1 dynamic relations between order imbalance, volatility and return of top losers dr. yong-chern su,...

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Dynamic Relations between Order Imbalance, Volatility and Return of Top Losers

Dr. Yong-Chern Su, National Taiwan University, Taiwan

Dr. Han-Ching Huang, Chung Yuan Christian University, Taiwan

Po-Hsin Kuo, National Taiwan University, Taiwan

Pei-Wen Chen, National Taiwan University, Taiwan (presenter)

2008 NTU International Conference on Finance

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Agenda

1. Introduction

1.1 Motivation and Purpose

1.2 Main findings

1.3 Contributions

2. Data

3. Methodology

4. Empirical Results

5. Conclusion

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1. Introduction


Motivation

• Investors are always seeking useful indicators to predict the movements of their hol

ding stocks. Among many possible indicators, trading activity has been proven to be

a great proxy to imply private information (Lo and Wang, 2000; Karpoff, 1987).

• Chordia, Roll and Subrahmanyam (2002) find that order imbalances, reflecting the

directions of the trading volume, exert significant influence on stock returns. Ord

er imbalances can reveal some private information behind the market markers and t

he big-deal traders.

• Chordia, Roll and Subrahmanyam (2005) document that imbalances predict futur

e returns over very short intervals, no more than thirty minutes. However, onl

y specialists (market makers) know order imbalances.

• In the real world, there is a channel such as TradeStation® to offer the automating r

ule-based trading based on the real-time volume signal, and hence we want to kno

w whether no-informed investors can use order imbalance information to trad

e and earn abnormal profits even without private information.

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1. Introduction


Objective

• The objective of our study is to examine the dynamic relations between order

imbalance, volatility and stock returns, and to design a valuable trading strategy

based on their relations.

• How to select stocks to achieve our objective?

Based on Llorente, Michaely, Saar and Wang (2002), investors trade for two

reasons: hedging for their stock holdings or speculating on their private information.

When investors trade stocks because of their private information, the patterns of

stock returns will continue in following periods. Once it works, we can predict the

movement of their stock prices. Therefore, we want to find the speculative stocks.

• We choose top losers (the stocks with the lowest returns on each date) to stand

for the speculative stocks, which might be possibly with more information inside,

and use this sample to prove that investors without any private information can use

order imbalance information to trade and earn profits.

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1. Introduction

1.2 Main findings

• First, we find that both in our time varying GARCH (1,1) model and the intraday tim

e-series regression models, there’s significant positive contemporaneous effect

between order imbalance and return in our top losers sample.

• Second, we develop a successful trading strategy based on the previous findings.

As our samples are daily top losers, our strategy is to short sell when the first negati

ve order imbalance appeared and buy back when the order imbalances become bu

yer-initiated.

The empirical results show that if we don’t truncate the smaller order imbalances, w

e can’t find abnormal returns. However, if we sift our data from trading volume, t

hat is above 99% volume, we document a significant profit based on our tradi

ng strategy.

• Third, we follow a complete procedure to examine the causality relationship betwee

n return and order imbalance to explain our significant profit, and find that in the mo

st case, order imbalance is a unidirectional indicator for predicting future retur

ns. Especially, order imbalance is a good indicator for price discovery in small firm

size quartile.

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1. Introduction1.3 Contributions

We contribute to the literature at three aspects.

• First, the existing articles use a comprehensive cross-sectional sample of exchanges s

tocks to document that order imbalances have a significant relationship with stock retur

ns. Ours is the first study to use the specific speculative stocks, top losers, to analy

ze the dynamic relations between trading activities and stock returns, and based on th

e relations to show that there exists a valuable trading strategy.

• Second, our success in trading strategy relies on truncations of smaller order imbal

ances. This implies that trading size offers more valuable information on making p

rofits than trading number, which is consistent with the findings of Chan and Fong (2

000). They show that the order imbalance in large trade size categories affects the ret

urn more than in smaller size categories.

• Third,by examining the dynamic causality relationship between return and order imbala

nce, we find that in most case, order imbalance is a unidirectional indicator for pre

dicting future returns, and is the main source to make profit of our trading strategy.

Although Chordia, Roll and Subrahmanyam (2005) find that order imbalances lose thei

r predictive ability in no more than thirty minutes, we document a significant profit ba

sed on our trading strategy.

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2. Data

2.1 Sample

• The transaction data sources are from the CRSP and TAQ databases.

• We first sought for the daily top losers within CRSP, then match the

corresponding intraday trading data on TAQ.

• Because transactions data are so voluminous, our study uses a limited sample of

stocks over a limited interval of time.

(a) The sample period is from Dec. 1st , 2005 to Dec. 31st , 2005.

