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The Relation Between Relative Order
Imbalance and Intraday Futures Returns:
An Application of the Quantile RegressionModel to Taiwan
Chiao Yi Chang and Fu Shuen Shie
ABSTRACT: Adopting the quantile regression model, this paper describes the positiverelation between relative order imbalance and intraday futures returns. The positive con-nection is relatively stronger for lower quantiles of intraday futures returns than for higherquantiles. However, the connection vanishes within 30 minutes. The results reflect thecompensation of the uncertainty and the absence of liquidity for relatively lower returns inthe Taiwan futures market. Furthermore, this paper finds evidence supporting an L-shapedpattern for intraday futures returns.
KEYWORDS: intraday data, order imbalance, quantile regression model.
Figlewski (1982) argued that heterogeneous information causes information diversity
among investors, which affects the markets in which investors participate. In the order-
driven market, because there is no centralized market maker; prices are determined by
the interactions of buyers and sellers, who are free to choose between limit and market
orders. Such orders measure trading activity and the intensity and strength of trading
directions intuitively. As such, an order imbalance exists due to the opposing views of the
buyers and sellers in regard to the same financial assets. The order imbalance, represent-ing the unsatisfied orders, arises due to the frictions associated with the costs of waiting,
because investors may need to pay higher buying prices or lower selling prices for im-
mediate trades. Because relative order imbalances (ROIBs) display positive or negative
signs reflecting their directions, they offer more information relating to market activity
than volume alone. Many of the previous papers investigating the relation between order
imbalance and the returns of financial assets are confined to stock markets (as evidenced
by the empirical results for the New York Stock Exchange (NYSE) in McInish and Wood
1990 and Chordia and Subrahmanyam 2004; for the NASDAQ in Chan et al. 1995; and
for 835 stocks on the London Stock Exchange in Abhyankar et al. 2003). In relation to
other stock markets, relatively fewer empirical results have been conducted on futuresmarkets in which a linkage is found to exist between order imbalance and futures returns.
Although prices in the spot and futures markets are highly correlated, there are differences
in intraday returns due to the different types of investors and market microstructures. In
Chiao Yi Chang ([email protected]) is an assistant professor in the Department of Insurance andFinance at National Taichung Institute of Technology, Taiwan. Fu Shuen Shie ([email protected])
is an assistant professor in the Department of Finance at National Taichung Institute of Technol-
ogy, Taiwan. The authors thank the anonymous referees for providing valuable feedback and many
insightful comments in support of this study. They also thank Ali Kutan, the editor, for numeroushelpful suggestions.
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contrast to the spot market, investors in futures markets are motivated primarily by hedg-
ing or speculation. In addition, because the underlying asset of index futures is a basket
of stocks rather than an individual stock, information that is private or firm specific has
little effect on the whole basket of stocks (Gorton and Pennacchi 1993).
International investors often consider the emerging market a form of risk diversificationin their portfolios. However, the financial markets of emerging countries are characterized
by high volatility, with asset prices that are more volatile relative to those in developed
countries. In particular, futures contracts transactions are implemented using margins
to create leverage, which carries with it a high degree of risk. Thus, the behavior of the
futures market in emerging markets is worthy of investigation.
The relatively higher or lower returns experienced in emerging markets occur in
relation to both risk and the absence of liquidity. Amihud and Mendelson (1986) found
support for the liquidity premium hypothesis, which states that investors require a pre-
mium when there is an absence of liquidity. The liquidity problem increases in severity
when there are lower asset prices or returns. The quantile regression model can assist in
understanding the behavior of the futures market under an entire conditional distribu-
tion of futures returns, thus incorporating the results under the conditions of relatively
higher or lower futures returns. Therefore, with the intention of better understanding
the connection between order imbalance and index futures returns, this paper employs
the quantile regression model to examine the relation under the conditions of relatively
higher or lower futures returns.
