1. 1 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

2. 2 Agenda 1. Introduction 1.1 Motivation and Purpose 1.2 Main findings 1.3 Contributions 2. Data 3. Methodology 4. Empirical Results 5. Conclusion

3. 3 1. Introduction 1.1 Motivation and Purpose Motivation Investors are always seeking useful indicators to predict the movements of their holding 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. Order imbalances can reveal some private information behind the market markers and the big-deal traders. Chordia, Roll and Subrahmanyam (2005) document that imbalances predict future returns over very short intervals, no more than thirty minutes. However, only specialists (market makers) know order imbalances. In the real world, there is a channel such as TradeStation ® to offer the automating rule-based trading based on the real-time volume signal, and hence we want to know whether no-informed investors can use order imbalance information to trade and earn abnormal profits even without private information.

4. 4 1. Introduction 1.1 Motivation and Purpose 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.

5. 5 1. Introduction 1.2 Main findings First, we find that both in our time varying GARCH (1,1) model and the intraday time-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 negative order imbalance appeared and buy back when the order imbalances become buyer-initiated. The empirical results show that if we don’t truncate the smaller order imbalances, we can’t find abnormal returns. However, if we sift our data from trading volume, that is above 99% volume, we document a significant profit based on our trading strategy. Third, we follow a complete procedure to examine the causality relationship between return and order imbalance to explain our significant profit, and find that in the most case, order imbalance is a unidirectional indicator for predicting future returns. Especially, order imbalance is a good indicator for price discovery in small firm size quartile.

6. 6 1. Introduction 1.3 Contributions We contribute to the literature at three aspects. First, the existing articles use a comprehensive cross-sectional sample of exchanges stocks to document that order imbalances have a significant relationship with stock returns. Ours is the first study to use the specific speculative stocks, top losers, to analyze the dynamic relations between trading activities and stock returns, and based on the relations to show that there exists a valuable trading strategy. Second, our success in trading strategy relies on truncations of smaller order imbalances. This implies that trading size offers more valuable information on making profits than trading number, which is consistent with the findings of Chan and Fong (2000). They show that the order imbalance in large trade size categories affects the return more than in smaller size categories. Third,by examining the dynamic causality relationship between return and order imbalance, we find that in most case, order imbalance is a unidirectional indicator for predicting 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 their predictive ability in no more than thirty minutes, we document a significant profit based on our trading strategy.

7. 7 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. 1 st, 2005 to Dec. 31 st, 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%.

8. 8 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.

9. 9 3. Methodology We use two models: GARCH(1,1) and time-series regression models to examine the 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 arguments of contemporaneous OI-return relation (Chordia and Subrahmanyam, 2004) and contemporaneous OI-volatility relation (Chan and Fong, 2000) separately with GARCH(1,1) model, which has been proven to successful model for capturing time-varying volatility properties of individual stock returns. We use an OI coefficient in the conditional mean equation and conditional volatility equation separately to fit our intraday data. ….. (1) ….. (2) Where R t is the return in period t, defined as ln(P t /P t-1 ); OI t is the explanatory variable; ε t is the residual of the stock return in period t; h t is the conditional variance in period t; Ω t-1 is the information set in period t-1; α, β, A 1, B 1, C 1, D 1 are coefficients

10. 10 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 current 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 R t is the stock return in period t, defined as ln(P t /P t-1 ) OI t is the current order imbalance in period t OI t-i,i=1,2,3,4,5 are lagged order imbalance at time t-1, t-2, t-3, t-4, t-5 β i,i=1,2,3,4,5 are the coefficients of the impact of OI on returns ε t is the residual of stock return in period t …..(3).….(4)

11. 11 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 trading strategy, we employ Chen and Wu (1999) procedure to explore the dynamic causal relations between return and order imbalances. According to CW(1999), there are 4 dynamic relations between two random variables, including independency (x 1 Λ x 2 ), contemporaneous (x 1 ＜－＞ x 2 ), unidirectional (x 1 = ＞ x 2 ) and feedback (x 1 ＜ = ＞ x 2 ) relations (Appendix 1). (Appendix 1 We first construct a VAR model to describe the temporal behaviors of return and order imbalance, and then use a systematic multiple hypotheses testing method for identifying the dynamic relations between them (Appendix 2).Appendix 2 The procedure consists of four test sequences, which implement a total of six pair- wise hypotheses tests (Appendix 3).Appendix 3 Multiple hypotheses testing method can avoid the potential bias induced by restricting the causal relation to a traditional single alternative hypothesis. For example, to conclude that x 1 ＜－＞ x 2, we need to establish that x 1 ＜ ≠x 2 as well as x 1 ≠ ＞ x 2 and also to reject x 1 Λ x 2.

12. 12 4. Empirical Results 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 imbalance-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 moving down 7.4×10 -5 %. About 70% order imbalances have a significantly positive relation with stock returns. 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)

13. 13 4. Empirical Results 4.2 Dynamic relations between order imbalances and volatility It is intuitively that higher order imbalances cause higher volatility, since higher order imbalances could signal private information and lead market makers to adjust inventory by revising quotes, thereby inducing price fluctuations. We expect to see a significantly positive relation between order imbalances and volatility. However, our result is mixed. About 40% of our sample have a significantly positive 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 % 95%41.0 % 99%39.3 % ….. (2)

14. 14 4. Empirical Results 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), investors 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 order. (b) The leverage effect: According to Christie (1982), a fall in stock price increases the degree of leverage in firm’s capital structure, thereby inducing an increase in stock volatility. One potential explanation for the negative OI-volatility relation of other 40% top losers: Since market makers also have the responsibility to control and maintain the stability of stock markets, high seller-initiated orders could be accompanied by small volatility.

15. 15 4. Empirical Results 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, and above 80% of lagged-one order imbalances have negative effect on current returns in our intraday study. This result is consistent with Chordia and Subrahmanyam (2004) proposed in the daily data. However, the intraday lagged two to four order imbalances don’t have such significant 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 % 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 % Negative and significant (Percent) 90%8.2 % 0.0 % 88.5 %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 % …..(3)

16. 16 4. Empirical Results 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.

17. 17 4. Empirical Results 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 % 3.2 %4.8 %7.9 %3.2 % 95%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 % …(4)

18. 18 4. Empirical Results 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.

19. 19 4. Empirical Results 4.4 Trading strategy based on return-order imbalance relation We develop an order imbalance truncated trading strategy based upon our empirical findings. Since our samples are daily top losers, our strategy is to short sell when the first 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 trading price or by bid-ask price basis, with the average return of our sample stocks (benchmark).

20. 20 4. Empirical Results 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 becomes positive. The OI truncated trading strategy is a successful strategy that turns 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

21. 21 4. Empirical Results 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 significant return, we further investigate the dynamic causality relation between return and order imbalance. From the nested causality empirical results, we find that in most case, order imbalance 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) X 1 represents stock returns; X 2 represents order imbalances

22. 22 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.

23. 23 Appendix 1 Source: Chen and Wu (1999), Journal of Empirical Finance

24. 24 Appendix 2 Hypotheses on the dynamic relations of a bivariate system Source: Chen and Wu (1999), Journal of Empirical Finance

25. 25 Appendix 3 Test flow chart of a multiple hypothesis testing procedure Source: Chen and Wu (1999), Journal of Empirical Finance