatility of financial assets at specific times or days. If there exists a significant seasonal phenomenon in the market, it means there is a form of market inefficiency. In the case of any obvious seasonal effects in financial assets, it means that the retums of the financial assets are predictable. At this junctu時， the market tends to be inefficient and there may be arbitrage opportunities. Frequently seen abnormalities include weekday effects and weekend effects. Cross (1973) uses a theoretic model to illustrate weekday effects of share price returns. Jaffe and Westerfield (1985) also support weekday effects. However, other scholars such as Smirlock and Starks (1986) argue otherwise. They do not think weekday effects exist. Also, Milonas (1986) examines the maturity effects of futures and finds that the c10ser it is to maturity dates, the greater the volatility of fuωre prices is. His study proves that there are maturity effects for futures. However, Chen and Williams (1994) indicate that there are no maturity effects for fuωre.

Some scholars provide explanations for the reasons con甘ibuting to seasonal effects. First, Keim and Stambough (1984) indicate that the trading on Fridays and Mondays may be subject to measurement errors and hence they propose the concept of symmetric errors. Some scholars argue that weekend effects are mainly due to measurement errors. Patell and Wolfson (1979) suggest that Monday effects are caused by the announcement of negative news by govemments usually after the c10se ofthe stock markets on Fridays. More often than not, such negative or positive news are reflected on the trading on Mondays. Miller (1988) argues that weekday effects are subject to the influence of investment decisions. Ritter (1988) explains pre-holiday effects with parking the proceeds hypothesis. Some scholars explain seasonal effects with window dressing and price reversal effects.

Chiao Da Managemenl ReviewVol. 30 No. 2, 2010 65

Previous studies on transaction taxes in Taiwan mainly focus on the influence of transaction taxes on market quality. Few studies on futures price discovery examine the impact of transaction tax cuts on trading behavior of investors. Meanwhile, most studies do not incorporate the effects of time trends or seasonal effects. In fact, the Taiwanese futures market has grew rapidly in trading volume. As a result, both trading volumes and open interests grow over time with the market and result in time trends (Figure 1). It should be possible to mitigate the interferences of these factors in the study on the reduction of transaction taxes with the time trend factors taken into account.

Thepu叩oses ofthis paper are as follows:

l.It aims to examine the reduction of transaction taxes by Taiwan Futures Exchange and explore the impact of time trends and seasonable factors on the relationship between stock index futures return volatility and trading activities. It intends to gain an understanding of the efficiency of the Taiwan futures market by investigating the seasonal effects of return volatility or 虹ading actlvltles.

2.This paper plans to refer to the return volatility of four different levels of information contents, i.e. the squared return volatility, the high-low price volatility, GK volatility and the sum of intraday return volatility to examine the effects of transaction taxes, time trends and seasonal factors on futures retum volatility and compare whether the test results on the volatility of different information contents show any differences.

3.This paper also measures the proxy variables such as trading volume, open interest and speculative trading activities to evaluate trading activities so as to c1ari命 the relationship between transaction taxes, seasonable effects and trading activities. The purpose is to understand how transaction taxes, time trends and seasonal factors affect the breadth, depth and speculative 仕ading activities of the futures market.

4.This paper intends to compare the effects oftransaction taxes, time trends and seasonal factors on four different indexes, i.e. TX futures, MTX futures, TE futures and TF futures. Meanwhile, the research finding of this paper serves

66 ξfJect of transaction tax on the relationship between volatility and trading activities ofTaiwan stock index戶tures

as another robustness checks on the empirical effects of the transaction tax

cuts on the Taiwan stock index futures market.

Figure 1

Time Series Plots of the Monthly Trading Volume and Open Interest on the

Taiwan's Stock Index Futures Market: 2003.1.1.-2007.6.31.

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This paper applies Flexible Fourier Forrn to test the inf1uence of seasonal

Chiao Da Management Reνlew 則. 30No. 2. 2010 67

Fourier Fonn can appropriately capωre the smooth wave relationship between

time series, time-to-market and time-to-maturity (Luu and Martens, 2003).

However, before applying Flexible Fourier Fonn to examine the impact of

seasonal factors on futures return volatility (trading activities), it is necessary to

test whether the time series of return volatility (trading activities) are static. The test of seasonal factors with Flexible Fourier Fonn should be perfonned whilst the

time series ofreturn volatility (trading activities) are static. Meanwhile, assuming

the time variables are the endogenous variables of return volatility (trading

activities), this paper perfonns a stepwise regression to identify the optimal

explanatory model for the seasonal factors before incorporating the dummy

variable regarding tax cuts and examining the tax effec尬， time trends and seasonal

effects. Also

,

this paper runs the seemingly unrelated regression (SUR) to

estimate the two structural equations for volatility and 甘ading volume

(speculative trading activities) so as to investigate the dynamic and cross effects of the sum of intraday return volatility and trading volume (speculative trading

activities) on the relationship between transaction taxes, time trends and

seasonable factors.

This paper consists of five sections. This section explains research motives

and purposes. Section Two reviews literature. Section Three describes research

methods, samples and empirical models. Section Four outlines the empirical

findings and analyzes the key results. Section Five summarizes the conc1usions.

2. Literature Review

Stock Index futures, specific to stock markets, are the futures contracts with

indexes as the underlying at a fu仙re point in time. Generally speaking, index

futures serve three functions, i.e. hedging, price discovery and speculation. If the

index futures market provides a trading environment of high leverage and high

liquidity, it can serve as a good hedging channel for equity investors by

transferring the price fluctuation risks they are not willing to take to the

68 Effect of transaction tax on the relationship between volatility and trading activities ofTaiwan stock index戶的res

more active. Hence, this paper hopes to gain a deep understanding of the futures market by examining the influence of transaction taxes and seasonal factors on the volatility and trading activities of index futures. Below is a summary of the relevant studies in Taiwan and overseas.

2.

1. Tr

ansaction Taxes

Umlauf(1993) examines the Swedish stock market in 1980-1987 and finds that after the transaction tax was raised from 1 % to 2% in 1986, the volatility of the stock market rose and the trading volume significantly shifted to the London market. Campbell and Froot (1994) also find that the hike of transaction taxes prompts investors to seek alternative markets overseas. Meanwhile

,

Westerholm (2003) performs an empirical study to prove that the Finn stock market experienced a marked reduction in share price volatility after transaction tax cuts. However, Roll (1989) argues that 甘ansaction taxes are irrelevant to volatility. In other words, volatility does not change due to changes in transaction taxes. Hu (1998) investigates the effects of the changes of transaction taxes on the four stock markets in Asia and finds that such changes do not significantly affect price volatility, but do have adverse effects on returns. Ericsson and Lindgren (1992) analyze the impact of transaction taxes on trading volumes and find that an increase in transaction taxes lowers the average turnover of the markets. Baltagi and Li (2006) perform an empirical study and find that in the Shanghai and Shenzhen stock markets, the increase of stamp duties by 113 (from 0.3% to 0.5%) reduces the trading volume by 113. Meanwhile, tax hikes also increases market volatility. The structural shift indicates a deterioration of the market after t阻

mcreases.

