Pacific-Basin Finance Journal Manuscript Draft Manuscript ... · Manuscript Draft Manuscript Number: PBFJ-D-12-00036 Title: The Restudy of the Relationship between Market Orders and

Pacific-Basin Finance Journal Manuscript Draft Manuscript Number: PBFJ-D-12-00036 Title: The Restudy of the Relationship between Market Orders and Stock Returns in Taiwan Article Type: Research Paper Keywords: Reference point; Order imbalance; Panel model. Abstract: Unlike previous studies that adopted "price" as the reference point, this paper employs the adjusted order imbalance related to "volume" as a reference point to examine the relationship between a firm's characteristics and stock returns. Adjusted order imbalance, including trading direction of stock index and trading volume of individual stock and stock index, is freely and easily obtained by investors in Taiwan. Employing the panel regression model, this paper found prior adjusted order imbalance has a significantly positive relationship with individual stock returns. Additionally, empirical results show that adjusted order imbalance enhances the impacts of value and size effect.

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The Restudy of the Relationship between Market Orders and

Stock Returns in Taiwan

Highlights

>>We found the positive impacts of adjusted order imbalance.

>>We examine the effect of reference points related to "volume" to stock returns.

>>We collected numerous observations (number of data is 1,434,768) in the panel

model.

>> The adjusted order imbalance could enhance the value and size effects.

*highlights

i

The Restudy of the Relationship between Market Orders and

Stock Returns in Taiwan

Abstract: Unlike previous studies that adopted "price" as the reference point, this paper

employs the adjusted order imbalance related to “volume” as a reference point to

examine the relationship between a firm’s characteristics and stock returns. Adjusted

order imbalance, including trading direction of stock index and trading volume of

individual stock and stock index, is freely and easily obtained by investors in Taiwan.

Employing the panel regression model, this paper found prior adjusted order imbalance

has a significantly positive relationship with individual stock returns. Additionally,

empirical results show that adjusted order imbalance enhances the impacts of value and

size effect.

Keywords: Reference point; Order imbalance; Panel model.

*Manuscript, excluding Author DetailsClick here to view linked References

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1. Introduction

Following the 1980s, many researchers found that asset prices often violate the

theoretical expectative prices and were referred to as financial puzzles. Alpert and

Raiffa (1982) pointed out that there are two reasons for violating the market

effectiveness. One is that asymmetric information exists for investors and investors

catch the different quantitative quality of information at different times. The other is that

cognition and awareness are different for investors even given the same information.

Figlewski (1982) mentioned that investors have different information perspectives of

the public information. The investors’ divergence of views of the same information

reflects the fact that the investors’ behaviors contribute to explaining the security price.

Kahneman (1992) supported the viewpoint that the investors participate in

anchoring-and-adjustment of their views as investing. That is, the investors would

choose specific information as a reference when they make investment decisions. The

specific information is like the anchors of a boat that keep it located at a fixed position

rather than drifting out to sea somewhere. Previous research has looked at the

“anchoring effect” (Slovic and Lichtenstein, 1971; Tversky and Kahneman, 1974). The

famous expectative theory also applies the concepts of reference point to explain the

nonlinear utility function (Kahneman and Tversky, 1979; Tversky and Kahneman,

1992). The expectative theory argues that the investors judge their gains or losses

depending on some reference points or relative value rather than an objective or

absolute value.

However, what are the reference points for investors? Past studies supported that

the price variables could be a reference point, such as the purchase cost (Shefrin and

Statman, 1985), and the history price of individual stock, like a recent 52-week high.

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George and Hwang (2004) supported that the recent 52 week-high could be a reference

point for investors and the zero-costing strategy based on the 52 week-high can create

more positive profits than momentum strategy. Chang (2011) documented the positive

connection between the 5-day high, 20-day high, 60-day high, and 52-week high of a

stock price and its returns.

