Effects of order flow imbalance on short-horizon contrarian strategies in the Australian equity market

Pacific-Basin Finance Journal 14 (2006) 291 – 310 www.elsevier.com/locate/pacfin

Effects of order flow imbalance on short-horizon contrarian strategies in the Australian equity market Kevin Lo, Richard Coggins * Discipline of Finance, School of Business, Faculty of Economics and Business, University of Sydney, NSW 2006, Australia Received 23 February 2004; accepted 29 September 2005 Available online 27 January 2006

Abstract We use Lo and MacKinlay’s [Lo, A.W., MacKinlay, C., 1990. When are contrarian profits due to stock market overreaction? The Review of Financial Studies 3, 175–205] contrarian portfolio approach to examine the profitability of short-horizon contrarian strategies in the context of the Australian Stock Exchange. The results show that simple contrarian strategies lead to small but still statistically significant profits when applied to daily and intra-day portfolio formation. However, the profits are not sufficient to cover transaction costs for institutional investors. The source of contrarian profits is also analyzed leading to the conclusion that stock market overreaction is found to be the primary source of contrarian profits. We also examine the relation between the degree of return reversal and order flow activity after abnormal price changes. We find that the degree of return reversal is positively related to the level of order flow imbalance. Larger profits are generated from order flow based contrarian strategies when the order flow imbalances are high. D 2005 Elsevier B.V. All rights reserved. JEL classification: G10; G14 Keywords: Contrarian strategies; Order flow; Market overreaction; Return autocorrelation

1. Introduction Some empirical studies suggest price movements in the stock market are to some extent predictable based on past price history. This view is largely based on empirical evidence that a contrarian strategy of buying previous losers and selling previous winners generates significant profits. For example, Lehmann (1990) has documented evidence of statistically significant * Corresponding author. Tel.: +61 2 93514768; fax: +61 2 93516461. E-mail address: [email protected] (R. Coggins). 0927-538X/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.pacfin.2005.09.002

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profits using contrarian strategies over weekly returns, even after corrections for plausible transaction costs.1 However, the interpretation of the sources of contrarian profits have been heavily debated in the finance literature. Some research such as Conrad et al. (1997) and Boudoukh et al. (1994) argue that the majority of contrarian profits are due to market microstructure biases like nonsynchronous trading and bid–ask spreads. They find contrarian profits would disappear once these errors are accounted for. Another stream of research hypothesizes contrarian profits come from stock market overreaction. For example, Jegadeesh and Titman (1995a) suggest that investors overreact to information, and consequently a subsequent correction generates negative correlation in stock returns. Contrarian strategies could then be profitable because in the presence of negative autocorrelation, current losers would become future winners and current winners then become losers. The suggestion that stock market overreaction is the only source of contrarian profits has been questioned by Lo and MacKinlay (1990). They have proposed return forecastability across securities is another important source of contrarian profits. They have argued that even when there is no stock market overreaction and an individual security’s returns are serially independent, a contrarian strategy can still be profitable simply because of price lead–lag effects among securities. The first objective of this paper is to adopt Lo and MacKinlay’s (1990) contrarian portfolio methodology and to investigate both the profitability and the sources of contrarian strategies on daily and hourly horizons in the context of the Australian market. With the majority of prior research based on the US market, there are relatively few papers that have examined contrarian strategies in a non-US context.2 Prior research examining the profitability of contrarian strategies over time scales shorter than weekly returns is also relatively scarce. The second objective is to investigate the role of trading activity and liquidity in explaining return reversals and overreaction. Some researchers have argued that return reversals and overreaction are results of irrational trading behaviour. Another possibility is that as the market lacks sufficient liquidity to dissipate unexpected price pressures, this results in short-term return reversals. We analyze the relation between return reversals and order flow imbalance, which is a measure of liquidity pressure and trading activity first proposed by Chordia et al. (2002), by examining order imbalances following large price changes. Trading and liquidity measures can also convey information that cannot be deduced from share prices. Traders are generally divided into informed and uninformed traders in the market microstructure literature. Since informed traders would want to trade larger quantities when they have valuable information, uninformed traders would interpret excess liquidity demand as an indication of private information. A number of authors have studied whether trading information can help explain stock returns. For example, Blume et al. (1994) show that bvolume provides information on information quality that cannot be deduced from the price statistic.Q Conrad et al. (1994) find price reversals for heavily traded securities and price continuation for low volume 1

Other papers have also found contrarian strategies are profitable over longer time scales. Jegadeesh (1990) has examined monthly returns of individual stocks and found bthe negative first-order serial correlation in monthly stock returns is highly significantQ, while Conrad and Kaul (1998) have further shown that contrarian strategies are apparently profitable over even longer terms (3 to 5 years). 2 For example, Hameed and Ting (2000) have investigated the short-term predictability of stock returns on the Malaysian stock market.

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293

securities, suggesting there is a significant relationship between lagged volume and the current returns of securities. Campbell et al. (1993) also find that bprice changes accompanied by high volume will tend to be reversedQ. The organization of this paper is as follows. Section 2 describes the contrarian portfolio strategy and presents empirical results addressing contrarian profits. Section 3 analyzes the relationship between return reversal and order flow imbalance by conditioning abnormally large price changes on order flow imbalance. The profitability of order flow based contrarian strategies is discussed in Section 4. Section 5 concludes the paper. 2. The contrarian portfolio strategy 2.1. Lo and MacKinlay’s (1990) methodology We use a simple contrarian trading strategy formulated in a similar manner to Lo and MacKinlay (1990). Generally, a contrarian strategy involves buying previous losers and selling previous winners. Such a contrarian strategy can take advantage of any stock market overreaction and lead–lag relationships that exist among the stock returns. Lead–lag relationships exist among stock returns because some securities react more quickly to information than other securities. For example, if the returns of security A lead the returns of security B, then a contrarian strategy can generate a profit from buying B whenever there is a price increase in A and selling B following a price fall in A. The portfolio is constructed with investment weight x it in each security i at time t, given by xit ¼ 

1 ðritk  rmtk Þ N

ð1Þ

where r it is the turn on the ith security at time t and r mt represents the return on the equally weighted market index, k is the number of lags and N is the number of securities. The investment weight in each security is negatively proportional to each security’s past return less the return on the market index. For example, a security will have a greater positive weighting in the portfolio in period t if it has under-performed compared to the market index, and vice versa. By construction, this portfolio is an arbitrage portfolio since the total investment at any given time is zero. In addition, the long or short investment position at any time t is given by: It ðk Þ ¼

N 1 X jxit ðk Þj 2 i¼1

ð2Þ

and the profit p t (k) from this strategy is pt ðk Þ ¼

N X

xit ðk Þrit :

ð3Þ

i¼1

Following Lehmann (1990) and Conrad et al. (1997), we can also calculate the total transaction costs incurred at any time t as T Ct ðk Þ ¼ c 