Also, Wang and Yau (2000) examine the four futures contracts in the US market to analyze the relationship among trading volumes, bid-ask spreads and price volatility. The result indicates that transaction taxes and bid-ask spreads move in the same direction. Although tax levies increase tax revenues, they also reduce trading volumes and enhances price volatility. Chou and Lee (2002) compare TX futures listed in Singapore and futures listed in Taiwan and find that in Taiwan, relatively speaking, transaction taxes undermines the efficiency of

Chiao Da Management Re νiewVo l. 30 No. 2. 2010 69

price discovery. They prove that after the reduction of transaction taxes in the

Taiwan futures market, Taiwan index futures lead TX futures listed in Singapore

in terms of price discovery. Habermeier and Kirilenko (2003) indicate that transaction taxes significantly affect the demand from investors and such effects are reflected in trading.

To put it differently, transaction taxes delay the process of price discove句，

enhance volatility and weaken market liquidity. Edwards (1993) indicates that the

levy of taxes in futures market cannot generate equivalent tax revenues, but raises

bid-ask spreads and push trading to altemative markets overseas. In other words,

it undermines intemational competitiveness. Transaction taxes cause indirect costs

of hedgers because they need to pay higher risk premiums to speculators, and this

lowers trading volumes. Finally, Chou and Wang (2006) also validate the effects

of transaction tax cuts on May 1, 2000 in the Taiwan futures market. They

examine the impact of the tax cut from 0.05% to 0.25% on the market quality and

find that tax cuts boost trading volumes and narrow bid-ask spreads. However,

there are no significant changes of retum volatility. Tax revenues increase in the

second and third year, from the level one year before tax cuts.

2.2. Seasonal Effects and Futures Maturity Effects

Many studies indicate that there are seasonal effects on average retums or

retum volatility in equity or futures markets. Ho and Cheung (1994) perform an

empirical study on a number of emerging stock markets in Asia and find that there

are weekday effects in most markets, including Taiwan. The retum volatility on

Monday is significantly higher than other weekdays. Clare et. al. (1997) apply the

ARCH model to estimate the conditional variances for the five stock markets in Asia Pacific and find the similar results. Keef and Roush (2005) examine S&P 500 from the 1930s through 1999 in order to validate whether there are significant

variances on the pre-holiday retums. The results indicate that in 1987, there were

strong pre-holiday effects, but such effects weakened after 1987. Lucey and Tully

(2006) sample the futures contracts for gold and silver in 1982-2002 in order to verify whether there are seasonable effects for conditional and unconditional daily means and variances. The study suggests that means are weak but variances are

70 芝加ct of transaction tax on the relationship between νolatility

and trading activities ofTaiwan stock index futures

strong, indicating the existence of seasonal effects. Tu (2003) examines the weekday effects of Taiwan index futures and finds that Monday retums are

abnormal, indicating Monday and Tuesday effects on futures retums in Taiwan.

Regarding the literature on maturity effects of futures, Walls (1999) examines the maturity etfects of electricity futures contracts by estimating

volatility with the squares of logarithms of high-low price retums and con甘olling

the effect of trading volumes on volatility. There is strong evidence indicating that volatility increases when maturity dates approach. Milonas (1986) sample agriculture produce 臼tures and TF futures and finds that the closer futures contracts reach maturi旬， the greater the volatility becomes. However, Moosa and Bollen (2001) argue the otherwise. They examine S&P 500 futures but the research finding does not support maturity e缸ects on TF futures. Stoll and Whaley (1991) investigate the S&P 500 and index futures 合om January 1985 through June 1989 and find that trading volumes and volatility decline when maturity dates approach. Hence, their study supports maturity effects on 甘ading volumes

and volatility. Chen, Duan and Hung (1999) sample Nikkei 225 lndex 企om

September 24, 1988 through June 6, 1999 and find that futures volatility goes down when maturity dates are near. Finally, when it comes to empirical studies in Taiwan, Chou, Chen and Chen (2006) examine the Taiwan index futures from

1998 to 2002 and find that maturity effects are not obvious in Taiwan. 2.3. Return Volatility and Trading Activities

There are currently a number of mainstream theories explaining the relationship between retum volatility and trading volume (trading activities) in the futures or stock markets. These theories are as follows:

I.Clark (1973) proposes Mixture of Distribution Hypothes時， which assumes daily trading volume is the proxy for the sum of information unobservable flowing into the futures market (Lamoureux and Lastrapes, 1990; Andersen,

1996; Bohl and Henke, 2003). Hence, the volatility of futures price each day can be considered the aggregation of the price volatility within that day. The amount of 甘ading volurne is therefore in a positive correlation with the number of information arrivals. To conclude, futures price volatility is

Chiao Da Management Review 他 1. 30 No. 2, 2010 71

relevant to trading volumes.

2.Copeland (1976) proposes Sequential 1nformation Arrival Model (S1AM).

This model assumes information flows are slow and investors pass

information to one another. Therefore, new information is gradual1y

generated and reflected. Therefore, prices are adjusted gradual1y in order to

reflect new information and produce the new equilibrium price.

3 . Karpoff (1987) proposes asymmetrγin price-volume relationship.

4.De Long et al. (1990) propose the trading noise hypothesis.

1n al1, there is extensive literature indicating that there is a certain

relationship between trading volumes and volatility.

Kalotychou and Staikouras (2006) argue that trading volumes are a proxy for the amount of information or width of the markets and open interests can be

seen as a proxy for market depth. Meanwhile, Kim (2005) refers the ratio of

trading volume/open interest as a proxy variable to measure speculative trading

activities. 1f futures volatility is a sure outcome of trading, it happens via the

arrival of information in the market where hedgers or speculators respond to the

information. Chain of reactions from investors wil1 drive futures prices to the

equilibrium after the arrival of information. The expected and subsequent movements will solely reflect on the market liquidity and trading volume of

contracts. 1f the abovementioned adjustment process is proceeded in a continuous

time and under the influence of information flows, there should be a triangle

relationship among information, liquidity and volatility.

To sum up, most scholars suggest that there is a significant correlation

among transaction taxes, market liquidity and bid-ask spreads of the futures

market. However, there are no consistent conc1usions regarding the re1ationship

between transaction taxes and futures return volatility. Also, scholars have varying

views conceming the maturity effect of futures. Final1y, this paper finds that most

scholars support that there is a positive and significant correlation between price volatility and trading volume in stock or futures markets after they have

72 互fJect of transaction tax on the re/ationsh伊 between vo/ati/ity and trading activities ofTaiwan stock indexfutures

3. Methodology

3.1. Data and Samples

This paper examines the impact of the transaction tax cuts on the

correlation between retum volati\ity and trading activities ofTaiwan index futures.

