do stock prices underreact to information conveyed by investors' trades? evidence from china

Do Stock Prices Underreact to InformationConveyed by Investors’ Trades? Evidencefrom China*

Fei Wu**International Institute for Financial Studies and RCFMRP, Jiangxi University of Finance and Economics

Received 31 August 2012; Accepted 6 January 2013

Abstract

We examine the process of stock prices adjusting to information conveyed by the trading

process. Using the price impact of a trade to measure its information content, we show that

the weekly price impact has significant cross-sectional predictive power for returns in the

subsequent week. The effect is sensitive to the level of informational asymmetry. We find that

the price impact contains information that is not fully captured by public order flows and

that a lead–lag effect exists regarding the arrival of information to different groups of inves-

tors. Our finding suggests a price under-reaction to trading information, which can be

explained by the gradual-information-diffusion theory.

Keywords Under-reaction; Information; Price impact; Trading process; Return predictability

JEL Classification: G02, G14, G15

1. Introduction

One of the important functions of financial markets is to facilitate the incorpora-

tion of information through the trading process. The speed of this process is a cru-

cial determinant of the extent to which a market is informationally effcient. While

the traditionally accepted view of efficient markets contends that stock prices reflect

news immediately when it arrives, in the last decade studies have uncovered

evidence suggesting that stock prices may respond too slowly to public news

announcements. For example, numerous empirical studies in finance and

*Acknowledgments: Fei Wu was supported by the National Natural Science Foundation of

China (Grant No.71072083 and 71003012) and the Jiangxi University of Finance and Eco-

nomics’s Innovative Research Team Development Grant. All remaining errors are our own

responsibility.

**Corresponding author: Fei Wu, International Institute for Financial Studies and RCFMRP,

Jiangxi University of Finance and Economics, Nanchang 330013, Jiangxi, China. Tel: +86 (0)

791 8381-6750, Fax: +86 (0)791 8380-2306, email: [email protected].

Asia-Pacific Journal of Financial Studies (2013) 42, 442–466 doi:10.1111/ajfs.12020

442 © 2013 Korean Securities Association

accounting have documented that stock prices appear to drift for several months

after important corporate events.1

In light of the studies of public information releases, the question of how prices

adjust to private information has received much less attention. In this paper, we

examine whether prices also underreact to private information conveyed by the

trading process, and if so, how price underreaction may occur. Our contribution is

twofold. First, we identify a predictable price reaction to the inferred (by the econo-

metrician) information content of trades. The finding is interpreted to indicate

price underreaction to trading information. Second, we provide evidence that,

because of investor heterogeneity, value-relevant information diffuses gradually

among investors. The gradual diffusion of information offers an explanation for

price underreaction.

To estimate the information content of investors’ trades, we rely on a micro-

structure measure, the price impact of a trade, to determine when a trade contains

information and the extent of that information. Asymmetric information models

posit that investor orders contain private information about fundamentals. When

an order with value-relevant information is executed in the market, it will cause a

persistent impact on stock prices (see, e.g., Glosten and Milgrom, 1985; Kyle, 1985).

Thus, the price impact of a trade reflects a likely action of an informed trader.

Applying this methodology to a large set of proprietary account-level data from

emerging Chinese stock markets, namely, the Shanghai Stock Exchange (SSE), our

analysis supports the predictive value of price impact for future returns.

We show that the cross-section of stock returns varies with the beginning-of-

period price impact differential (PID) between buying trades and selling trades.

Stocks with high PIDs in a week yield significantly higher excess returns in the sub-

sequent week than do stocks with low PIDs. An increase in the PID of one standard

deviation leads to an increase in average weekly returns of 0.26%. On an annualized

basis, a one-standard-deviation increase in the PID implies an increase in returns of

14.48%. These findings remain after controlling for various firm characteristics that

are believed to capture cross-sectional return variations, return reversals and the

illiquid nature of some stocks. When we extend the baseline analysis to time hori-

zons of approximately 1 month, 6 months, 1 year and 2 years, the predictive power

of weekly PIDs disappears in longer horizons without subsequent reversals.

If the predictive effect of the PID is driven by the informational component of

the price impact, our results should depend on the level of informational asymme-

try in a crucial way (Ni et al., 2008). We find that the level of the PID successfully

predicts surprises of earnings announcements and that the association between PIDs

and future returns appears to be more pronounced for stocks that have experienced

an intense probability of informed trading in the past. We also find that the mea-

sure of the PID information net of the measure of public information remains posi-

tive and is significantly related to future returns. These findings support the notion

1See Daniel et al. (1998) for a complete list of relevant literature.

Price Under-Reaction to Trading Information

© 2013 Korean Securities Association 443

that the PID contains value-relevant private information. Finally, we find that the

traditional Fama–French three factors and the momentum factor explain, at best,

less than 32% of the variability of portfolio returns and the positive significant

intercepts indicate weekly excess returns of 0.3% that are not compensated by vari-

ous risk factors. This finding rules out the possibility that excess returns on high

PID stocks are ultimately traced to differences in loadings on economically mean-

ingful risk factors.

Stock prices may underreact or overreact to private information contained in

PIDs, which generate the patterns of short-term return predictability. In the models

of overreaction, Daniel et al. (1998) and De Long et al. (1990) argue that short-

term price continuation is due to an initial overreaction followed by even more

overreaction. When prices are pushed up too far relative to fundamentals, the mod-

els predict a long-term return reversal. We do not find evidence of subsequent

return reversals in the longer term following high PIDs in support of the overrerac-

tion hypothesis. Price underreaction to information may arise as a result of the cog-

nitive biases of representative agents or the gradual diffusion of information. For

example, the conservatism bias of Barberis et al. (1998) means that investors react

insufficiently to private information revealed by stock prices, pushing the price up

too little. Since the price is too low, subsequent returns will, on average, be higher,

thereby generating return predictability. Alternatively, the gradual information dif-

fusion (GID) theory of Hong and Stein (1999) predicts that price underreaction

occurs when information diffuses slowly among the investing population. Prices

that slowly reflect private information, through investors’ trading, lead to short-run

return continuation.

In our context of empirical designs, the conservatism bias hypothesis and the

GID hypothesis differ in their implications in two ways. First, the GID theory sug-

gests that some investors receive private information at a point in time earlier than

others do, so the price impacts of some investors’ trades predict those of other

investors’ trades. The cognitive bias theory does not assume a lead–lag effect for the

PIDs of different investors. Second, owing to a large heterogeneity of trading

sophistication, the conservatism bias hypothesis suggests that there is a more slug-

gish reaction to information for some investors than others. For example, Hvidkjaer

(2006) argues that small (large) trades are more likely to reflect trading by individ-

ual (institutional) investors. He finds that underreaction among small traders con-

tributes to the momentum effect; but large traders, by contrast, show no evidence

of underreaction. In our robustness checks (as discussed in Section 3.2.1), we find

that the predictive effects of PID are present significantly for both large and small

trades as well as for both trades initiated by large traders and trades initiated by

small traders. There is no supportive evidence of the cross-sectional variations in

the magnitude of underreaction among investor populations.

We proceed to look for evidence of the GID theory. We argue that if some

investors (i.e., informed investors) receive private information at a point in time

earlier than others do, then the PID calculated based on these investors’ trades

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should lead (predict) the PID calculated based on other investors’ trades. Using

institutional investor and large individual investor accounts (small individual inves-

tor accounts) as a proxy for more (less) informed investors, our results show a

lead–lag effect for the arrival of the PID information to the two groups of investors.

The PID values of hypothetically informed investors, up to four weeks in the past,

predict the current PID values of hypothetically uninformed investors, with no sig-

nificant relation found for the reverse direction. Our finding thus confirms that the

gradual diffusion of information is the likely explanation for price underreaction.