N X i¼1

jxit  xitk j

ð4Þ

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where c is the transaction cost per dollar transaction. |x it  x itk | represents the transactions required to change from the original investment weight x itk to the new weight x it for security i at time t. 2.1.1. Decomposition of contrarian profits According to Lo and MacKinlay (1990), the expected profits can be easily decomposed into three components by expressing the expected profits as E[p t (k)] = C k + O k  r l2: P 1. Cross-serial covariance of returns ðCk Þ ¼ cov½rmtk ; rmt   N12 Ni¼1 cov½ritk ; rit  P N N 1 2. Serial autocovariances of returns  ðOk Þ¼  P i¼1 cov½ritk ; rit  N2 N 2 2 1 3. Dispersion of expected returns rl ¼ N ð l i  lm Þ . i¼1 Therefore, the expected profits of the contrarian strategy can be expressed as: ( ) ( ) N N 1 X N 1 X E½pt ðk Þ ¼ cov½rmtk ; rmt   2 cov½ritk ; rit  þ  cov½ritk ; rit  N i¼1 N 2 i¼1 ( ) N 1 X 2  ð l  lm Þ ð5Þ N i¼1 i This decomposition allows the sources of contrarian profits to be determined, i.e. what percentages of contrarian profits are due to stock market overreaction or lead–lag relationships among securities. The cross-serial covariances (C k ) measure the contribution of lead–lag structure to contrarian profits. The serial autocovariances (O k ) measure the contribution of overreaction, and represent the profit due to the variation in the mean returns of individual securities (l i ) compared to the mean returns of the market index (l m ). Eq. (5) also shows the profitability of the contrarian strategy is consistent with positive autocorrelation in portfolio returns and negative correlation in individual security returns. Positive cross-autocovariances between securities implies C k is positive, and negative serial autocorrelation for individual securities implies O k is also positive. The major limitation of Eq. (5) is the assumption of covariance-stationarity. To relax this assumption, we follow Lo and MacKinlay’s (1990) sampling theory for C k and O k whereby the assumption is replaced with weaker assumptions to allow for heterogeneity and serial dependence. The estimators Cˆ k and Oˆ k are given by

ˆC k ¼

T T X X 1 1 Ckt and ˆO k ¼ Okt T  k t¼kþ1 T  k t¼kþ1

ð6Þ

where T is the total number of time periods and Ckt ¼ rmtk rmt  l2m 

Okt ¼ 

N   1 X ritk rit  l2i 2 N i¼1

N   N 1 X ritk rit  l2i : 2 N i¼1

ð7Þ

ð8Þ

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2.2. Sample data The data for this study comprise the daily and intra-day price at 1-h intervals of the top 200 stocks on the ASX from 2000 to 2002.3 From the returns of each security, a contrarian trading strategy was constructed based on Eq. (1).4 An equally weighted market index was constructed from the entire set of securities. 2.2.1. Minimizing measurement errors Microstructure effects such as bid–ask spread and nonsynchronous trading may cause the profits of a contrarian strategy to be biased upwards, and in turn may induce negative autocovariance of stock returns. Conrad et al. (1997) show that by comparing results using transaction returns and bid returns, contrarian profits are largely generated by bid–ask bounce and the profits disappear once these costs are controlled for. In an attempt to minimize the effect of bid–ask bounce, the mid-spread price between bid and ask is used for this analysis.5 Infrequent trading is another important source of measurement errors. According to Miller et al. (1994), there are two forms of infrequent trading: nonsynchronous trading and nontrading. Nonsynchronous trading occurs when stocks trade every consecutive interval, but not necessarily at the close of each interval. Treating nonsynchronous data as if they are observed at the same time can create false autocorrelation. As a result, apparent lead–lag effects may exist among securities even though this is purely an artifact of the manner in which returns are measured. In contrast, nontrading occurs when stocks do not trade in every consecutive interval. For short trading intervals such as daily and hourly, the problem of nonsynchronous trading is minimal. However, as the trading interval shrinks nonsynchronous trading gives way to the problem of nontrading. The effect of nontrading and nonsynchronous trading can be substantially minimized by concentrating the analysis on the large-capitalization and most actively traded securities. The probability of nontrading in an hourly interval for the largest 100 securities from the ASX is 0.0153. The probability increases to 0.0527 if the subset of securities is extended to the top 200 securities. As more small-sized securities are included, the results would be affected by nontrading to a greater degree. Therefore, this paper chooses the top 200 securities that are presented on the ASX from 2000 to 2002. These 200 stocks constitute approximately 90% of total market capitalization on the ASX. However, there is a downside to focusing the analysis on the largest securities. By doing so, only a relatively small subset of the securities listed on the ASX was examined. Therefore, the possibility of finding evidence of contrarian profits due to lead–lag effects between large and small securities is diminished.

3 We select the 200 largest stocks based on market capitalization that were listed on the ASX for the entire sampling period. Stocks are then divided into four quartiles. The quartiles are allocated by sorting the stocks based on market capitalization at the end of the sampling period. 4 Simple return series were computed from the price series of each security. For intra-day analysis, overnight returns were eliminated to remove any overnight effects. 5 Conrad et al. (1994) and Jegadeesh and Titman (1995b) have shown that using returns based on either the bid or the ask quotes (or any combination of the two) will contain no measurement errors due to bid–ask bounce.

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2.3. Empirical results on basic contrarian strategies 2.3.1. Autocorrelation results This section investigates both the individual security’s and the portfolio’s autocorrelation. Contrarian strategies can be profitable due to overreaction if individual securities are negatively autocorrelated. Lo and MacKinlay (1990) further suggests that the profitability of contrarian strategies can also be attributed to forecastability across securities. Their perspective has been based on the empirical evidence that when securities are grouped together to form a portfolio, the portfolio returns tend to be positively autocorrelated. Since the autocovariance of a portfolio can be written as the sum of the self-autocovariances and cross-autocovariances of the securities, if the self-autocovariances of individual securities are generally weakly negative and the portfolio autocovariance is positive, then the cross-autocovariances must be positive and larger in magnitude than the sum of the negative autocovariances. This evidence implies securities in a portfolio may be positively cross-autocorrelated. For this reason, contrarian strategies are profitable if there are strong cross-autocorrelations among securities in the portfolio. Table 1 shows the cross-sectional average of the first five autocorrelation coefficients of hourly and daily returns on individual securities, respectively. The lag 1 autocorrelation coefficients are weakly negative for both hourly and daily returns. Negative autocorrelation might be an indication of stock market overreaction to an individual security’s return. Higher lag autocorrelation coefficients, however, are not statistically significant at the 95% confidence level. Table 2 reports the first five lags of autocorrelation of hourly and daily equally weighted portfolio returns, respectively. The autocorrelation coefficients at the first and higher orders are Table 1 Cross-sectional average of autocorrelation coefficients on individual securities Sample

Lag 1

Lag 2

Lag 3

Lag 4

Lag 5

(% significant)

(% significant)

(% significant)

(% significant)

(% significant)

Panel A: Hourly All 200 stocks Largest quartile Second quartile Third quartile Smallest quartile

returns 0.0595 0.0047 0.0713 0.0804 0.0816

(76.00%) (62.00%) (76.00%) (82.00%) (84.00%)

0.0099 0.0084 0.0101 0.0203 0.0178

(33.00%) 0.0000 (26.50%) 0.0005 (28.00%) 0.0137 (20.00%) 0.0054 (30.00%) 0.0011 (26.00%) 0.0007 (36.00%) 0.0093 (30.00%) 0.0045 (38.00%) 0.0033 (30.00%) 0.0020

Panel B: Daily returns All 200 stocks 0.0107 Largest quartile 0.0234 Second quartile 0.0152 Third quartile 0.0309 Smallest quartile 0.0199

(43.50%) (40.00%) (48.00%) (38.00%) (48.00%)

0.0214 0.0432 0.0272 0.0108 0.0044

(17.00%) (26.00%) (14.00%) (14.00%) (14.00%)