(b) The observation period each day is from 9:30 A.M. to 4:00 P.M (the regular

trading time), due to different transaction rule and pricing mechanism.

(c) 61 NASDAQ stocks are collected from the databases.

• The average return of our 61 sample is -18.8%.

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2. Data

2.2 Order imbalance variable

• Following the Lee and Ready (1990) rule, we sign each trade as either buyer-

initiated or seller-initiated.

If a trade occurs above the prevailing quote mid-point, it is regarded as a buyer-

initiated and vice versa.

• The order imbalance (OI) is defined as daily net share volume, which is

computed as the difference between the buyer-initiated share and the seller-

initiated share.

• Our sample, either per day or per trade basis, shows that seller-initiated share

volume is larger than the buyer-initiated share volume. It is self-explained that

negative order imbalances push stock prices move downward and lead these

stocks to the top losers.

(a) The average OI of our sample is -203,483 shares per day.

(b) The average mean of OI per trade is -120 shares; the average standard

deviation of OI per trade is reaching for 2,124 shares.

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3. Methodology

We use two models: GARCH(1,1) and time-series regression models to examine th

e relations between order imbalance, volatility and stock returns.

3.1 Dynamic return-OI and volatility-OI GARCH(1,1) models

• To examine the dynamic relations of return-OI and volatility-OI, we associate the a

rguments of contemporaneous OI-return relation (Chordia and Subrahmanyam, 2

004) and contemporaneous OI-volatility relation (Chan and Fong, 2000) separat

ely with GARCH(1,1) model, which has been proven to successful model for capturi

ng time-varying volatility properties of individual stock returns.

• We use an OI coefficient in the conditional mean equation and conditional volat

ility equation separately to fit our intraday data.

….. (1)

t t tR OI

(0, )1 tN ht t

21 1 1 1 1t t th A B h C

….. (2)

t tR

(0, )1 tN ht t

21 1 1 1 1 1t t t th A B h C DOI

Where Rt is the return in period t, defined as ln(Pt/Pt-1); OIt is the explanatory variable;

εt is the residual of the stock return in period t; ht is the conditional variance in period t;

Ωt-1 is the information set in period t-1; α, β, A1, B1, C1, D1 are coefficients

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3. Methodology

3.2 Intraday time series regressions of return on order imbalance

• According to Chordia and Subrahmanyam (2004), traders tend to split their orders

over time to minimize the price impact of trades.

• To figure out whether the previous order imbalances can also have influence on c

urrent stock returns, and how long do they last for, we apply CS (2004) empirical

regression models of daily data to our intraday data.

• Conditional contemporaneous OI-return regression

• Unconditional lagged OI-return regression

Where Rt is the stock return in period t, defined as ln(Pt/Pt-1)

OIt is the current order imbalance in period t

OIt-i ,i=1,2,3,4,5 are lagged order imbalance at time t-1, t-2, t-3, t-4, t-5

βi ,i=1,2,3,4,5 are the coefficients of the impact of OI on returns

εt is the residual of stock return in period t

ttttttt OIOIOIOIOIR 453423121

…..(3)

1 2 3 4 51 2 3 4 5t t t t t t tOI OI OI OI OIR .….(4)

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3. Methodology

3.3 Dynamic causal relations between return and order imbalance

• To clarify the dynamic lead-lag relation to explain the abnormal return from our tradi

ng strategy, we employ Chen and Wu (1999) procedure to explore the dynamic ca

usal relations between return and order imbalances .

• According to CW(1999), there are 4 dynamic relations between two random variable

s, including independency (x1 Λ x2), contemporaneous (x1＜－＞ x2), unidirectional

(x1 =＞ x2) and feedback (x1＜ =＞ x2) relations (Appendix 1).

• We first construct a VAR model to describe the temporal behaviors of return and ord

er imbalance, and then use a systematic multiple hypotheses testing method for

identifying the dynamic relations between them (Appendix 2).

The procedure consists of four test sequences, which implement a total of six pair-w

ise hypotheses tests (Appendix 3).

• Multiple hypotheses testing method can avoid the potential bias induced by restricti

ng the causal relation to a traditional single alternative hypothesis. For exam

ple, to conclude that x1＜－＞ x2 , we need to establish that x1＜≠ x2 as well as x1≠

＞ x2 and also to reject x1 Λ x2 .

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4.1~4.3 Results of relations between OI, volatility and stock return of top losers

4.4 Results of our order imbalance truncated trading strategy

4.5 Results of return-order imbalance dynamic causality relation

4.1 Dynamic relations between order imbalances and returns

• In our intraday study with time varying GARCH(1,1) model to examine order im

balance-return relation of 61 top losers, the mean of OI coefficients is 7.4E-

05. It implies that increasing one negative order will lead the stock return to m

oving down 7.4×10-5%.

