The Relation Between Relative Order Imbalance and Intraday Futures ReturnsAn Application of the...

8/12/2019 The Relation Between Relative Order Imbalance and Intraday Futures ReturnsAn Application of the Quantile Regre

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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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70 Emerging Markets Finance & Trade

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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MayJune 2011 71

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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MayJune 2011 73

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


6/20


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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MayJune 2011 75

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.


8/20


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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MayJune 2011 77

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

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