0.0125 0.0147 0.0162 0.0142 0.0050

(12.00%) (14.00%) (10.00%) (8.00%) (16.00%)

0.0080 0.0288 0.0043 0.0016 0.0005

(20.50%) 0.0047 (10.00%) 0.0104 (20.00%) 0.0043 (26.00%) 0.0050 (26.00%) 0.0008

(21.00%) (22.00%) (12.00%) (18.00%) (32.00%)

(10.50%) 0.0055 (7.50%) (12.00%) 0.0051 (2.00%) (10.00%) 0.0075 (8.00%) (4.00%) 0.0100 (10.00%) (16.00%) 0.0096 (10.00%)

Panel A reports the autocorrelation coefficients for intra-day hourly returns. Panel B reports the autocorrelation coefficients for daily returns. Lag i represents the average ith order autocorrelation coefficients of returns on individual securities. The significance of each autocorrelation coefficient is tested by calculating the p-value of the null-hypothesis of no correlation for each individual security. If the correlation coefficient has a p-value of less than 0.05, it is considered significant. The percentage of all securities that have significant autocorrelation coefficients is reported inside the brackets (% of significant securities).

Portfolio

Mean return

Standard deviation

Lag 1

Lag 2

Lag 3

Lag 4

Lag 5

( p-value)

( p-value)

( p-value)

( p-value)

( p-value)

Panel A: Hourly returns All 200 stocks 0.0000 1–50 stocks 0.0001 51–100 stocks 0.0001 101–150 stocks 0.0001 151–200 stocks 0.0001

0.0012 0.0018 0.0015 0.0017 0.0019

0.1089 0.0371 0.0472 0.0178 0.0148

(0.0000)* (0.0125)* (0.0015)* (0.2304) (0.3200)

0.0624 0.0019 0.0088 0.0241 0.0335

(0.0000)* (0.8964) (0.5540) (0.1053) (0.0243)*

0.0820 0.0393 0.0402 0.0425 0.0443

(0.0000)* (0.0081)* (0.0068)* (0.0042)* (0.0029)*

0.0246 0.0033 0.0170 0.0462 0.0056

(0.0984) (0.8252) (0.2541) (0.0019)* (0.7087)

0.0283 0.0082 0.0241 0.0264 0.0190

(0.0573) (0.5793) (0.1056) (0.0753) (0.2007)

Panel B: Daily returns All 200 stocks 0.0004 1–50 stocks 0.0003 51–100 stocks 0.0005 101–150 stocks 0.0005 151–200 stocks 0.0003

0.0054 0.0062 0.0057 0.0063 0.0072

0.0496 0.0231 0.0698 0.0802 0.0555

(0.1736) (0.5262) (0.0555) (0.0277)* (0.1281)

0.0687 0.0283 0.0408 0.0940 0.0619

(0.0593) (0.4374) (0.2639) (0.0097)* (0.0897)

0.1370 0.0687 0.0601 0.0977 0.1157

(0.0002)* (0.0597) (0.0994) (0.0073)* (0.0015)*

0.0908 0.0118 0.0494 0.1430 0.1066

(0.0128)* (0.7477) (0.1760) (0.0001)* (0.0035)*

0.0984 0.0116 0.0626 0.1490 0.0983

(0.0070)* (0.7517) (0.0869) (0.0001)* (0.0070)*

Panel A reports the autocorrelation coefficients for intra-day hourly returns. Panel B reports the autocorrelation coefficients for daily returns. Lag i represents the ith order autocorrelation coefficients of returns. The p-value tests the hypothesis of no correlation, with an asterisk (*) indicating that the autocorrelation coefficients are statistically significant at a 95% confidence level.

K. Lo, R. Coggins / Pacific-Basin Finance Journal 14 (2006) 291–310

Table 2 Average of autocorrelation coefficients on an equally weighted portfolio

297

298

Table 3 Analysis of the profitability of the contrarian strategy applied to intra-day hourly returns for the sample of top 200 ASX stocks k

Cka

(z-stat.)

Oka

(z-stat.)

r l2

a

E[p t (k)]a

(z-stat.)

I(k)a

%C k

%O k

%r l2

1–200

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

0.0018 0.0009 0.0011 0.0003 0.0004 0.0015 0.0000 0.0012 0.0001 0.0002 0.0019 0.0003 0.0010 0.0004 0.0005 0.0021 0.0010 0.0013 0.0013 0.0006 0.0023 0.0016 0.0016 0.0003 0.0005

(270.69)* (181.28)* (298.87)* (82.04)* (88.68)* (197.74)* (0.58) (174.63)* (22.44)* (22.75)* (272.67)* (63.27)* (201.67)* (65.73)* (84.06)* (190.09)* (116.04)* (161.68)* (171.75)* (87.75)* (119.78)* (106.09)* (137.06)* (27.50)* (48.90)*

0.0557 0.0099 0.0005 0.0011 0.0057 0.0137 0.0029 0.0053 0.0018 0.0035 0.0371 0.0062 0.0002 0.0000 0.0041 0.0799 0.0173 0.0049 0.0006 0.0050 0.0889 0.0182 0.0016 0.0032 0.0100

(696.87)* (328.18)* (16.99)* (41.62)* (209.47)* (57.22)* (163.87)* (309.77)* (117.45)* (191.69)* (661.50)* (213.64)* (4.96)* (1.26) (151.28)* (578.46)* (222.23)* (69.47)* (8.45)* (88.63)* (744.47)* (217.77)* (20.34)* (43.05)* (124.94)*

0.0006 0.0006 0.0006 0.0006 0.0006 0.0002 0.0002 0.0002 0.0002 0.0002 0.0004 0.0004 0.0004 0.0004 0.0004 0.0006 0.0006 0.0006 0.0006 0.0006 0.0008 0.0008 0.0008 0.0008 0.0008

0.0570 0.0103 0.0001 0.0014 0.0059 0.0150 0.0031 0.0043 0.0022 0.0035 0.0386 0.0061 0.0007 0.0001 0.0041 0.0814 0.0178 0.0055 0.0013 0.0049 0.0904 0.0190 0.0009 0.0043 0.0103

(713.1)* (342.22)* (4.04)* (50.36)* (219.52)* (62.79)* (186.44)* (285.70)* (151.19)* (223.89)* (666.05)* (216.04)* (20.91)* (2.43) (154.83)* (584.11)* (225.78)* (77.96)* (19.06)* (89.25)* (770.24)* (228.65)* (11.16)* (58.95)* (130.62)*

22.9880 22.9890 22.9890 22.9910 22.9930 17.7190 17.7210 17.7220 17.7240 17.7250 20.9610 20.9620 20.9610 20.9640 20.9660 25.4210 25.4190 25.4190 25.4220 25.4240 29.7180 29.7220 29.7210 29.7240 29.7260

3.17 9.03 1007.09 24.97 6.21 9.90 0.13 26.99 6.60 5.55 4.85 5.47 139.33 609.82 11.90 2.61 5.71 22.93 101.98 12.76 2.59 8.29 180.40 6.15 4.63

97.81 96.42 417.26 83.84 96.77 91.38 93.91 122.57 84.61 100.13 96.26 101.55 23.71 52.90 101.31 98.12 97.59 87.71 44.85 100.78 98.34 96.16 182.57 74.11 96.46

0.98 5.45 489.83 41.12 9.43 1.28 6.22 4.42 8.79 5.42 1.12 7.03 63.03 656.92 10.59 0.72 3.31 10.64 46.83 11.98 0.93 4.45 97.83 19.75 8.17

1–50

51–100

101–150

151–200

Profits are given by E[p t (k)] = C k + O k  r l2, where C k depends on cross-autocovariances, O k depends on self-autocovariances, and r l2 is the cross-sectional variance of the mean returns. k is the lag term. Investment I(k) reports the average long (or short) position. C k , O k and r l2 are expressed as a percentage of profit. All z-statistics are asymptotically N(0, 1) under the null hypothesis that the relevant population value is zero. The z-statistics are corrected for heteroskedasticity and autocorrelations up to 8 lags based on adjustments described in Newey and West (1987). a Multiplied by 10,000. * The coefficients are statistically significant at a 1% level.

