Download Price Volatility, Trading Activity and Market Depth

Wen-Hsiu Kuo
al./AsiaManagement
Pacific Management
Review
(2005)
10(1), 131-143
AsiaetPacific
Review (2005)
10(1),
131-143
Price Volatility, Trading Activity and Market Depth: Evidence from Taiwan and
Singapore Taiwan Stock Index Futures Markets
Wen-Hsiu Kuoa,*, Hsinan Hsub, and Chwan-Yi Chiangc
a
Doctoral Student in Department of Business Administration, National Cheng Kung University, Tainan, Taiwan ;
and a lecturer in Department of Finance, Ling Tung College, Taichung, Taiwan
b
Department of Finance, Southern Taiwan University of Technology, Tainan County, Taiwan.
c
Department of Business Administration, National Cheng Kung University, Tainan, Taiwan.
Accepted March 2004
Available online
Abstract
This study empirically investigates the relations among price volatility, trading activity and market depth for some selected futures
contracts traded on the Taiwan Futures Exchange (TAIFEX) and Singapore Exchange Derivatives Trading Division (SGX-DT). Two different methodologies, the OLS-based and GARCH-based models, are used to test the robustness of the result and to obtain a sensitivity check.
The major findings of this investigation are as follows. First, the estimates of the conditional mean function of the two futures markets are
consistent with weak-form efficiency. Second, the evidence suggests that volatility is higher during periods of high futures trading volume
for the TAIFEX and SGX-DT futures markets, supporting the mixture of distribution hypothesis by Clark (1973). Lastly, inconsistent with
market depth theories, this study demonstrates that existing market depth does not mitigate volatility in the SGX-DT and TAIFEX futures
markets. This result is noteworthy because it provides evidence that the relation between price volatility and market depth may vary with the
market maturity.
Keywords: Price volatility; Trading activity; Market depth; Stock index futures; GARCH
1. Introduction
Numerous works have examined the relation between
trading volume and price volatility for equities and futures.
Considerable evidence exists a positive contemporaneous
correlation between price volatility and trading volume.
Karpoff (1987) extensively reviews previous theoretical
and empirical research on the price-volume relation, and
finds 18 studies documenting the positive relation. Regarding the theoretical aspect, the two leading models,
namely the sequential information model of Copeland
(1976) and the mixture of distribution hypothesis of Clark
(1973), explain for the positive relationship between volume and price volatility. As for the empirical aspect, various studies such as Crouch (1970), Epps and Epps (1976),
Cornell (1981), Harris (1986), Tauchen and Pitts (1983),
Gallant, Rossi and Tauchen (1992), Chen, Firth and Rui
(2001), and Ciner (2002) demonstrate the positive contemporaneous correlation between volatility and volume in
equities and futures markets. The most recent model developed by Blume, Easley, and O’Hara (1994) describes the
informational role of volume, and documents in which
volume conveys information to the market and then improves the accuracy of price movement forecasts. Furthermore, this model demonstrates how volume can affect
market be- havior, rather than simply describing the corre-
This study documents the relations among price volatility, trading activity and market depth for selected futures
contracts traded on the Taiwan Futures Exchange (TAIFEX)
and Singapore Exchange Derivatives Trading Division
(SGX-DT) Taiwan Stock Index Futures markets. This
subject has been extensively investigated for U.S. capital
markets, and also for some developed international markets.
However, this issue has been little examined in less-developed markets. The reason for our particular interest in
empirical work on the Taiwan Stock Index Futures markets
is that it is a rapidly expanding emerging market1 and is
characterized by high volatility in Asia. Therefore, this
study provides additional empirical evidence by exploring
whether the volatility patterns and contribution of market
depth of emerging markets differ from those of developed
markets. That is, we will test the mixture of distribution
hypothesis that there is a positive contemporaneous correlation between price volatility and trading volume, and the
market depth theory that price volatility is affected by existing market depth. The main contribution of this work is
to present empirical comparisons to fill this gap in the literature.
* Corresponding author. E-mail: [email protected]
1
See Hsu and Lin (2002), Lin and Hsu (2003) and Lin, Hsu and
Chiang (2004).
131
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
lation between trading volume and price movements.
Therefore, the literature widely uses volume as a proxy for
information arrival.
appears to serve as a good proxy for the order flow concept
that relates directly to market depth. Therefore, Bessembinder and Seguin (1993) use expected open interest as a
proxy for market depth since it reflects order flow of the
futures transactions and willingness of traders to risk their
capital.
Lamoureux and Lastrapes (1990) first apply Bollerslev’s (1986) GARCH methodology to investigate the price
volatility-volume relationship in equity markets, employing
daily trading volume as a measure of the information flow
(the rate of information arrivals) based on Clark’s (1973)
MDH.2 Lamoureux and Lastrapes find that autoregressive
conditional heteroscedasticity (ARCH) effects disappear
when trading volume is introduced into the conditional
variance equation, suggesting that using trading volume as
a proxy for the information variable causes price volatility
and largely explains the GARCH effects. Jones, Kaul and
Lipson (1994) also obtain findings similar to those of
Lamoureux and Lastrapes (1990). Unlike the study by
Lamoureux and Lastrapes (1990), Najand and Yung (1991)
and Foster (1995) show that GARCH effects remain when
current volume is included in the conditional variance
equation. These authors find a positive relation between
trading volume and price volatility, which is consistent with
the theoretical models provided by Clark (1973), Copeland
(1976) and Blume, Easley, and O’Hara (1994).
Consistent with earlier studies, Bessembinder and Seguin (1993) identify a strong positive relation between
contemporaneous price volatility and trading volume, but
unexpected volume shocks influence price volatility more
than expected volume shocks. Additionally, Bessembinder
and Seguin find that expected open interest is negatively
related to price volatility in all eight futures markets, indicating that increased depth (larger expected open interest)
mitigates price volatility and supporting market depth theory.
Following the method developed by Bessembinder and
Seguin (1993), Ragunathan and Peker (1997), Watanabe
(2001) and Fung and Patterson (1999) all investigate the
relationships between price volatility, trading activity and
market depth in the Australian futures market, the Japanese
stock index futures market and the USA futures market,
respectively. Their empirical results resemble those of
Bessembinder and Seguin (1993) despite differences in
sample data .
The volume-volatility relationship frequently has been
examined, but few works include market depth in the
volume-volatility analysis. Kyle (1985) develops a theoretical model of market depth, and defines market depth as
the volume of order flows required to move prices by one
unit. His model suggests that market depth changes with
trading activity and a deep market helps create market
conditions that reduce price pressures when trading provides new information. Consequently, market depth theory
says that lower price volatility frequently may exist in
deeper markets that facilitate trading activity. That is, observed price volatility, conditional on contemporaneous
volume, is expected to decrease with increasing market
depth.
The purpose of this work extends previous research and
further examines the relationships between price volatility,
trading activity and market depth in TAIFEX and SGX-DT
Taiwan Stock Index Futures markets using two different
methodologies for testing the robustness of our results. This
paper provides insights into the different methodologies
specified. First, this work adopts the methodology of Bessembinder and Seguin (1993), in which the conditional
mean and volatility equations are estimated sequentially
using OLS. Second, rather than selecting a OLS-based
volatility estimation framework, we also generalize the
methodology of Bessembinder and Seguin (1992, 1993) to
a GARCH-based framework following Gulen and Mayhew
(2000). The conditional mean and volatility equations are
jointly estimated numerically by maximizing the likelihood
function (MLE) in GARCH-based model.
Earlier studies measure trading activity in futures
markets based on volume alone. Recently, various studies3
have examined the relation between open interest and price
volatility in developed futures markets. Particularly, Bessembinder and Seguin (1993) first investigate the relations
between price volatility, trading activity variables (trading
volume and open interest) and market depth for eight futures markets in the U.S. As the level of open interest is a
measure of trading activity and reflects the current willingness of futures traders to risk their capital in the futures
position in the presence of price volatility, open interest
Overall, the findings of this study indicate that, with the
exception of slight differences in the estimation results of
Monday effect, expected volume and unexpected open
interest variables, the estimation results of the remaining
variables for the two models are similar for both the
TAIFEX and SGX-DT futures markets. Further comparisons with developed markets are as follows. First, like
Bessembinder and Seguin (1993), Ragunathan and Peker
(1997), Gulen and Mayhew (2000) and Watanabe (2001),
the results of this study show that the TAIFEX and
SGX-DT futures markets are consistent with weak-form
efficiency and support the mixture of distribution hypothesis by Clark (1973). Second, this study tests the market
2
The framework that the MDH can be represented as GARCH model is
refered to Lamoureux and Lastrapes (1990).