This paper adopts the intraday data in the Taiwan Futures Exchange (TAIFEX) with
an order-driven mechanism because the unique intraday data of orders from buyers or
sellers can be identified directly and the positive or negative signs of orders are avail-
able. As such, we need not identify seller-initiated or buyer-initiated trades using Lee
and Readys (1991) approach or other similar approaches. The seller-initiated or buyer-initiated trades are ex post, whereas the buyer or seller orders are ex ante, to represent the
respective needs of investors. In addition, due to the absence of index futures markets in
some emerging markets, this paper provides a sample case study as a reference for other
emerging countries in similar situations.
The results of this paper show that a higher ROIB (i.e., excess demand) results in
higher futures returns in the time series and vice versa. In particular, this phenomenon
is more significant in the case of relatively lower futures returns because lower futures
returns reflect a more serious liquidity problem. The connection vanishes within a period
of 30 minutes.
Because investors can inquire about the accumulated unexecuted buy or sell orders
through the futures price terminal, which is released by TAIFEX every 5 seconds during
the trading session, profitable trading strategies may result from using the intraday order
imbalance. When traders observe excess demand or supply, they can submit orders during
an interval of about 30 minutes.
Another aim of our research is to report the pattern of intraday futures returns in
the TAIFEX. We found that an L-shaped pattern exists for intraday futures returns. It
is possible that high futures returns result from opening trade due to the overnight halt
in trade and the accumulated effect of information released. Lack of high returns at the
close of trading in Taiwanese futures markets suggests that informed traders with private
information prefer not to trade during the closing stages of the market. Because the larg-
est proportion of investors in Taiwan comprises individuals, it is suggested that there arefewer informed traders in the market.
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Literature Review
The buy and sell orders, which normally provide an important information source for
the market maker in the quote-driven market, are crucial for market participants in the
order-driven market. The buy and sell orders represent the collective views of the buyers
and sellers and reflect their interpretation of the information and imbalances represent-
ing the pricing conflicts between both types of traders. Thus, the order imbalances can
directly represent the excess market demand.
Excess demand or supply exists when the numbers of buy orders and sell orders do
not match. Order imbalances with positive or negative signs represent the excess demand
or excess supply, respectively. Different combinations of buy and sell orders lead to
different implications in the same set of transactions. Therefore, the order imbalances
are more useful information for investors because volume is reflected in the activities
from the directions of buying or selling orders. Chan and Fong (2000) pointed out that
order imbalance is an important trading variable because the volatilityvolume relation
becomes much weaker after controlling for the impacts of order imbalance in NYSEand the NASDAQ.
Regarding the order-driven spot market, Brown et al. (1997) confirmed the presence
of such an order-imbalance return relation in the Australian stock market. Liu (1997)
demonstrated that order imbalances play an influential role in the Taiwanese stock market.
Lee et al. (2004) supported the persistence in the daily order imbalance and the positive
relation between contemporaneous stock returns and the order imbalance in Taiwan. Bai-
ley et al. (2009)documented the strong positive contemporaneous relationship between
daily order imbalances and individual stock returns in China.
Almost the entire automated system of futures markets is order driven. However, Wester-
holm and Swan (2004) indicated that the existence of a market-making system could assist
the reduction of price volatility and transaction costs more effectively than under a purely
order-driven system. Jain (2003) pointed out that market makers can improve liquidity. In
the emerging futures market, their volatility is relatively high, whereas liquidity is relatively
low. Therefore, the emerging futures market, which has adopted an order-driven mechanism
without the intervention of market makers, is worthy of discussion.
In developed futures markets, Ning and Tse (2009) documented that neither a contem-
poraneous nor a lagged positive daily order imbalance exhibited effects on futures returns
for FTSE 100 index futures contracts in the order-driven market. Other studies have also
investigated the relation between order imbalance and futures returns in emerging futures
markets. Huang and Chou (2007) investigated Taiwan stock index futures and found that
contemporaneous and lagged order imbalance has a positive significant impact on futuresreturns over 5-minute intervals.1Owing to the higher volatility and lower trading volume
of emerging markets in Taiwan as opposed to developed countries, investors might pay a
higher premium to trade in the event of excess demand or supply. Price pressures caused
by the order imbalance result in a positive relation between lagged order imbalances and
futures returns, especially for relatively higher or lower returns. Because investors are
afraid to leave their orders unfulfilled and are eager to trade under extreme returns, we
expect the relation between order imbalance and futures returns under higher or lower
futures returns to be stronger. However, there is absence of literature on this issue.