(Note: The Taiwan futures transaction tax was lowered from 0.025% to 0.01% on

January 1, 2006.) In contrast to existing \iterature focusing only on TX futures,

this paper samples a wider range of trading data by investigating the four nearby

contracts, i.e. TX futures, MTX futures, TE futures and TF futures \isted on the Taiwan Futures Exchange for a long period and with significant trading volumes. The daily trading data is sourced from the website of the Taiwan Futures Exchange; the intraday trading data is sourced from Taiwan Economic Joumal

(TEJ). (All the data is confirmed to be accurate). The research period covers from

July 1, 2004 through June 31, 2007. This paper selects the 18 months before the

tax cut on January 1, 2006 and the 18 months after the tax cut. The daily trading

volume and 5-minute intraday trading data over a period of three years are

sampled. The 5-minute intraday trading data is used to estimate the sum of

intraday retum volatility, which is an approximation of the actual retum volatility.

This paper sources a total of 44,520 entries of 5-minute intraday trading data and

742 entries of daily trading for all the index future contracts.

3.2. Trading Activity Measurement

This paper measures the trading activities of futures with three metrics, i.e.

daily trading volumes, open interests and trading volume/open interest. Generally

speaking, trading volumes can serve as a proxy for the information flowing into the futures markets or a measurement for the breadth of the futures markets. Open

interests can be regarded as a proxy for market depth (Kalotychou and Staikouras ,

2006). In addition, this paper refers to trading volume/open interest as a proxy

variable for the measurement of speculative trading activities (Kim, 2005). If

speculative trading activities rise, trading volumes will increase more than open

Chiao Da Management Review 的 1. 30 No. 2, 2010 73

speculative trading activities increase, trading volumes/open interest wi11 go up

significantly.

Luu and Martens (2003) also suggest that trading volume/open interest can

reflect the impact of speculative and hedge trading activities in the futures market.

Assuming that there are two trading days, T 1 and T 2 on the futures market and the

trading volume is the same on either day. The trading volume on day T1 is mainly

a result of hedge trading activities; whereas the trading volume on day T2 is speculative or arbitrage trading activities. As speculators or hedgers tend to close

their positions on the same day, the open interest on day T2 is significantly

smaller than that of day T I. Hence, the trading volume/open interest on day T2 is

greater than that of day T 1. In other words, when there are more speculative

trading activities on the futures market, trading volume/open interest will be

markedly greater.

3.3.

Return Volatility Measurement

Some studies indicate that the test results of the price-volume relationship for futures with squared return volatility and the sum of intraday return volatility

are significantly different (Luu and Martens, 2003). Hence, this paper estimates

return volatility with the data of four different levels of information contents in order to understand whether the same phenomenon exists in the Taiwan index

futures market. These four methods to measure daily return volatility are:

(1) Squared return volatility (卅). This is one of the most frequently used

methods. The calculation method is to square the daily

return而= ln(

p,

/

P,

-l ) X 100, to measure return volatility. The symbol

p,

denotes the closing price on day t.

(2)High-low price volatility. The method to estimate high-low price volatility

is based on Parkinson (1980), Chou and Wang (2006) and Webb et al.

(2007) who perform empirical studies on the index futures markets. Daily

high-low price volatility is calculated as

Ô'~L = (In(Hp' / L

P')

X 100)2/(4 .ln 2) . The symbols H

P'

and L

P'

74 勾Tect of transaction tax on the re/ationsh伊 belween vo/ati/ity and trading activi1的ofTaiwanstock indexfutures

(3)GK volatility: This is proposed by Gannan and Klass (1980), who indicate that the use of daily highest price, lowest price, closing price and opening price to estimate volatility is more efficient than the use of squared retum volatility. Meanwhile, Saunders (1986) applies GK volatility to test the maturity effects and the impact of trading volumes on the futures market and argues that closing prices should not be the only description for price paths. Webb et al. '(2007) also refer to GK volatility to measure Taiwan index futures retum volatility. GK volatility is ca1culated as follows: δ~K = 0.511. (u - d)2 一 0.019.[c.(u+d) 一 2ud]-0.383 .c2 where u = ln(H

,

/

C

,

_l) x 100 一 ln(0

,

/

Ct-l ) X 100 d = ln(L

,

/

Ct-l ) X 100 -ln( 0

,

/

Ct-l) X 100 c = ln(C

,

/

C

,

_l) X 100 -ln(O

,

/

C

,

_l) X 100 、 -F 咀且 , .. 、

Let H

,

be the higher intraday price on the t晶 trading day; let L

,

be the lowest intraday price on the t-th trading day; let 0

,

be the open price on the t-th

tradingσay; let C

,

be the closing price on the t-th 甘ading day.

Finally, this paper refers to more detailed data, i.e. 5-minute intraday trading da徊， to estimate futures retum volatility. Andersen and Bollerslev (1998b), Andersen et al. (2001) and Luu and Martens (2003) indicate that the use of intraday retums to estimate daily retum volatility is more precise than the use of daily average squired retum or highest daily bid-ask spread. Chou and Wang

(2006) also perfonn a test on tax cut e位ects with intraday retum volatility, but do not take into consideration ovemight volatility.

This paper refers to Luu and Martens (2003) for the measurement of intraday retum volatility. It is ca1culated as the sum of intraday retum volatility,

i.e. the summation of squared ovemight retum and squared intraday 5-minute retums. It is computed as the following.

N

σ 2__，

r

;

n .

+ )'

r

Chiao Da Managemenl ReviewVol. 30 No. 2, 2010 75

In the above equation, the symbol â-;eal.t denotes the sum of int叫ay

retum volatility on the t-th trading day and the symbol _rc-_o.t denotes the ovemight retum, i.e. the profit from the difference between the c10sing price of the day before the t-th trading day and the opening price of the t-th trading day. Therefore, the symbol

r

Lo.t

d由如枷e臼叩n削1

from the c10sing price of the day before the tι叫-t由h trading day and the opening price

of t由he t←拈th trading day. The symbol rJ~TRA i.t denotes the int叫ay mean squared

retum ofthe i-由于minute band on the t-th trading day. At this juncture, N is equal to 60. As the trading hours in the Taiwan futures market start on 8:45am and finish on 1 :45pm, the daily trading hours can be divided into 60 5-minute bands. The adoption of 5-minute band as the time frequency to capture intraday pattems is mainly based on the recommendations 企om Luu and Martens (2003), Andersen and Bollerslev (1998b) and Andersen et al. (2001) who perform empirical studies

on stock markets, forex markets and futures market. This approach avoids market microstructure related issues resultant from bid-ask bounces.