3
See Bessembinder and Seguin (1992, 1993), Harris and Raviv (1993),
Bessembinder, Chan and Seguin (1996), Ragunathan and Peker (1997),
Watanabe (2001), Fung and Patterson (1999), Ferris, Park and Park
(2002) and Girma and Mougoue (2002).
132
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
equation based on Clark’s (1973) MDH.4 The conclusion
indicates that trading volume used as a proxy for the information variable explains much of the GARCH effects,
supporting the information-based variance structure.
depth theory and finds that existing market depth does not
mitigate price volatility in the TAIFEX and SGX-DT futures markets. That is, the finding of this investigation is
inconsistent with market depth theory. This evidence contrasts with the findings of developed markets by Bessembinder and Seguin (1993) and Watanabe (2001), who find
that large expected open interest (e.g. market depth) mitigates volatility. Therefore, this study concludes that market
maturity affects price volatility.
Recently, some researchers have studied the relation
between price volatility and trading activity measured by
trading volume and open interest in futures markets. Using
open interest as a proxy for market depth, Bessembinder
and Seguin (1993) first investigate the relations between
price volatility, trading activity variables (trading volume
and open interest) and market depth in eight futures markets
in the USA. Bessembinder and Seguin find a strong positive relation between contemporaneous price volatility and
trading volume, supporting the mixture of distribution
hypothesis by Clark (1973). Besides, the findings of Bessembinder and Seguin also support the market depth hypothesis, namely that expected open interest is positively
related to number of traders or total capital dedicated to a
market at the beginning of a trading session, and that an
increase in the number of traders or amount of capital involved in a market enhances market depth and thus lessens
volatility.
The remainder of this paper is organized as follows.
Section 2 reviews the literature on the relationship between
price volatility, trading activity and market depth. Section 3
then describes our data set and the empirical methodology.
Subsequently, section 4 presents the empirical results. Finally, section 5 makes concluding remarks.
2. Literature Review
The “mixture of distributions hypothesis” (MDH) by
Clark (1973) postulates that price volatility and volume
jointly and simultaneously respond to the common (mixing)
directing variable, which is interpreted as the rate of information flow to the market. Based on the MDH, price
volatility and trading volume should be positively correlated.
Ragunathan and Peker (1997) investigate the nature of
the relationship between volumes, price variability and
market depth for four futures contracts traded on the Sydney Futures Exchange, and obtain analytical results that
confirm the empirical findings of Bessembinder and Seguin
(1993).
Copeland (1976) constructs a “sequential arrival of
information” model in which the sequential arrival of new
information to the market causes both volume and price
movements through numerous information shocks and a
final equilibrium is established. The model of sequential
information arrival indicates a positive relationship between volume and price volatility and suggests that price
volatility potentially is predictable based on trading volume
knowledge.
Watanabe (2001) examines the relation between price
volatility, trading volume and open interest for the Nikkei
225 stock index futures traded on the Osaka Securities
Exchange (OSE). The OSE gradually changes regulations
such as margin requirements, price range and time interval
in updating quotaion several times. The regulations were
relaxed beginning February 14, 1994. Therefore, the samples prior to and beginning February 14, 1994 are examined
separately. The results obtained by Watanabe for the period
beginning February 14, 1994 resemble the findings of
Bessembinder and Seguin (1993). However, no relationship
between price volatility, volume and open interest is found
for the period before February 14, 1994. This analytical
result shows that the relation between price volatility, volume and open interest may vary with the regulations.
Blume, Easley and O’Hara (1994) develop a model that
traders can use to learn valuable information regarding a
security by observing past price and volume information.
The model demonstrates how volume affects market behavior and argues that volume provides data on the quality
or precision of about past price movement information.
Numerous studies such as Crouch (1970), Epps and
Epps (1976), Cornell (1981), Harris (1986), Gallant, Rossi
and Tauchen (1992), Chen, Firth and Rui (2001), and Ciner
(2002) use equity and futures market data to investigate the
price-volume relationship. These empirical results support
an almost positive relationship between price volatility and
volume, consistent with the theoretical models developed
by Clark (1973), Copeland (1976) and Blume, Easley, and
O’Hara (1994).
Fung and Patterson (1999) also investigate the relationship between price volatility, trading volume and market depth for seven U.S. futures markets.5 Fung and Patterson identify a strong, positive relation between volume
and price volatility. Furthermore, Fung and Patterson also
find an negative relationship between market depth and
volatility, suggesting that increased depth reduces price
Lamoureux and Lastrapes (1990) investigate the efficacy of the GARCH effects in GARCH specification in
equity markets when the information variable (e.g., trading
volume) is incorporated into the conditional variance
4
The framework in which the MDH can be represented as GARCH model
is refered to Lamoureux and Lastrapes (1990).
5
The futures data were obtained from the Futures Industry Institute and
consist of five currency futures prices and two interest-rate futures prices.
133
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
volatility.
Table 1. Features of Sampled Futures Contracts
1. Futures Exchange
2. Underlying asset
3.Contract size
4.Contract month
5.Trading Hours
6.Last Trading Day
7.Tick size
TX
TF
TE
Mini-TX
TAIFEX
Taiwan Capitalization
Weighed Index
TWD 200 × TX index
Spot month, the next
calendar month, and the
next three quarter
months
8:45am-1: 45pm
TAIFEX
Taiwan Banking &
Insurance Sector Index
TWD 1000× TF index
Spot month, the next
calendar month, and the
next three quarter
months
8:45am-1: 45pm
TAIFEX
Taiwan Electronic Sector
Index
TWD 4000× TE index
Spot month, the next calendar month, and the next
three quarter months
TAIFEX
Taiwan Capitalization
Weighed Index
TWD 50 × TX index
Spot month, the next
calendar month, and the
next three quarter
months
8:45am-1: 45pm
8:45am-1: 45pm
SGX-DT
MSCI Taiwan Index
USD100 × TiMSCI index
March, June, September,
December and two nearest
serial months
8:45am-12: 15pm
14:45pm-19:00pm
The third Wednesday of The third Wednesday of The third Wednesday of the The third Wednesday of Second last business day of
the delivery month of the delivery month of delivery month of each
the delivery month of the contract month
each contract
each contract
contract
each contract
0.1 index point
1 index point
0.2 index point
0.05 index point
1 index point
The findings of these studies suggest that an inverse
relationship exists between market depth and the price
volatility. However, previous studies have neglected the
relations between price volatility, trading activity and
market depth in emerging futures markets. This work addresses this deficiency and provides an additional evidence
by empirically assessing the TAIFEX and SGX-DT Taiwan
Stock Index futures markets.
from January 2001 to March 2003. Since the Mini-TX is
not introduced until April 9, 2001, its sample period runs
from April 9, 2001 to March 2003. Following Bessembinder and Seguin (1993), the index futures prices are taken
from the nearby futures contracts to obtain a representative
futures price series, since the nearby futures contracts usually are most actively traded. The return Rt is computed
using the natural logarithmic difference in the price levels.
That is, Rt = ln( Pt / Pt −1 ) where Pt denotes the closing price
of the nearby contract on day t. Additionally, trading vol-
3. Data and Methodology
3.1 Data
ume and open interest are summed across all outstanding
maturities to obtain an aggregate measure of activity for
each futures contract. Table 1 details the specifications of
the five futures contracts investigated here.
The Singapore Exchange Derivatives Trading Limited
Division (SGX-DT) and Taiwan Futures Exchange
(TAIFEX) introduce futures contracts of the Taiwan stock
index on January 9, 1997 and July 21, 1998, respectively.