In addition to the price variables being used as a reference point, investors often

adopt the relevant volume variables as reference points in intuition when they make

investment decisions. Nevertheless, there is a paucity of literature on this subject. In

this paper, we try to choose the “order imbalance” that is one of relevant volume

variables as a reference point to determine their impact on individual stocks. In Taiwan,

both the Taiwan Stock Exchange (TSE) and news services report daily buying and

selling orders of the stock index. The TSE releases the data of accumulated buying or

selling orders of the TAIEX (Taiwan Stock Exchange Capitalization Weighted Stock

Index) everyday. The data is free and easy to obtain from the TSE's website or other

media, such as TV or newspapers. 1

Therefore, market investors can get information

on the order imbalance, which means buying orders greatly outnumber selling orders

on the Taiwan stock index. A reasonable expectation is that the stock prices the next

day reflect the news of order imbalance. The convenience of getting the information

pertaining to order imbalance may lead investors to follow the market orders that could

represent the sentiments of investors. Therefore, order imbalance of the TAIEX should

affect individual stocks the next day.

1The information of orders or order imbalance of “individual” stocks is not easy to obtain for common

investors because the free data only reveals unfilled or unsatisfied orders for the “best five” ticks, not

accumulation of all the orders of individual stocks. Therefore, the order imbalance of individual stocks is

inconvenient to obtain and cannot be used as a reference point for investors.

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It is worth noticing that we need not identify seller-initiated or buyer-initiated

trades using Lee and Ready’s (1991) approach or other similar approaches. The

seller-initiated or buyer-initiated trades are ex-post, while the buyer or seller orders are

ex-ante, to represent the respective needs of investors. The order imbalance this paper

adopted is the ex-ante concept to show the power of buying or selling.

The trading volume is abandoned for use as a reference point because the order

imbalance offers more useful information for investors. The trading volume does not

include the directions of trades. That means the powers of buying or selling is only

aware of the order imbalance, not trading volume. The power of buying or selling

could reflect the willingness of investors to trade at some point. This is important for

common investors to observe the sentiments of other investors in this market. The

order imbalance provides an indication of the stocks’ potential movement in terms of

being in a positive or negative direction. When a positive order imbalance occurs,

investors will believe that the sentiment of the market is high, optimistic, or brilliant in

the future. In contrast, in the case of a negative order imbalance, investors will believe

that the sentiments of other investors are pessimistic, conservative, or dark. When the

order imbalance is positive (negative), traders adjust their expectations regarding stock

returns in the future, then push the price upwards (downwards).

There is another explanation for the importance of order imbalance －

attention-grabbing news. The “glitter stocks” means the stocks that exist in the news or

information avenues that grab the attention of investors. Odean (1999) argued that

investors choose those glitter stocks to trade. Barber and Odean (2008) pointed out that

the stocks reflecting news such as abnormal trading volume or extremely high or low

daily returns, grabs the attentions of investors and, thereby, are purchased. The research

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called this behavior of buying stocks with attention-grabbing news “attention-driven

buying”. Previous literature focused on the characteristics of individual stocks that grab

investors’ attention, and the common news of the stock index was ignored by scholars.

However, the latter contributes more toward investing adjustments because the single

measure makes the decision making process simpler for varied stocks, and it is easy to

understand and adopt these investing indexed financial assets. Considering large trading

volume of individual stock grabs investors’ attention and the order imbalance of the

TAIEX motivates investors’ sentiments, this paper investigates the impact of interaction

term and trading volume of a firm and the order imbalance of the TAIEX.

Employing the panel regression model, which could both consider the time series

and cross-section data, this paper finds that the order imbalance of stock index has

positive effects on individual stocks in Taiwan. The important control variables,

including the PE ratio, firm size, and book-to-market ratio, have been considered in the

models. This finding could be explained by the investors’ sentiments. When the buying

orders outnumber the selling orders, the investors prefer to hold positive positions or to

buy stocks. By contrast, when the selling orders outnumber the buying stocks, the

investors prefer to hold negative positions or to sell stocks.

2. Brief Literature Review and Hypotheses

2.1 The relationship between order imbalance and stock returns

The orders of investors seem to have content full of significant information. For

example, Subrahmanyam (2009) agreed that the order flows have profound implications

for all of the finance areas. Fan, Hu, and Jiang (2012) documented the negative price

impact after block trades in China. A substantial body of research has documented the

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positive relationship between the order imbalance and stock returns. Chan and Fong

(2000) pointed out that order imbalance could explain the greatest movement of stock

prices because the volatility-volume relationship becomes much weaker after

controlling for the impact of order imbalance on the NYSE and NASDAQ. Chordia,

Roll, and Subrahmanyam (2002) pointed out the significant relationship between the

daily order imbalances and contemporaneous market returns in the S&P 500 index.