3.4. The Model

Based on the above research motives and purposes, this section provides a detai!ed description of the empirical methods and steps. At fir哎， this paper tests the impact of transaction taxes, time trends and seasonal factors on futures trading activities or retum volatility. This paper applies Flexible Fourier Form and the dummy variable for transaction taxes (D_tTax ). Flexible Fourier Form is proposed by Andersen and Bollerslev (l 998a). 此1artens et al. (2002) use it to validate

high-企equency (intraday) data because it is a model able to accurately capture time trends. It is also able to test whether the futures market report factors such as time trends, time-to-maturity and Monday effects. Meanwhile, the dummy variable for transaction taxes is incorporated in order to explore the impact of transaction taxes, time trends and seasonal factors on futures retum volatility or trading activities. Flexible Fourier Form is described in the following:

76 Effect of transaction t叫 on 1he rela1ionship between vola1ility

and 1rading activities ofTaiwan slock index戶tures

FFF, =a

,

.DMON+b

,

'l+b

,

'1' +c

,

.ttm

,

+c，

叫+封熱 C自己立旦)+8， .sin紅旦旦)

1

(3)

;:;;'\. ttmmu ttmmu )

TSr=α。 +FFFr + λ .D戶+~ ~

In Eq. (4), the symbol TS_r denotes the time series at time t. Such series inc1ude futures trading activities, e.g. daily trading volumes, daily open interests and speculative variable, and the fo叮 types of return volatility, i.e. squared return volatility, high-low price volatili旬， GK volatility and total intraday retum volatility.

The symbol FF

F,

denotes Flexible Fourier Form. This form can be divided into the following in Eq. (3).

1. The symbol D MON denotes the dummy variable for Monday. At the trading time is Monday (i.e. t),_{D MON} = 1; otherwi凹， DMON=O

2.The trading days ( and (2 are referred to capωre the time trends.

Generally speaking, the start day of the research period is defined as the initial value ( = 1, and the number of days is added.

3.The symbol ttm_m且 denotes the further time (days) to maωrity of the futures contract at the nearest month.

4.The symbol n denotes the number of sinusoids. This variable, along with Flexible Fourier series, can capture the smooth wave relationship between time series and days to maturity. When this relationship exists

,

the trading activities (retum volatility) of futures change in a cyc1ical manner (regular1y) according to time-to-maturity. The symbol n denotes the optimal number of sinusoids. This paper chooses to use SIC (Schwarz's Information Criterion) to determine the minimum value.

Finally, in Eq. (4), the symbol DrTax denotes the dummy variable for transaction tax cuts. The value is assigned to be zero for time t (before tax cuts

on J anuary l, 2006) and to be one after time t. If the effect of transaction tax cuts is significant， λvalue has to be significant1y different 台om zero. Ifλ> 0, the time series and transaction taxes are in a reverse relationship. If otherwise, the time series and 甘ansaction taxes are in a positive relationship. The symbol &j r

Chiao Da Management ReviewVol. 30 No. 2. 2010 77

The next step is to examine the cross effects of tax cuts, time trends and seasonable effects on futures retum volatility and trading activities. This paper incorporates Flexible Fourier Form (FFF;) and dummy variable for transaction

taxes， D戶， in Eq. (3) into the dynamic two-equation structural model consisting of retum volatility and trading activity variables. Meanwhile, this paper uses the SUR method to estimate this structural equation. The SUR estimation is based on the absence of a diagonal relationship in the co-variance matrix of error items in the structural equation. It is applicable when the error items of respective equations are correlated. After the confirmation of such a correlation, this paper uses the SUR estimation to test the impact of tax cuts, time trends and seasonable effects on the Taiwan index futures retum volatility and trading activities. The dynamic two-equation structural model is described as follows:

σf =C10+αl1 .41 +K+αIp ﹒σip +β:10 -TAl'; +K +βIq .TAl';_q +FF.罰， +AaD戶 +C"

TA v， =c，o+ α10 σfz +K+α1，﹒σL+β11 -TA l';-I +K +β1， -TA 仁 +FFF" +λ， .D戶 +6"" (5)

In Eq. (5)

,

the symbol σ，2 denotes the retum volatility ofthe t-th trading day. At this juncωre， this paper se\ects detailed data of the sum of intraday retum volatility for measurements. The symbol TA V

,

denotes the trading activity variable, measured with daily trading volume (咒) and speculative trading activities (VO,). The symbols p , q , r and s denote the four lag lengths, respectively. The number of lengths is determined with stepwise regression. The symbol FFF; denotes Flexible Fourier Form, which is used to test Monday effects

,

time trends and time-to-maturity. The symbol D

,

Tax denotes the dummy

variable for transaction taxes. Ifλi value (i = 1 , 2) is significantly different from zero, the tax cut effects do exist. lt means that tax reductions have significant effects on the volatility or trading activities of futures. The symbols

C IO and c20 denotes drift items whereas the symbols "1' and "2' denote error ltems.

78 E加ct of transaction t.ω on the 何如ionship between volatility and trading activities ofTaiwan stock ind，臼戶tures

4.

Results and Analysis

Below is a summary of test results based on the empirical study performed in the abovementioned method.

4.1. Basic Descriptive Statistics and Unit Root Tests of Futures Trading Activities and Return Volatility

Table 1 summarizes the descriptive statistics and unit root tests of the trading activities ofthe nearby contracts offour Taiwan stock index futures during the 18 months before the transaction tax cuts on January 1, 2006 and the 18 months after the tax cuts. This paper finds that under the 5% significance level,

the t-value tests are significantly greater than zero. The average daily trading volume ofTX fu仙res， MTX futures and TE futures rose significantly from 25,393,

4,710 and 4308 contracts before tax cuts to 35,665, 6,503 and 4,546 contracts after tax cuts (under the 5% significance level, t-statics significantly more than zero). However, the average daily trading volume of TF futures dropped noticeably from 3,770 contracts before tax cuts to 2,677 contracts after tax cuts (under the 5% significance level, t-statics significantly smaller than zero). Hence,

this paper finds that transaction tax cuts cannot enhance the average daily trading volumes for all the index futures contracts on the market.

Secondly, the average daily open interests of MTX futures and TF futures significantly dropped from the before-tax-cut levels of 6,541 and 8,910 contracts to 5,134 and 5,712 contracts, respectively, after tax cuts (under the 5% significance level, the t-value significantly smaller than zero). The average daily open interests of TX futures and TE futures significantly dropped 企om the before-tax-cut levels of 33,357 and 7,752 con甘acts to 35,142 and 8,242 contracts,

respectively, after tax cuts (under the 5% significance level, the t-value significantly greater than zero). If open interests are considered a proxy variable

Chiao Da Management ReviewVol. 30 No. 2, 2010 79

Table 1

SummaryS胸前stics and Unit Root Tests for Daily Futures Trading Activiti肘。n

theTaiwan 訕。ckIndex Futures Market: 2004.7.1-2007.6.31呵 742 Trading Days.