The SGX-DT offers Morgan Stanley Capital International
Taiwan Stock Index Futures (MSCITX), which contains 77
large capitalization stocks on the Taiwan stock exchange.
Moreover, the TAIFEX offers the Taiwan Stock Exchange
Capitalization Weighted Stock Index Futures (TX), which
includes all of the stocks6 listed on the Taiwan Stock Exchange (TSE). Subsequently, TAIFEX also successively
launched Taiwan Stock Exchange Electronic Sector Index
Futures (TE), Taiwan Stock Exchange Banking and Insurance Sector Index Futures (TF) and Mini Taiwan Stock
Exchange Capitalization Weighted Stock Index Futures
(Mini-TX).
Table 2 lists some basic descriptive statistics of the
returns, absolute returns, trading volume and open interest
for each futures contract examined here. The most volatile
futures contract is TE, with daily returns standard deviation
of approximately 2.598% per day. In contrast, the least
volatile futures contract is TX, which has daily standard
deviation in returns of 2.115%. The partial autocorrelations
of returns at all lags are statistically insignificant, implying
that no evidence exists predictability of returns. MSCITX is
the most active futures contract, measured in terms of
volume and open interest, while the least active is TF. First
order autocorrelation coefficients are significant for every
trading volume and open interest, showing that high autocorrelation exists in volumes and open interests. The presence of unit roots in volume and open series is tested using
the Augmented Dickey-Fuller (ADF) tests. The empirical
findings of the tests firmly reject the null hypothesis of a
unit root at the 5% significance level for all volume series
and open interest series, implying that the series need not be
differenced to achieve stationarity, a condition necessary to
The daily closing prices, trading volumes, and open
interests of TX, TF, TE, Mini-TX and MSCITX are obtained from the TAIFEX and the SGX-DT, respectively.
The sample period for TX, TF, TE, and MSCITX extends
6
MSCITX
The TSE Weighted Index does not include full-delivery stocks, preferred
stocks, and newly listed stock, which are listed for less than one calendar month.
134
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
avoid spurious regressions.
Table 2. Summarized Statistics of Futures Returns, Volume and Open Interest
Contract
Mean
TX
Return (%)
Absolute Return (%)
Volume
Open Interest
-0.0242
1.585
14406
11699
TF
Return (%)
Absolute Return (%)
Volume
Open Interest
Standard
Deviation
Partial Autocorrelation at Lag
1
2
2.115
1.399
5294
3405
-0.060
-0.016
0.705**
0.968**
0.052
0.098**
0.360**
-0.108**
-0.0058
1.6138
1792
2177
2.156
1.4283
1330
1172
-0.024
0.115**
0.86**
0.981**
TE
Return (%)
Absolute Return (%)
Volume
Open Interest
-0.0502
1.9411
3175
3151
2.5977
1.7251
1286
1126
Mini-TX
Return (%)
Absolute Return (%)
Volume
Open Interest
-0.0489
1.5881
3459
3721
MSCITX
Return (%)
Absolute Return (%)
Volume
Open Interest
-0.0463
1.8299
15542
41414
Unit Root
Test Statistic
4
5
0.054
0.103**
0.173**
0.000
0.069
0.061
0.238**
-0.030
-0.037
0.034
0.200**
-0.027
-4.11**
-4.69**
0.051
0.169**
0.253**
-0.203**
0.066
0.057
0.199**
0.042
-0.004
0.061
0.057
-0.045
-0.042
0.091
0.024
0.052
-4.13**
-3.71**
-0.06
-0.007
0.654**
0.975**
0.082
0.072
0.330**
0.012
0.017
0.119**
0.127**
-0.035
0.027
0.014
0.275**
-0.043
-0.008
0.039
0.226**
0.037
-3.81**
-3.81**
2.1522
1.4516
1504
1392
-0.079
-0.013
0.72**
0.966**
0.062
0.101**
0.369**
-0.062
0.056
0.106**
0.206**
-0.035
0.082
0.098**
0.244**
0.031
-0.049
0.042
0.169**
0.026
-3.77**
-5.00**
2.4072
1.5624
5234
7071
-0.025
-0.056
0.245**
0.740**
-0.018
0.075
0.109
0.064
-6.65**
-8.57**
0.072
0.060
0.089
0.009
3
0.073
0.009
0.019
0.127**
-0.035
-0.065
0.022
0.079
1. To test for the stationarity of the volume and open interest series, we use the augmented Dickey and Fuller (1981) test to perform the unit root test. We
employ the Akaike Information Criterion (AIC) to determine the appropriate lag structure in ADF test. The critical value for ADF test at the 5% is –3.42. H0 :
unit root, HA : no unit root.
2.** indicate statistically significant at 5% level.
Additionally, to capture the evidence8 that past volatilities can predict volumes, the forecast errors are regressed
against lags in volatility, volume, and open interest. Finally,
the following equation is used to estimate the expected and
unexpected trading activity variables:
3.2 Measurement of Trading Activity Variables and Market
Depth
Following previous studies,7 this work uses trading
volume and open interest as proxies for trading activity in
futures markets. Employing a technique similar to that of
Bessembinder and Seguin (1992, 1993), the trading activity
series are decomposed into expected and unexpected components. First, the expected trading activity series is the
fitted value from the univariate ARMA model, while the
unexpected trading activity series is defined as εˆit , which
is the actual trading activity series minus expected trading
activity. This step yields ten series of forecast errors, εˆit ,
{
εˆit = activity it − E activity it activity i ,t −τ , τ = 1,..., n
}
εˆit = ϕ +
j =1
ρijσˆ i ,t − j +
n
k =1
λikVoli ,t − k +
n
µmOIi ,t − m + ν it (2)
m =1
where Voli and OIi denote the trading volume and open
interest of futures contract i, respectively. This study utilizes the Akaike information criterion (AIC) to determine
the appropriate lag structure in Eqs. (1) and (2). Therefore,
this study employs a different model for each time series.
The residuals νˆit from the Eq. (2) serve as the unexpected component of each trading volume and open interest
series, while the expected component is defined as the
difference between the actual trading activity series and the
unexpected component, activityit-νˆit .
(1)
for activity = trading volume or open interest
i = TX, TF, TE, Mini-TX, MSCITX
7
n
Bessembinder and Seguin (1992, 1993), Ragunathan and Peker (1997),
Watanabe (2001) and Fung and Patterson (1999).
8
2
See Schwert (1990), Gallant, Rossi and Tauchen (1992).
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
According to market depth theory by Kyle (1985),
Bessembinder and Seguin (1993) argue that market depth
varies with recent trading activity, which is proxied by
endogenously determined open interest. As the level of
open interest is a measure of trading activity and reflects the
current willingness of futures traders to risk their capital in
the futures position in the presence of price volatility, expected open interest is a good proxy for market depth.
Therefore, this study also uses expected open interest as a
proxy for market depth. We will test the market depth theory that observed volatility, conditional on contemporaneous volume, is expected to decrease with increasing market
depth (larger expected open interest) in TAIFEX and
SGX-DT Taiwan stock index futures markets.
lagged volatility variables are included in Eq. (4) to measure and accommodate the effect of persistence in price
volatility, a phenomenon called volatility-clustering.
According to Bessembinder and Seguin (1992, 1993),
estimates of daily standard deviations are obtained using
the following transformation.
σˆ t = Uˆ t
To improve study robustness, two commonly used
price volatility measures, the OLS-based and GARCHbased models, are employed to examine the relationship
between price volatility, trading activity and market depth
for selected futures contracts traded on the TAIFEX and the
SGX-DT.