They argued that the order imbalances are significantly associated with daily changes in

liquidity after controlling for volume, as well as using the excess buying or selling

trades as another determinant of the market price movements. Madhavan and Smidt

(1993), Huang and Stoll (1994), Chordia and Subrahmanyam (2004), and Chordia, Roll,

and Subrahmanyam (2008) also found the positive connection between order imbalance

and stock returns.

For special events, such as the financial crisis on October 19, 1987, Blume,

MacKinlay, and Terker (1989) found a strong relationship existed between order

imbalance and stocks on the New York Stock Exchange (NYSE). The positive impact of

order imbalance to stock returns has been confirmed in different countries. Brown,

Walsh, and Yuen (1997) supported the connection in the Australian stock market. Liu

(1997) and Lee et al. (2004) demonstrated that order imbalances play an influential role

in the Taiwan stock market. Bailey et al. (2009) documented the strong positive

relationship between daily order imbalances and contemporaneous individual stock

returns in China.

As this review shows, there has been extensive research on the relationship

between order imbalance of individual stock and its returns. This study would like to

confirm the adjusted order imbalance in Taiwan because the order of the TAIEX is

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easily available for investors. Investors tend to take a familiar target as a reference point

to judge the value (Slovic and Lichtenstein, 1971). Tversky and Kahneman (1974)

called it the “anchoring effect.” Purchase cost had been supported to be a good

reference point (Shefrin and Statman, 1985) and the recent 52 week-high of individual

stocks (George and Hwang, 2004) and stock index (Chang, 2011) could also be

anchoring. Similarly, the past price variables could also be a reference point, the volume

variables could too. Because the case investors use volume variables as a reference

point, this study adopted the adjusted order imbalance, which is defined as the relative

proportion of trading volume multiplied y the order imbalance of the Taiwanese stock

index. The factors of adjusted order imbalance are due to the easy availability of volume

variables. The trading volumes of individual stock, the overall trading volume, and the

order imbalance of the TAIEX can be surveyed via the web, newspaper, and TV every

day. We construct the hypothesis of relevant volume variable as a reference point. The

adjusted order imbalance considering the liquidity of individual stock, stock index, and

order imbalance of stock index has a positive impact on stock returns.

2.2 Size, Value, and P/E effects

This paper includes the most common firm characteristics that are important

factors in predicting stock returns mentioned in a number of studies: Firm size, book

to market ratio (B/M), and PE ratio.

The size effect means that small stocks earn higher returns than larger ones and

there is a negative relationship between firm size and stock returns. Some researchers

believe that size is a critical factor in determining the expectations for stock returns [e.g.,

Banz (1981), Reinganum (1981a), Jaffe et al. (1989), and Rouwenhorst (1998)]. The

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value effect means that the stocks with low market value (high book-to-market ratio)

yield higher returns than those with high market value and there is a positive

relationship between book-to-market ratio and stock returns. Other studies agreed that

the value effect is indispensible and an important factor, [e.g., Bauman and Miller

(1997), Rosenberg et al. (1985), Chan et al. (1991), Capual et al. (1993), Fant and

Peterson (1995), Piotroski (2000), Chan and Lakonishok (2004)]. Pontiff and Shall

(1998) agreed that the B/M ratio has more predicting power than other variables, such

as interest rate spread and dividend yields. Huang (2011) documented that the strategies

based on value spread in B/M ratio earns significantly positive expected returns. Brown,

Rhee, and Zhang (2008) found the impact of value exists but differs across four Asian

stock markets.

Some empirical studies have argued that the size and value effects should not be

ignored in such an analysis [e.g., Fama and French (1992), Fama and French (1996),

Barber and Lyon (1997), Bauman et al. (1998), Piotroski, (2000), Daniel et al. (2001)].

Reinganum (1981b) argued that the value effect is related to the size effect because

value effect mitigates after controlling firm size; while Chan, Hamao, and Lakonishok

(1991) found the value effect included in their model weakened the size effect in the

Japanese stock market. The results of Loughran’s (1997) study found that the stocks that

are larger in size have a smaller impact of B/M on stock returns, while the stocks that

are smaller in size have a larger impact of B/M effect. De Groot and Verschoor (2002)

find a strong size effect in five Asian emerging markets and a significant value effect in

Korea, Malaysia, and Thailand.