This paper relates to the existing literature in two ways. First, it relates to stud-

ies exploring the slow response of prices to information as the underlying cause of

predictable patterns in stock returns (see, e.g., Fama, 1998 for a review of the litera-

ture). Our study differs in that we analyze the predictable price patterns due to

underreaction to private information that is contained in the trading process, while

previous studies focus on public information releases.

Second, this paper relates to research that aims to understand the economic

drivers of investors’ underreaction. Our findings, adding support to the concept of

slow, rather than immediate, diffusion of information among investors, is consistent

with Hong and Stein’s (1999) theoretical framework. Our study is closely related to

the empirical work of Hong et al. (2000), who set out to test empirically the predic-

tions of the GID theory. Using firm size and analyst coverage as proxies for the rate

of information flow, they find that stocks with slower information diffusion exhibit

more pronounced momentum. Our results complement their findings. The differ-

ence lies in the approach employed to search for evidence in support of GID. Men-

zly and Ozbas (2010) explore the delayed price responses to shocks that originate in

related firms in the supplier and customer industries. They present evidence sup-

porting the hypothesis that value-relevant information diffuses gradually in financial

markets.

The remainder of this paper proceeds as follows. The next section describes the

data and defines the main variables used. Section 3 examines whether returns can

be predicted on the basis of trading information. Section 4 considers alternative

mechanisms underlying the predictability of returns. Section 5 concludes the paper.

2. Data and Variable Measurement

2.1. Data

We obtained a sample of daily trading data compiled by the SSE for the purpose of

an audit trail between the exchange and member brokerage firms. Our primary

sample contains a large set of 77.4 million daily detailed transaction records of 676

SSE A shares (common stocks) conducted by 7.12 million institutional and individ-

ual brokerage accounts across mainland China for the period between April 2001

and August 2002. The data include identifiers for the buying trader and the selling

trader, the price and quantity of buying or selling trades, the stock code, and the

date when the trade occurred.



We use this proprietary data instead of market transaction data, such as the

Trade and Quotes (TAQ) data, because the data possess a number of distinct fea-

tures that enable a more accurate analysis of the matter of interest. First, each trans-

action in the data is flagged with a buy/sell indicator. This feature is important in

the context of our analysis because the construction of aggregate price impact

across different trades requires an accurate identification of the direction of each

trade. Second, the data include an account identifier that reveals the status of the

trader who initiates a trade. By identifying the status of different investors, that is,

an institutional investor or a retail investor, we are able to assume, in the latter part

of the analysis, a particular group of investors as being hypothetically more

informed than others.

Nonetheless, our data have two limitations. First, the time dimension of the

data is relatively short and old. Ideally, we would study a longer and more updated

sample period, but this is not possible given the availability of the proprietary data.

Second, the data are limited to an emerging market, namely, the Chinese stock

market. Our results are subject to the problem of generalizability. It would be useful

to conduct an international study that includes data from other emerging markets

and developed markets, but this is not possible given the data availability. Since the

market structure in China is different from that in other markets (Hsiao and Tu,

2012), and the key mechanism underlying the price underreaction may also be dif-

ferent across countries, we must interpret our results with caution in terms of gen-

eralizing the conclusions to other markets.

Table 1 provides descriptive statistics. Over a 16-month period, the sample trad-

ers executed 211.55 billion shares with a Renminbi (RMB) trade value of

1688.95 billion. The turnover of trades accounts for approximately 32% of total

market activities. Account identifiers indicate that 99.57% of the accounts are

individual investor accounts while the remaining 0.43% are institutional investor

accounts. The compositions are very similar to the aggregate proportions of

individual and institutional accounts reported by the Chinese Securities Depository

& Clearing Co. Ltd in 2002. With less than 0.5% of the accounts, institutional

investors trade 13.24% of the total share volume (6.32% of the total trade value).

In light of the exceptional size of individual investor trades, it is imperative to

classify individual investors into groups to allow for an in-depth analysis of the het-

erogeneity of individual investor accounts. Following Ng and Wu (2007), we classify

an individual investor whose average value of a single trade is greater than or equal

to RMB 50 000 as a large individual. Other individual investors are small investors.

As shown in Table 1, large individual investors are clearly different from small indi-

vidual investors in terms of trading activity. For example, their average purchase

(sale) value of a single trade is RMB 161 556 (RMB 167 425), which is approxi-

mately 13 times the size of that of small individual investors. The average trade size

is relatively close to that of institutional investors, with an average trade of RMB

391 334 (RMB 245 723) for a single purchase (sale). Trade size offers a good proxy

for the wealth level of investors because margin trading was prohibited in China

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during our sample period. The wealth level, in turn, reflects investors’ resources

and the ability to collect value-relevant information for their trading.

Stock returns, quarterly earnings announcements, and other information relating

to stock trading and firm characteristics are obtained from the China Stock Market

& Accounting Research Database (CSMAR), a Chinese stock trading and corporate

research database. The CSMAR is compiled similarly to CRSP and Compustat by

GTA Information Technology Co. Ltd.

Table 1 Summary statistics

This table provides a descriptive summary for the proprietary data used in the study. The primary sample

contains 77.4 million daily detailed transaction records of 676 SSE A shares (common stocks) conducted

by 7.12 million brokerage accounts across mainland China for the period from April 2001 to August

2002. Brokerage accounts are classified into institutional investors and individual investors on the basis

of account identifiers. Individual investor accounts are further classified on the basis of their average

trade sizes. Accounts with an average trade value greater than or equal to RMB 50 000 are classified as

large individual investors. The remaining accounts are classified as small individual investors.

All accounts Institutions Large individuals

Small

individuals

No. of accounts (1000) 7119.96 30.64 390.99 6698.32

(0.43%) (5.49%) (94.08%)

No. of buys (1 million) 40.47 0.12 1.96 38.38

No. of sells (1 million) 36.89 0.18 1.9 34.82

Total no. Of trades

(1 million)

77.36 0.30 3.86 73.2

(0.39%) (4.99%) (94.62%)

No. of shares purchased

(1 billion)

106.09 14.13 33.12 58.84

No. of shares sold

(1 billion)

105.47 13.88 33.55 58.04

Total no. Of

shares traded

(1 billion)

211.55 28.00 66.67 116.88

– (13.24%) (31.51%) (55.25%)

Values of buys

(1 billion RMB)

848.03 53.71 319.74 474.58

Values of sells

(1 billion RMB)

840.92 53.14 319.99 467.79

Total values of trades

(1 billion RMB)

1688.95 106.84 639.73 942.38

– (6.32%) (37.88%) (55.80%)

Average no. of shares

purchased

1723 32,504 13,181 1043

Average no. of

shares sold

1877 21,791 13,666 1129

Average values of

buys (RMB)

20,474 391,334 161,556 12,126

Average values of

sells (RMB)

22,288 245,723 167,425 13,188



2.2. Measuring the Information Content of a Trade

We use price impact as a measure for the information content of a trade. This mea-

sure is motivated by the concepts of asymmetric information models. These models

state that the trading process of investors is the mechanism through which value-

relevant private information is incorporated into asset prices (see, e.g., Glosten and

Milgrom, 1985; Kyle, 1985). Trades containing information about a security’s true

value will have a persistent impact on its price. Price impact thus reflects a likely

action of informed investors.