Futures TX MTX TE TF

Study Before After wholeBefore Aaer wholeBefore Aaer wholeBefore After whole Period

Part 1: Daily trading volume

Mean 25393 35665 30474 u 4710 6503 5597U _{4308 4546 4426}U _{3770 2677 3230}0 Median 25114 35217 29800 4119 6422 5401 4180 4360 4284 3291 2396 2776 Std. Dev. 8365.7 10111 且 10594.1 2312.8 2177.4 2417.8 1477.8 1615.5 1551.0 1941.9 1320.8 1750.4 Skew 0.7186 0.5548 0.6279 1.1956 0.3263 0.5887 0.7474 0.5175 0.6351 1.4126 2.0184 1.7098 Kurt. 3.7079 4.0780 3.6599 4.6078 2.8750 3.0090 4.2518 2.8783 3.4633 5.5630 9.2783 6.9269 ADF/ _-4.479* / -28.515* -4.920* / -22.683* -5.411* / -25.646* -3.747* / -18.316* PP

Part 11: Daily open interest

Mean 33357 35142 34240 u 6541 5134 58450 _{7752 8242 7994}U _{8910 5712 7328}0 Median 33724 36375 34707 6576 5143 5614 7912 8402 8161 8979 5605 6860 Std. Dev. 8808.2 8209.1 8558.1 1942.8 1349 1816.3 1889.8 1932.2 1925.3 3049.0 1469.7 2884.4 Skew. Kurt. ADF/ PP -0.0580 -0.8386 -0.4190 -0.0472 -0.2104 0.2709 -0.4790 -1.0629 -0.7505 0.5035 -0.3789 0.9844 3.2992 4.1819 3.5359 2.9580 3.9001 3.3412 3.7025 4.7897 4.0676 4.2357 3.1112 4.8392 -8.893* / -8.771* -6.414* / -6.644* -10.321* / -9.737* -6.914* / -6.106.

Part I1I: Speculation ratio

Mean 0.8124 1.0717 0.9406 0.7599 1.3 106 1.0323 0.5902 0.6057 0.5979 0.4617 0.4983 0.4798 U U U Median 。 7682 1.0123 0.8854 0.6863 1.2511 0.9830 0.5400 0.5357 0.5385 0.4049 0.4256 0.4136 Std. Dev. 0.3256 0.3785 0.3756 0.3651 0.4309 0.4847 0.2474 0.3397 0.2966 0.2517 0.2689 0.2608 Skew. 0.9364 1.0493 0.9747 1.1126 0.8873 0.7414 1.3645 2.3498 2.1665 1.2180 1.8973 1.5921 Kurt. 4.0129 4.8779 4.5878 4.5793 4.3665 3.6781 7.3591 10.7961 11.1089 4.6568 8.4670 6.9207 ADF / -5.831* / -22.360. -7.696./ -7.559* -16.357* / -16.862 * -11.345* / -14.138* PP

note: Before-period: 2004.7.1-2005.12.31., 375 trading days; After-period: 2006.1.1-2007.6.31., 372 trading days. • indicates significance at the 1 % level. ADF is the unit root test of Augmented Dickey-Fuller test; PP is the unit root test ofPhillips-Perron test. Uindicates significance at the

5% level in the mean increase in after-period with reduced tax ratio; DIndicates significance at the

80 Effect of transaction t囚 on the relationship between volatility and trading activities ofTaiwan stock indexfutures

Table 2

Summary statistics and unit root tests for daily futures return and volatility

on the Taiwan stock index futures market: 2004.7.1-2007.6.31.

,

742 tradin2 days.

Futures TX MTX TE TF

Study

Before After Whole Before After Whole Before After Whole Before After Whole

Period

Part 1: Daily futures retum

Mean 0.0364 0.0792 0.0576 0.0364 0.0792 0.0576 0.0633 0.0734 0.0683 -0.0111 0.0399 0.0141 扎1edian 0.0000 0.1506 0.0685 -0.0164 0.1471 0.0634 0.0000 0.1914 0.1002 0.0199 0.1192 0.0810 Std. Dev. 0.9860 1.1328 1.0607 0.9726 1.1586 1.0681 1.2633 1.3016 1.2815 1.1783 1.2446 1.211 0 Skew. -0.3183 -0.8301 -0.6197 -0.1352 -0.8295 -0.5635 -0.0542 -0.8249 -0.4524 -0.1173 -0.2426 -0.1810 Kurt. 4.9761 6.0484 5.7268 4.6947 6.1538 5.7924 4.8189 6.1707 5.5262 9.6144 4.6711 6.9104 ADF IPP -28.435. / -28.413. -28.829. / -28.801. -29.001. / -29.026. -28.307. / -28.314. Part II: Squared retum volatility

Mean 0.9337 1.2313 1.0809 0.9710 1.2860 1.1268 1.5957 1.6948 1.6447 1.3848 1.5463 1.4647 Median 。 2652 0.4324 0.3327 。 2526 0.4072 0.3132 0.4695 0.5963 0.5220 0.3714 0.4449 0.3968 Std. Dev 1. 7708 2.6681 2.2630 1.9260 2.8179 2.4123 3.1142 3.7817 3.4585 4.0705 2.9529 3.5604 Skew. 4.0901 6.2482 6.1198 4.6226 6.2902 6.2067 4.4861 6.7814 6.0363 8.3836 3.3788 7.2496 Kurt. 25.4164 57.375660.6045 31.475757.995560.7372 29.9327 66.2350 56.7837 91.713415.466382.1169 ADF IPP -9.912. / -26.975. -10.233. / -26.924. -12.237. / -9.737. -20.866. / -20.908. Part III: High-Iow price volatility

Mean 。 6369 0.7456 0.6907 0.6308 0.8049 0.7169u 1.0010 1.0684 1.0343 0.8256 1.0127 0.9181 Median 。 3876 0.4645 0.4258 0.3642 0.4607 0.4255 0.5920 0.6564 0.6301 0.4944 0.6097 0.5459 Std. Dev. 0.7866 1.0236 0.9126 0.7796 1.3624 1.1096 1.2001 1.5891 1.4055 1.3583 1.1582 1.2659 Skew 3.4101 4.9426 4.5905 3.3632 6.5244 6.6692 3.4996 5.4894 5.0350 8.2058 2.8504 6.1556 Kurt. 17.875735.8261 33.5388 18.185456.486067.310520.561243.358640.7399100.896 12.393270.5528 ADF IPP -8.953. / -28.194. -5.935* / -28.470. -5.678. / -27.735. -9.770. / -26.488. Part IV: GK volatility

Mean 。 .6413 0.7079 0.6742 0.6064 0.7459 0.6754 0.9531 1.0121 0.9823 0.7815 0.9419 0.8608u Median 。.4004 0.5017 0.4473 0.3707 0.4751 0.4307 0.6495 0.6884 0.6686 0.48980.6072 0.5386

Chiao Da Management Re叫ewVol. 30No. 2, 2010 81

Study

Before After Whole Before After Whole Before After Whole Before After Whole

Period

Skew. 4.3910 3.6599 4.0322 4.2330 9.3879 9.5274 3.0025 6.6574 5.8014 4.4972 2.2560 3.5317