The majority of research in firm characteristics has focused on the firm size and

B/M, the price-to-earnings (PE) ratio that represents the earnings yield effect, which is

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also emphasized by previous studies. Basu’s (1983) research supported the view that the

PE effect is not independent of firm size. The investors overstate growth expectations

creating over-optimism (over-pessimism) for high (low) P/E stocks. Bleiberg (1989)

supported that the longer the observed sample period, the stronger the relationship

between high PE and S&P 500 stocks’ future returns. Basu (1977), Cook and Rozeff

(1984), Jaffe et al. (1989), Peavy and Goodman (1983), and Fairfield and Harris (2010)

all agreed that stocks with low PE ratios generate higher returns.

In relation to the opposite views on interactions between size and P/E effects, Cook

and Rozeff (1984) argued that the interaction does not exist and size and E/P are

independent effects, unlike what was claimed by Reiganum (1981a) and Basu (1983).

Jaffe et al. (1989) employed the Seemingly Unrelated Regression (SUR) model to

compare the significance of the coefficients of E/P and size in different observation

periods. Their results were consistent with Cook and Rozeff (1984).

The style investing means that investors prefer small size, High B/M, and low P/E.

In this study, we allow the effects of adjusted order imbalance and the impact of the

main firm characteristics such as size, B/M, and P/E. We constructed the enhanced style

effect because the large trading volume grabs investor attention (Barber and Odean

(2008), as does adjusted order imbalance. When investors notice some glittering stocks

they then choose those stocks with their favorite firm characteristics. Therefore, the

hypothesis of enhanced style effect should be supported; the interaction terms of

adjusted order imbalance and firm characteristics are significant and have the same

signs as firm characteristics.

3. Data and Methodology

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3.1 Data

Investors in Taiwan can get information pertaining to order imbalance of the

Taiwan stock index easily and they may adopt the order imbalance into their

information set to make investment decisions. Therefore, this paper adopts the daily

data of order imbalance of the Taiwanese stock index to find its impact on the next day’s

individual returns. Our sample data is comprised of the daily data of stocks traded on

the Taiwanese stock market. The sample period was from January 1, 1998 to December

31, 2007, totaling 2541 days. The data was collected from the Taiwan Economic Journal

Data Bank. Given that the number of stocks did not stay the same at every sample point

because the number of stocks increased due to initial public offerings and decreased due

to delisting, the panel data is unbalanced. Thus, the total number of firms is up to 704

and the number of data is 1,434,768.

3.2 Measures of Variables

The variables used in the regression model and their definitions are described as

follows.

(1) Stock Returns (RET)

tiRET , ＝( tiP , - 1, tiP )/ 1, tiP ×100% (1)

where tiP , is the stock closed price of firm i at day t, while 1, tiP is the corresponding

price of firm i at day t-1. tiRET , denotes the stock i returns at time t. The stock returns

are adjusted when the dividend is distributed.

(2) Adjusted Order Imbalance (AOI)

First, we calculated the order imbalance tTWOI , , which is defined as the order

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imbalance of Taiwanese stock index at day t:

tTWtTWtTw NSNBOI ,,,

(2)

The variables NBTW,t and NSTW,t, denote the buy and sell orders on the Taiwan

stock index at day t, respectively.

Second, considering the difference of trading size and liquidity of individual

stocks i, we adjusted the information for order imbalance of the Taiwan stock index. We

calculated the adjusted order imbalance of firm i tiAOI , , which is defined as the

proportion of the tTWOI , .

tTW

ti

tTWtiVOL

VOLOIAOI

,

,

,,

(3)

The variables VOLi,t, is the trading volume of firm i at day t, and VOLTW,t is the

trading volume.

(3) Price-to-earnings ratio (PE)

tiPE , ＝ tiP , / tiEPS , (4)

where tiEPS , , is yearly earnings divided by outstanding shares of firm i in the latest

season on day t under the assumption that the expected per-share earnings in the coming

year will be the same as the earnings per-share of the last season. Again, tiP , is the

closing stock price for firm i at day t.