To determine the existence of an asymmetry effect,
namely, the effects of unexpected changes in trading activity variables on price volatility varying according to shock
sign, dummy variables are defined as 0 for a negative shock
(lower than expected trading activities) and 1 for a positive
shock (higher than expected trading activities). The product
of the dummy variable and the unexpected trading activity
variable thus is created. Consequently, the estimated equation is expressed as follows,
3.3.1 Model 1(OLS-Based Volatility Estimate)
First, this study measures the unbiased estimate of
daily futures price volatility using the same procedure as
Davidian and Carroll (1987) and Bessembinder and Seguin
(1992, 1993). The procedure involves iteration between the
following two equations: a conditional mean Eq. (3) and a
conditional volatility Eq. (4),
Rt = α +
γ j Rt− j +
j =1
σˆ t = δ +
n
j =1
ω j Uˆ t − j +
4
ρidi +
i =1
4
i =1
ηi di +
n
π j σˆ t − j + U t
σˆ t = δ 0 +
k =1
µ j Ak +
n
β jσˆ t − j + et
ω j Uˆ t − j +
4
ηidi +
i =1
m
k =1
µ j Ak +
n
β jσˆ t − j
j =1
(6)
+ δ 1Un exp Voldum t + δ 2Un exp OIdum t + et
where UnexpVoldumt represents the product term of the
unexpected volume and the dummy variable, which is 1 for
a positive shock on day t and 0 otherwise, and UnexpOIdumt represents the product term of the unexpected
open interest and the dummy variable, which is 1 for a
positive shock and 0 otherwise.
(3)
(4)
j =1
where Rt denotes futures return on day t, di (i=1,..., 4)
represents four dummy variables9 which captures differences in mean and volatility for the ith day of the week and
Ut (residuals) is unexpected returns from Eq. (3). σ̂ t is the
conditional standard deviation, which is called price volatility in this paper. The method for estimating σ̂ t will be
explained below. Ak are the trading activity variables,
which are divided into expected and unexpected components, and indicate how trading activity variables affect
price volatility in Eq. (4). Lagged unexpected returns are
included in Eq. (4) to capture this possible asymmetry (e.g.,
leverage effect10) in the relation between returns and volatility. That is, negative unexpected return shocks impact
volatility more than positive unexpected return shocks. The
9
n
j =1
j =1
m
(5)
Davidian and Carroll (1987) recommend that Eqs. (3)
and (4) are estimated sequentially. Equation (3) first is
estimated without the lagged volatility estimates by using
OLS. The obtained residuals then are transformed into the
volatility estimates using Eq. (5), and subsequently Eq. (4)
is estimated. Fitted values calculated from Eq. (4) are used
as regressors in reestimating Eq. (3). Equation (4) is finally
reestimated using the residuals from Eq. (3).
3.3 Measurement of Price Volatility-Empirical Model
Specification
n
π /2
3.3.2 Model 2(GARCH-Based Volatility Estimate)
Second, using a procedure inspired by Gulen and
Mayhew (2000), this study transforms Eqs. (3) and (4) to
the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model proposed by Bollerslev (1986). In
contrast to the regression Eqs. (3) and (4) estimated by OLS,
the GARCH model empirically has been demonstrated to
capture reasonably well the time-varying volatility of financial data returns.11 The estimated GARCH(p, q) specification can be expressed as below,
Rt = a +
n
j =1
d1t takes one when day t is Monday and otherwise takes zero; d2t takes one
when day t is Tuesday and otherwise takes zero, and so on.
See Black (1976), Christie (1982), Nelson (1991). The leverage effect
means a reduction in stock price increases the debt/equity ratio (or leverage) and thus raises equity returns volatility.
10
11
136
bj Rt − j +
4
ci di + εt , εt Ωt −1 ~ N ( 0, ht )
(7)
i =1
See Bollerslev (1986), French,Schwert and Stambaugh (1987), Nelson
(1991), Bollerslev ,Chou and Kroner (1992).
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
p
ht = α 0 +
α i ε t2− i +
i =1
q
4
β j ht − j +
j =1
η i d i + ω 1 ExpVol
i =1
+ ω 2 Un exp Vol + ω 3 ExpOI
different from 0, then negative unexpected return shocks
impact volatility more than positive unexpected return
shocks. Trading activity variables also are decomposed into
expected and unexpected components, and then are inserted
into the EGARCH conditional volatility equation as additional explanatory variables.
(8)
+ ω 4 Un exp OI
t
If the asymmetric term, , is negative and statistically
t
where Rt denotes futures return on day t, di (i=1,…, 4) represents four dummy variables12 which captures differences in
mean and volatility for the ith day of the week, ε t (residuals) is unexpected returns from Eq. (7), ExpVolt and UnexpVolt represent the expected and unexpected volume, and
ExpOIt and UnexpOIt are the expected and unexpected open
interest, respectively. The conditional mean equation provided in Eq. (7) can be expressed as a function of exogenous variables with an error term. The ht is the one- period
ahead forecast variance based on past information (Ω t −1 ) ,
and is called the conditional variance, which denotes price
volatility in this paper. The conditional variance equation
specification in Eq. (8) is a linear function of lagged
squared residuals and lagged residual conditional variance.
Furthermore, Equation (8) can be extended to permit the
inclusion of exogenous independent variables such as daily
dummies and trading activities in this investigation.
4. Empirical Results
Table 3 presents the estimated results of the conditional
mean Eq. (3) for each of the five futures contracts. The
findings of this study are consistent with those of Bessembinder and Seguin (1993) and Ragunathan and Peker
(1997). The largest adjusted R2 is 1.39% for TF. Moreover,
none of the day-of-the-week dummies are significant across
all contracts. Lagged returns do not have significant explanatory power for all contracts. This evidence can be
attributed to weak-form efficiency, indicating that past
returns are of limited use in predicting present returns.
Nevertheless, lagged volatilities for TE, Mini-TX and
MSCITX are positive and statistically significant at the
10% level.
Additionally, to determine whether an asymmetry in
volume and open interest shocks exists, the UnexpVoldumt
and UnexpOIdumt terms are included in Eq. (8). Equation
(9), given below, shows that the allowed variation in the
effects of unexpected changes in volume and open interest
with shock sign is reestimated.
p
ht = α 0 +
q
α i ε t2−i +
4
β j ht − j +
i =1
Table 4 reports the estimation results of the conditional
volatility in Eq. (4). Monday dummy exhibits significant
day-of-the-week effect across all contracts. Moreover, all
ten coefficient estimates for expected and unexpected
volume are positive. However, magnitudes and statistical
significance levels show that expected and unexpected
volume has heterogeneous effects on volatility. The estimated coefficient on expected volume is significant at the
10% level for two of five contracts, while the estimated
coefficient on unexpected volume is significant at the 5 %
level for all five contracts. Furthermore, the coefficients of
unexpected volume are larger than expected volume. The
ratio of unexpected volume to expected volume varied from
2 for the TF to 111 for the Mini-TX, indicating that unexpected volume impacts volatility more than expected
volume. This analytical result is consistent with the findings of Bessembinder and Seguin (1993), Ragunathan and
Peker (1997) and Watanabe (2001).
j =1
η i d i + ω1ExpVolt + ω2Un exp Volt
i =1
(9)
+ ω3 ExpOIt + ω4Un exp OI + ω5Un exp Voldumt + ω6Un exp OIdumt
However, the GARCH is a symmetric volatility model
and its conditional variance depends on the magnitude
rather than the sign of the unexpected disturbance term.
Thus, GARCH fails to capture the “leverage effect”. The
EGARCH model proposed by Nelson (1991) overcomes
this problem. The conditional variance in the model depends on both the sign and magnitude of the unexpected
returns, and thus is asymmetric in its response to positive
and negative unexpected returns. This study designs a more
rigorous model that is used to investigate the relationship
between price volatility, trading activity and market depth
for the TAIFEX and SGX-DT Taiwan Stock Index Futures
under the framework of EGARCH specification. The
EGARCH (1,1) specification replaces Eq. (9) with the
following Eq. (10).
log h t = ω 0 + φ log h t − 1 + α
+ ω 1 ExpVol
t
+ ω 2 Un exp Vol
+ ω 5Un exp Voldum
12
t
ε t −1
ht −1
t
−
2
π
+ ω 3 ExpOI
+ ω 6Un exp OIdum
+γ
t
t
ε t −1
ht − 1
4
Except for TF, the coefficient estimates for expected
open interest are negative and statistically significant. This
measurement result contrasts with the findings of Bessembinder and Seguin (1993) and Watanabe (2001), who find
that all coefficients relating expected open interest to volatility are negative and significant. Bessembinder and Seguin (1993) note that a significant negative coefficient for
the effect of expected open interest on volatility is consistent with the market depth hypothesis that expected open
interest is positively related to the number of traders or
amount of capital dedicated to a market at the beginning of
a trading session, and moreover increasing the number of
traders or amount of capital involved in a market improves
market depth and thus reduces volatility. Accordingly, inconsistent with theories of market depth, this study does not
η idi
+
i =1
+ ω 4 Un exp OI
t
(10)
d1t takes one when day t is Monday and otherwise takes zero, d2t takes
one when day t is Tuesday and otherwise takes zero, and so on.