Another interesting issue is the intraday pattern. Many studies point to the evidence of
high returns, trading volume, and volatility at both the opening and closing of the market.
Past studies have often focused on the U-shaped pattern of the variation in stock returns
(McInish and Wood 1990; Wood et al. 1985), and other papers have also mentioned the
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U-shaped pattern of stock returns (Jain and Joh 1988; Lockwood and Linn 1990; Tian
and Guo 2007). The reasons for such a pattern include the mechanism of the periodic call
supported by Amihud and Mendelson (1987); the strategic trading model in which trade is
concentrated in a particular period during the day, as supported by Admati and Pfleiderer
(1988); and delays resulting from the market closing that lead to information uncertainty,with traders facing excessive risk, as argued by Slezak (1994) regarding spot markets.
Regarding futures markets, Daigler (1997) found that trading activity and volatility follow
a U-shaped pattern in Major Market Index, S&P 500, and T-bond futures contracts. Ding
(1999) found support for similar results for foreign exchange futures markets, and Tang
and Lui (2002) also found similar results in China. Although most studies often mentioned
the U-shaped pattern, some special patterns are also found in the empirical results, such
as a W-shaped return pattern corresponding to the Tokyo Stock Exchanges two trading
sessions (Chang et al. 1993) and the Istanbul Stock Exchange in Turkey (Bildik 2001).
This paper also observes the intraday pattern in Taiwan and finds evidence of an L-shaped
pattern of futures returns, as well as a U-shaped pattern for the ROIB.
Measures of Variables and the Empirical Model
This paper employs the quantile regression model supported by Koenker and Bassett
(1978). The quantile regression model estimates the models for the median and other
conditional quantile functions. Thus, the entire range of quantiles is observable, aid-
ing further understanding of the connections between the independent and dependent
variables.
Ifxt1is a set of independent variables, it will be represented as follows:Rt=xt1+t,where is the coefficient vector. We can then measure the coefficients by the quantile
regression model through minimizing the value of Equation (1) as follows:
min
: :
1
11 1
1 1T
R x R xt t
t R x
t t
t R xt t t t
+ ( )
<
.
(1)
The conditional th quantile functions as depicted by Equation (1) are estimated byminimizing an asymmetrically weighted sum of absolute errors. We construct the regres-
sion model as follows:
Rt= 0+ 1ROIBt1+ t . (2)
In this model,Rtis the dependent variable representing the intraday futures returns for
each 5-, 15-, and 30-minute interval. The relative order imbalance,ROIBt, is defined asthe proportion of order sizes at time t:
ROIB
NB NS
VOL
t
i t i t
i
m
i
n
i t
i
k=
==
=
, ,
,
.11
1
(3)
The subscript tdenotes the time interval t for each 5-, 15-, and 30-minute interval. The
subscript iis the frequency of orders from buyers or sellers.NBandNSdenote the order
sizes of futures contracts bought and sold, respectively. VOLis the trading volume in
futures contracts. Using the trading volume as the denominator to eliminate the size
problem, the relative order imbalances eliminate the size distortion present in the order
imbalances themselves, which follows increases in trading volume.
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After confirming the base connection between the intraday futures returns and ROIB,
we considered several important control variables in our model.
Past literature has argued that liquidity is a primary driving factor of the execution
costs in stock index futures (Berkman et al. 2005; Tse et al. 2006). To measure liquidity,
we calculated the absolute value of futures returns associated with the number of trades,TradeNt,at each 5-, 15-, and 30-minute interval.LIQUItis defined as follows:
LIQUIR
TradeNt
t
t
= .