Kurt. 29.855722.2463 26.1599 29.0257 109.685 131.043 14.627370.065762.647430.3002 9.3815 21.7703

ADF IPP -10.956* 1-26.713* -12.496* 1-27.328* -10.685 * 1 -26.262 * -11.076* 1-25.355*

Part V: Sum ofintraday return volatility

Mean 0.9142 1.0037 0.9585 0.9368 1.0031 0.9696 1.4288 1.4875 1.4579 1.3761 1.2755 1.3263 Median 。 6151 0.7112 0.6586 0.6208 0.7348 0.6801 1.0322 1.0335 1.03285 0.7220 0.8958 0.8032 Std. Dev 1.0468 1.1506 1.0995 0.9609 0.9156 0.9387 1.4525 1.8527 1.6617 4.0737 1.0461 2.9865 Skew 4.7618 6.7563 5.9055 3.1053 2.9306 3.0170 3.8804 6.2600 5.602710.5059 2.241513.5406 Kurt. 36.489575.7891 60.2442 15.1590 13.99414.600324.895761.138754.1476124.229 8.9890217.747 • ----* -- ..~. ----* ADF 1 PP -10.044' 1-27.362' -9.755' 1 -23.418' -9.272' 1-26.871 . -13.200' 1-17.225

note: Before-period: 2004.7.1-2005.12.31., 375 甘adingdays; After-period: 2006.1.1-2007.6.31.,

372 個din恆 days.• indicates si伊 ificanceat the 1 % level. ADF is the unit root test of Augmented Dickey-Fuller 臼st;PP is the unit root test ofPhillips-Perron test. U indicates significance at the

5% level in the mean increase in aftcr-period with reduced tax ratio

for market depth, the result summarized in Table 1 suggests that the cuts of

transaction taxes enhance the market depth for TX futures and TE futures but weaken the market depth for MTX futures and TF futures. The speculative trading

activities (trading volume/open interest) ofTX futures and MTX futures increased

dramatically from 0.8124 and 0.7599 before tax cuts to 0.0717 and 1.3106,

respectively, after tax cuts (under the 5% significance level, the t-value

significantly greater than zero). Hence, this paper infers that the speculative

trading activities of TX futures and MTX futures will rise significantly due to tax

cuts. However, TE futures exhibit no significant variance. Finally, under the 1 %

significance level, all the ADF and PP unit root tests on all the series report

significant results and reject the unit roots. Hence, this paper infers that the series

ofthe trading activities ofthe four index futures are all stationary.

Table 2 summarizes the descriptive statistics and unit root tests of the daily log returns and return volatility of the nearby contracts of four Taiwan stock index

futures during the 18 months before the transaction tax cuts on January 1, 2006

82 Effect of transaction t位 on the relationship be/Ween volatility

and trading actiνities ofTaiwan stock index futures

this paper finds that under the 5% significance level, the t-value tests on the average daily log return of the four index futures cannot suppo此 that there are any significant variances before and after tax cuts, although the average daily log return of TX futures and MTX futures increase from 0.0364 % and 0.0364 % before tax cuts to 0.0792 % and 0.0792% after tax cuts. Secondly, the coefficients of skewness of the daily log return of these four index futures are all negative and skewed to the right. All the coefficients of kurtosis are greater than three, consistent with the leptokurtic characteristics of typical financial assets. Meanwhile, this paper also finds that among the four index futures, only the t-value tests on the average high-low price volatility of MTX futures and the GK volatility of TF futures are significantly greater than zero under the 5% significance level. Other volatility does not significantly increase or decrease after tax cuts. Finally, under the 1 % significance level, the ADF and PP unit root tests of the return volatility series are all significantly different 企om zero so the unit roots are rejected. Therefore, this paper infers that the series of the return volatility ofthe four index futures are all stationary.

4.2

Model Fit and Tests on Impacts of Transaction Taxes

,

Time Trends and Seasonal Factor 00 Trading Åctivities and Return Volatility

Table 3 summarizes the effects of transaction taxes, time trends and seasonable factors on the trading activities of the nearby contracts of four stock index futures, i.e. TX futures, MTX futures, TE futures and TF futures. Firstly, this paper considers the inf1uence of time factors, such as Mondays, time trends and time-to-maturity on futures trading activities and return volatility by identi冉ling the optimal explanatory variables with stepwise regression and deriving the optimal explanatory model. Finally, this paper incorporates the dummy variable for tax cuts, D，T.肘， to further test the impact of transaction tax reductions and seasonal factors on the futures trading activities and return volatility. At this junc切時， this paper selects the optimal model by choosing the smallest SIC value. Test results are listed in Table 3. The λcoefficients in Table 3 show the relationship of 甘ansaction taxes with futures trading activities and the

Chiao Da Management ReνiewVol. 30 No. 2, 2010 83

relationship of transaction taxes with retum volatility. Secondly, this paper refers to Ql coefficients to test Monday effects. It refers b₁ and b₂ coefficients to

test time trends. It also uses the C₁ and C₂ coefficients to test time-to-maturity and 仇 and θi coefficients to test the cyclical relationship of smooth waves between futures trading activities (or retum volatility) and time-to-maturity.

Part 1 of Table 3 indicates the test results of daily trading volumes. It shows

thatλcoefficients of the four index futures are all significantly greater than zero

(p=0.000) and supports the significant reverse relationship between daily trading volumes and transaction tax rates for all the four index futures. In other words,

transaction tax cuts markedly enhance daily trading volumes of the four Taiwan index futures. However, the trading volume of TF futures is greater before tax cuts if time trends are not taken into account (Table 1). After time trends are taken into the equation, the inf1uence of transaction taxes on the trading volume of TF futures is the same as the inf1uence on the other three index futures. Meanwhile,

test results indicate that the Ql coefficients for TX futures and TE futures are

-2232.18 and -436.899, respectively and their p values are 0.006 and 0.001. These numbers are statistically significant and hence support the conclusion that Monday trading volumes of TX futures and TE futures are significantly smaller than those on other trading days. In other words, Monday effects do exist. This paper then continues to perform a test on b₁ or b₂ coefficients to validate whether Monday effects are relevant to the correlation of TX futures and TE futures with intemational equity markets (as Mondays in Taiwan are Sundays in Europe and the US).

Except for the b₂ coefficient of TX futur闊， the trading volumes of these four futures are significantly correlated with time or time squares. Hence, this paper infers that there are time trends in the trading volumes of Taiwan index futures. Meanwhile, this paper also finds that the test results on c₁' c2 ' 的 and θl

coefficients of TX futures and MTX futures are significantly different from zero (p values all smaller than 0.01). Therefore, this paper infers that the trading volumes of TX futures and MTX futures are significantly correlated with time-to-maturity. Meanwhile, it is also in a cyclical (regular) relationship of a smooth sine wave with time-to-maturity.