(4) Book to market ratio (BM)

tiBM , ＝ tiValueBook , / )( ,, titi SharesP (5)

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where tiShares , is the outstanding shares of firm i at day t, tiValueBook ,

represents

the book value of equity.

(5) Firm size (SIZE)

tiSIZE , ＝ titi SharesP ,, (6)

3.3 Methodology

We propose the following equations to examine the impact of order imbalance of

the stock index on individual stock returns.

Model 1:

tititititititi AOISIZEBMPERET ,1,41,31,21,1,, (7)

where tiRET , is the stock returns of firm i at day t , ),,3,2,1( Jjj

1, tiPE , 1, tiBM , 1, tiSIZE , and 1, tiAOI are the price to earning ratio, book-to-market

ratio, the market value, and adjusted order imbalance of firm i on day t-1, respectively.

ti , is the coefficient to estimate,

and ti ,

is the error term.

Model 2:

tititititititi DUMSIZEBMPERET ,1,41,31,21,1,, (8)

where tiDUM , is the dummy variable, which takes on the value 1 if the sign of

adjusted order imbalance is positive, and the value is zero if the sign is negative. If the

coefficient of tiDUM , is not significantly zero, the intercept term equals 4, ti ,

while, if the coefficient of tiDUM , is significant, the intercept term still equals to

ti , .

Model 1 and 2 could test the hypothesis of relevant volume as a reference point.

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Model 3:

1,1,41,31,21,1,, tititititititi PEDUMSIZEBMPERET

titititititi DUMSIZEDUMBMDUM ,1,71,1,61,1,5 (9)

where the interaction terms of dummy variable products on the other independent

variables allow us to observe the impacts of adjusted order imbalance to firm

characteristics. Hence, with a significant coefficients of interaction terms, the total

impacts for 1, tiPE are 41 , for 1, tiBM

are 52 , and for 1, tiSIZE are

63 ,

respectively. Model 3 could test the hypothesis of enhanced style effect, if the

interaction term is not zero.

This study employs the panel regression analyses, rather than the ordinary least

squares (OLS) model. Kalton, Kasprzyk, and McMillen (1989) argued that the OLS

model may have biased coefficients that make empirical results different between the

whole sample and the individual sample. The panel regression model could include the

time series and cross-section data, and more information from the sample could be

shown in the model than those in the OLS model.

ti

K

k

tkiktiti XY ,

1

1,,,

(10)

where, Ni ,,2,1 , representing the firm i at the day t, and Tt ,,2,1 ,

representing each day during the sample period. tiY , represents the dependent

variable of firm i at the same day t while 1, tkiX represents the k independent variable

of firm i at day t-1. ti , is the residual error and 0)( itE , 2)( itVar for

ji or 0, jitE for t . k for Kk ,,2,1 represents the coefficients of

each dependent variable k. ti , for Ni ,,2,1 represents the intercept term of firm i

13

at day t.

The three different sub-models are dependent on the intercept term ti , :

(1) OLS model: The model is under the assumption that every sample has the same

intercept term. That is ti, .

(2) Fixed Effects model: The model is under the assumption that firm i has a different

intercept term but the same intercept term for each day t. That is iti , .

(3) Random Effects model: The model is most relaxed for the assumption that firm i

has the different intercept term on day t. That is iti , , where λ represents the

random term and i represents the error of the random term.

Before estimating the models, we chose the model by using the F-test to compare

the explanation powers of the fixed model and OLS model, and employing the

Lagrange Multiplier (LM) test supported by Breusch and Pagan (1980) to compare the

Random Effects model and OLS model. The F-test is as follows:

),1(~

)(

)1(

)1(

)(

2

22

knnTnF

knnT

R

n

RR

Ffix

olsfix

(11)

where 2R is the coefficient of determination,

2

fixR is the coefficient of determination

under the Fixed Effects model, while 2

olsR is the coefficient of determination under the

OLS model. If we do not reject the hypothesis 0H , the OLS model is better.

The LM test is as follows:

14

)1(~1

12

2

2

1 1

2

1

2

1

n

i

T

t

it

n

i

T

t

it

e

e

T

nTLM (12)

where e is the error term under the OLS model. If we do not reject the hypothesis 0H ,

the OLS model is better. Otherwise, the Random Effects model is more adequate than

the OLS model.