137
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
Table 3. Estimation Results of the Autoregressive Model for Daily Futures Returns
Rt = α +
Futures contracts
Intercept
n
j =1
γ j Rt− j +
4
i =1
TX
ρ id i +
TF
n
j =1
π j σˆ t − j + U
t
TE
Mini-TX
MSCITX
-0.00364
(-0.81585)
0.00065
(0.17174)
-0.00604
(-1.36766)
-0.00400
(-1.45935)
-0.01538
(-1.89779)
-0.00189
(-0.63259)
-0.00256
(-0.86081)
0.00071
(0.24139)
-0.00019
(-0.06338)
0.20228
(1.00145)
0.05631
(0.33818)
-0.00234
(-0.78531)
-0.00434
(-1.44190)
-0.00259
(-0.85164)
0.00337
(1.12764)
0.00342
(0.00045)
0.03443
(0.13016)
-0.00232
(-0.66441)
-0.00175
(-0.49276)
0.00114
(0.32781)
-0.00153
(-0.43640)
0.25482
(2.81211)*
0.02035
(0.09741)
0.00009
(0.02902)
-0.00213
(-0.67522)
0.00157
(0.50080)
-0.00063
(-0.19907)
0.29254
(3.30876)*
0.01681
(0.03786)
-0.00382
(-1.02495)
0.00034
(0.09468)
0.00069
(0.18327)
0.00247
(0.66704)
0.64834
(3.60275)*
0.03271
(0.11005)
Daily dummies
Monday
Tuesday
Wednesday
Thursday
Sum of lagged volatilities
Sum of lagged returns
Ljung-Box Q (12)
Ljung-Box Q2 (12)
Adjusted R2
Regression F-statistic
4.2827
3.8209
7.4793
8.3059
6.4976
38.997**
-0.00232
0.91257
121.39**
0.01391
1.53094
45.607**
0.01271
1.85095*
41.845**
0.00475
1.22647
20.160*
0.008753
1.30275
1. Test statistics in parentheses for individual coefficients are t–statistics. Test statistics in parentheses for lagged coefficients are F–statistics for the hypothesis
that the sum of the lagged coefficients is zero.
2. Ljung-Box Q (k) statistic tests the joint significance of the autocorrelations of the daily return series up to the k-th order. Ljung-Box Q2 (k) statistic tests the
joint significance of the autocorrelations of the squared daily return series up to the k-th order.
3. * and ** indicate statistically significant at the 10% and 5% level, respectively.
4. The appropriate lag-length specification of each equation is determined using Akaike’s Information Criterion (AIC).
unexpected volume shocks influence volatility more than
negative unexpected volume shocks.
find any evidence that higher levels of expected open interest significantly mitigate volatility. Four of the five estimated coefficients relating unexpected open interest to
volatility are negative and significant. This analytical result
resembles that of Bessembinder and Seguin (1993), implying that an increase in open interest during the trading
day lessens the influence of a volume shock on volatility.
The sum of the estimated coefficients on the lags of the
volatility series is positive and significant for all contracts,
displaying significant persistence in volatility in financial
markets. The sum of estimated coefficients on lagged unexpected returns is negative and significant for TE and
MSCITX, indicating that negative return shocks have a
larger effect on subsequent volatility than positive return
shocks do, otherwise known as the “leverage effect”.
This study reports Ljung-Box test statistics for the 12th
order serial correlation including both the residuals and
squared residuals in Table 3. The Ljung-Box test statistics for
the residual levels are insignificant at the 5% level, revealing
that no serial autocorrelation remains in the five futures
contracts. However, the Ljung-Box test statistics for the
squared residuals are highly significant for all contracts,
indicating the existence of time-varying index returns volatility. Furthermore, Tables 4 and 5 also demonstrate that the
sum of estimated coefficients on the lags of the volatility
series is positive and significant for all contracts. Therefore,
these analytical results indicate the volatility-clustering phenomenon observed in the present volatility series. This study
Table 5 reports the estimation results of Eq. (6) that
allow the effects of unexpected changes in volume and
open interest to vary with the shock sign. The coefficients
associated with the UnexpVoldumt and UnexpOIdumt are
not statistically significant for all contracts, indicating no
asymmetries for unexpected volume and open interest. This
finding is inconsistent with the findings by Bessembinder
and Seguin (1993) and Watanabe (2001), who find positive
Additionally, the 1 and 1 coefficients for the persistence
of volatility measures are statistically positive for all contracts when current volume and open interest are included
in the conditional variance equation simultaneously.
Therefore, current volume and open interest do not remove
the ARCH effects in the SGX-DT and TAIFEX futures.
This finding is consistent with the findings of Najand and
Yung (1991) and Foster (1995), but differs from those of
138
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
Table 4. Regressions of Futures Returns Volatility on Expected and Unexpected Trading Activity
σˆ t = δ +
Futures contracts
Intercept
Daily dummies
Monday
Tuesday
Wednesday
Thursday
Expected volume
Unexpected volume
Expected open interest
Unexpected open interest
Sum of lagged volatilities
Sum of lagged unexpected returns
Adjusted R2
Regression F-statistic
n
j =1
ω j Uˆ t − j +
4
i =1
ηid i +
m
k =1
µ j Ak +
n
j =1
β j σˆ t − j + e t
TX
0.01186
(3.34560)**
TF
0.018215
(7.35168)**
TE
0.00981
(2.5436)**
Mini-TX
0.01271
(4.03618)**
MSCITX
0.03360
(3.11148)**
0.00752
(3.49979)**
0.00004
(0.02049)
0.00313
(1.46045)
-0.00056
(-0.26353)
4.57E-07
(1.69090)
1.91E-06
(8.54184)**
-2.61E-07
(-0.79992)
-4.94E-06
(-5.6621)**
0.21238
(3.67422)**
-0.10259
(1.93938)
0.22044
9.18490**
0.00389
(1.83411)*
-0.00287
(-1.35707)
-0.00140
(-0.65788)
-0.00341
(-1.58038)
5.21E-06
(3.80526)**
1.05E-05
(9.52388)**
-4.54E-06
(-3.54286)**
-8.60E-06
(-2.591493)**
0.14487
(2.94785)*
-0.04863
(0.71218)
0.20179
10.46253**
0.00771
(2.90466)**
0.00266
(1.01856)
0.00333
(1.26180)
-0.00105
(-0.39339)
3.21E-06
(1.88732)*
7.85E-06
(7.47906)**
-1.24E-06
(-0.99024)
-2.26E-05
(-6.66454)**
0.35699
(4.18475)**
-0.264952
(6.13189)**
0.20803
5.86893**
0.00814
(3.59289)**
0.000667
(0.29810)
0.00215
(0.95247)
-0.00103
(-0.45849)
9.49E-08
(0.08660)
1.06E-05
(12.2295)**
-1.69E-07
(-0.17595)
-4.88E-06
(-2.07135)**
0.27227
(8.66916)**
-0.04985
(0.58856)
0.30943
14.21835**
-0.00706
(-2.66275)**
0.00202
(0.77245)
-0.00820
(-3.04590)**
-0.00474
(-1.80079)*
3.07E-08
(0.05643)
1.08E-06
(6.48034)**
-2.24E-07
(-1.44620)
-1.07E-07
(-0.56401)
0.22482
(2.75632)*
-0.17657
(4.58891)**
0.15236
4.55372
1. * and ** indicate statistically significant at the 10% and 5% levels, respectively.
2. Test statistics in parentheses for individual coefficients are t–statistics. Test statistics in parentheses for lagged coefficients are F–statistics for the hypothesis
that the sum of the lagged coefficients is zero.