(4)
A higher number forLIQUItimplies greater market liquidity. In addition, we used two
other measures of liquidity. The numerator of the first alternative measure is replaced by
the summation of the change of futures price for every tradejover 5-, 15-, and 30-minute
intervals, being Sj |DPjt| /TradeNt. The other measure of liquidity is the squared futuresreturns divided by volume for each time interval, beingRt
2/VOLt. These measures have also
been used in several empirical studies (Chang et al. 1999; Lehmann and Modest 1994).Chordia et al. (2002) argued that order imbalances are significantly associated with
daily changes in liquidity, after controlling for volume. The trading volume variable, VOLt,
is also added as a control variable in this paper. We consider that the volatility can thus
help improve predictive power (Andersen et al. 1999; Huang and Stoll 1994). Finally, the
variable of intraday time intervals for each day provides controls for the intraday variation
(Ahn et al. 2001; Goh and Kok 2006). The model is represented as follows:
R ROIB TIME LIQUI VOL VFt m t m k k t t t t t k
K
m
= + + + + + +==
0 1 2 31
, ,11
M
(5)
where TIMEk,trepresents the kth time-of-day dummy variable, which takes the value of
one if the futures returns for time tcorresponding with the time interval k, and zero oth-erwise. There are 59, 19, and 9 time-of-day dummy variables in Equation (5) for 5, 15,
and 30 minutes of trading time, respectively. The volatility variable, VFt, represents the
conditional intraday return volatility and is built using a GARCH(1, 1) model (Laurini
et al. 2008).
Given that the dynamic model and order imbalance is autocorrelated (Chordia and
Subrahmanyam 2004; Ning and Tse 2009), we extend the specification of Equations (2)
and (5) to include the lag, limited to 12 lagged-order imbalance terms. To determine the
best model, we employ Akaikes information criterion (AIC) and the Schwarz Bayesian
criterion (SBC), whereby the lagged-order model with the smallest AIC and SBC among
all the competing models is the best model.
Data and Empirical Findings
Data
We selected the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX)
futures (TX) traded on TAIFEX to serve as our representative futures market. Taiwanese
data allow direct identification of whether a trade is initiated by the buyer or the seller.
The data set allows us to identify the originator of each order as it is submitted by a seller
or a buyer. Although the buyer or seller orders submitted to the exchange might not be
matched, the original orders can still reveal the price pressures from investor intuition.The orders are executed under a price and time priority system.2
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The TAIEX futures contract is the most actively traded index futures contract on the
TAIFEX. Given that the nearby futures contracts are usually the most actively traded
contracts, we utilized data for these contracts. The data were also adjusted by rolling
over to the next nearest-to-deliver contract on the 5 days prior to expiry in order to cre-
ate a time series of futures returns, thereby avoiding thin markets and expiration effects.Chou, Chen, and Chen (2006) found that the expiration effect is stronger in Taiwan than
in Hong Kong, although weaker than in the United States. The sample period extended
from October 1, 2006, to September 30, 2007, with a total of 3,338,242 orders being
spread over 245 trading days. The trading day is divided into 5-, 15-, and 30-minute
intervals from the markets opening to its closing. There are 14,945, 5,145, and 2,695
observations from the 5-, 15-, and 30-minute intervals, respectively.
The TAIFEX is traded in a computer-based continuous orderdriven trading system to
improve liquidity. The Taiwan futures market changed the price formation process from
call auction to continuous auction. Comparing the two trading mechanisms, Cheng and
Kang (2007) supported the conclusion that the continuous auction improves information
efficiency. The TAIFEX futures contracts are traded from 8:45 A.M.to 1:45 P.M.on each
trading day, and orders that accumulate in the 15 minutes before opening and the 5 minutes
before closing must be matched by a call auction. The electronic trading system matches
the orders in the form of a continuous auction from 8:45 A.M.to 1:40 P.M.