Finally, to compare the Fixed and Random models the Hausman Test, supported by

Hausman (1978), helped us determine which model is better:

)(~ˆˆˆˆ 21kH randomfixrandomfixrandomfix

(13)

where, fix is the vector of estimated coefficients under the Fixed Effects model,

random is the vector of estimated coefficients under the random effects model, fix is

variance-covariance matrix under the Fixed Effects model, and random fix is

variance-covariance matrix under the Random Effects model. If we do not reject

hypothesis 0H , the Random Effects model is better. Otherwise, the Fixed Effects model

is more adequate than the Random Effects model.

4. Empirical Findings

Table 1 summarizes the descriptive statistics of the variables used in the

regression models. The average daily returns across individual stocks was 0.042%. The

adjusted order imbalance, on average, was negative.

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[Insert Table 1 about here]

To investigate the relationship between stock returns and the adjusted order

imbalance, we implemented the panel model with control variables including PE, firm

size, and book-to-market ratio. Table 2 reports the F-test, LM test, and Hausman test,

which can help us choose the type of panel model.


For Model 1, the statistic of F-test answers which is more adequate for the OLS

model or Fixed Effects model. The F statistic was 1.4022 and rejected the hypothesis.

The Fixed Effects model is adequate for Model 1. The LM statistic was 68.8281 and

rejected the hypothesis, which means the Random Effects model is more adequate than

the OLS model. However, the Hausman test conducts that the statistic, 590.1289,

rejected the null hypothesis and suggests that the results of the Fixed Effects model

should be statistically preferred over the results from the Random Effects model. Finally,

the Fixed Effects model was most adequate for Model 1. The comparisons of the OLS,

Fixed Effects model, and Random Effects model for Model 2 and Model 3 are similar to

Model 1. The Fixed Effects model is supported as the most adequate for Model 2 and

Model 3. We then adopted the Fixed Effects model to estimate in Tables 3, 4, and 5.


Employing the Fixed model, the coefficients in Table 3 reveal that the adjusted

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order imbalance of the Taiwan stock index has a positive impact (2.219) on individual

stock returns at a 1% significance level in Model 1. The results agree with the

hypothesis of relevant volume variables as a reference point. The information related to

the adjusted order imbalance is easily available via the TSE web, newspaper, or news

media. We found that the impact of the PE effect, value effect, and size effect on stock

returns exists. For comparison, the base model without AOI variable is shown in Table 3.

Both the base model and model 1 agree that the expectative signs of coefficients of PE,

BM, and SIZE are supported.

For both the firm size and PE ratio, we found significant negative impacts on stock

returns and the BM were found to have a positive impact on stock returns. The last

bottom row in Table 3 is the F-test to find whether the AOI variable adds significant

explanatory power to the base model. The F-test was used for the comparison of nested

models, which are the two sets of estimates in Model 1. The first set of regression

models includes the firms’ characteristics variables and the AOI variable, while the

second set of results comes from a restricted model in which the AOI variable is omitted.

The F-test for the coefficient of AOI variable is based on a simple comparison of the

residual sum of square from this restricted regression and the residual sum of squares

from the unrestricted model. The F-test was 6.72 and its p-value was less than 1%, this

means that the increase in explanatory power of the full model versus the model only,

including variables of firms’ characteristics and intercept term, is significant.


Table 4 shows the estimates from Model 2 in which the dummy variable,

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depending on the signs of adjusted order imbalance of the Taiwan stock index, was

added. We used a dummy variable to capture these effects, which are possibly different

between positive and negative adjusted order imbalance. The coefficient for the dummy

variable represents the change in the intercept for the positive adjusted order imbalance.

The intercept term represents the impact of the omitted variable, which is a set of other

factors possibly affecting the individual stock returns but not included in the regression

model. The coefficient of dummy variable is significantly positive. The higher the

adjusted order imbalance, the higher the individual stock returns. Again, the signs of

characteristic variables are the same as those in Table 3.


Because the signs of adjusted order imbalance of stock index may have differing

responses to other independent variables, the interaction terms are shown in Table 5.

