Time-Varying Arrival Rates of Informed and Uninformed Trades

We propose a dynamic econometric microstructure model of trading, and we investigate how the dynamics of trades and trade composition interact with the evolution of market liquidity, market depth, and order flow. We estimate a bivariate generalized autoregressive intensity process for the arrival rates of informed and uninformed trades for 16 actively traded stocks over 15 years of transaction data. Our results show that both informed and uninformed trades are highly persistent, but that the uninformed arrival forecasts respond negatively to past forecasts of the informed intensity. Our estimation generates daily conditional arrival rates of informed and uninformed trades, which we use to construct forecasts of the probability of information-based trade (PIN). These forecasts are used in turn to forecast market liquidity as measured by bid-ask spreads and the price impact of orders. We observe that PINs vary across assets and over time, and most importantly that they are correlated across assets. Our analysis shows that one principal component explains much of the daily variation in PINs and that this systemic liquidity factor may be We thank Mark Ready, Schmuel Baruch, and seminar participants at New York University and the 2002 AFA meetings for helpful comments. Address correspondence to Robert F. Engle, Stern School of Business,NewYorkUniversity, 44West 4th Street, Suite 9-62,NY10012-1126, or e-mail: [email protected]. doi: 10.1093/jjfinec/nbn003 Advance Access publication February 26, 2008 C © The Author 2008. Published by Oxford University Press. All rights reserved. The online version of this article has been published under an open access model. Users are entitled to use, reproduce, disseminate, or display the open access version of this article for non-commercial purposes provided that: the original authorship is properly and fully attributed; the Journal and Oxford University Press are attributed as the original place of publication with the correct citation details given; if an article is subsequently reproduced or disseminated not in its entirety but only in part or as a derivative work this must be clearly indicated. For commercial re-use, please contact [email protected] 172 Journal of Financial Econometrics important for asset pricing. We also find that PINs tend to rise before earnings announcement days and decline afterwards. ( JEL: C51, C53, G10, G12, G14) keywords: Arrival rates, informed trades, uninformed trades, autoregressive process, market depth, liquidity A fundamental insight of themicrostructure literature is that order flow is informative regarding subsequent pricemovements. This informational role arises because orders arrive from both informed and uninformed traders, and market observers can infer new information regarding the value of the asset from the composition and existence of trades. Thus, market parameters such as volume, volatility, market depth, and liquidity are all linked in the sense that each is influenced by the underlying order arrival processes. In this paper, we propose a dynamic econometric microstructure model of trading, and we investigate how the dynamics of trades and trade composition interact with the evolution of market liquidity, market depth, and order flows. There are many reasons why understanding market liquidity and depth are important. From a practical perspective, the cost of trading in a security is inextricably linked to these market variables, and market professionals devise trading strategies that explicitly incorporate these factors. From a more academic perspective, understanding the evolution of liquidity and its interaction with information flow provides insight into the price formation process as well as into more fundamental asset pricing issues as formulated by Easley, Hvidkjaer, and O’Hara (2002), O’Hara (2003), and Acharya and Pedersen (2005). We argue in this paper that understanding market parameters such as liquidity requires understanding a more basic market variable, the order arrival process. Our dynamic microstructure model follows Easley and O’Hara (1992) by letting the arrival of informed and uninformed traders dictate the order flow and the price formulation. Different from them, however, our model explicitly allows the arrival rates of informed and uninformed trades to be time-varying and predictable. We propose a forecasting relation for the bivariate arrival rate process which is analogous to the GARCH (Bollerslev 1986) specifications on volatilities. We estimate the parameters that govern the forecasting dynamics using a maximum likelihood method. The likelihood function is determined by the probability of having a given set of buy and sell orders each day, as a function of the arrival rate forecasts. Thus, our model specification allows us to forecast the arrival rates of informed and uninformed orders, and then to forecast the resultant measures of liquidity based on these order arrival processes. Our modeling approach is a blending of model-based microstructure (see, for example, Easley and O’Hara 1992) with the literature analyzing the econometric determinants of the joint dynamics between trades and prices. Examples of the latter include Hasbrouck (1991), Dufour and Engle (2000), Engle (2000), Engle and Russell (1998), Manganelli (2000), Engle and Lange (2001), Chordia, Roll, and Subrahmanyam (2000, 2001a, 2001b, 2002, 2005), Chordia and Subrahmanyam (2004), Hasbrouck and Seppi (2001), and Korajczyk and Sadka (2006). In common with EASLEY ET AL. | Informed and Uninformed Arrival Rates 173 this econometric literature, our model generates direct forecasts on market liquidity anddepth.Different from them, however,we do not rely on exogenous dynamic specifications of trade and price linkages. Instead, our inclusion of a GARCH-style specification into a microstructure model allows us to show why particular components of order imbalance matter, thus providing an econometric structure for investigating order flow information and its resultant effects on market liquidity and depth. To illustrate the potential of ourmethodology, we estimate the dynamicmodel for 16 actively traded stocks using daily numbers of buys and sells over 15 years from January 1983 to December 1998. We find that both the informed and uninformed order flows are highly persistent. More trade today generates more trade tomorrow by both kinds of traders. However, the uninformed arrival forecasts respond negatively to past forecasts on the informed arrival. Informed trade arrival responds more to past order imbalance than it does to overall trade volumes, with the impulse responses to both variables positive and the decay exponential. Uninformed trade responds more to past uninformed trade than it does to past informed trade. The impulse responses suggest a slower decay to the uninformed trading behavior. We use the estimated model to generate forecasts on the arrival rates of informed and uninformed traders. Based on the arrival rate forecasts, we compute forecasts of the probability of information-based trading (PIN), which has been shown to have explanatory power for both spreads and returns.We also use the arrival rate forecast to predict trading-cost relevantmeasures such as bid-ask spreads and price impacts. For example, ourmicrostructuremodel directly links the arrival rates of informed and uninformed traders to the bid-ask spread, and so our arrival rate forecasts can be used to predict bid-ask spreads.We illustrate the power of this approach by predicting opening spreads for a sample of stocks, andwe find significantly positive results for most stocks. Similarly, given the arrival rate forecasts, we can use Bayesian updating to calculate the price impact of any given sequence of order flows. As an illustration, we define a measure of market depth we term the half-life. This measure is defined as the number of consecutive buys needed for the price impact to exceed half of the exogenously specified maximum impact. The half-life estimates provide a compact forecast of the market depth based on the forecasts of arrival rates of informed and uninformed traders. We also illustrate the value of our dynamic model of trading by showing how our estimated PINs vary around earnings announcement days. One might expect PINs to be high before earnings announcements, and low afterwards as earnings announcements turn private information about earnings into public information. In a recent working paper, Benos and Jochec (2007) ask whether constant PINs estimated from the static model over time periods of at least 28 trading days before and after earnings announcement have this property. They find that their PIN estimates do not have the expected property. Our belief is that this occurs because the variation in trade based on private information occurs in short periods before and after announcements and using long periods to estimate PINs obscures this effect. Using our dynamic model, we find significant variation in PIN, in the predicted direction, in the week or so before and after earnings announcement 174 Journal of Financial Econometrics days. This result suggests that with our dynamic specification PIN can be used in event studies. We believe that our results will have an impact in three areas of finance. First, institutional investors need to predict trading costs in order to evaluate the efficiency of alternative trading strategies. In order to do this, it is necessary to predict the price impact of hypothetical trades. Our approach allows us to do a better job of making these predictions than standard microstructure models. We provide an illustrative example in Section 4. Second, the liquidity of assets is important for riskmanagement as one of the risks associatedwith an asset position is the cost of reversing the position. We can predict the PIN, which in turn allows us to forecast liquidity. Third, our more sophisticated model of PIN shows that PINs are both autocorrelated and cross-correlated. Since PIN can be viewed as a simple measure of liquidity, our results show that liquidity covaries across assets. Acharya and Pedersen (2005) argue that liquidity risk matters for asset pricing and our PIN analysis shows that there is a systemic liquidity factor. Further, our new PINs should allow us to improve on the asset pricing results of Easley, Hvidkjaer, and O’Hara (2002). The paper is organized as follows. We begin in Section 1 by setting out our dynamicmicrostructuremodels. Section 2 describes the data set and our estimation procedure. Section 3 provides our estimation results on the order arrival processes, and we examine the impulse response functions to shocks to trade imbalances and overall volume levels. Section 4 investigates the application of the arrival rate forecasts to the prediction of bid-ask spreads and price impacts. This section also illustrates how to use our dynamic model of PINs in an event study. Section 5 provides some diagnostic analysis of the forecasting results. Section 6 concludes.