The main difference between trading rules in the spot and futures markets in Taiwan is
that the stock exchange operates under a call auction system that retains the orders peri-
odically and matches the transactions every 2535 seconds in a trading section, whereas
the futures exchange employs continuous auction. However, at the market opening and
closing, both exchanges are traded by a call auction.
Empirical Findings
Table 1 presents descriptive statistics for the Taiwan index futures.3The average for ROIB
decreased as the time interval increased. The relevant numbers ranged from 1.23 104 for5-minute intervals to 0.42 104 for 30-minute intervals, and the standard deviation wasfound to be decreasing. This supports the view that strategic traders concentrate their trading
activities within a given period of time, as suggested by Admati and Pfleiderer (1988).
The relation between the ROIB and futures returns was examined using the quantile
regression model, with the results presented in Table 2. The coefficients and t-statistics
in relation to ROIB are reported for the quantiles at each 5 percent interval.
The quantile regression coefficients can be interpreted as the marginal change in futures
returns for the th conditional quantile as a result of the marginal change in the relativeorder imbalance. In Table 2, the coefficients for the median quantiles (i.e., those from
the 25 percent quantile to the 70 percent quantile) were found not to be significantly dif-
ferent from zero. Their effects on the futures returns were not obvious where the power
of both the buyers and sellers were about the same.
For both extremes of the quantiles, which imply relatively higher or lower intraday
futures returns, the effects of order imbalance contributed more to the intraday futures
returns than the median quantiles of the intraday futures returns. Where the intraday
futures returns were lower, the coefficients increased from 26.5 106for the 20 percentquantile to 120 106for the 5 percent quantile. In contrast, where the intraday futures
returns were higher, the coefficients only increased from 11.6 106in the 75 percentquantile to 43.2 106in the 95 percent quantile.
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Table
1.
DescriptivestatisticsfortheTaiwanstockindexfuture
smarket
Descr
iptive
statistics
Price
Return
NB
NS
ROIBa
5min
utes
Mea
n
8,0
78.7
880
0.0
023
658.5
846
657.2
968
1.2
303
Med
ian
7,9
47.0
000
0.0
000
535.0
000
536.0
000
0.0
743
Max
imum
9,8
21.0
000
4.1
344
6,8
24.0
000
6,0
02.0
000
1
,104.0
000
Min
imum
6,8
59.0
000
3.1
720
2,2
98.0
000
2,1
42.0
000
1
,820.0
000
Standarddeviation
6
92.7
987
0.1
509
529.6
382
556.0
252
134.6
455
Ske
wness
0.4
232
0.1
514
1.9
451
1.6
916
0.2
024
Kur
tosis
2.3
413
126.3
244
10.4
661
9.1
311
12.8
448
Obs
ervations
14,9
45
14,9
44
14,9
44
14,9
44
14
,944
15minutes
Mea
n
8,0
78.7
100
0.0
066
1,9
13.0
260
1,9
09.4
610
0.4
171
Med
ian
7,9
47.0
000
0.0
124
1,5
87.0
000
1,6
08.0
000
0.1
109
Max
imum
9,8
21.0
000
4.1
344
14,7
85.0
000
14,0
01.0
000
987.0
000
Min
imum
6,8
61.0
000
3.1
720
1,5
87.0
000
1,6
65.0
000
459.0
000
Standarddeviation
6
92.7
426
0.2
564
1,2
85.6
390
1,3
05.7
290
51.6
892
Ske
wness
0.4
230
0.2
508
1.9
825
1.8
912
2.1
902
Kur
tosis
2.3
410
46.5
951
10.5
954
9.9
027
54.8
887
Obs
ervations
5,1
45
5,1
44
5,1
44
5,1
44
5
,144
30minutes
Mea
n
8,0
78.4
600
0.0
126
3,6
52.3
280
3,6
45.6
100
0.4
178
Med
ian
7,9
47.0
000
0.0
135
3,1
54.5
000
3,1
30.0
000
0.0
621
Max
imum
9,7
90.0
000
4.1
344
23,4
71.0
000
22,3
98.0
000
987.0
000
Min
imum
6,8
67.0
000
3.1
720
182.0
000
1,0
27.0
000
459.0
000
Standarddeviation
6
92.7
055
0.3
543
2,3
38.3
000
2,3
62.8
440
41.6
016
Ske
wness
0.4
223
0.1
065
1.8
309
1.7
805
8.0
040
Kur
tosis
2.3
387
26.0
601
10.0
020
9.3
039
216.8
669
Obs
ervations
2,6
95
2,6
94
2,6
94
2,6
94
2
,694
Notes:ThesamplecoversintradayobservationsfortheOctober1,2006,toSept
ember30,2007,period.NB=theord
ersizesoffuturescontractsbought,NS=theorder
sizeso
ffuturescontractssold,ROIB=theratioornetordersizesoffuturescontractsboughttothetradingvolume.a1
04.