The price impact of a transaction is defined as the deviation of the transaction

price from the unperturbed price that would have prevailed had the trade not

occurred. In its simplest terms, the unperturbed price can be the previous transac-

tion price or the previous closing price of a stock. Following Kraus and Stoll

(1972), Keim and Madhavan (1997) and Chiyachantana et al. (2004), we calculate

the price impact (PI) of a trade as:

PIj ¼ I � ðPej

Pc� 1Þ ð1Þ

where I is a buy/sell indicator that takes the value of 1 if the transaction j is a pur-

chase and �1 if the transaction j is a sale; Pej is the execution price of the transac-

tion j; Pc is the benchmark price, which is the closing price on the day before the

transaction occurs. If an investor has private information and uses it optimally, the

expected price impact of either a buyer-initiated trade or a seller-initiated trade will

most likely be positive. To adjust the price effects for market-wide price movements

during the transaction (Prasanna and Menon, 2012), we follow Chan and Lakonis-

hok (1995) and Chiyachantana et al. (2004):

PImj ¼ I � ðPej

Pc�Me

McÞ ð2Þ

where Me is the market index on the day the transaction occurs and Mc is the mar-

ket index on the day before the transaction is occurs. After calculating market-

adjusted price impacts for buyer and seller initiated trades, we construct weekly

PID between purchase and sale trades, denoted as PIDmi;w, which is the value-

weighted average difference of PI between purchase transactions and sale transac-

tions for stock i over the entire week w.

PIDmi;w ¼ VWPI

buy;mi;w � VWPIsell;mi;w ð3Þ

where VWPIbuy;mi;w (VWPIsell;mi;w ) is the average PI

buy;mi;w (PIsell;mi;w ), weighted by the

value of each trade occurring in week w. We also examine the past magnitude

of PID associated with each stock to determine whether a PID is at a normal

level in a particular week. We relate each weekly stock-specific PID to the aver-

age PID of the stock in the previous 5 weeks and calculate the abnormal PID

(AbPID) as:

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AbPIDmi;w ¼ PIDm

i;w � 1

5

X5

h¼1

PIDmi;w�h ð4Þ

Throughout the paper, this market-movement-adjusted AbPID will be used as the

main measure of the PID.

Table 2 provides a descriptive analysis of the weekly PIDs, with and without

adjusting for market-wide movements, for different investor groups and trade sizes.

Price impact differences between buying and selling trades appear to be stronger for

the large investor group (i.e., institutional investors and large individual investors)

and trades with large share volume. For example, trades in the largest trade-size

group (>RMB 50 000) have the largest average PID at 72 bps. The result is consistent

with prior research on block trades and institutional trades, which document that

large-size trades (e.g., block trades) have a greater price impact than small-size trades.

Table 2 Price impact differential

This table provides a descriptive summary for the price impact differential (PID) between buying trades

and selling trades, with and without adjusting for market-wide movements, in different investor groups

and trade sizes. The large investor group consists of both institutional investor accounts and large indi-

vidual investor accounts. Other individual investor accounts are classified into the small investor group.

Trades are classified into seven groups on the basis of the number of shares executed.

Price impact

differential (102)

Market-

movement-

adjusted price

impact

differential (102)

Trades associated with

All accounts 1.065 0.645

Insitutions vs. individuals

Insitutional accounts 1.462 0.714

Individual accounts 1.043 0.642

Ng and Wu (2007)’s classification

Large investors 1.190 0.670

Small investors 0.978 0.634

Trade size (share)

<1000 0.271 0.135

1000–5000 0.680 0.444

5001–10 000 0.811 0.556

10 001–20 000 0.884 0.614

20 001–30 000 0.924 0.604

30 001–40 000 0.954 0.612

40 001–50 000 1.014 0.633

>50 000 1.257 0.720



Table 2 also shows a generally positive PID, that is, purchases, on average, have a

greater price impact than sales. A larger price impact for purchases than sales can be

explained by information motivation. For example, Chan and Lakonishok (1995) and

Keim and Madhavan (1996) advocate that purchases are normally information moti-

vated because buying a stock reflects one choice out of many alternatives. Sales are

liquidity motivated over purchases; because of short-selling constraints, the decision

to sell a stock that is already in a portfolio does not convey negative information.

3. Can the PID Predict Stock Returns?

In this section, we examine whether stock prices adjust to trading information in a

timely fashion. Our hypothesis is that if trading information contained in the PID

is incorporated into stock prices in a timely fashion, the PID does not predict

future returns. In contrast, slow-adjustment of prices to information yields a predic-

tive ability of the PID about future returns.

3.1. Baseline Analysis

The relationship between the PID and the cross-section of future stock returns is

the starting point of our analysis. A regression approach that simultaneously exam-

ines the predictive value of the PID along with other return attributes, for future

returns, is used. First, we adopt a regression based on Fama and MacBeth (1973).

Each week, we run the predictive regressions cross-sectionally by regressing excess

returns in week w + 1 on the AbPID in week w and a set of firm-specific control

variables. We include firm characteristics of size and book-to-market ratio following

Daniel and Titman (1997); they suggest that these firm characteristics capture the

cross-section of expected returns. Researchers have identified reversal patterns in

stock returns at weekly intervals (see, e.g., Jegadeesh, 1990); to control for any pat-

terns of return reversal, prior week returns are included. The regression, thus, takes

the following form:

ERi;wþ1 ¼ aþ b1AbPIDi;w þ b2ERi;w þ b3LNSizei;wþ1 þ b4B=Mi;wþ1 þ ei;wþ1 ð5Þ

Models 1 through 3 of Table 3 report the mean coefficients of the Fama–MacBeth regressions along with the associated Newey–West corrected t-statistics.

The Newey–West approach is used to account for any resulting overlap. For the

hypothesis that the PID predicts the cross-section of stock returns in the following

period, we expect b1 in equation (5) to be statistically significant and positive.

As seen in Table 3, the coefficients for the AbPID are positive, large and signifi-

cant, indicating that the PID is strongly related to excess returns in the subsequent

week. In all cases, the significance of the predictive power does not depend on

including or excluding the controls for return autocorrelations, return co-move-

ments of stocks with similar size, or book-to-market characteristics. The economic

significance in Model (3), holding other variables fixed, can be interpreted as an

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increase in the AbPID by one standard deviation, which leads to an increase in

average weekly returns of 0.26%.2 On an annualized basis, a one-standard-deviation

increase in the AbPID implies an increase in returns of 14.48%.

Petersen (2009) argues that the Fama–MacBeth approach can lead to under-

stated standard errors if there are fixed or slowly decaying effects in the data. Alter-

natively, we use a panel regression that pools all data with firm and time dummies.

t -statistics are calculated using two-way clustered standard errors (as in Petersen,

2009), where the cluster is defined at the firm and time level. The results are

reported in Models 4 through 6 of Table 3. The coeffcient estimates of the AbPID

are all positive and statistically significant across different specifications. For brevity,

we report only the Fama–MacBeth regression results in the rest of the paper. The

results of panel regressions are qualitatively similar.

Table 3 Can price impact predict stock returns?

This table reports estimates of Fama–MacBeth regressions and panel regressions relating AbPID to future

stock returns. The dependent variable is excess (market-adjusted) returns on stock i in week w + 1. Ab-

PID(w) is the abnormal PID between buying trades and selling trades for stock i in week w. Excess return

(w) is the excess returns in week w. LN Size (w + 1) and B/M (w + 1) are the natural log of the firm’s

capitalization and the firm’s book-to-market ratio, respectively, in week w + 1. Specifications 1 through 3

are Fama–MacBeth regressions with Newey–West corrected standard errors. Specifications 4 through 6

are the panel regressions with time- and firm-fixed effects. t -statistics are calculated using two-way clus-

tered standard errors where the cluster is defined at the firm and time level. t–statistics are reported in

parentheses below the coefficient estimates. Statistical significance is indicated by ** for 1% and * for

5%.