K. Lo, R. Coggins / Pacific-Basin Finance Journal 14 (2006) 291–310

Portfolio

Table 4 Analysis of the profitability of the contrarian strategy applied to daily returns for the sample of top 200 ASX stocks k

Cka

(z-stat.)

Oka

(z-stat.)

r l2

a

E[p t (k)]a

(z-stat.)

I(k)a

%C k

%O k

%r l2

1–200

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

0.0141 0.0206 0.0401 0.0266 0.0283 0.0105 0.0072 0.0269 0.0018 0.0053 0.0214 0.0156 0.0203 0.0160 0.0204 0.0322 0.0385 0.0403 0.0559 0.0564 0.0257 0.0334 0.0607 0.0558 0.0487

(24.18)* (32.77)* (46.42)* (56.48)* (59.03)* (17.4)* (12.66)* (24.86)* (3.82)* (11.16)* (48.28)* (32.49)* (34.52)* (35.61)* (34.50)* (44.06)* (38.87)* (42.79)* (79.77)* (63.03)* (26.42)* (30.31)* (57.81)* (66.62)* (78.32)*

0.0661 0.1093 0.0445 0.0343 0.0390 0.0743 0.1791 0.0164 0.1280 0.0422 0.0614 0.1099 0.0335 0.0082 0.0059 0.0359 0.0849 0.1022 0.0016 0.0815 0.1607 0.0568 0.0233 0.0138 0.1203

(33.58)* (73.52)* (25.34)* (30.67)* (35.78)* (43.28)* (123.19)* (5.64)* (61.03)* (33.26)* (44.69)* (92.13)* (22.89)* (6.50)* (3.99)* (12.72)* (37.03)* (51.44)* (0.84) (38.10)* (30.55)* (13.97)* (5.97)* (3.66)* (42.99)*

0.0090 0.0090 0.0090 0.0090 0.0090 0.0031 0.0031 0.0031 0.0031 0.0031 0.0054 0.0054 0.0054 0.0054 0.0054 0.0108 0.0108 0.0108 0.0108 0.0108 0.0164 0.0164 0.0164 0.0164 0.0164

0.0610 0.1209 0.0756 0.0519 0.0198 0.0879 0.1688 0.0401 0.1231 0.0444 0.0453 0.1201 0.0484 0.0024 0.0209 0.0572 0.1126 0.1317 0.0467 0.0359 0.1515 0.0738 0.0676 0.0532 0.0880

(38.06)* (96.03)* (59.92)* (45.83)* (21.26)* (54.08)* (130.27)* (19.86)* (63.97)* (40.39)* (35.05)* (105.18)* (41.45)* (2.01) (16.97)* (22.62)* (60.72)* (77.55)* (27.15)* (20.53)* (31.59)* (18.82)* (17.85)* (13.77)* (32.03)*

71.6670 71.6970 71.7450 71.7840 71.7970 59.3080 59.3260 59.3710 59.4090 59.4160 63.2250 63.2670 63.3190 63.3520 63.3660 75.2160 75.2520 75.2910 75.3250 75.3050 88.8970 88.9190 88.9750 89.0300 89.0830

23.14 17.01 53.01 51.27 143.05 11.93 4.25 66.99 1.50 11.88 47.26 12.95 41.91 668.97 97.56 56.16 34.17 30.58 119.64 157.35 16.95 45.28 89.79 104.97 55.38

108.37 90.45 58.91 66.08 197.45 84.54 106.09 40.75 104.02 95.12 135.42 91.52 69.18 343.93 28.12 62.66 75.39 77.60 3.41 227.32 106.10 76.99 34.51 25.93 136.70

14.77 7.46 11.93  17.35 45.61 3.54 1.84 7.74 2.52 7.00 11.84 4.47 11.09 225.04  25.68  18.82 9.57 8.18  23.05 30.03 10.85  22.27  24.30  30.90 18.68

1–50

51–100

101–150

151–200

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Portfolio

Profits are given by E[p t (k)] = C k + O k  r l2, where C k depends on cross-autocovariances, O k depends on self-autocovariances, and r l2 is the cross-sectional variance of the mean returns. k is the lag term. Investment I(k) reports the average long (or short) position. C k , O k and r l2 are expressed as a percentage of profit. All z-statistics are asymptotically N(0, 1) under the null hypothesis that the relevant population value is zero. The z-statistics are corrected for heteroskedasticity and autocorrelations up to 8 lags based on adjustments described in Newey and West (1987). a Multiplied by 10,000. * The coefficients are statistically significant at a 1% level. 299

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positive, however not all coefficients are statistically different from zero. In addition, the autocorrelation coefficients at both hourly and daily levels are much smaller in magnitude than the weekly and monthly coefficients documented in Lo and MacKinlay (1990). From these results, it is inconclusive that portfolio returns at very short horizons exhibit significant positive autocorrelation. In summary, the autocorrelation properties of daily and hourly returns tend to support overreaction as the dominant source of contrarian profits, if contrarian strategies are found to be profitable. The source of contrarian profits can be investigated in more detail by decomposing the profits using the Lo and MacKinlay (1990) decomposition. The results from this decomposition are documented in the next section. 2.3.2. Profitability and sources of contrarian profits In this section, the magnitude of contrarian profit and its sources can be examined by decomposing the expected profits into three components according to Lo and MacKinlay (1990). The expected profits calculated from Eq. (3) are decomposed into three different terms by Eqs. (5), (6), (7) and (8). Tables 3 and 4 show the estimates of expected contrarian profits and its three sources C k , O k and r l2 implemented for hourly intra-day and daily returns, respectively. For the hourly returns (Table 3), the estimated profits are positive at short lags but the profits quickly diminish and the strategy becomes unprofitable at longer lags. Smaller securities tend to have higher profits at the first lag. The daily returns (Table 4) shows a different pattern, contrarian strategies are profitable except at the first lag with maximum expected profits at lag 2 and the profits gradually decreasing as the lag increases. Large securities seem to have higher profits at the second lag which is in contrast to the hourly results. The estimated profits also appear to be greater for daily returns, but are much smaller in magnitude than the weekly returns findings by Lo and MacKinlay (1990) and Conrad et al. (1997).6 This indicates that the shorter the return time scale, the smaller the estimated profits are. The last three columns in the tables show Cˆ k , Oˆ k and r l2 as percentages of expected profits. Both daily and hourly results indicate that while self-autocovariances contribute significantly and positively to the expected profits, the cross-autocovariances contribute modestly to the profits (even in some cases negatively). This finding implies contrarian profits are mainly due to an individual security’s price overreaction, while predictability across securities contributes little to the overall contrarian profits. This result is contrary to that of Lo and MacKinlay’s (1990) finding that ba systematic lead–lag relationship among returns of size-sorted portfolios is an important source of contrarian profitsQ. Table 5 shows the economic significance of the contrarian profits in terms of the relative size of the associated investment and execution costs. The contrarian profits are relatively small compared to the capital required for the strategy. The hourly strategy at the first lag for all stocks has a profit of 24.79 basis points of investment. This suggests that contrarian strategies require large amounts of capital investment to generate small profits. Hence, only large institutional

6

We conducted the same profitability analysis using weekly returns and found the weekly estimated profits have the same order of magnitude as Lo and MacKinlay (1990) and Conrad et al. (1997).