3. The appropriate lag-length specification of each equation is determined using Akaike’s Information Criterion (AIC).
Lamoureux and Lastrapes (1990) and Jones, Kaul and
Lipson (1994), who find that ARCH effects on price volatility are insignificant when volume is included in the conditional variance equation.
and Patterson (1999), few researchers have examined the
same relations for emerging markets. This study aims to
further extend the methodology used by Bessembinder and
Seguin (1993) and improve understanding of the relations
among price volatility, trading activity and market depth for
selected futures contracts in the Taiwan Futures Exchange
(TAIFEX) and Singapore Exchange Derivatives Trading
Division (SGX-DT) Taiwan Stock Index Futures markets.
Table 7 reports the estimation results of a standard
GARCH model [Eqs. (7) and (9)] that allows the effects of
unexpected volume and open interest shocks on volatility to
vary with shock sign by introducing the UnexpVoldumt and
UnexpOIdumt terms. The estimation results are almost
identical regardless of the presence of dummy variables,
except that the coefficients on the expected volume variable
for TE and MSCITX become negative and the coefficient on
unexpected open interest for TE becomes insignificant. The
coefficients associated with UnexpVoldumt and UnexpOIdumt are not statistically significant for all contracts,
indicating that neither of the unexpected trading activity
shocks are asymmetric in SGX-DT and TAIFEX. This result
also is consistent with the Schwert volatility estimates listed
in Table 5.
This study investigates this issue using two different
modeling methodologies, the OLS-based and GARCHbased models, to test the robustness of the results and to
obtain a sensitivity check. Essentially, the findings of this
study regarding the relationship among volatility, volume
and open interest are robust for different measures of price
volatility. Besides slight differences in the estimation results
for Monday dummy, expected volume and unexpected open
interest variables, the estimation results of the remaining
variables are similar across the two models for the TAIFEX
and SGX-DT futures markets. Further comparison with
developed markets is presented below.
5. Conclusion
First, the results of conditional mean function of the two
models in the TAIFEX and SGX-DT futures markets are
consistent with weak-form efficiency. The findings resemble those found for other developed markets in studies by
Bessembinder and Seguin (1993), Ragunathan and Peker
Despite extensive research on the relations among
trading activity, volatility and market depth in futures markets, including that by Bessembinder and Seguin (1993),
Ragunathan and Peker (1997), Watanabe (2001) and Fung
139
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
Table 5. Regressions of Futures Returns Volatility on Trading Activity (Allowing for Asymmetries)
σˆ t = δ 0 +
Futures contracts
Intercept
Daily dummies
Monday
Tuesday
Wednesday
Thursday
Expected volume
Unexpected volume
UnexpVoldum
Expected open interest
Unexpected open interest
UnexpOIdum
Sum of lagged volatilities
Sum of lagged unexpected returns
Adjusted R2
Regression F-statistic
n
j =1
ω j Uˆ t − j +
4
i =1
ηi d i +
m
k =1
µ j Ak +
n
j =1
β j σˆ t − j + δ 1Un exp Voldumt + δ 2Un exp OIdumt + et
TX
0.01177
(3.3156)**
TF
0.01798
(7.1292)**
TE
0.00972
(2.51604)**
Mini-TX
0.01124
(3.5929)**
MSCITX
0.03391
(3.0363)**
0.00749
(3.48117)**
0.00003
(0.01829)
0.00326
(1.51685)
-0.00051
(-0.23957)
4.28E-07
(1.5662)
1.80E-06
(4.0393)**
1.77E-07
(0.24913)
-2.91E-07
(-0.8881)
-6.00E-06
(-4.0320)**
2.43E-06
(0.87776)
0.38125
(4.28517)**
-0.10332
(1.96408)
0.21866
8.29627**
0.004087
(1.9098)*
-0.00279
(-1.31371)
-0.00133
(-0.62479)
-0.00333
(-1.5456)
5.00E-06
(3.4711)**
1.12E-05
(4.3101)**
-1.39E-06
(-0.36328)
-4.48E-06
(-3.4843)**
-1.27E-05
(-2.1228)**
8.67E-06
(0.85692)
0.15024
(3.18855)*
-0.05585
(0.92808)
0.20723
9.56114**
0.00765
(2.8762)**
0.00249
(0.95571)
0.00316
(1.20244)
-0.00066
(-0.24971)
2.88E-06
(1.6506)
6.11E-06
(2.8104)**
2.87E-06
(0.84442)
-1.36E-06
(-1.0784)
-2.58E-05
(-4.2724)**
7.13E-06
(0.67820)
0.38746
(5.09621)**
-0.25911
(5.90118)**
0.21372
5.70246**
0.008054
(3.60693)**
0.00058
(0.2662)
0.00144
(0.6468)
-0.00099
(-0.44852)
-6.30E-07
(-0.5699)
7.71E-06
(4.5213)**
4.09E-06
(1.48395)
-2.91E-07
(-0.3072)
-1.48E-05
(-3.9279)**
2.61E-06
(1.46801)
0.27185
(8.72858)**
-0.04916
(0.57127)
0.31817
13.23680**
-0.00701
(-2.6456)**
0.00199
(0.76674)
-0.00848
(-3.14368)**
-0.00503
(-1.90519)*
-3.42E-07
(0.5892)
1.79E-06
(3.6902)**
-1.06E-06
(-1.55929)
-2.83E-07
(-1.6481)
-7.14E-08
(-0.2348)
-8.76E-08
(-0.16226)
0.31854
(3.18756)**
-0.17741
(4.6917)**
0.15691
4.22498**
1. * and ** indicate statistically significant at the 10% and 5% levels, respectively.
2. Test statistics in parentheses for individual coefficients are t–statistics. Test statistics in parentheses for lagged coefficients are F–statistics for the hypothesis
that the sum of the lagged coefficients is zero.
3. The appropriate lag-length specification of each equation is determined using Akaike’s Information Criterion (AIC).
(1997), Gulen and Mayhew (2000) and Watanabe (2001).
the findings of Bessembinder and Seguin (1993) and Watanabe (2001), namely that positive unexpected volume
shocks impact volatility more than negative unexpected
volume shocks.
Second, as found for the developed markets, both
models also show that unexpected volume influences
volatility more than expected volume for the TAIFEX and
SGX-DT futures markets. This finding indicates that volatility increases with increasing futures volume, but this
behavior is driven by the unexpected volume component,
rather than the expected component. This finding seems to
support the mixture of distribution hypothesis by Clark
(1973).
Finally, empirical tests of the market depth theory
demonstrate that increased levels of expected open interest
(viewed as a proxy for market depth) do not mitigate volatility significantly. This finding suggests that market depth
does not have an effect on volatility in the SGX-DT and
TAIFEX futures markets, implying that existing market
depth does not mitigate price volatility. This analytical
result contrasts with the findings of the developed markets
examined by Bessembinder and Seguin (1993) and Watanabe (2001). Because the Taiwan Stock Index Futures
market is a emerging market and characterized by high
volatility, this difference can be attributed to market maturity. This result is noteworthy because it provides evidence that the relation between price volatility and market
depth may vary with the market maturity. It can be concluded that market maturity affects price volatility. Thus,
the findings of this study have implications for financial
market regulators concerned with how to enhance market
Third, both models demonstrate the volatility-clustering phenomenon observed in the present volatility series
for the TAIFEX and SGX-DT futures markets when current
volume and open interest are included in the conditional
variance equation. This analytical result is consistent with
those of Bessembinder and Seguin (1993), Ragunathan and
Peker (1997), Watanabe (2001), but is inconsistent with the
findings of Lamoureux and Lastrapes (1990).
Fourth, no asymmetric relationship is found between
unexpected trading activity and volatility in the TAIFEX
and SGX-DT futures markets. This finding contrasts with
140
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
depth in the SGX-DT and TAIFEX futures markets.