Fama–MacBeth regressions Panel regressions

(1) (2) (3) (4) (5) (6)

Intercept 0.000 0.000 0.010 �0.002** �0.002** 1.401**

(�0.028) (�0.269) (0.419) (�3.895) (�3.713) (7.385)

AbPID (w) 0.041** 0.096** 0.093** 0.036* 0.084** 0.055**

(3.860) (5.005) (5.417) (2.264) (3.430) (2.874)

Excess

return (w)

– �0.069** �0.069** – �0.065* �0.046

– (�2.668) (�2.835) – (�2.228) (�1.710)

LN Size

(w + 1)

– – �0.001 – – �0.065**

– – (�0.569) – – (�7.480)

B/M

(w + 1)

– – 0.011** – – 0.054*

– – (3.006) – – (3.112)

Firm fixed

effects

No No No Yes Yes Yes

Time fixed

effects

No No No Yes Yes Yes

Cluttering No No No Firm & Time Firm & Time Firm & Time

R2 – – – 3.10% 3.37% 7.13%

2The standard deviation of the AbPID is 0.028.



3.2. Robustness

3.2.1. Representativeness and Sample Selection Issues

We conduct several robustness checks. The first one relates to whether the sample

is sufficiently representative of the population. As the sample does not cover all

market activity, it could be problematic if it includes only transactions from a sub-

set of unrepresented investors. This is unlikely to be the case for two reasons: (i)

the sample accounts for approximately one-third of total market activity; (ii) the

sample is representative as the investor compositions in our data are very similar to

those reported contemporarily by the Chinese Securities Depository & Clearing Co.

Ltd.

If our sample is suffciently representative, the results in Section 3.1 will survive

further sub-classifications of the sample. We perform two tests. First, we provide a

separate analysis of return predictability for different investor groups, namely, the

large investor group and the small investor group. Second, we examine results for

small and large trades originating from either institutional or individual investors.

We define large and small trades using a fixed cut-off trade value; a large trade has

an RMB value equal to or greater than 50 000 while a small trade has an RMB

value less than 50 000. We then run Fama–MacBeth regressions for observations

constructed from two investor groups and two trade-size categories. The results are

reported in Panel A and B of Table 4. The predictive effects are present for not only

large and small investor groups but also large and small trade sizes.

As discussed in Section 1, if price underreaction is driven by cognitive biases

such as the conservatism bias, there may be a cross-sectional variation in the mag-

nitude of underreaction among different investor groups, as documented by

Hvidkjaer (2006). However, the results reported in Table 4 do not seem to suggest

a significant difference in the predictive effects of the PID either between trades ini-

tiated by large traders or trades initiated by small traders.

3.2.2. Illiquidity Concerns

Our results may be driven by the negative relationship between returns and the

illiquid nature of some stocks, if the PID is correlated with time-varying stock illi-

quidity. This makes intuitive sense as the price impact of a trade is widely consid-

ered to be a measure of transaction costs. Illiquidity reflects the impact of order

flow-on price—the higher the price impact, the higher the illiquidity (Glosten and

Milgrom, 1985).

To control for this possibility, we include Amihud’s (2002) illiquidity measure

of a stock in the baseline regression. The results, reported in Panel C of Table 4,

show that the predictable patterns in returns based on the PID are not affected by

the inclusion of the illiquidity ratio. The coeffcient of the AbPID remains positive

and statistically significant at the 1% level.

3.2.3. PID Sensitivity to Changes in Market Conditions

Chiyachantana et al. (2004) argue that traders are forced to pay a premium for

liquidity when they trade on the same side of the market, resulting in higher

(lower) price impacts for purchases (sales) in bullish markets and lower (higher)

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Table 4 Robustness: sample selection and illiquidity issues

This table reports results of robustness checks for issues in relation to the sample selection and the illi-

quidity nature of sample stocks. Panel A reports regression results for observations constructed on the

basis of trades associated with large and small group investors, respectively. Panel B reports regression

results for observations associated with large and small trades. Large trades are trades that execute with a

value equal to or greater than RMB 50 000. Small trades are trades that execute with a value less than

RMB 50 000. Panel C reports estimates of Fama–MacBeth regressions with the illiquidity measure of a

stock as an additional control variable. Statistical significance is indicated by ** for 1% and * for 5%.

Panel A: Fama–MacBeth regressions for large and small investors

Large investors Small investors

(1) (2) (3) (4) (5) (6)

Intercept �0.000 �0.000 0.010 0.000 �0.000 0.009

(�0.022) (�0.282) (0.4130 (0.031) (�0.173) (0.381)

AbPID (w) 0.041** 0.097** 0.094** 0.033** 0.080** 0.077**

(3.969) (5.077) (5.506) (3.057) (4.441) (4.867)

Excess return (w) – �0.069** �0.069** – �0.062* �0.063*

– (�2.672) (�2.850) – (�2.278) (�2.493)

Log Size (w + 1) – – �0.001 – – �0.001

– – (�0.564) – – (�0.529)

B/M ratio (w + 1) – – 0.011** – – 0.011**

– – (3.010) – – (3.032)

Panel B: Fama–MacBeth regressions for large and small trades

Large trades Small trades

(1) (2) (3) (4) (5) (6)

Intercept �0.000 �0.000 0.010 0.000 �0.000 0.009

(�0.029) (�0.289) (0.413) (0.040) (�0.313) (0.367)

AbPID(w�1) 0.042** 0.097** 0.094** 0.033** 0.081** 0.079**

(4.023) (5.077) (5.497) (2.955) (5.087) (5.782)

Excess return (w) – �0.069** �0.069** – �0.070** �0.070**

– (�2.684) (�2.859) – (�2.969) (�3.252)

Log Size (w + 1) – – �0.001 – – �0.001

– – (�0.564) – – (�0.520)

B/M ratio (w + 1) – – 0.011** – – 0.011**

– – (3.022) – – (3.099)

Panel C: Fama–MacBeth regression with additional illiquidity control variable

Intercept AbPIA Excess Log Size B/M ratio Illiquidity

(w) return (w) (w + 1) (w + 1) ratio (w)

Coeffcient �0.002 0.089** �0.072** �0.000 0.011** 0.464

t-stat. (�0.073) (4.916) (�3.053) (�0.117) (3.107) (1.910)



price impacts for purchases (sales) in bearish markets. This argument implies that

our key independent variable, PID, may capture, instead of the information effects,

merely the liquidity effects of the trading process.

To address this concern, we examine whether the PID value and its predictive

effect for future returns varies significantly with market movements over the sample

period. We define four phases of large fluctuations in the SSE composite index over

the sample period if a phase lasts at least more than 30 trading days and the phase

is associated with a rise or drop in the index greater than 15%. We calculate the

average PID and run the baseline regressions for each extreme market-movement

phase.3 Unlike Chiyachantana et al. (2004), we do not find evidence indicating

either a particularly large PID when the market is in a bullish phase or a particu-

larly small (or even negative) PID when the market is in a bearish phase, and that

the predictive power of the PID for returns varies significantly across extreme mar-

ket-movement phases.

4. Why can the PID Predict Future Returns?

In addition to slow price adjustment to information conveyed by the trading pro-

cess, at least two potential explanations for the cross-sectional predictive power of

the PID arise from either a non-information or information channel. First, the price

effect of a trade could be generated by the trading process itself because of market

frictions. Second, even if the price impact succeeds in capturing the consequence of

information asymmetry, the predictable patterns in returns may ultimately be traced

to differences in loadings on economically meaningful risk factors. Either explana-

tion is irrelevant to price underreaction.

4.1. Non-Informational Component of Price Impact

4.1.1. Distribution Effect Due to Short-term Cost of Liquidity

In a frictional market, the process of trading itself generates price movements

because of various market imperfections and frictions. Investors face the diffculty of

distributing shares among potential buyers/sellers because of different investor pref-

erences and/or high short-run liquidity costs (Kraus and Stoll, 1972). First, trading

induces discernible price impact patterns because securities are not necessarily per-

fect substitutes, and the excess-demand curve is downward-sloping (Shleifer, 1986).