The coefficients of interaction terms can help us to understand how the firm’s

characteristics, including PE, BM, and SIZE, affect the individual stock returns under

the conditions of either positive or negative adjusted order imbalance. Including the

cross term of DUMt-1×PE t-1, DUM t-1×BM t-1, and DUM t-1×SIZE t-1, we found the

interaction terms remain the same signs of the characteristics term: PE t-1, BM t-1, and

SIZE t-1, respectively. For example, the coefficient of SIZE t-1 was -0.446 and the

coefficient of interaction term DUM t-1×SIZE t-1 was also negative, -0.631. Similarly, the

coefficients of PE ratio and interaction term of market order imbalance and PE ratio are

negatively significant. The coefficients of B/M ratio and the interaction of market order

imbalance and B/M ratio are positively significant. Therefore, the hypothesis of enhance

18

style effect is supported and the individual firms’ characteristics and the information set

of adjusted order imbalance interact with each other, and the relationships between the

characteristics and stock returns is stronger for positive adjusted order imbalance. This

suggests that ignoring the adjusted order imbalance leads to an under-estimation of the

impact of the firms’ characteristics variables.

5. Conclusion

The order imbalance represents the excess demand and the common sentiments of

investors. The information of adjusted order imbalance, which is easily available in

Taiwan, is an important reference for investors. However, previous literature focused on

the order imbalance of individual stocks, which may not easily be available for

investors and the order imbalance of stock index was omitted. In Taiwan, the

information of order imbalance of stock index is easily available for investors from the

TSE website or news media but not of order imbalance of an individual stock. We

employed the adjusted order imbalance that considers the liquidity of individual stock

and stock index and order imbalance of stock index, and confirmed the positive

relationship between the order imbalance of stock index and the individual stock

returns.

Besides agreeing to the positive connection between the adjusted order imbalance

and the individual stock returns, the empirical results suggest the interaction of the

adjusted order imbalance and characteristics variables. First, the size effect, value effect,

and PE effect are supported in this paper. There is a positive relationship between the

stock returns and BM, while there are negative relationships between the stock returns

and firm size or PE. We then found that the coefficients of interaction term of

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characteristics variables and the adjusted order imbalance keep the same signs of the

coefficients of characteristics variables. The relationship between individual stock

returns and a firm’s characteristics, including firm size, BM, and PE, is enhanced for the

positive adjusted order imbalance. Therefore, ignoring the adjusted order imbalance

may lead to an under-estimation of the impact of firms’ characteristics variables.

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Table 1 Descriptive Statistics

This table reports the descriptive statistics for listed stocks in Taiwan. The sample covers daily

observations for the 1998/1/1-2007/12/31 period, totaling 2541 days. RET is stock returns, AOI is the

adjusted order imbalance, PE is price to earnings ratio, BM is book-to-market ratio, and SIZE is the

market value. Given that the number of stocks did not stay the same at every sample point, as the number

of stocks increased due to initial public offerings and decreased due to delisting, the panel data is

unbalanced. Thus, the total number of firms is up to 704.

Average Medium Std. Dev. Number of

Observation

RET 0.0420 0.0000 2.8656 1434768

AOI -0.2808 -0.0282 28.08 1434768

PE 23.4564 12.8200 76.9659 1429524

BM 0.9473 0.7576 0.8460 1434768

SIZE 20631.26 4497 76733.99 1434768

21

Table 2 The Tests for Adequate Models

This table reports the statistics of F-test, LM test, and Hausman test. The sample covers daily

observations for the 1998/1/1-2007/12/31 period, totaling 2541 days. Given that the number of stocks did

not stay the same at every sample point, as the number of stocks increased due to initial public offerings

and decreased due to delisting, the panel data is unbalanced. Thus, the total number of firms is up to 704.

The three models are as follows:

Model 1: tititititititi AOISIZEBMPERET ,1,41,31,21,1,,

Model 2: tititititititi DUMSIZEBMPERET ,1,41,31,21,1,,

Model 3: 1,1,41,31,21,1,, tititititititi PEDUMSIZEBMPERET

titititititi DUMSIZEDUMBMDUM ,1,71,1,61,1,5

where RET is stock returns, AOI is the adjusted order imbalance, PE is price to earnings ratio, BM is

book-to-market ratio, SIZE is the market value, and DUM is the dummy variable, which take value 1 for

the positive AOI and 0 for negative AOI.