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Table 5 Economic significance of the contrarian profits in terms of the relative size of the associated investment and execution costs E½pt ðk Þ b Eap½pt ðk Þ  TC ðk Þ b Portfolio k E[p t (k)]a I(k)a TC(k)a Break even I ðk Þ I ðk Þ transaction costb Panel A: Intra-day hourly strategies 1–200 1 0.0570 22.9880 1–200 2 0.0103 22.9890 1–200 3 0.0001 22.9890 1–50 1 0.0150 17.7190 51–100 1 0.0386 20.9610 51–100 2 0.0061 20.9620 51–100 3 0.0007 20.9610 101–150 1 0.0814 25.4210 101–150 2 0.0178 25.4190 101–150 3 0.0055 25.4190 101–150 4 0.0013 25.4220 151–200 1 0.0904 29.7180 151–200 2 0.0190 29.7220

24.79 4.46 0.05 8.47 18.39 2.93 0.33 32.03 7.01 2.18 0.49 30.41 6.38

0.1666 0.1666 0.1666 0.1196 0.1492 0.1492 0.1492 0.1866 0.1866 0.1866 0.1866 0.2187 0.2187

47.70 68.02 72.44 59.05 52.78 68.24 70.85 41.37 66.39 71.22 72.90 43.18 67.20

7.87 1.42 0.02 2.89 5.94 0.95 0.11 10.04 2.20 0.68 0.15 9.50 1.99

Panel B: Daily strategies 1–200 2 0.1209 1–200 3 0.0756 1–200 4 0.0519 1–50 2 0.1688 1–50 3 0.0401 1–50 4 0.1231 1–50 5 0.0444 51–100 2 0.1201 51–100 3 0.0484 51–100 4 0.0024 51–100 5 0.0209 101–150 1 0.0572 101–150 2 0.1126 101–150 3 0.1317 101–150 4 0.0467 151–200 2 0.0738 151–200 3 0.0676 151–200 4 0.0532

16.86 10.53 7.23 28.45 6.76 20.72 7.47 18.98 7.65 0.38 3.30 7.61 14.96 17.49 6.20 8.30 7.60 5.97

0.4761 0.4764 0.4765 0.3807 0.3809 0.3809 0.3810 0.4210 0.4213 0.4214 0.4215 0.5041 0.5044 0.5046 0.5047 0.5941 0.5945 0.5948

49.54 55.87 59.15 35.71 57.40 43.40 56.65 47.56 58.88 66.14 63.22 59.41 52.06 49.54 60.80 58.51 59.21 60.84

5.84 3.65 2.51 10.20 2.42 7.43 2.68 6.56 2.64 0.13 1.14 2.61 5.13 6.00 2.13 2.86 2.62 2.06

71.6970 71.7450 71.7840 59.3260 59.3710 59.4090 59.4160 63.2670 63.3190 63.3520 63.3660 75.2160 75.2520 75.2910 75.3250 88.9190 88.9750 89.0300

Panel A reports the contrarian profits and the associated investment and execution costs for the intra-day hourly strategies. Panel B reports profits and execution costs for the daily strategies. E[p t (k)] is the estimated profit at lag k. Investment I(k) reports the average holding position. TC(k) is the average transaction costs assuming the one-way execution cost is 0.0023 per dollar transaction. E[p t (k)] / I(k) is the profit before transaction costs expressed as basis points of investment. (E[p t (k)]  TC(k)) / I(k) is the profit after transaction costs expressed as basis points of investment. The last column reports the one-way transaction cost (c) necessary to break even. Only contrarian strategies in Tables 3 and 4 that are profitable before transaction costs are reported. a Multiplied by 10,000. b In basis points.

investors are more likely to find contrarian strategies profitable, since they have a relative advantage in their ability to command leverage to take positions. To assess the economic significance of the profits, we consider execution costs for institutional investors. Comerton-Forde et al. (2005) have estimated the average execution costs of institutional investors in Australia are around 23 basis points for buys and 14 basis points for

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sells.7 We used these execution-cost estimates to determine whether contrarian strategies are profitable for institutional investors after execution costs are included. The total execution costs can be calculated by Eq. (4), we assume the one-way transaction cost per dollar transaction (c) is 0.23%. Table 5 shows the potential profits after considering execution costs. The contrarian profits disappear once institutional execution costs are included. The hourly strategy at the first lag has a pre execution cost profit of 24.79 basis points of investment, however after execution cost, the strategy has a loss of  47.70 basis points. The one-way transaction cost required to break even is 7.87 basis points. In summary, this section has documented the profitability and sources of contrarian profits using hourly and daily returns. Contrarian strategies are found to generate only small but statistically significant profits. However, the profits cannot be economically exploited by institutions as the profits are exceeded by institutional execution costs. These strategies are potentially economically profitable only for traders who have one-way transaction costs of lower than 7.87 basis points. Numerous studies have examined whether incorporating other information such as trading volume can help improve the profitability of purely returns-based contrarian strategies.8 The remainder of this paper examines whether there is any relation between return reversal and order flow activity, and whether contrarian profits can be improved if order flow information is incorporated. 3. Return reversal and order flow imbalance In the last section, we found that the profitability of contrarian strategies is mainly due to overreaction. Several studies in the contrarian literature have focused on return behaviour after extreme stock price changes to examine the overreaction hypothesis.9 As the hypothesis suggests, the more extreme the initial movements in stock prices are, the more extreme the subsequent movements in the opposite direction to correct the initial overreaction. Some papers attempt to study large price changes accompanied by news announcements.10 In this section, we condition large price changes on trading and liquidity indicators rather than on firm-specific news or market announcements as in other papers.11 The aim is to investigate whether liquidity pressure can help explain the reversal and overreaction effects, and whether large order flow imbalances can be used as a contrarian trading signal. In most papers that examine the association between trading activity and stock market returns, trading activity is measured by volume. We focus on an alternative measure of trading activity: net order flow. Net order flow can be considered as a measure of net liquidity demand or 7

Comerton-Forde et al. (2005) measure execution costs as the sum of temporary and permanent measures. Temporary measures the return between the post execution benchmark and the average traded price of the trade package, while permanent measures the return between the post and the pre-execution benchmark. Bikker et al. (2004) have also found average execution costs equal 27 basis points for buys and 38 basis points for sells, using data from worldwide trades. Bikker et al. (2004) define execution costs as the sum of price impact costs and commission. 8 For example, Blume et al. (1994), Campbell et al. (1993), Hameed and Ting (2000). 9 Studies that focused on extreme price changes include DeBondt and Thaler (1985), Atkins and Dyl (1990), Cox and Peterson (1994), Cooper (1999), Pritamani and Singal (2001) and Larson and Madura (2003). 10 For example, Larson and Madura (2003) have found that there is no overreaction in response to informed events such as news announcements cited in the Wall Street Journal (WSJ), but there is overreaction in response to uninformed events that are not explained in the WSJ. 11 Pritamani and Singal (2001) condition large price changes on both trading volume and public announcements.