Second, the distribution effect can also occur even if willing buyers or sellers exist,

but finding a match is diffcult. Stocks are then sold (bought) at a price lower

(higher) than the equilibrium price in the case of sales (purchases). Such price

effects are temporary as prices quickly reverse to the equilibrium after excess liquid-

ity demand is subsequently absorbed (e.g., Campbell et al., 1993).

The distribution effect due to investor preferences predicts a negative correlation

between the PID and future stock returns. This prediction is a flat contradiction to

3For brevity, we do not report the results, which are available upon request.

F. Wu


the pattern found in previous analyses. To investigate whether the distribution

effect from the short-term cost of liquidity affects our results, we examine whether

prices reverse in longer time horizons. We calculate cumulative stock returns over

four future time horizons: (w + 1, w + g), where g = 4, 26, 52, and 104 weeks. The

four weekly horizons are approximately equivalent to 1-month, half-year, 1-year,

and 2-year horizons. Table 5 presents Fama–MacBeth regressions of equation (5)

with returns calculated on using longer-time horizons. It shows that the positive

effects of weekly PIDs on future cross-sectional returns are only significant in

Model (1) without additional controls for g = 4, and disappear in economic and

statistical significance as time horizons move from 26 to 104 weeks. The weekly

returns’ predictability is unlikely to be affected by transitory demand pressure as

there is no obvious pattern of return reversals in weeks following w.

Our finding of no subsequent reversals followed by high short-term returns is

also inconsistent with the overreaction explanation for the predictive power of PID.

The literature in overreaction argues that, due to investors’ self-attribution bias

(Daniel et al., 1998) or the involvement of positive feedback traders (De Long et al.,

1990), an initial overreaction is followed by even more overreaction, leading to a

short-term price continuation. However, since the price has now risen above what

is justified by fundamentals, subsequent returns will, on average, be too low, gener-

ating a long-term reversal.

4.2. Informational Component of Price Impact

To differentiate the informational component of price impact from its pure

demand–pressure component, we follow Ni et al.’s (2008) assertion that the non-

informational component of price impact is insensitive to the level of informational

asymmetry. The information-based component is highly dependent on the level of

informational asymmetry.

4.2.1. Earnings Announcement Events

If information is an important attribute of the predictive value of PIDs for future

returns, then the informational effects should be stronger in periods of high infor-

mation asymmetry (e.g., periods before earnings announcement dates) or when

more informed trading occurs. For example, the differential information content

between purchases and sales should be greater (more positive) before announce-

ments of large positive earnings surprises and weaker (more negative) before

announcements of large negative earnings surprises.

To examine this issue, we use quarterly earnings announcements. Following

Garfinkel and Sokobin (2006), we measure the earnings surprise of an announce-

ment by taking the average market-adjusted returns of the stock in the window of

(t-1, t) where day t is the announcement date. We define 5 days prior to the earn-

ings-surprise-estimation window, (t�6, t�2), as the event window. To determine

the abnormal level of PIDs, we compare daily PIDs within the event window to the

average value of PIDs in a 30-day estimation window, (t�36, t�7). More specifi-

cally, the abnormal daily market-movement-adjusted PID is calculated by



AbPIDmi;t�d ¼ PIDm

i;t�d �1

30

X36

j¼7

PIDmt;t�j ð6Þ

where d = {2,…,6}. The event window, AbPID, is simply the average across the five

days prior to the earnings announcement dates. Panel A of Table 6 compares

Table 5 Non-informational component of price impact

This table reports estimates of Fama–MacBeth regressions relating AbPIDs to longer-term future stock

returns. The dependent variable is the excess (market-adjusted) returns on stock i for a future time hori-

zon: (w + 1, w + g), where g = 4, 26, 52, and 104 weeks. The AbPID (w) is the abnormal PID between

buying trades and selling trades for stock i in week w. Excess return (w�g, w�1) is the excess returns for

a period of (w�g, w�1) where g = 4, 26, 52, and 104 weeks. LN Size (w + 1, w + g) and B/M (w + 1,

w + g) are the natural log of the firm’s capitalization and the firm’s book-to-market ratio over a horizon

of (w + 1,w + g). Statistical significance is indicated by ** for 1% and * for 5%.

Dependent

variable=

Excess return (w�g)

g = 4 g = 26

(1) (2) (3) (1) (2) (3)

Intercept 0.000 �0.000 �0.147 �0.004 �0.003 �0.765**

(0.025) (�0.163) (�1.912) (�0.945) (�0.778) (�4.757)

AbPID (w) 0.110** 0.033 0.018 �0.003 �0.033 �0.037

(2.925) (1.032) (0.538) (�0.042) (�0.506) (�0.520)

Excess return

(w�g)

– �0.073* �0.076** – �0.020 �0.018

– (�2.375) (�2.688) – (�1.423) (�1.490)

Log size (w + g) – – 0.007 – – 0.035**

– – (1.990) – – (4.868)

B/M (w + g) – – �0.001 – – 0.018

– – (�0.064) – – �1.026

Dependent

variable=

Excess return (w�g)

g = 52 g = 104

(1) (2) (3) (1) (2) (3)

Intercept �0.024** �0.022** �1.789** �0.104** �0.075** �4.777**

(�2.952) (�2.680) (�8.421) (�15.90) (�10.84) (�46.05)

AbPID (w) 0.021 0.001 �0.001 0.011 �0.018 �0.032

(0.274) (0.019) (�0.015) (0.111) (�0.178) (�0.371)

Excess return

(w�g)

– �0.018** �0.012** – �0.058** �0.041**

– (�3.723) (�2.988) – (�16.03) (�10.96)

Log size

(w + g)

– – 0.081** – – 0.214**

– – (8.615) – – (47.97)

B/M (w + g) – – 0.042 – – 0.113**

– – (1.745) – – (8.133)

F. Wu


directly the average AbPIDs for events with positive earnings surprises and average

AbPIDs for events with negative earnings surprises. The average daily AbPIDs for

positive events (15.2 bp) is significantly greater than the average daily AbPID for

negative events (0.1 bp). The difference is significant at the 1% level.

We then regress event window AbPID on corresponding levels of earnings sur-

prises as well as earnings-surprise-ranking deciles to avoid the linearity assumption.

Panel B reports the coefficient estimates. Earnings surprise coefficients in both

Models (1) and (2) are positive and significant at the 5% level or above, suggesting

that the value of event window PID increases in the level of earnings surprises. The

PID seems to contain value-relevant information for forthcoming earnings

announcements. This information content leads to more informed purchases (sales)

relative to sales (purchases) in the event of positive (negative) earnings surprises.

4.2.2. Probability of Informed Trading

As argued earlier, it is likely that disproportionately more value-relevant private

information is revealed through buying and selling activities when more informed

trading is present in the market. If information drives the predictive value of PIDs

for future returns, then we expect to see stronger return predictability under cir-

cumstances where more informed trading is present.

To assess the frequency of informed trading across firms, we use the probability

of informed trading (PIN) as a proxy. PIN is computed from the probability that

an order is submitted by an informed trader (Easley et al., 1997). We estimate PIN

Table 6 Informational component of price impact: earnings announcement events

This table reports cross-sectional variations in daily AbPIDs within an event window. The event window

is the 5-day window prior to quarterly earnings announcements. AbPID is the daily PID minus the aver-

age value of PIDs in a 30-day estimation window, (t�36, t�7). Panel A reports the event window average

values of AbPIDs for positive earnings surprises and for negative earnings surprises. Earnings surprises

are measured by taking the average market-adjusted abnormal stock returns in a window of (t�1, t)

where day t is the quarterly announcement date. The statistical tests for differences are reported. Panel B

reports regression estimates of event window AbPID on corresponding levels of earnings surprises as well

as earnings-surprise-ranking deciles. Statistical significance is indicated by ** for 1% and * for 5%.