• About 70% order imbalances have a significantly positive relation with stock r

eturns. This result is consistent with the daily results of previous studies.

The significance test of the OI coefficients (in percentage)

Confidence Level

Positive and significant

Negative and significant

90% 72.1 % 4.9 %

95% 68.8 % 4.9 %

99% 68.8 % 4.9 %

….. (1)

t t tR OI

(0, )1 tN ht t

21 1 1 1 1t t th A B h C

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4.2 Dynamic relations between order imbalances and volatility

• It is intuitively that higher order imbalances cause higher volatility, since higher ord

er imbalances could signal private information and lead market makers to adjust in

ventory by revising quotes, thereby inducing price fluctuations.

We expect to see a significantly positive relation between order imbalances and v

olatility.

• However, our result is mixed. About 40% of our sample have a significantly positi

ve relation between volatility and order imbalances, namely a negative coefficient

on OI, while other 40% have a significantly negative relation.

The significance test of the OI coefficients(in percentage)

Confidence Level

Positive and significant

Negative and significant

90% 42.6 % 42.6 %

95% 41.0 % 41.0 %

99% 39.3 % 39.3 %

….. (2)

t tR

(0, )1 tN ht t

21 1 1 1 1 1t t t th A B h C DOI

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4.2 Dynamic relations between order imbalances and volatility (cont.)

• Besides the inventory adjustment story, we give two additional reasons why high

seller-initiated orders of top losers are accompanied by large volatility.

(a) The investors behavior: According to Kahneman and Tversky (1979), investo

rs tend to hold their stocks when stock price quotations going up, but tend to

overreact and sell them in panic, such as observing a large seller-initiated or

der.

(b) The leverage effect: According to Christie (1982), a fall in stock price increas

es the degree of leverage in firm’s capital structure, thereby inducing an incr

ease in stock volatility.

• One potential explanation for the negative OI-volatility relation of other 40% top l

osers: Since market makers also have the responsibility to control and maintain t

he stability of stock markets, high seller-initiated orders could be accompanied by

small volatility.

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4.3 Intraday time-series regressions

4.3.1 Conditional contemporaneous OI-return relation

• Most of the contemporaneous OI have positive influences on current returns, an

d above 80% of lagged-one order imbalances have negative effect on current re

turns in our intraday study. This result is consistent with Chordia and Subrahmany

am (2004) proposed in the daily data.

• However, the intraday lagged two to four order imbalances don’t have such signific

ant influences on current stock returns as CS(2004) daily study.

Time-series regression of return on OI- lagged 0 through lagged 4

Confidence Level Intercept (OI) t (OI) t-1 (OI) t-2 (OI) t-3 (OI) t-4

Positive and significant (Percent)

90% 1.6 % 90.2 % 1.6 % 3.3 % 3.3 % 8.2 %

95% 1.6 % 82.0% 1.6 % 0.0 % 3.3 % 4.9 %

99% 0.0 % 80.3 % 1.6 % 0.0 % 1.6 % 1.6 %

Negative and significant(Percent)

90% 8.2 % 0.0 % 88.5 % 8.2 % 8.2 % 8.2 %

95% 6.6 % 0.0 % 85.3 % 4.9 % 3.3 % 4.9 %

99% 1.6 % 0.0 % 80.3 % 1.6 % 3.3 % 1.6 %

ttttttt OIOIOIOIOIR 453423121

…..(3)

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4.3.1 Conditional contemporaneous OI-return relation (cont.)

• The positive contemporaneous relation between order imbalance and return is

consistent with both inventory and asymmetry information effects of price formation.

• Both in the GARCH (1,1) model and the time-series regression model, we obtain

the same significant contemporaneous effect.

The significance is even higher in the time-series regression model than the 70% in

the GARCH(1,1) relation. The higher percentage shows that the longer time span

has the effect to restore the hidden information.

• The negative relation between lagged one imbalance and current return is

because auto-correlated imbalances cause the effects of the lagged one imbalance

to be reversed in the current return.

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4.3.2 Unconditional lagged OI-return relation

• Only lagged-one order imbalances have significant effect on current stock

returns and the relationship between these two variables is negative.

• This result is different from Chordia and Subrahmanyam (2004) in the daily study.

They argue that about 77% of the coefficients on first lag imbalances are

significantly positive. Their result indicates that the price movement continues

while ours indicates that the price pressure reverses in the lagged-one period.