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Table
2.
Coefficientestimationsofthequantileregressionmod
el
Qua
ntileregressionresult
Symmetricquantilestest
R
estriction
Quantile
Coefficient
t-value
Quantile
Coefficient
t-value
value
Interc
ept
0.0
5
0.1
69
49.9
89***
0.9
5
0.1
67
52.0
84***
0.4
55
0.1
0
0.1
11
56.5
15***
0.9
0
0.1
14
68.9
73***
1.1
03
0.1
5
0.0
83
64.7
14***
0.8
5
0.0
88
69.1
99***
2.6
29***
0.2
0
0.0
64
56.6
73***
0.8
0
0.0
68
64.6
48***
2.5
74**
0.2
5
0.0
49
50.6
22***
0.7
5
0.0
54
56.5
93***
3.5
74***
0.3
0
0.0
37
40.9
02***
0.7
0
0.0
41
46.7
67***
3.9
26***
0.3
5
0.0
25
29.6
22***
0.6
5
0.0
29
35.6
99***
3.7
98***
0.4
0
0.0
13
16.3
17***
0.6
0
0.0
24
32.0
63***
16.4
09***
0.4
5
1.7
35a
0.0
02b
0.5
5
0.0
13
17.1
71***
26.6
91***
0.5
0
0.0
02a
0.0
68b
ROIBt1
0.0
5
120.0
08c
5.8
25***
0.9
5
43.1
85c
3.7
40***
7.0
26***
0.1
0
57.2
00c
3.4
68***
0.9
0
35.3
02c
2.8
08***
4.7
19***
0.1
5
36.7
73c
4.3
28***
0.8
5
20.4
22c
2.5
51**
5.1
53***
0.2
0
26.4
61c
3.1
33***
0.8
0
18.8
17c
2.3
70**
4.3
98***
0.2
5
9.8
72c
1.3
90
0.7
5
11.5
62c
1.6
82*
2.5
72**
0.3
0
6.8
15c
1.0
59
0.7
0
6.7
89c
1.0
74
1.9
24*
0.3
5
1.3
51c
0.2
23
0.6
5
5.4
78c
1.0
43
1.1
82
0.4
0
0.9
46c
0.1
63
0.6
0
0.7
15c
0.1
40
0.3
57
0.4
5
0.0
01a
20.7
40a
0.5
5
0.1
49c
0.0
28
0.0
46
0.5
0
0.0
04a
0.0
07
Slope
equalitytest
c2
61.1
5***
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Goodnes
s-of-fitstatistics
Adjusted
Adjusted
R2
R2
Quantile
(percent)
Quantile
(perc
ent)
0.0
5
3.5
39
0.9
5
0.887
0.1
0
1.5
46
0.9
0
0.581
0.1
5
1.2
24
0.8
5
0.413
0.2
0
0.4
57
0.8
0
0.357
0.2
5
0.1
28
0.7
5
0.157
0.3
0
0.0
60
0.7
0
0.061
0.3
5