Panel A: Average abnormal PID over 5 days before positive and negative earnings surprises

Abnormal PID Earnings surprise > 0 Earnings surprise < 0 Diff. t-stat

Mean 0.152 0.001 0.151** �2.289

Panel B, regression of avgerage abnormal PID over five days before the announcement date

on earnings surprise measures

Intercept Earnings surprise Earnings surprise decile R2

Model (1) 0.067* 7.714* – 0.36%

(2.061) (2.210) – –

Model (2) �0.157 – 0.039** 0.51%

(�1.949) – (2.999) –



on an annual basis.4 For each year, we classify stocks that have the largest (smallest)

50% of PIN in the previous year as those stocks with more (less) informed trading.

Fama–MacBeth regressions in equation (5) are then estimated by including an addi-

tional dummy, (DPINv), which takes the value of 1 for observations of stocks in the

highest 50% PIN group and 0 otherwise, and an interactive variable between the

dummy and the AbPID, DPIN 9 AbPIDw, which is designed to capture the incre-

mental predictive power of the AbPID for the next week’s returns for stocks with

intense informed trading.

Table 7 reports the regression coefficient estimates. Conditional on the previous

week’s PID, stocks with a higher probability of informed trading (a previous period

PIN higher than median) earn higher subsequent returns than stocks with a lower

probability of informed trading (a previous period PIN lower than median). All

coefficients of the interactive variable across three specifications are positive and sta-

tistically significant (at 5% or more).

In summary, the results presented in Sections 4.2.1 and 4.2.2 support the notion

that the PID’s predictive value is likely driven by the informational component of

price impact. When prices respond too slowly to the informational content of the

PID, predictable patterns in returns may result.

4.2.3. Private Information Content of PIDs

If the PID contains information, what is the nature of the information? Is it possi-

ble that the PID consists purely of information that does not extend to anything

more than public knowledge? In this section, we address these questions.

While a large order imbalance could be induced by either public or private

information (Chordia and Subrahmanyam, 2004), it makes intuitive sense that

investor order flows, at the very least, ought to reflect the effect of public informa-

tion release on the trading decisions of investors. If the PID contains nothing more

than public information, we expect that PIDs should not explain stock returns

beyond the extent to which public order flows could have been able to explain

them. On the other hand, the PID provides additional explanatory power if it con-

tains information that is not fully captured by public order flows.

To test this hypothesis, we will perform a two-stage regression analysis. The

first-stage regression regresses the PID on order imbalances of various investor

groups on a stock-by-stock basis. In our data, order flows are classified on the basis

of investor accounts, namely, large investor group and small investor group. The

two groups should, a priori, capture different sources of information (c.f., Ng and

Wu, 2007). For each group, the order imbalance (OI) for stock i in week w is calcu-

lated as (purchases-sales)/(purchases + sales) where purchases (sales) is the total

value of buying (selling) trades from an investor group. Specifically, we run the

following regression:

4To calculate firm-specific PIN, we obtain intra-day transaction data on Chinese markets

from the Global Taqtic database managed by the Securities Industry Research Center of Asia-

Pacific.

F. Wu


AbPIDi;w ¼ ai þ bLargeðSmallÞi OI

LargeðSmallÞi;w þ eAbPIDi;w ð7Þ

The first-stage creates a PID measure net of price pressure from investor order

imbalances. We then run the second-stage regression, the baseline Fama–MacBeth

regressions with the AbPID being replaced by the residuals, eAbPIDi;w , generated from

equation (9).

The Fama–MacBeth regression results are reported in Table 8. The coefficients

on residuals that are generated from the first-stage regressions as a measure of the

PID net of public information effects are statistically significant for both large inves-

tor group regressions and small investor group regressions. After controlling for

past returns and firm characteristics in Model (3) for small investor order imbal-

ances, an increase in the PID net of public information effects by one standard

deviation leads to an increase in average weekly returns of 0.18%.5 The results indi-

cate that the PID increases the explanatory power of future returns beyond investor

order flows, implying that PIDs contain additional information that might not be

fully captured by order flows.

Table 7 Informational component of price impact: probability of informed trading

This table reports estimates of Fama–MacBeth regressions to analyze how the predicative power of the

AbPID for future returns varies according to the extent of informed trading of individual stocks. The

extent to which informed trading occurs in a stock is measured by the probability of informed trading

(PIN). Stocks that have the largest 50% of PIN in the previous year are classified as those with more

informed trading. Fama–MacBeth regressions are then estimated by including an additional dummy,

(DPIN), which takes the value of 1 for observations of stocks in the highest 50% PIN group, 0 otherwise,

and an interactive variable between the dummy and the AbPID, DPIN 9 AbPIDw. Statistical significance

is indicated by ** for 1% and * for 5%.

(1) (2) (3)

Intercept �0.000 �0.000 0.009

(�0.044) (�0.348) (0.351)

AbPID (w) 0.006 0.060** 0.064**

(0.386) (2.809) (3.536)

DPIN 0.000 0.000 0.001

(0.242) (0.579) (1.111)

AbPID (w) 9 DPIN 0.060** 0.059** 0.049**

(2.778) (3.049) (2.720)

Excess return (w) – �0.067* �0.068**

– (�2.591) (�2.811)

LN Size (w + 1) – – �0.001

– – (�0.510)

B/M (w + 1) – – 0.011**

– – (2.973)

5The standard deviation of the AbPID is 0.027.



The magnitude of the residual coefficients varies between the two groups. The

PID exhibits predictive power over future returns more strongly than the net of

variations in small group investor order flows. This result suggests that the large

group investors may have access to private sources of information to a greater

extent than small group investors.

4.3. Risk-based Explanation: Factor Analysis

It is possible that the returns being earned on high-PID portfolios are simply com-

pensation for risks already captured by the Fama–French, momentum and/or other

factor-mimicking portfolios. A risk-based explanation does not relate to the slow

adjustment of prices to news in forming the positive PID–returns relation.To address this issue, we sort stocks into quintiles on the basis of the AbPID in

each week. Zero-cost portfolios are then formed on a weekly basis (w) by taking

long (short) positions in stocks with the greatest (smallest) 20% PIDs in week

(w�1). The portfolios are rebalanced weekly. Portfolio returns are then regressed

on the Fama–French three factors and the momentum factor.

RL�Sw ¼ cþ d1MKTPFw þ d2SMBw þ d3HMLw þ d4UMDw þ ew ð8Þ

where RL�Sw is the excess returns of the largest PID portfolio minus the excess

returns of the smallest PID portfolio. MKRPF, SMB, HML, and UMD factors are

Table 8 Information content of price impact: Marginal predicative power of PID over inves-

tor order flows

This table reports estimates of Fama–MacBeth regressions to analyze the predictive power of the AbPID

net of price pressure from investor order imbalances. The analysis is conducted using a two-stage regres-

sion approach. Investor accounts are first classified into large investor group and small investor group. For

each group, the order imbalance (OI) for stock i in week w is calculated as (purchases-sales)/(purchases +sales), where purchases (sales) are the total value of buying (selling) trades from an investor group. The

first-stage regression regresses AbPID on order imbalances of various investor groups on a stock-by-stock

basis. The residuals obtained from the first-stage regressions represent an AbPID measure net of price pres-

sure from investor order imbalances. The second-stage regression runs a modified baseline Fama–MacBeth

regression, which replaces AbPID with the residuals generated from the first-stage regression. This table

reports the second-stage regression results. Statistical significance is indicated by ** for 1% and * for 5%.