84 Effect of transaction t，ι on the relationship between volati/i，抄

and trading activities ofTaiwan stock index戶tures

According to the test results on daily open interests shown in Section 2 of Table 3, the λcoefficients of these four index futures are all significantly smaller than zero (p=0.000). Therefore, this paper there is a significantly positive correlation between daily open interests and transaction taxes. In other words, the reduction of transaction taxes lowers daily open interests. Meanwhile, this paper also finds that only the O[ coefficient of the open interests for TX futures is significantly smaller than zero (o[ = -0.0978; p-values = 0.000). This shows that the open interest of TX futures is significantly smaller on Mondays and hence Monday effects do exist. As far as the b[ or b₂ time trend coefficients are concerned, the b[ coefficient of TX futures is 27.4189 and the b₂ coefficient is -0.0107; the b[ coefficient of MTX futures is -5.7667 and the b₂ coefficient is 0.0043; the b[ coefficient ofTF futures is -5.1211 and b₂ coefficient is 0.0031.

Chiao Da Management ReviewVo/. 30 No. 2. 2010

Table 3

Tax

,

Time Trend and Seasonal Factors for the Effect of Futures Trading

Activities on the Nearby Contracts of Four Stock Index Futures in the

Taiwan Futures Market: 2004.7.1-2007.6.31.,742 Trading Days.

85

令 a ι，I .2:r. i . ttm. . .2:r. i-ttm.. ) _ _ T

Variable=ao +a

,

.DMON +b

,

.t+b

,

.t' +c

,

.ttm

,

+c

,

.ttm,' + 之|然 .cos(一一一~)+θ" .sin(一一一~)I+λ-DY+Er

ï:õ'\. ttmmu ttm 制 j

Coeff. n SIC _ao a

,

_b

,

b_{2 C}

,

C ₂ 的 向

Ø

2

θ2 λ

Part 1: D團 ily trading volume

TX 21.0363 -2232.18 -7.8679 4223.31 -102.879 14648.3 -4429.41 14686.2 (0.006) (0.000) (0.000) (0.000) (0.000) (0.007) (0.000) 恥叮X 17.8676 -13.2552 0.0092 1050.75 -24.7187 3376.32 -734.440 3553.21 (0.000) (0.000) (0.000) (0.000) (0.000) (0.030) (0.000) TE _。 17.3055 ~~O~~~，I -~!~.~~9 13156 -0.0047 2331.1 1 (0.000) (0.001) (0.054) (0.000) (0.000) TF _。 l74880 5(70l070054 ) -8.6602 0.0044 1014.44 (0.000) (0.000) (0.000)

Part 11: Daily open interest

TX MTX TE TF -27975.7 -0.0978 27.4189 -0.0107 7069.62 -157.17625257.9 2020.50 3813.62 478.598 -6782.24 2 20.1948 (0.001) (0.003) (0.000) (0.000) (0.000) (0.000) (0.007) (0.586) (0.000) (0.653) (0.000) 2 17.1656 -5.7667 0.0043 977.267 -21.7171 3060.29 357.266 509.529 115.297 -820.431 (0.000) (0.000) (0.000) (0.000) (0.000) (0.465) (0.000) (0.365) (0.000) 2 l7283l -9600.39 _(0.000) 2457.55 _(0.000) -57.5425 _(0.000) 94_{(0.000) (0.258) (0.000) (0.189) (0.000)} 77.79 -987.218 1226.00 -328.876 -499.883 2 17.9899 -5.1211 0.0031 1080.01 -20.97373494.71 1907.48 595.041 394.534 -2.<73.53 (0.000) (0.000) (0.000) (0.000) (0.000) (0.010) (0.000) 0.040) (0.000)

Part III: Speculation ratio

TX MTX TE TF 1.6571 -0.1017 -4.53E-07 -0.1070 0.0025 -0.3201 0.0186 0.6135 (0.000) (0.001) (0.000) (0.000) (0.00 1) (0.001) (0.809) 。 9051 -0.0957 -J.79E-07 -0.0197 0.0006 。 1.0161 (0.000) (0.009) (0.017) (0.00 1) (0.000) 3.2982 -0.0936 0.0004 -6.14E-07 -0.4065 0.0097 -1.6434 0.3097 -0.2355 0.0890 2 0.0467 (0.000) (0.000) (0β10) (0.000) (0.000) (0.000) (0.000) (0.048) (0.000) (0.047) 1.6615 -0.0567 -0.0008 3.32E-07 -0.1384 0.0032 -0.4294 0.0428 -0.2973 (0.000) (0.003) (0.000) (0.000) (0.000) (0.000) (0.000) (0.379)

note: The selection factor of the model is the minimum SIC value; Numbers in parentheses are z-values. 0.5301 (0 ∞0) 。 6559 (0.000) 。 1429 (0.000) 0.2668 (0.000)

86 局Tect

01

transaction t，ω on the relationship between volatili秒

and trading activities

01

Taiwan stock index戶tures

Table 4

Tax

,

Time Trend and Seasonal Factors for the Effect of Futures Return

and Volatility on the Nearby Contracts of Four Stock Index Futures in

the Taiwan Futures Market: 2004.7.1-2007.6.31.,742 Trading Days.

司 街品，( 2Jr.j.(tm. 2Jr.j.(Im. \

Variable;a_o +a1 .ÐMON +b1 .I+b

,

'1' +C1 • 1

1m,

+C

,

'1

1m:

+ 主 1

ø

,

.cos(一一一:2.)+0， .sin(一一一:2.) 1+λ D/QX +E

i:õ\帥max ttmmax )

Coeff. n SIC G_{o 。1} b₁ b₂ C₁ C₂

_Øl

_θl λ

Part 1: Squared retum volatility

TX _。 4.4847 0.8385 。 4961 。 2955 (0.000) (0.018) (0.074) MTX _。 4.6125 0.8691 0.5308 0.3127 (0.000) (0.018) (0.077) TE _。 5.3372 1.4506 。 7558 0.0960 (0.000) (0.019) (0.705) TF _。 5.3935 1.3848 0.1616 (0.000) (0.537)

Part II: High-low price volatility

TX _。 2.6682 。 7774 -0.0089 。.1109 (0.000) (0.012) (0.097) MIχ 。 3.0584 。 7749 。 2003 -0.0116 0.1762 (0.000) (0.050) (0.007) (0.029) TE _。 3.4906 1.5586 -0.0020 1.1709 (0.000) (0.000) (0.000) TF _。 3.3205 0.8256 0.1870 (0.000) _{。 044)}

Part III: GK volatility

TX _。 2.3627 1.0633 -0.0012 -0.0059 。 7194 (0.000) (0.000) (0.053) (0.000) MTX _。 3.0547 。 7751 -0.0107 。 1422 (0.000) (0.013) (0.079) TE _。 3.2542 1.6294 -0.0020 -0.0085 1.1347 (0.000) (0.000) (0.075) (0.000) TF _。 2.7916 。 7815 0.1605 (0.000) (0.025)