Time-series regression of return on OI- lagged 1 through lagged 5

Confidence Level Intercept (OI) t-1 (OI) t-2 (OI) t-3 (OI) t-4 (OI) t-5

Positive and significant (Percent)

90% 1.6 % 1.6 % 3.2 % 4.8 % 7.9 % 3.2 %

95% 1.6 % 1.6 % 0.0 % 1.6 % 7.9 % 3.2 %

99% 0.0 % 1.6 % 0.0 % 1.6 % 4.8 % 3.2 %

Negative and significant(Percent)

90% 27.9 % 82.5 % 1.6 % 3.2 % 4.8 % 1.6 %

95% 18.0 % 79.4 % 1.6 % 3.2 % 1.6 % 0.0 %

99% 6.6 % 77.1 % 1.6 % 0.0 % 0.0 % 0.0 %

1 2 3 4 51 2 3 4 5t t t t t t tOI OI OI OI OIR …(4)

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4.3.2 Unconditional lagged OI-return relation (cont.)

• We attribute this situation to the reason as follow.

When market makers observe a huge negative order, they would be expected to

respond by keeping the quote down. However, if bid-ask price is pressed lower,

traders have a good opportunity to buy stocks with a lower price and market

makers’ inventories will be reduced. Once market makers were cornered,

discretionary traders won and the stock price continued to go up.

This is the unique characteristic of speculative stocks. Our sample stocks are

top losers and they are speculative while the data which Chordia and

Subrahmanyam (2004) employed include all individual stocks.

• Furthermore, our empirical result of top losers is more consistent with the findings

of Chordia and Subrahmanyam (2002) in the aggregate market. They report

that there is evidence that large-negative-imbalance, large-negative-return

days are accompanied by strong reversals in S&P 500.

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4.4 Trading strategy based on return-order imbalance relation

• We develop an order imbalance truncated trading strategy based upon our e

mpirical findings.

• Since our samples are daily top losers, our strategy is to short sell when the fir

st negative order imbalance appeared and buy back when the order imbalances

become buyer-initiated.

• All actions ignore the transaction costs and taxes.

• We trade the above strategy based on four scenarios: no truncation, 50%, 90%

and 99% truncations of smaller order imbalances.

• Then, we compare the the average returns of our trading strategies, either by tra

ding price or by bid-ask price basis, with the average return of our sample stocks

(benchmark).

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4.4 Trading strategy based on return-order imbalance relation (cont.)

• The average returns of our trading strategy by trading price basis with no, 50%, 90

%, and 99% truncations are -77.4%, -26.2%, -10.6% and 1.1%, respectively.

• Although the first three strategies have negative returns and even the first two are

worse than the original average return, we observe the trend that when trimming

the smaller order imbalances, the strategy yield a higher average return.

• When trimming off the 99% smaller order imbalances, the average return even bec

omes positive. The OI truncated trading strategy is a successful strategy that tur

ns daily top losers, with an average return of -18.8%, to a positive return.

• The paired comparisons test show that the 99%-truncated trading strategy earned

a significant return than no-truncated one.

Original(Benchmark)

No 50% 90% 99% truncated truncated truncated truncated

Average return-18.8%

By trading price basis

-77.4% -26.2% -10.6% 1.1%

Average return-18.8%

By bid-ask price basis

-167.9% -35.3% -12.4% 2.6%

Average return of all sample stocks from speculative trading strategy

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4.5 Return-order imbalance causality relation in explaining the successful trading strategy

• In order to explore why our order imbalance truncated trading strategy earns a signif

icant return, we further investigate the dynamic causality relation between return an

d order imbalance.

• From the nested causality empirical results, we find that in most case, order imbala

nce is a good indicator for predicting future returns.

• Order imbalance is a better indicator for price discovery in small firm size quartile.

Dynamic nested causality relations between returns and order imbalances (in percentage)

X1 represents stock returns; X2 represents order imbalances

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5. Conclusions

• This paper uses the specific speculative stocks, top losers, to analyze

the dynamic relations between order imbalance and stock returns, and

based on their relations to show that there exists a valuable trading

strategy.

• Our successful trading strategy relies on truncations of smaller order

imbalances. This implies that trading size provides more valuable

information on making profits from individual stocks than trading

number.

• The dynamic causality relationship between return and order imbalance

shows that order imbalance is a unidirectional indicator for predicting

future returns in most case, and is valuable information to make

profits.

Thanks for your attention.

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Appendix 1

Source: Chen and Wu (1999), Journal of Empirical Finance

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Appendix 2

Hypotheses on the dynamic relations of a bivariate system


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Appendix 3

Test flow chart of a multiple hypothesis testing procedure


1 dynamic relations between order imbalance, volatility and return of top losers dr. yong-chern su,...

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