Table 6. Effect of Futures Trading Activity on Volatility-GARCH Model
Rt = a +
ht = α 0 +
p
i =1
α i ε t2− i +
Panel A Conditional Mean Equation
Futures contracts
Intercept
Daily dummies
Monday
Tuesday
Wednesday
Thursday
Sum of lagged returns
q
j =1
n
j =1
β j ht − j +
b j Rt− j +
4
i =1
4
i =1
c i d i + ε t , ε t Ω t −1 ~ N ( 0 , h t )
η i d i + ω 1 ExpVol t + ω 2Un exp Vol t + ω 3 ExpOI t + ω 4Un exp OI
TX
-0.00048
(0.7855)
TF
-0.00069
(0.6989)
TE
-0.00073
(0.8363)
Mini-TX
-0.00076
(0.7309)
TiMSCI
-0.00185
(0.3880)
-0.00109
(0.6773)
-0.00193
(0.4672)
0.00136
(0.6042)
0.00074
(0.7763)
0.02196
(0.8679)
-0.00172
(0.4997)
-0.00311
(0.2141)
-0.00064
(0.8023)
0.00082
(0.7206)
0.06446
(0.5066)
-0.00168
(0.7039)
4.21E-05
(0.9931)
0.00080
(0.8570)
-8.96E-05
(0.9858)
0.02192
(0.8710)
0.00019
(0.9548)
-0.00047
(0.8812)
0.00113
(0.6871)
0.00039
(0.9151)
-0.0033
(0.9743)
-0.00139
(0.6470)
0.00266
(0.4389)
0.00188
(0.5715)
0.00266
(0.3328)
0.0720
(0.5439)
TE
GARCH (2,2)
0.00051
(0.0228)**
0.17565
(0.0102)**
0.04000
(0.6282)
0.47999
(0.0771)*
0.03999
(0.8975)
-1.80E-05
(0.9323)
-0.00011
(0.5244)
-0.00014
(0.4205)
-3.25E-05
(0.8535)
3.38E-08
(0.5678)
1.24E-07
(0.0018)**
-2.11E-08
(0.6611)
-4.48E-07
(0.0001)**
Mini-TX
GARCH (2,2)
0.00036
(0.0088)**
0.15000
(0.0713)*
0.04000
(0.6468)
0.48000
(0.0078)**
0.04000
(0.8557)
-4.78E-05
(0.7762)
-0.00016
(0.1922)
-8.68E-05
(0.5034)
-6.41E-05
(0.6330)
2.10E-08
(0.3700)
1.06E-07
(0.0000)**
-1.52E-08
(0.4908)
-4.32E-08
(0.4206)
TiMSCI
GARCH (2,1)
0.00062
(0.0018)**
0.13332
(0.1071)
0.04444
(0.5939)
0.53333
(0.0000)**
Panel B Conditional Variance Equation
Intercept
1
TX
GARCH (1,2)
1.17E-05
(0.8524)
0.13332
(0.0415)**
TF
GARCH (1,1)
9.01E-05
(0.0673)*
0.14994
(0.0040)**
0.53333
(0.0334)**
0.04444
(0.8423)
9.37E-05
(0.3083)
-2.51E-05
(0.7374)
4.17E-05
(0.5884)
-1.61E-05
(0.8249)
1.67E-09
(0.7949)
2.97E-08
(0.0000)**
-9.70E-10
(0.8767)
-7.84E-08
(0.0012)**
0.59996
(0.0000)**
2
1
2
Monday
Tuesday
Wednesday
Thursday
Expected volume
Unexpected volume
Expected open interest
Unexpected open interest
5.78E-06
(0.9404)
-0.00013
(0.1194)
-2.77E-05
(0.6158)
-0.00016
(0.0067)**
4.07E-09
(0.8974)
2.65E-07
(0.0000)**
-4.21E-08
(0.0285)
-2.12E-07
(0.0379)**
-0.00018
(0.0321)**
0.00010
(0.2570)
-0.00013
(0.2029)
-0.00027
(0.0014)**
2.84E-08
(0.0069)**
3.39E-08
(0.0000)**
-2.74E-09
(0.3471)
1.81E-09
(0.7094)
Model Diagnostics Test on Standardized Residuals
Ljung-Box Q (12)
Ljung-Box Q2 (12)
ARCH (12)
5.8042
(0.926)
16.728
(0.160)
15.4364
(0.2184)
4.0047
(0.9830)
8.0298
(0.783)
7.8705
(0.7951)
9.4180
(0.667)
8.3470
(0.106)
17.0041
(0.118)
12.828
(0.382)
24.231
(0.029)**
25.050
(0.034)**
9.8115
(0.632)
7.3806
(0.112)
15.9548
(0.1933)
1. The number in parentheses are the p-values.
2. LB Q (12) and LB Q2 (12) are the Ljung-Box statistics applied on the standardized and squared standardized residuals, respectively. ARCH (12) is the
statistics used to test whether standardized residuals exists ARCH effect up to the order 12.
3. * and ** indicate statistically significant at the 10% and 5% levels, respectively.
141
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
Table 7. Effect of Futures Trading Activity on Volatility-GARCH Model with Dummy Variables
Rt = a +
ht = α 0 +
p
i =1
αiε t2−i +
q
j =1
β j ht − j +
4
i =1
n
j =1
b j Rt− j +
4
i =1
c i d i + ε t , ε t Ωt −1 ~ N ( 0 , h t )
ηi di + ω1ExpVolt + ω 2Un expVolt + ω3 ExpOIt + ω 4Un exp OI + ω5Un expVoldumt + ω6Un exp OIdumt
Panel A Conditional Mean Equation
Futures contracts
Intercept
TX
-0.00054
(0.7602)
TF
-0.00097
(0.6143)
TE
-0.00073
(0.8319)
Mini-TX
-0.00075
(0.8271)
TiMSCI
-0.00180
(0.3732)
-0.00032
(0.9172)
-0.00057
(0.8673)
0.00042
(0.8908)
0.00022
(0.9402)
0.0219
(0.871)
-0.00151
(0.5730)
-0.00309
(0.2283)
-0.00063
(0.8123)
0.00074
(0.7537)
0.06439
(0.5074)
-0.00168
(0.6943)
4.25E-05
(0.9929)
0.00080
(0.8587)
-8.94E-05
(0.9856)
0.03508
(0.7804)
0.00022
(0.9577)
-0.00047
(0.9142)
0.00113
(0.7898)
0.00039
(0.9315)
-0.00692
(0.9525)
-0.00138
(0.6647)
0.00267
(0.3782)
0.00190
(0.5774)
0.00266
(0.4202)
0.08536
(0.7158)
Daily dummies
Monday
Tuesday
Wednesday
Thursday
Sum of lagged returns
Panel B Conditional Variance Equation
Intercept
1
TX
GARCH (1,2)
0.00010
(0.1212)
0.13333
(0.0215)**
TF
GARCH (1,1)
0.00010
(0.0549)
0.14985
(0.0015)**
8.07E-06
(0.9233)
-0.00015
(0.0047)**
-3.82E-05
(0.4683)
-0.00016
(0.0139)**
1.15E-08
(0.7395)
2.44E-07
(0.0001)**
-1.89E-09
(0.9869)
-2.97E-08
(0.2320)
-3.81E-07
(0.0499)**
4.20E-07
(0.1843)
TE
GARCH (2,2)
0.00050
(0.0335)**
0.12000
(0.1118)
0.04000
(0.6148)
0.67999
(0.0195)**
0.04000
(0.8949)
-4.09E-05
(0.8381)
-7.96E-05
(0.6163)
-9.72E-05
(0.5798)
-2.67E-05
(0.8770)
-3.00E-08
(0.5031)
1.46E-07
(0.0441)**
-2.11E-08
(0.8562)
-1.77E-08
(0.6525)
-1.54E-07
(0.5019)
-3.79E-07
(0.30900)
Mini-TX
GARCH (2,2)
0.00037
(0.0001)**
0.12000
(0.1974)
0.04000
(0.6196)
0.48000
(0.0412)**
0.04000
(0.8512)
-5.49E-05
(0.6658)
-0.00014
(0.1296)
-6.23E-05
(0.5889)
-7.74E-05
(0.4825)
1.92E-08
(0.3386)
1.28E-07
(0.0000)**
5.56E-08
(0.4333)
-1.53E-08
(0.3910)
-2.18E-08
(0.3812)
-2.83E-07
(0.2169)
TiMSCI
GARCH (2,1)
0.00055
(0.0039)
0.13333
(0.1092)
0.04444
(0.6191)
0.53333
(0.0002)**
0.0720
(0.5522)
-2.47E-05
(0.7713)
5.66E-05
(0.5407)
-6.77E-05
(0.4408)
-5.08E-05
(0.6865)
-1.06E-08
(0.5216)
3.78E-08
(0.0037)**
-1.58E-08
(0.5105)
-3.41E-09
(0.4985)
1.14E-09
(0.8786)
-1.63E-08
(0.1012)
3.9760
(0.9840
7.3295
(0.835)
7.1379
(0.8483)
8.6695
(0.731)
19.772
(0.072)
20.3916
(0.060)
12.940
(0.373)
22.575
(0.032)**
23.3324
(0.025)**
8.1982
(0.769)
20.962
(0.051)
17.505
(0.1315)
2
0.53333
(0.0093)**
0.04444
2
(0.8027)
7.30E-05
Monday
(0.4570)
-8.44E-05
Tuesday
(0.2937)
-8.02E-05
Wednesday
(0.2812)
-5.96E-05
Thursday
(0.4376)
9.89E-10
Expected volume
(0.8732)
2.05E-08
Unexpected volume
(0.0053)**
2.44E-08
UnexpVoldum
(0.2123)
-9.87E-10
Expected open interest
(0.7378)
-1.24E-07
Unexpected open interest
(0.0118)**
9.58E-08
UnexpOIdum
(0.1927)
Model Diagnostics Test on Standardized Residuals
8.9643
Ljung-Box Q (12)
(0.706)
11.563
Ljung-Box Q2 (12)
(0.481)
11.4361
ARCH (12)
(0.4919)