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303

imbalance. One measure of net order flow is the difference between buyer and seller initiated volumes. Order flow conveys information beyond trading volume. Chordia et al. (2002) suggest that order flow sometimes signals private information. A change in demand or supply, and hence an order flow imbalance, may reveal some private information. 3.1. Measures of order flow imbalance In addition to the mid-point price data that was used in the last section, this analysis also uses transaction data for the top 200 stocks on the ASX from 2000 to 2002. In US markets, each transaction has to be explicitly designated as either buyer or seller-initiated according to the Lee and Ready (1991) algorithm. In contrast, for the ASX data we are able to infer initiation directly from the submitted orders, thus ensuring 100% accuracy in trade directions for on market trades. The transaction data are aggregated at hourly intervals. The net order flow is measured as the difference between the number of buyer-initiated trades ( Q Bt ) and seller-initiated trades ( Q St ) over an hourly interval t.12 To standardize net order flow across securities, we define the imbalance ratio IR t as follows: ( QB t QBt NQSt Q St : ð9Þ IRt ¼ Q St  QB QBt bQSt t

The imbalance ratio IR t is positive if there are more buyer-initiated trades than seller-initiated, that is when there is net buying demand during interval t. Similarly, the ratio is negative when there are more seller-initiated trades than buyer-initiated. On occasions when there are no buyerinitiated or seller-initiated trades during a time interval, this interval is excluded in our analysis. Thus, the infrequent trading problem is also eliminated. 3.2. Abnormal returns and order flow imbalance We condition large price changes on order imbalances. Firstly, we need to standardize stock returns across securities. For each security i, the market-adjusted returns MAR it are calculated by subtracting the equally weighted portfolio returns r mt from the stock returns. Stock returns r it are calculated at hourly mid-point prices. MARit ¼ rit  rmt

ð10Þ

We call those hourly market-adjusted stock returns that represent a large abnormal price change an abnormal event. A price change is considered dabnormalT if the market adjusted return is more than three standard deviations away from the historical mean over the preceding 30 days.13 If there

12

Hasbrouck (1991) defines absolute order imbalance as the volume difference between buyer-initiated and sellerinitiated trades. 13 Since there are six intervals over a single trading day, the historical mean is measured over 180 preceding hourly trading intervals. This definition of large price change is very similar to the definition used by Pritamani and Singal (2001). They calculate the historical mean and standard deviation of stock returns over the preceding 250 trading days as their analysis is based on a longer time scale of daily stock returns. The advantage of this definition is that it represents a significant change in investor expectations rather than an absolute percentage price change, resulting in a lower likelihood of biases towards more volatile stocks.

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is more than one abnormal event identified on the same day for a security, then only the first abnormal event is included to ensure that we do not count related events more than once. Abnormal events are divided into positive and negative based on positive or negative market adjusted returns. Table 6 presents the market-adjusted returns of abnormal events conditioned on order flow imbalance. Small order flow imbalances are designated as an imbalance ratio of 1–2, while ratios N10 designate extreme order flow imbalances. The size of market-adjusted returns increases as the magnitude of order imbalance increases. For example, for the negative events sample, mean market-adjusted return increases from  2.646% for small imbalances (ratio 1–2) to  3.067% for extreme imbalances (ratio N 10). Mean reversing behaviour is observed when market-adjusted returns reverse from negative at time t to positive at time t + 1 for the negative events sample. Similar results are obtained from the positive events sample as market-adjusted returns reverse from positive to negative. The degree of return reversal also increases as the size of imbalance increases. For example, mean market-adjusted return at t + 1 increases from 0.199% for small imbalances (ratio 1–2) to 0.286% for large imbalances (ratio 5–10) for the negative events sample. Abnormal returns also take longer to reverse under extreme imbalances (ratio N 10) as evidenced by significant market-adjusted returns even after

Table 6 Abnormal market-adjusted hourly returns conditioned on order imbalance ratio Ratio

Imbalance Small 1–2a (z-stat.)

Medium 2–5a (z-stat.)

Panel A: Positive events and positive imbalance ratio Number of events: 1161 1554 Market adjusted return: Mean MARt 2.767% (42.30)* 3.067% 0.121% (3.16)* 0.136% Mean MARt+1 Mean MARt+2 0.016% (0.55) 0.025% Mean MARt+3 0.038% (1.45) 0.021% 0.005% (0.18) 0.036% Mean MARt+4 Mean MARt+5 0.018% (0.62) 0.034% Panel B: Negative events and negative imbalance ratio Number of events: 1005 1249 Market adjusted return: Mean MARt 2.646% (29.89)* 2.836% Mean MARt+1 0.199% (2.14)* 0.246% 0.084% (2.30)* 0.018% Mean MARt+2 Mean MARt+3 0.043% (1.33) 0.041% Mean MARt+4 0.039% (1.20) 0.011% Mean MARt+5 0.009% (0.28) 0.028%

Large 5–10a (z-stat.)

Extreme N10a (z-stat.)

682

749

(49.14)* 3.120% (3.71)* 0.128% (0.73) 0.007% (0.81) 0.029% (1.29) 0.022% (1.20) 0.003%

548 (52.27)* 3.049% (5.65)* 0.349% (0.52) 0.079% (1.46) 0.037% (0.35) 0.135% (0.88) 0.018%

( 40.62)* 2.953% (2.36)* 0.163% (0.15) 0.056% (0.69) 0.007% (0.52) 0.013% (0.06) 0.006%

(41.72)* (3.08)* (1.44) (0.19) (0.36) (0.16)

572 (36.31)* 3.067% (5.02)* 0.286% (1.47) 0.154% (0.81) 0.024% (2.37)* 0.043% (0.29) 0.006%

(34.62)* (3.84)* (2.24)* (0.55) (0.93) (0.11)

Panel A reports the mean adjusted returns for positive events and positive imbalance ratio, which are Large positive price changes associated with net buying imbalances. Panel B reports the mean adjusted returns for negative events and negative imbalance ratio, which are large negative price changes associated with net selling imbalances. All z-statistics are used to test whether the abnormal returns are statistically different from zero. There are two other possibilities: positive events — negative imbalance ratio and negative events — positive imbalance ratio, however there are only a few events for these two possibilities so the results are not reported. a These are the absolute value of order imbalance ratios. * Indicates statistically significant at the 5% level.

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Table 7 Abnormal events conditioning on order imbalance ratio: comparison between using market-adjusted returns and spreadreduced market-adjusted returns Ratio

Imbalance Small 1–2a (z-stat.)

Medium 2–5a (z-stat.)

Panel A: Positive events and positive imbalance ratio Market adjusted return: Mean MARt 2.767% (42.30)* 3.067% Mean MARt+1 0.121% (3.16)* 0.136% Spread-reduced MAR: Mean SRMARt 2.250% (28.96)* 2.413% Mean SRMARt +1 0.011% (0.35) 0.023% Panel B: Negative events and negative imbalance ratio Market adjusted return: Mean MARt 2.646% (29.89)* 2.836% Mean MARt+1 0.199% (2.14)* 0.246% Spread-reduced MAR: Mean SRMARt 2.058% (39.94)* 2.252% Mean SRMARt +1 0.077% (2.52)* 0.117%

Large 5–10a (z-stat.)

