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This study investigates the convergence process toward efficiency of daily top gainers. The convergence process toward efficiency is much clearer as a result of using a GARCH(1, 1) model compared to the OLS model, and exhibits a monotonic decline as the time interval increases. The relationship between volatility and order imbalances is, however, not strong enough, suggesting that market makers do have the capability to reduce price volatility. This study develops an imbalance-based trading strategy, which earns a positive profit but fails to outperform the buy-and-hold strategy (i.e., open-to-close returns). A nested causality approach, which examines the dynamic return–order imbalance relationship during the price-formation process, confirms the results.

The concept of market efficiency was both developed and refined by Fama (1970), who defines “efficient” as any market in which prices always “fully reflect” available information. In an efficient market, nobody can earn abnormal returns based on any trading strategy since the relevant information will, as soon as it is revealed, be impounded into stock prices by rational investors. While the majority of financial research assumes a broad rationality, many recent studies highlight market anomalies and the link between psychology and behavioral finance, e.g., the January effect, the weekend effect, the small firm effect, and the momentum effect (Durham, 2001, Rachev et al., 2007 and Huang and Wang, 2009). The irrationalities of individual investors seem to move the stock prices away from the fundamental values, making the stock market less efficient. However, professionals and money managers seldom beat passive investment strategies. To some extent, this means that the market is efficient enough. Although these phenomena appear to be self-contradictory, many researchers translate this feature as “aggregation.” All investors, as they gather together and engage in diversified investment behavior, push the market toward efficiency.1 It needs, however, to be asked how the market converges to efficiency? A good example is that of Chordia et al. (2005) who interpreted convergence based on individual actions. First, order imbalances arise from traders who demand immediacy for liquidity or informational needs. These order imbalances are positively auto-correlated, suggesting that traders are either herding or spreading their orders out over time, or both. Second, NYSE specialists react to initial order imbalances by altering quotes away from the fundamental value in an effort to control inventory. Finally, outside arbitragers intervene to add market-making capacity by performing countervailing trades in the opposite direction. This arbitrage activity takes at least a few minutes since arbitragers must ascertain whether or not there is new relevant information regarding values. Chordia et al. (2005) indicate that efficiency does not happen immediately, and they examine the process in which markets converge to efficiency based on the data of large NYSE firms. They declare that order imbalances are highly positively dependent over both short and long intervals, and that these imbalances predict future returns only over very short intervals. They find that it takes more than 5 min but less than 60 min2 for the market to achieve weak-form efficiency.3 In contrast to Chordia et al. (2005), we narrow the range of our study to daily top gainers. Top gainers play an important role in market efficiency because of information diffusion.4 Usually these stocks provide extremely valuable information to the general public. We use intra-day data to examine not only the impact of discretionary traders on returns but also the impact of discretionary traders on volatility and especially the according responses from uninformed market makers who have the responsibility to reduce volatility. We are interested in the process by which the news is incorporated into stock prices. We use order imbalances as an indicator of the price movements. Chordia and Subrahmanyam (2004) document the market order imbalance, defined as aggregated daily market purchase orders less sell orders for stocks, as being highly predictable from 1 day to the next while returns are independent. They find that price pressures caused by auto-correlated imbalances give rise to a positive relationship between lagged imbalances and returns. Under different time intervals, we examine the predictive and explanatory ability of imbalances on returns and explore the convergence process of top gainers. Su and Huang (2008) investigate the intra-day behavior of NASDAQ speculative top gainers in examining the relationship between returns and order imbalances in light of extraordinary events and conclude that order imbalances convey more information than trading volume. Besides, they observe a negative relationship between firm size and order imbalances, i.e., order imbalances serve as a better return predictor in the small trading volume quartile. In this paper, we investigate how long it takes for the stock price of the daily top gainers to reach market efficiency. Finally, we try to develop a trading strategy based on the return–order imbalance relationship. Several hypotheses have been established in order to examine whether the strategy earn a positive return and beat the original open-to-close return, and whether time intervals matter. We have several marginal contributions besides Chordia et al. (2005). First of all, we argue that the direct relationship between order imbalances and returns should consider the linkage with volatility. Secondly, market maker behavior plays a very important role in mitigating volatility from discretionary trades through inventory adjustments. Finally, we investigate the nested causality between order imbalances and returns as we explore the intra-day dynamics that is essential in convergence process. The remainder of this paper is organized as follows. Section 2 describes the data and methodology. Section 3 presents the empirical results, and Section 4 concludes.

All kinds of investors push the market toward efficiency to the extent that no one can earn an abnormal profit by adopting the same trading strategies continuously. Efficiency cannot occur instantaneously in the real world. Some time is needed for the stock to converge to efficiency. The central purpose of our study is to investigate the convergence process of daily top gainers in the stock market toward efficiency. From the unconditional lagged return–order imbalance OLS model, we observe a convergence path from 5-min interval to 15-min interval. Consistent with Chordia and Subrahmanyam (2004), the lagged-one imbalances have a positive impact on returns except for the 10-min interval, which implies that the 10-min interval provides the best fit for market makers to control inventories, and thus the relationship between returns and lagged-one imbalances becomes negative at 10-min interval. In the conditional contemporaneous return–order imbalance OLS model, the positive relationship between the contemporaneous order imbalances and returns is consistent with Chordia and Subrahmanyam (2004). Being conditional upon the current order imbalances, the returns are negatively related to the lagged-one imbalances, which is also consistent with Chordia and Subrahmanyam (2004). Moreover, the path of convergence is also perceptible from 5-min interval to 15-min interval although there is a hump at the 10-min interval. To resolve the weaknesses embedded in the OLS regression model, we use the GARCH(1, 1) model to again examine the relationship between contemporaneous imbalances and returns, and find that the explanatory ability of these imbalances in terms of explaining the returns is lower than that of the OLS regression model. We attribute this to volatility. Because the GARCH(1, 1) model controls volatility more appropriately, some of the explanatory power of imbalances in the OLS regression model might come from the risk premium. In addition, the convergence process is much clearer from the use of the GARCH(1, 1) model, and exhibits a monotonic decline as the time interval increases. From the volatility–order imbalance GARCH(1, 1) model, we infer that market makers control volatility so well that as a result the relationship between volatility and order imbalances is not strong. Moreover, we can still observe an apparent decline in the explanatory power of the order imbalances as the time interval increases. After investigating the relationships among returns, order imbalances, and volatility as mentioned above, we attempt to build a trading strategy for the sample stocks. We use two kinds of prices (quote prices and trade prices) to implement our strategy, but only one strategy using trade prices earns a positive return. Nevertheless, neither strategy can beat the buy-and-hold strategy (i.e., the original open-to-close return) of top gainers. We also employ a nested causality approach to examine the dynamic return–order imbalance relationship during the price-formation process. The results explain our imbalance-based trading strategy.