F-test

LM test

Hausman test

Models

0H ：OLS is more adequate

1H ：Fixed effect model is

more adequate

0H ：OLS is more adequate

1H ：Random effect model

is more adequate

0H ：Random effect model

is more adequate

1H ：Fixed effect model is

more adequate

Model 1 F＝1.4022***

( P<0.0001 )

LM＝68.8281***

( P<0.0001)

Hausman statistic＝

590.1289***

( P<0.0001 )

Reject H0 Reject H0 Reject H0

The adequate model: Fixed effect model

Model 2 F＝1.3233***

( P<0.0001 )

LM＝29.3697***

( P<0.0001)

H＝536.9451***

( P<0.0001 )



Model 3 F＝1.2619***

( P<0.0001 )

LM＝52.2358***

( P<0.0001)

H＝508.5189***

( P<0.0001 )



Note: The notation *** represents that the value is significant at 1%.

22

Table 3 Empirical Results of Panel Regression Model

This table reports regression results. The sample covers daily observations for the 1998/1/1-2007/12/31

period, totaling 2541 days. Given that the number of stocks did not stay the same at every sample point,

as the number of stocks increased due to initial public offerings and decreased due to delisting, the panel

data is unbalanced. Thus, the total number of firms is up to 704. The model is as follows:

Base Model: titititititi SIZEBMPERET ,1,31,21,1,,

Model 1: tititititititi AOISIZEBMPERET ,1,41,31,21,1,,

where RET is stock returns, AOI is the adjusted order imbalance, PE is price to earnings ratio, BM is

book-to-market ratio, and SIZE is the market value.

Model 1 (Unrestricted) Base Model (Restricted)

Independent

variables

coefficient

(t statistic) p-value

coefficient

(t statistic) p-value

intercept -0.0198*** <0.0001 -0.0208***

<0.0001

(-4.2783) (-4.4996)

PEt-1 -55.7942a* 0.0799 -56.6

a*

0.0752

(-1.7514) (-1.7795)

BM t-1 0.0791*** <0.0001 0.0794***

<0.0001

(22.2819) (22.3768)

SIZE t-1 -0.6683a*** <0.0001 -0.6641a***

<0.0001

(-8.2950) (-8.2487)

AOI t-1 2.2187a*** 0.0095

(2.5929)

F(1,1428113)=6.7231***

Note: The notation *, *** represents that the value is significant at 10%, and 1%, respectively. The

superscript “a” represents to multiply 10-6

.

23






Model 2: tititititititi DUMSIZEBMPERET ,1,41,31,21,1,,

where RET is stock returns, PE is price to earnings ratio, BM is book-to-market ratio, SIZE is the market

value, and DUM is the dummy variable, which takes value 1 for the positive adjusted order imbalance

and 0 for the negative adjusted order imbalance.

Independent

variables coefficient (t statistic) p-value

intercept -0.0857*** (-17.7474) <0.0001

PE t-1 -54.4727a* (-1.7123) 0.0868

BM t-1 0.0704*** (19.8163) <0.0001

SIZE t-1 -0.7183a*** (-8.9311) <0.0001

DUM t-1 0.2362*** (46.3441) <0.0001

Note: The notation *, *** represents that the value is significant at 10%, and 1%, respectively.

The superscript “a” represents to multiply 10-6

.

24






Model 3: 1,1,41,31,21,1,, tititititititi PEDUMSIZEBMPERET

titititititi DUMSIZEDUMBMDUM ,1,71,1,61,1,5

where RET is stock returns, PE is price to earnings ratio, BM is book-to-market ratio, SIZE is the market

value, and DUM is the dummy variable, which takes a value of 1 for the positive adjusted order

imbalance and 0 for negative adjusted order imbalance.

Independent

variables coefficient (t statistic) p-value

intercept -0.0443*** (-8.2938) <0.0001

PE t-1 -31.500a*** (-0.8320) 0.4054

BM t-1 0.0192***

(4.5687) <0.0001

SIZE t-1 -0.4460a*** (-5.2439) <0.0001

DUM t-1×PE t-1 -92.500a (-1.3933) 0.1635

DUM t-1×BM t-1 0.1329***

(22.7450) <0.0001

DUM t-1×SIZE t-1 -0.6310a*** (-9.6100) <0.0001

DUM t-1 0.1228***

(15.2283) <0.0001

Note: The notation *** represents that the value is significant at 1%. The superscript “a”

represents to multiply 10-6

.

25

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