Extreme N10a (z-stat.)

(49.14)* 3.120% (3.71)* 0.128%

(40.62)* 2.953% (2.36)* 0.163%

(41.72)* (3.08)*

(56.97)* 2.463% (0.62) 0.044%

(39.68)* 2.317% (1.10) 0.014%

(42.23)* (0.34)

(52.27)* 3.049% (5.65)* 0.349%

(36.31)* 3.067% (5.02)* 0.286%

(34.62)* (3.84)*

(53.20)* 2.384% (3.79)* 0.109%

(36.22)* 2.395% (2.16)* 0.135%

(35.34)* (2.69)*

Panel A compares the mean adjusted returns and spread-reduced market-adjusted returns for positive events and positive imbalance ratio. Panel B compares the two returns for negative events and negative imbalance ratio. Market-adjusted returns are calculated from subtracting market returns from stock returns. Stock returns are calculated using midpoint prices. Spread-reduced market-adjusted returns are calculated in the same manner, except that the half spreads are subtracted from stock returns. All z-statistics are used to test whether the abnormal returns are statistically different to zero. a These are the absolute value of order imbalance ratios. * Indicates statistically significant at the 5% level.

two hourly intervals for the negative events sample. However, the positive events sample does not show the same behaviour.14 The results in Table 6 show that statistically significant profits can be made to take advantage of the return reversals after large price changes associated with order flow imbalances. However, the bid–ask spread would tend to widen during periods of high volatility or illiquidity due to increases in inventory risk.15 As the stock returns were calculated based on mid-point prices, these statistically significant profits may not be economically realized because of higher bid–ask costs. Thus, we need to remove bid–ask spreads from the stock returns. We define spreadreduced stock returns (r itspread) as: ritspread ¼

Pit  Pit1 1=2dit b Pit1 Pit1

ð11Þ

where 1 / 2d it is the half-spread of security i at time interval t and P it represents the mid-point price. The half-spread is subtracted from stock return if the return is positive and is added if 14

A similar analysis was conducted on daily intervals but not reported. The results show that market-adjusted returns increase as order imbalance increases, but a subsequent return reversal following the imbalance for hourly intervals is not observed. This suggests that the order flow imbalance effect is more likely to be evidenced over short horizons, particularly on an intra-day level. 15 A number of studies have discussed the impacts of volatility and liquidity on bid–ask spread, for example Huang and Stoll (1997).

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the return is negative. Spread-reduced market-adjusted returns (SRMAR t ) are calculated by subtracting the market return (rmt ) from spread-reduced stock returns (r it-spread ). The comparison between spread-reduced market-adjusted returns (SRMAR t ) and marketadjusted returns (MAR t ) for abnormal events conditioning on order flow imbalance is illustrated in Table 7. The magnitude of abnormal returns decrease after the bid–ask spread is taken into account. For the positive events sample, returns one interval after abnormal events (SRMAR t+1) become on average non-statistically significant after the spreads are incorporated. For the negative events sample, returns one interval after abnormal events are still statistically significant, but on average the reversal effect diminishes. 4. Order flow based contrarian strategies 4.1. Formation of order flow based strategies To test if order flow imbalances are related to the magnitude of contrarian profits, we develop order flow based contrarian strategies which is a variant of Lo and MacKinlay’s (1990) original strategy. Hameed and Ting (2000) have examined the relation between contrarian profits and trading activity by categorizing securities into different groups based on trading activity. However, the same methodology cannot be applied here as the order flow imbalance of a security is not uniform across time. A security can have periods of high order flow imbalance and low order flow imbalance. We adopt a different methodology in which additional portfolio formation rules are applied. Firstly, the same basic contrarian methodology is applied as in Section 2, however a security i is only included in the contrarian portfolio during the time interval t if a filter rule is passed.16 In each interval t, we select securities from the entire portfolio size N = 200 that pass the extra filter rule. We denote N´t as the number of securities that pass the filter rule during interval t. N´t is always smaller than the maximum number of securities N since not all securities can pass the filter rule. The investment weight in each security i that passes the filter rule at time t is defined as: xit V ¼ 

1 ðritk  rmtk V Þ Ntk V

ð12Þ

where rVmtk represents the mean return of those securities and Ntk V is the number of securities that passed the filter rule at the kth lag. This representation involves buying previous losers and selling previous winners that have passed the filter rule. The net investment is maintained at zero. The investment position, profits from the strategy and the decomposition of contrarian profits are calculated in the same manner as the original Lo and MacKinlay’s (1990) contrarian strategy using Eqs. (2), (3) and (5), respectively. To illustrate the general relation between contrarian profits and order flow imbalance, we define three strategies denoted general imbalance strategy, high imbalance strategy and low imbalance strategy. The main intention of constructing the general imbalance strategy is to eliminate the nontrading problem discussed in Section 2.2.1. In the general imbalance strategy, the nontrading problem is then removed by filtering out non-trading periods. The filter rule requires that the security must have an imbalance ratio magnitude greater than or equal to one. Specifically, the security must have both buyer and 16

Cooper (1999) formed portfolios by screening on absolute magnitudes of stock returns and volume. A security was included in the portfolio only if its return and volume were within the filter level.

Table 8 Analysis of the profitability of the order flow based contrarian strategy applied to intra-day hourly returns k

Cka

(z-stat.)

Oka

(z-stat.)

r l2

a

E[p t (k)]a

(z-stat.)

I(k)a

General imbalance (tradable portfolio)

1 2 3 4 5 1 2 3 4 5 1 2 3 4 5

0.0021 0.0008 0.0013 0.0002 0.0005 0.0057 0.0021 0.0023 0.0011 0.0015 0.0015 0.0009 0.0015 0.0001 0.0000

(256.49)* (128.09)* (233.90)* (27.32)* (78.75)* (380.03)* (169.38)* (205.30)* (102.28)* (141.62)* (188.47)* (134.39)* (235.67)* (9.37)* (5.43)*

0.0390 0.0007 0.0058 0.0024 0.0088 0.0437 0.0032 0.0054 0.0000 0.0108 0.0344 0.0014 0.0033 0.0034 0.0042

(336.58)* (18.36)* (153.43)* (68.47)* (249.73)* (653.85)* (58.61)* (106.70)* (0.22) (211.32)* (138.90)* (25.07)* (66.58)* (68.47)* (93.87)*

0.0054 0.0054 0.0054 0.0054 0.0054 0.0060 0.0060 0.0060 0.0060 0.0060 0.0095 0.0095 0.0095 0.0095 0.0095

0.0357 0.0039 0.0099 0.0077 0.0137 0.0434 0.0006 0.0091 0.0048 0.0153 0.0264 0.0101 0.0114 0.0129 0.0137

(308.83)* (111.97)* (261.69)* (219.19)* (399.06)* (650.89)* (11.59)* (177.44)* (101.47)* (303.12)* (106.31)* (171.96)* (224.03)* (251.43)* (303.49)*

25.5890 25.5910 25.5930 25.5940 25.5940 27.8880 27.8900 27.8920 27.8930 27.8940 22.9970 23.0000 23.0010 23.0020 23.0000

High imbalance (imbalance ratio N 2)

Low imbalance (imbalance ratio b 2)