Part IV: Sum of in甘adayretum volatility

TX _。 2.9942 1.3673 -0.0016 0.9863 (0.000) (0.025) (0.000) MTX _。 2.6753 1.3335 -0.0014 0.8513 (0.000) (0.014) (0.000) TE _。 3.8112 2.1712 -0.0027 1.5277 (0.000) (0.000) (0.000) TF _。 5.0422 1.3761 -0.1007 。 000) (0.647)

Part V: Squared ovemight retum

TX _。 2.6765 0.7081 -0.0016 8.16E-07 0.3940

(0.000) (0.000) (0.029) (0.003)

MTX _。 1.9225 0.5356 -0.0011 6.19E-07 0.2420

Chiao Da Management ReviewVol. 30 No. 2, 2010 87 Coeff. n SIC _{ao a}

,

_b

,

b_{2 C}

,

C₂ 納 吭 λ TE _。 33799 0(O4O7O503 ) 。 0399 (0.677) TF _{。 4.5062}

(õ:ûõó

0.4697

i)

-0.1891 (0.260) Part VI: Squared intraday 5-minute retums

TX _。 l4lB5 0.8199 -0.0009 0.5849 (0.000) (0.000) (0.000) 恥叮X _。 1.9051 。.9199 -0.0010 0.6037 (0.000) (0.000) (0.000) TE TF 。 2.4873 1.4068 -0.0016 (0.000) (0.000) 。 40553 09064 (0.000)

note: 甘le se1ection factor of the mode1 is the minimum SIC va1ue; Numbers in parentheses are p-values.

0.9157 (0.000) 0.0884 (0.509)

This indicates that the daily open interests of these three index futures are relevant to time and time squares so time trends do exist. Meanwhile爪 'C₂,Øl

and

Ø2

coefficients of these four index futures are all significantly different from

zero. It suggests that the daily open interests are relevant to time-to-maturity or time squares. There is also a cyclical relationship of a smooth sine wave.

According to the test results on speculative trading activities listed in Section 3 of Table 3, this paper finds that the λcoefficients of the four index futures are all significantly greater than zero and the p values are all smaller than 0.05. Hence,

this paper infers that there is a significantly reverse relationship between transaction taxes and speculative trading activities. In other words, tax cuts noticeably enhance the speculative trading activities in the futures market.

Meanwhile, this paper finds that the a

,

coefficients of the speculative trading activities of the four futures are all signi日cantly smaller than zero. This indicates that the speculative trading activities in the Taiwan index futures market are significantly reduced on Monday and Monday effects do exist. Similarly, this paper finds that speculative trading activities report in part or in all a significant correlation with time trends (a

,

and a2 ) and time-to-maturity (c" c2， 吭， θ，,

88 Effect of transaction tax on the relationship between ν'olatility and trading activities ofTaiwan stock indexfutures

Secondly, Part 1 to IV of Table 4 summarize the test results of the squared

retum volatility, the high-low price volatility, GK volatility and the sum of

intraday retum volatility based on the four degrees of information contents.

According to Part 1, the effect of tax cuts on the squared retum volatility is not

obvious, because all the p values of the λcoefficients of these four index

futures are greater than 0.05. Meanwhile, Part 11 and Part III list the test results on

λcoefficients. They show that the λcoefficients of the high-low price

volatility of MTX futures, TE futures and TF futures and the λcoefficients of

the GK volatility of TX futures, TE futures and TF futures are significantly

greater than zero (with p values all smaller than 0.05). The above results indicate

that for most index fuωre contracts, there is a significantly reverse re1ationship

between retum volatility and transaction taxes. The test results of detailed data, i.e.

5-minute intraday trading data and the estimation of the volatility (Part IV of

Table 4) also suggest that the λcoefficients of the sum of intraday retum

volatility for TX futures, MTX futures and TE futures are all significantly greater

than zero (with p values all smaller than 0.05). Therefo間， this paper infers that

there is a significantly reverse relationship between the sum of intraday retum

volatility and transaction taxes for TX futures, MTX futures and TE futures.

This paper continues to examine whether the enhanced sum of intraday retum volatility stems from the squared intraday retum volatility or ovemight volatility during trading hours. This paper applies the method listed in Table 4 to test ovemight volatility and the squared intraday retum volatility. The results are summarized in Part V and Part VI of Table 4. This paper finds that the intraday volatility and transaction taxes are in a significantly reverse relationship as far as

the ovemight volatility and the squared intraday retum volatility of TX fuωres

and MTX futures are concemed. However, in the case of TE futur郎， only the

squared intraday retum volatility and transaction taxes are in a significantly

reverse relationship. To sum up the results shown in Table 4, the impacts of

transaction taxes on the retum volatility estimated with information of different

levels of contents are different. This paper does not find any significant tax

effects on volatility if daily trading data is used to perform tests. However, if

Chiao Da Management Review 均 1. 30 No. 2, 2010 89

intraday retum volatility is subject to significant tax effects.

According to the test results on _C1, _{C 2}, Øl' 吭 ， Ø2 and ()2 coefficients

shown in Table 4, only the high-low price volatility ofMTX futures (c₁ = -0.0116)

and its GK volatility (c₁ = -0.0107, p<0.05) report a significant negative

relationship, all the other coefficients are significantly different from zero. Hence,

this paper infers that the retum volatility and time-to-maturity for these four index

futures are not heavily related. So, the research finding tends to support that there

is no time-to-maturity effect on futures retum volatility. The test results on b₁

coefficients shown in Table 4 suggest that the high-low price volatility, GK

volatility and the sum of intraday retum volatility of TX futures and TE futures and the sum of intraday retum volatility of MTX futures are significantly smaller

than zero (p<0.05). Therefore, this paper tends to support that the retum volatility

and market timing are in a reverse relationship for TX 臼ωres ， MTX futures and

TE futures. Time trends for the volatility do exist. Meanwhile, the test results on

time 甘ends with mean squared retum and the sum of intraday retum volatility show significant variances. Time trends do not exist for the squared retum

volatility of these four futures. However, there is a significant reverse relationship

between the sum of intraday retum volatility and market timing for FX futur間，

MTX futures and TE futures.

The test results on a₁ coefficients reported in Table 4 suggest that the a₁

coefficients of TX futures (a₁ =0.4961), MTX futures (a₁ =0.5308) and TE futures

(a₁ =0.7558) are significantly greater than zero. The research finding tends to

support that there are Monday effects for Taiwan stock index futures because the mean square volatility on Mondays is obviously greater than that on other

weekdays. This conc1usion is similar with Ho and Cheung (1994) and Clare et al.

(1997) whose empirical results support Monday effects in the Taiwanese stock

market. However, this paper performs a test with detailed data, i.e. the sum of

intraday retum volatility, but finds that all the a1 coefficients ofthese four index

futures are all significantly different from zero. Hence, this paper infers that there

is no Monday effect on the sum of intraday retum volatility for all these four index futures.