Large investors’ order imbalance Small investors’ order imbalance

(1) (2) (3) (4) (5) (6)

Intercept �0.000 �0.000 0.007 �0.000 �0.000 0.010

(�0.002) (�0.265) (0.272) (�0.006) (�0.270) (0.428)

eAbPID (w) 0.036** 0.069** 0.067** 0.040** 0.082** 0.079**

(3.249) (3.771) (4.063) (3.609) (4.623) (4.880)

Excess

return (w�1)

– �0.067** �0.069** – �0.059* �0.058*

– (�2.977) (�3.314) – (�2.371) (�2.466)

LN Size (w) – – �0.001 – – �0.001

– – (�0.422) – – (�0.588)

B/M (w) – – 0.012** – – 0.011**

F. Wu


constructed using Chinese data based on the methods described on Kenneth

French’s website. The 3-month interest rate for savings deposits is used as the risk-

free rate, adjusted to a weekly frequency. The risk-free rates are obtained from

China Statistical Yearbooks. If the predictable returns patterns are due to changes

in risk characteristics, the intercept should be indistinguishable from zero.

The results are reported in Table 9. Panel A reports regression results of equally

weighted PID-sorted portfolios while Panel B reports regression results of value-

weighted PID-sorted portfolios. Even though the multi-factor model does possess

some explanatory power, it explains, at best, less than 30% of the variability of portfo-

lio returns. More importantly, the intercept is positive and significant at the conven-

tional 5% level, indicating weekly excess returns of approximately 0.3% after adjusting

for various risk factors. The 0.3% weekly return is economically large, translating into

a 16.8% annual return. The finding thus rules out the possibility of time-varying risks as

a potential explanation for the positive relationship between PIDs and future returns.

4.4. The Gradual Diffusion of PID Information

Our prior results suggest that stock prices slowly incorporating information con-

tained in PIDs may then be the most likely explanation for predictable patterns in

returns. The mechanism underlying price underreaction is still unclear because both

the conservatism bias of representative agents and the gradual diffusion of informa-

tion can give rise to price underreaction. As discussed in Section 3.2.1, we find that

the predictive effects of PID hold for trades initiated by both large traders and small

traders. This result does not seem to support the implication of the conservatism

bias hypothesis, namely, a cross-sectional variation in underreaction among differ-

ent investor groups as documented by Hvidkjaer (2006).

Table 9 Risk-based explanation: Factor analysis

This table reports performance results for zero-cost portfolios that are constructed on the basis of the previ-

ous period’s AbPID. Sample stocks are sorted into quintile by AbPID in each week. Zero-cost portfolios are

then formed on a weekly basis by taking long (short) positions in stocks with the greatest (smallest) 20%

PIDs in a week (w�1). The portfolios are rebalanced weekly. Portfolio returns are then regressed on the

three Fama–French factors (MKTRF, SMB, and HML) and the momentum factor (UMD). Panel A reports

regression results of equally weighted PID-sorted portfolios while Panel B reports regression results of value-

weighted PID-sorted portfolios. Statistical significance is indicated by ** for 1% and * for 5%.

Alpha MKTRF SMB HML UMD R2

Panel A: Equally weighted return

Coeffcient 0.003** �0.011 �0.150 0.332** �0.179 28.66%

t-stat. (3.615) (�0.161) (�1.408) (2.960) (�0.995) –

Panel B: Value-weighted return

Coeffcient 0.003* �0.104 0.263 0.240 �0.130 6.16%

t-stat. (2.181) (�1.082) (1.450) (1.800) (�0.544) –



We turn to the alternative explanation of underreaction—Hong and Stein’s

(1999) GID model. The key prediction of the GID theory is that information dif-

fuses slowly through the investing population, and as such, investors receive infor-

mation at different points in time. It follows that if some investors (i.e., informed

investors) receive private information at a time earlier than others, the PID

calculated based on these investors’ trades should lead (predict) the PID calculated

based on other investors’ trades. In this section, we provide empirical evidence in

support of this hypothesis.

Because the timing of private information arriving to individuals is unobserv-

able, we have to assume that investors are classified into different groups in which

each group is, a priori, more or less likely to possess the resources for collecting

information. Large investors are considered hypothetically informed investors

because their wealth level allows them more resources for collecting value-relevant

information (as discussed in Section 2.1). For the same reasoning, small investors

are considered hypothetically uninformed investors. Section 4.1 has provided evi-

dence suggesting that the large investors use private sources of information in their

trading to a greater extent than small investors.

We then estimate a two-variable vector auto-regression (VAR) model where

both the PID of large investors and the PID of small investors are treated as endog-

enous.

PIDLw ¼ si þ

XH

h¼1

hhPIDLw�h þ

XH

h¼1

khPIDSw�h þ wRw�5;w�1 þ e

w;PIDL ð9Þ

PIDSw ¼ gi þ

XH

h¼1

uhPIDLw�h þ

XH

h¼1

whPIDSw�h þ wRw�5;w�1 þ l

w;PIDS ð10Þ

where PIDLw is the PID calculated from the trades of large investors (i.e., hypotheti-

cally informed investors), and PIDSw is the PID calculated from trades of small

investors (i.e., hypothetically uninformed investors).

We perform two sets of VAR regressions. First, we run regressions at the indi-

vidual stock level. To ensure that the analysis is not affected by a lack of observa-

tions in some stocks, we restrict the sample to those stocks that have been

continuously traded for a number of weeks greater than or equal to 50.6 More than

90% of the sample stocks are used. We then report the mean and median coeffi-

cient estimates of individual stock regressions. Second, we perform a VAR model

jointly estimated across firms by allowing the intercept i to vary across firms, i.e.,

by introducing τi and gi. For both methods, we select a lag number of 5.

Coeffcient estimates of the two methods are reported in Table 10. Panel A

reports mean and median coefficients for stock-by-stock VAR analysis whereas

6A threshold of 25 trading weeks yields qualitatively the same results.

F. Wu


Table

10Does

PID

inform

ationdiffuse

slowly?VectorAuto-Regressive(V

AR)analysis

Thistable

reportsestimates

oftwo-variable

vectorauto-regressions(V

AR)onthePID

calculatedbythetrades

oflarge-groupinvestors

andthePID

calculatedbythe

trades

ofsm

all-groupinvestors.Twosets

ofVARregressionsareestimated.First,regressionsarerunonastock-by-stock

basis.Panel

Areportsthemeanandmedian

coefficientestimates

ofindividual

stock

regressions.Second,regressionsarerunonaVARmodel

jointlyestimated

across

stocksbyallowingtheinterceptvaries

across

stocks.Forboth

methods,alagnumber

of5ischosen.Statisticalsignificance

isindicated

by**

for1%

and*for5%

.

Panel

A:Meanandmediancoefficients

ofstock-by-stock

VARregressions

PID

Large

PID

Small

Excessreturn

w�1

w�2

w�3

w�4

w�5

w�1

w�2

w�3

w�4

w�5

(w�6

,w�1

)Intercept

Dependentvariable:PID

Small

Independentvariables

Mean

0.106**

0.092**

0.102**

0.106**

0.137**

�0.148**

�0.136**

�0.110**

�0.118**

�0.195**

�0.112**

�0.000*

t-stat.

(4.363)

(3.583)

(4.323)

(4.297)

(5.602)

(�6.199)

(�5.390)

(�4.786)

(�4.903)

(�8.306)

(�37.72)

(�2.193)

Median

0.079**

0.079**

0.092**

0.102**

0.138**

�0.125**

�0.106**

�0.106**

�0.112**

�0.210**

�0.108**

�0.000**

z-value

(4.193)

(3.167)

(4.625)

(4.512)

(5.662)

(�6.026)

(�5.245)

(�5.071)

(�5.151)

(�8.304)

(�20.57)

(�2.770)


Large

Mean

0.015

�0.042

�0.023

�0.064**G16

�0.041

�0.056*

�0.004

0.015

0.049*

�0.016

�0.112**

�0.000**

t-stat.