E½pt ðk Þ b I ðk Þ 13.94 1.54 3.89 3.01 5.37 15.57 0.23 3.28 1.73 5.47 11.48 4.39 4.95 5.61 5.96

TC(k)a

0.1886 0.1886 0.1886 0.1886 0.1886 0.2273 0.2273 0.2273 0.2273 0.2273 0.1880 0.1881 0.1881 0.1881 0.1881

E½pt ðk Þ  TC ðk Þ b I ðk Þ 59.77 75.25 77.59 76.71 79.07 65.92 81.73 84.77 83.23 86.96 70.29 86.16 86.71 87.37 87.73

General imbalance strategy (tradable portfolio) filter: any order flow imbalance. High imbalance strategy filter: order imbalance ratio N 2. Low imbalance strategy filter: order imbalance ratio b 2. Profits are given by E[p t (k)] = C k + O k  r l2, where C k depends on cross-autocovariances, O k depends on own-autocovariances, and r l2 is the cross-sectional variance of the mean returns. Investment I(k) reports the average long (or short) position. TC(k) is the estimated average transaction costs. E[p t (k)] / I(k) represents the profit before transaction costs expressed as basis points of investment, while (E[p t (k)]  TC(k)) / I(k) is the profit after transaction costs expressed as basis points of investment. All zstatistics are asymptotically N(0, 1) under the null hypothesis that the relevant population value is zero. a Multiplied by 10,000. b In basis points. * The coefficients are statistically significant at a 1% level.

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sell-initiated trades during the interval if the security i is to be included in the portfolio during interval t. In this case, time intervals that contain no trades on either bid or ask sides are filtered out. Therefore, the general imbalance strategy can be interpreted as a tradable portfolio. High and low imbalance contrarian strategies are constructed in a similar manner. The high imbalance strategy includes only securities that have a large degree of order flow imbalance during interval t, while the low imbalance strategy consists of securities that have only a small order flow imbalance at t. We choose an imbalance ratio of two as the threshold to separate high imbalances and low imbalances. The choice of this threshold is arbitrary, however this choice ensures both high and low imbalance strategies have at least 50 securities in the portfolios at any time.17 4.2. Empirical results for imbalance based contrarian strategies Table 8 presents the estimated contrarian profits of the three order flow based contrarian strategies on an hourly horizon. The contrarian profits are only positive at the first lag. However, the strategies become unprofitable after execution costs are considered. At longer lags, contrarian strategies are unprofitable even before transaction costs are included. This finding is similar to the evidence from the basic hourly contrarian strategies (Table 3) that are profitable at short lags but not at longer lags. The results are also consistent with the finding in Table 6 that on an hourly interval when there are temporary order flow imbalances causing prices to change, subsequently the price quickly moves in the opposite direction, which suggests order flow based strategies are more likely to be profitable at shorter lags. The estimated profits from the general imbalance strategy is smaller than the profits from the basic contrarian strategy in Table 3. This result is expected since the general imbalance strategy is limited to those securities that have both buyer and seller initiated trades, thus lessening the nontrading problem faced by the original contrarian strategy. Part of the profits from the original contrarian strategy cannot be realistically exploited as only limited trading can be achieved for liquidity reasons. On the other hand, the general imbalance strategy, a tradable portfolio, ensures that whenever trades occur there is some liquidity in the market as there were both buyer and seller-initiated trades. Comparing the results from high and low imbalance strategies, the high imbalance strategy has higher expected contrarian profits which is attributed to bigger contributions from both Cˆ k and Oˆ k terms. This evidence suggests not only bigger overreaction and reversal effects are the results of large order imbalances (bigger Oˆ k term), the cross-autocovariances among these securities also increase (larger Cˆ k ). This is perhaps an indication that there are order flow imbalances on the portfolio level. As suggested by Jegadeesh and Titman (1995a), lead–lag structure in security returns arises because of differences in the timeliness of stock price reactions to common factors. Our results may indicate different securities react to order flow imbalances at different rates, thus lead–lag relationships are created among securities as the trades of some securities can respond to temporary order flow imbalances more quickly than the trades of other securities.

17 Alternatively, we could choose an imbalance ratio of ten as the threshold. However, this would result in too few securities in the high imbalance portfolio, and introduce biases in comparisons between high and low imbalance portfolios.

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5. Conclusion This paper has shown short horizon contrarian strategies that are constructed from 200 securities on the ASX generate small but statistically significant profits. However, after execution costs are considered, these strategies become unprofitable even for large institutional investors. We also find that the degree of return reversal is positively related to order flow imbalance. Our results suggest that market overreaction can be caused by temporary liquidity imbalance. The temporary lack of liquidity causes the price to overshoot, and subsequently moves in the opposite direction once the temporal liquidity imbalance is dissipated. We also investigated the dependence of the profitability of contrarian strategies on the liquidity conditions of each individual security. Specifically, we find contrarian trading during high levels of order flow imbalance generates higher paper profits. A possible extension of this work is to investigate whether the optimal lag of contrarian strategies is dependent on the size of securities, and also on the liquidity conditions. Some securities will react to information faster than others, and some are more resilient to change in liquidity conditions than others. Acknowledgement The authors acknowledge the provision of intra-day data and the preprocessing software provided through the Australian Capital Markets Co-operative Research Centre (CMCRC) and its industrial partners. We appreciate the comments and suggestions by an anonymous referee. The authors would also like to thank Mr. Scott Slack-Smith from ABN Amro for helpful guidance. References Atkins, A., Dyl, E., 1990. Price reversals, bid–ask spreads, and market efficiency. Journal of Financial and Quantitative Analysis 25, 535 – 547. Bikker, J., Spierdijk, L., Van der Sluis, P.J., 2004. Market impact costs of institutional equity trades, working paper, Netherlands Central Bank. Blume, L., Easley, D., O’Hara, M., 1994. Market statistics and technical analysis: the role of volume. Journal of Finance 49, 153 – 181. Boudoukh, J., Richardson, M., Whitelaw, R., 1994. A tale of three schools: insights on auto-correlations of short-horizon stock returns. The Review of Financial Studies 7, 539 – 573. Campbell, J., Grossman, S., Wang, J., 1993. Trading volume and serial correlation in stock returns. The Quarterly Journal of Economics 108, 905 – 939. Chordia, R., Roll, R., Subrahmanyam, A., 2002. Order imbalance, liquidity, and market returns. Journal of Financial Economics 65, 111 – 130. Comerton-Forde, C., Frino, A., Oetomo, T., 2005. Managing institutional execution costs. The Journal of the Securities Institute of Australia Winter 2005, 22 – 25. Conrad, J., Kaul, G., 1998. An anatomy of trading strategies. The Review of Financial Studies 11, 489 – 519. Conrad, J., Hameed, A., Niden, C., 1994. Volume and autocovariances in short-horizon individual security returns. Journal of Finance 49, 1305 – 1329. Conrad, J., Gultekin, M., Kaul, G., 1997. Profitability of short-term contrarian strategies: implications for market efficiency. Journal of Business and Economic Statistics 15, 379 – 386. Cooper, M., 1999. Filter rules based on price and volume in individual security overreaction. Review of Financial Studies 12, 901 – 935. Cox, D., Peterson, D., 1994. Stock returns following large one-day declines: evidence on short-term reversals and longerterm performance. Journal of Finance 49, 255 – 267. DeBondt, W., Thaler, R., 1985. Does the stock market overreact? Journal of Finance 40, 793 – 805.

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