1
0.59992
(0.0000)**
1. The number in parentheses are the p-values.
2. LB Q (12) and LB Q2 (12) are the Ljung-Box statistics applied on the standardized and squared standardized residuals, respectively. ARCH (12) is the
statistics used to test whether standardized residuals exists ARCH effect up to the order 12.
3. * and ** indicate statistically significant at the 10% and 5% levels, respectively.
142
Wen-Hsiu Kuo et al./Asia Pacific Management Review (2005) 10(1), 131-143
References
Fung, H.G. and Patterson, G.A. (1999). The dynamic relationship of volatility, volume, and market depth in currency futures markets. Journal
Bessembinder, H. and Seguin, P.J. (1992). Futures trading activity and
of International Financial Markets, Institutions & Money, 9, 33-59.
stock price volatility. Journal of Finance, 47, 2015-2034.
Gallant, R.A., Rossi, P.E. and Tauchen, G. (1992). Stock prices and volume.
______ and ______. (1993). Price volatility, trading volume, and market
Review of Financial Studies, 5, 199-242.
depth: Evidence from futures markets. Journal of Financial and
Girma, P.B. and Mougoue, M. (2002). An empirical examination of the
Quantitative Analysis, 28, 20-39.
relation between futures spreads volatility, volume, and open interest.
______, Chan, K. and Seguin, P.J. (1996). An empirical examination of
The Journal of Futures Markets, 22, 1083-1102.
information, differences of opinion, and trading activity. Journal of
Gulen, H. and Mayhew, S. (2000). Stock index futures trading and volatility
Financial Economics, 40, 105-134.
in international equity markets. Journal of Futures Markets, 20,
Black, F. (1976). Studies of stock, price volatility change. Proceedings of
661-685.
the 1976 Meetings of the Business and Economics Statistics Section,
Harris, L. (1986). Cross-security tests of mixture of distribution hypothesis.
American Statistical Association, 177-181.
Journal of Financial and Quantitative Analysis, 21, 39-46.
Blume, L., Easley, D. and O’Hara, M. (1994). Market statistics and tech-
Harris, M. and Raviv, A. (1993). Differences of opinion make a horse race.
nical analysis: The role of volume. Journal of Finance, 49, 153-181.
Review of Financial Studies, 6, 473-506.
Bollerslev, T. (1986). Generalized autoregressive conditional heteroske-
Hsu, H. and Lin, B.J. (2002). The kinetics of the stock market. Asia Pacific
dasticity. Journal of Econometrics, 33, 307-327.
Management Review, 7 (1), 1-24.
______, Chou, R.Y. and Kroner, K.F. (1992). ARCH modeling in finance:
Jones, C.M., Kaul, G. and Lipson, M.L. (1994). Transactions, volume, and
A review of the theory and empirical evidence. Journal of Econo-
volatility. Review of Financial Studies, 7, 631-651.
metrics, 52, 5-59.
Karpoff, J.M. (1987). The relationship between price change and trading
Chen, G., Firth, M. and Rui, O.M. (2001). The dynamic relation between
volume: A survey. Journal of Financial and Quantitative Analysis, 22,
stock returns, trading volume, and volatility. The Financial Review,
109-126.
38, 153-174.
Kyle, A. (1985). Continuous auctions and insider trading. Econometrica,
Christie, A. (1982). The stochastic behavior of common stock variance:
53, 1315-1335.
Value, leverage and interest rate effects. Journal of Financial Eco-
Lamoureux, C. and Lastrapes, W. (1990). Heteroskedasticity in stock return
nomics, 10, 407-432.
data: Volume versus GARCH effects. Journal of Finance, 45, 221-
Ciner, C. (2002). Information content of volume: An investigation of Tokyo
229.
commodity futures markets. Pacific-Basin Finance Journal, 10,
Lin, C.C., Hsu, H. and Chiang, C.Y. (2004). The information transmission
201-215.
between two substitutes of index futures: The case of TAIEX and
Clark, P. (1973). A subordinated stochastic process model with finite
Mini-TAIEX stock index futures. Asia Pacific Management Review,
variance for speculative prices. Econometrica, 41, 135-155.
forthcoming.
Copeland, T. (1976). A model of asset trading under the assumption of
Lin, C.H. and Hsu, H. (2003). The impacts of foreign capital and price
sequential information arrival. Journal of Finance, 31, 1149-1168.
discovery process between Taiwan and Singapore futures contracts.
Cornell, B. (1981). The relationship between volume and price variability
Asia Pacific Management Review, 8 (1), 13-26.
in futures markets. Journal of Futures Markets, 1, 303-316.
Najand, M. and Yung, K. (1991). A GARCH examination of the relation-
Crouch, R. (1970). A nonlinear test of the random-walk hypothesis.
ship between volume and price variability in futures markets. Journal
American Economic Review, 60, 199-202.
of Futures Markets, 11, 613-621.
Davidian, M. and Carroll, R.J. (1987). Variance function estimation.
Nelson, D. (1991). Conditional heteroscedasticity in asset returns: A new
Journal of American Statistical Association, 82, 1079-1168.
approach. Econometrica, 59, 347-370.
Dickey, D.A. and Fuller, W.A. (1981). Likelihood ratio statistics for auto-
Ragunathan, V. and Peker, A. (1997). Price volatility, trading volume, and
regressive time series with a unit root. Econometrica, 49, 1057-1072.
market depth: evidence from the Australian futures market. Applied
Epps, T.W. and Epps, M.L. (1976). The stochastic dependence of security
Financial Economics, 7, 447-454.
price changes and transaction volumes: Implications for the mix-
Schwert, G.W. (1990). Stock volatility and the Crash of 87. Review of
ture-of-distributions hypothesis. Econometrica, 44, 305-325.
Financial Studies, 6, 77-102.
Ferris, S.P., Park, H.Y. and Park, K. (2002). Volatility, open interest, volume,
Tauchen, G.E. and Pitts, M. (1983). The price variability-volume relation-
and arbitrage: Evidence from the S&P 500futures market. Applied
ship on speculative markets. Econometrica, 51, 485-505.
Economics Letters, 9, 369-372.
Watanabe, T. (2001). Price volatility, trading volume, and market depth:
Foster, A.J. (1995). Volume-volatility relations for crude oil futures markets.
Evidence from the Japanese stock index futures market. Applied Fi-
Journal of Futures Markets, 15, 929-951.
nancial Economics, 11, 651-658.
French, R.K., Schwert, G.W. and Stambaugh, R.F. (1987). Expected stock
returns and volatility. Journal of Financial Economics, 19, 3-29.
143