(0.622)

(�1.668)

(�0.996)

(�2.666)

(�1.739)

(�2.408)

(�0.160)

(0.666)

(2.0814)

(�0.711)

(�41.78)

(�4.152)

Median

�0.015

�0.064*

�0.043

�0.073**

�0.062*

�0.023

0.015

0.037

0.053*

�0.031

�0.104**

�0.000**

z-value

(�0.099)

(�2.339)

(�1.136)

(�3.160)

(�2.154)

(�1.869)

(�0.280)

(�0.772)

(�2.450)

(�0.696)

(�20.92)

(�5.634)

Panel

B:VARregressionsjointlyestimated

across

strocks

PID

Large

PID

Small

Excessreturn

w�1

w�2

w�3

w�4

w�5

w�1

w�2

w�3

w�4

w�5

(w�6

,w�1

)


Small

Independentvariables

Mean

0.090**

0.02

0.072**

0.055**

0.099**

�0.110**

�0.045**

�0.107**

�0.094**

�0.213**

�0.088**

t-stat.

(5.259)

(1.163)

(4.149)

(3.148)

(5.6340

(�6.644)

(�2.714)

(�6.414)

(�5.598)

(�12.59)

(�42.30)


Large

Mean

0.013

�0.055**

�0.042*

�0.090**

�0.103**

�0.035*

0.029

0.009

0.050**

�0.007

�0.090**

t-stat.

(0.809)

(�3.349)

(�2.517)

(�5.369)

(�6.143)

(�2.176)

(1.845)

(0.543)

(3.126)

(�0.457)

(�45.25)



Panel B reports coefficients for a jointly estimated VAR model. Both results indicate

that the lagged PID of the large investor group (i.e., hypothetically informed inves-

tors) has a positive significant correlation with the current PID of the small investor

group (i.e., hypothetically uninformed investors) for up to 4 weeks in the past.

These results control for the explanatory power of lagged values of the small

investor group’s PID and past returns. No significant relationship exists when the

reverse direction is considered. This finding, along with those in previous sections,

confirms the hypothesis that some investors receive private information with a time

lag and that the information being reflected in their trading decisions, also with a

time lag, causes price underreaction to the information (i.e., returns predictability),

as predicted by GID theory.

5. Conclusion

In an attempt to explain the existence of previously documented anomalies in

returns, the GID model of Hong and Stein (1999) was built upon the assumption

that firm-specific information diffuses slowly through the investor population.

When some investors receive the information at a time lag, this causes an underre-

action of prices, constituting returns continuation. In this paper, we provide direct

empirical evidence in support of this prediction. We show that the extent of returns

predictability depends on the level of private information content contained in

investors’ transactions.

There are several avenues for future work. First, in studying security price for-

mation, a better understanding of the information content of the price impact of

market transactions may shed light on how price evolves and how private informa-

tion is impounded into price through the trading process. Second, our results sug-

gest that the price impact variable, which captures the consequence of information

asymmetry in markets, may be useful in depicting the activity of informed traders.

In corporate finance, the variable measuring the information content of stock price

has important implications for empirical studies on managerial decisions that may

be made upon the information content of stock prices. These issues are open ques-

tions for future research.

References

Amihud, Y., 2002, Illiquidity and stock returns: Cross-section and time-series effects, Journal

of Financial Markets 5, pp. 31–56.

Barberis, N., A. Shleifer, and R. Vishny, 1998, A model of investor sentiment, Journal of

Financial Economics 49, pp. 307–343.

Campbell, J.Y., S.J. Grossman, and J. Wang, 1993, Trading volume and serial correlation in

stock returns, Quarterly Journal of Economics 108, pp. 905–939.

Chan, L.K.C., and J. Lakonishok, 1995, The behavior of stock prices around institutional

trades, Journal of Finance 50, pp. 1147–1174.

F. Wu


Chiyachantana, C.N., P.K. Jain, C. Jiang, and R.A. Wood, 2004, International evidence on

institutional trading behavior and price impact, Journal of Finance 59, pp. 869–898.

Chordia, T., and A. Subrahmanyam, 2004, Order imbalance and individual stock returns:

Theory and evidence, Journal of Financial Economics 72, pp. 485–518.

Daniel, K., and S. Titman, 1997, Evidence on the characteristics of cross sectional variation

in stock returns, Journal of Finance 52, pp. 1–33.

Daniel, K., D. Hirshleifer, and A. Subrahmanyam, 1998, Investor psychology and security

market under- and over-reactions, Journal of Finance 53, pp. 1839–1885.

De Long, J.B., A. Shleifer, L. Summers, and R. Waldmann, 1990, Positive feedback

investment strategies and destabilizing rational speculation, Journal of Finance 45,

pp. 375–395.

Easley, D., N.M. Kiefer, and M. O’Hara, 1997, One day in the life of a very common stock,

Review of Financial Studies 10, pp. 805–835.

Fama, E.F., 1998, Market effciency, long-term returns, and behavioral finance, Journal of

Financial Economics 49, pp. 283–306.

Fama, E.F., and J. MacBeth, 1973, Risk, return and equilibrium: Empirical tests, Journal of

Political Economy 81, pp. 607–636.

Garfinkel, J.A., and J. Sokobin, 2006, Volume, opinion divergence, and returns: A study of

post-earnings announcement drift, Journal of Accounting Research, pp. 85–112.

Glosten, L.R., and P.R. Milgrom, 1985, Bid, ask and transaction prices in a specialist market

with heterogeneously informed traders, Journal of Financial Economics 14, pp. 71–100.

Hong, H., and J.C. Stein, 1999, A unified theory of underreaction, momentum trading and

overreaction in asset markets, Journal of Finance 54, pp. 2143–2184.

Hong, H., T. Lim, and J.C. Stein, 2000, Bad news travels slowly: Size, analyst coverage, and

the profitability of momentum strategies, Journal of Finance 55, pp. 265–295.

Hsiao, J.-L., and T.-T. Tu, 2012, The effect of abnormal turnover on asymmetric

autoregressive behavior of index returns: Evidence from the Chinese a-share stock

markets, Asia-Pacific Journal of Financial Studies 41, pp. 563–589.

Hvidkjaer, S., 2006, A trade-based analysis of momentum, Review of Financial Studies 19, pp.

457–491.

Jegadeesh, N., 1990, Evidence of predictable behavior of security returns, Journal of Finance

45, pp. 881–898.

Keim, D.B., and A. Madhavan, 1996, The upstairs market for large-block transactions:

Analysis and measurement of price effects, Review of Financial Studies 9, pp. 1–36.

Keim, D.B., and A. Madhavan, 1997, Transaction costs and investment style: An inter-

exchange analysis of institutional equity trades, Journal of Financial Economics 46,

pp. 265–292.

Kraus, A., and H.R., Stoll, 1972, Price impacts of block trading on the New York stock

exchange, Journal of Finance 27, pp. 569–588.

Kyle, A.S., 1985, Continuous auctions and insider trading, Econometrica 53, pp. 1315–1335.

Menzly, L., and O. Ozbas, 2010, Market segmentation and cross-predictability of returns,

Journal of Finance 65, pp. 1555–1580.

Ng, L., and F. Wu, 2007, The trading behavior of institutions and individuals in Chinese

equity markets, Journal of Banking and Finance 31, pp. 2695–2710.

Ni, S.X., J. Pan, and A.M. Poteshman, 2008, Volatility information trading in the option

market, Journal of Finance, 63, pp.1059–1091.



Petersen, M.A., 2009, Estimating standard errors in finance panel data sets: Comparing

approaches, Review of Financial Studies 22, pp. 435–480.

Prasanna, K., and A. Menon, 2012, The speed of stock price adjustments to market wide

information in India, Asia-Pacific Journal of Financial Studies 41, pp. 541–562.

Shleifer, A., 1986, Do demand curves for stocks slope down? Journal of Finance 41,

pp. 579–590.

F. Wu


do stock prices underreact to information conveyed by investors' trades? evidence from china

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