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Informed Traders and Limit Order Markets$ ARTICLE IN PRESS Journal of Financial Economics 93 (2009) 67–87 Contents lists available at ScienceDirect Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec Informed traders and limit order markets$ Ronald L. Goettler a,Ã, Christine A. Parlour b, Uday Rajan c a Booth School of Business, University of Chicago, USA b Haas School of Business, University of California, Berkeley, USA c Ross School of Business, University of Michigan, Ann Arbor, USA article info abstract Article history: We consider a dynamic limit order market in which traders optimally choose whether to Received 1 January 2008 acquire information about the asset and the type of order to submit. We numerically Received in revised form solve for the equilibrium and demonstrate that the market is a ‘‘volatility multiplier’’: 17 June 2008 prices are more volatile than the fundamental value of the asset. This effect increases Accepted 6 August 2008 when the fundamental value has high volatility and with asymmetric information Available online 5 April 2009 across traders. Changes in the microstructure noise are negatively correlated with JEL classification: changes in the estimated fundamental value, implying that asset betas estimated from G14 high-frequency data will be incorrect. C63 & 2009 Published by Elsevier B.V. C73 D82 Keywords: Limit order market Informed traders Endogenous information acquisition Computational game 1. Introduction Understanding dynamic order choice under asym- metric information is important because rational agents Many financial markets around the world, including use different trading strategies for different assets. The the Paris, Stockholm, Shanghai, Tokyo, and Toronto stock characteristics of an asset (such as the volatility of exchanges, are organized as limit order books. In addition, changes in the fundamental value of the asset) affect aspects of a limit order book are also incorporated into whether agents acquire information about the asset, markets such as Nasdaq and the NYSE. In spite of the which in turn affects the trading strategies they employ, dominance of this market form, there is no dynamic and thus the relationship between the fundamental value model of information-based trade in which investors can of an asset and its price or other market observables. choose to submit either market or limit orders. Specifically, the information content in a limit order book differs depending on whether informed agents submit limit orders and the prices at which they do so. Therefore, $ We have benefited greatly from comments by an anonymous referee and Elena Asparouhova, Kerry Back, Ekkehart Boehmer, Dmitry Livdan, to infer the fundamental characteristics of an asset from Bill Lovejoy, Ben Van Roy, and seminar participants at Aladdin, CFS market observables, or the information content in ob- (Eltville), Michigan, Carnegie Mellon, Stanford, Texas A&M, HKUST servables, it is important to understand how agents’ Symposium, Oxford Summer Symposium, Utah WFC, INFORMS, NBER trading behavior differs across assets. We conduct a Market Microstructure, and WFA meetings. systematic study of a limit order market with asymmetric à Corresponding author. Tel.: +1773 702 7549. E-mail addresses: [email protected] (R.L. Goettler), information to determine the effect of asset character- [email protected] (C.A. Parlour), [email protected] (U. Rajan). istics on trading behavior and market outcomes. 0304-405X/$ - see front matter & 2009 Published by Elsevier B.V. doi:10.1016/j.jfineco.2008.08.002 ARTICLE IN PRESS 68 R.L. Goettler et al. / Journal of Financial Economics 93 (2009) 67–87 In our model, risk-neutral agents arrive randomly at There is a ‘‘volatility multiplier’’ effect: assets with the market for an asset that has both common and private high fundamental volatility also exhibit greater vola- components to its value. Agents have different informa- tility in the microstructure noise (i.e., the deviation of tion about the common value (i.e., the present value transaction price from estimated fundamental value). of the future cash flows on the asset). Each agent chooses In an ideal frictionless market, all trades should occur either to buy or sell one share. If his order does not at the fundamental value, and the microstructure noise execute, he revisits the market and can revise his order. A should be identically zero. Thus, the volatility of the trader may reenter the market an arbitrarily large number microstructure noise is a measure of the level of of times before execution. Thus, agents face a dynamic trading frictions in the market. The effect is exacer- problem: the actions they take at any point in time bated when only speculators are informed, since incorporate the possibility of future reentries. In addition, quotes are more often set by uninformed traders. an agent may face adverse selection: prior to his first entry into the market, each agent chooses whether to buy More broadly, the set of agents posting the best limit information about the fundamental value of the asset. An prices (on either the buy or sell side) changes across time, informed agent views the current expected value of the leading to transaction prices that depart from the cash flows on each entry, whereas an uninformed agent fundamental value of the asset. In our model, agents’ forms an estimate of this value based on market responses to market frictions naturally create a time observables. variance in transaction prices. This suggests that one A model that incorporates the relevant frictions of limit explanation for time-varying expected returns or betas order markets (such as discrete prices, staggered trader may be changes in the composition of the types of agents arrivals, and asymmetric information) does not readily wishing to trade at any particular point of time. admit a closed-form solution. As a result, we use In our simulations, transaction prices do not respond numerical methods to solve for equilibrium. Once the instantaneously to changes in the fundamental value, and algorithm has converged, we then simulate trader arrivals the degree of inertia depends on both the volatility in the and analyze the results to determine the properties of fundamental value and the proportion of agents who market outcomes. Our paper is methodologically related acquire information. The inertia, in turn, implies that the to Goettler, Parlour, and Rajan (2005) but examines a microstructure noise displays positive autocorrelation, different set of questions, and therefore presents a richer and is negatively correlated with changes in the funda- model. Most importantly, in this paper we model asym- mental value. Further, changes in the microstructure noise metric information about the fundamental value of the are negatively correlated with changes in the estimated asset. Thus, we can analyze the relationship between the fundamental value, with the degree of correlation varying volatility of changes in the fundamental value, the degree with the asset volatility, and the extent of asymmetric of asymmetric information, and transaction prices. information. In our model, all traders are risk-neutral. Thus, the These properties are important to account for in volatility of the fundamental value matters because it decomposing the transaction price into the efficient price affects the value of the option provided to other agents by (i.e., the fundamental value) and microstructure noise. a limit order submitter. As a result, in equilibrium, this Further, the negative correlation between changes in the volatility affects liquidity provision, and hence, the overall microstructure noise and changes in the fundamental informativeness of market observables such as transaction value implies that betas estimated in an asset prices and order depths. pricing regression will be too low. This opens up the Overall, our findings include: possibility that microstructure effects (including proxies for liquidity or idiosyncratic risk) may spuriously Agents with no intrinsic motive for trade (i.e., spec- attain explanatory power in cross-sectional asset pricing ulators) are willing to pay the most for information, regressions. and also submit the bulk of limit orders to the market. Our theoretical predictions are consistent with recent Competition among speculators results in private work that uses high-frequency stock market data. For information often being reflected in the limit order example, Hansen and Lunde (2006) consider the stocks in book. the Dow Jones Index, and find that in many cases the However, speculators supply less liquidity when the microstructure noise is negatively correlated with the asset is more volatile. Instead, they opportunistically fundamental value. Aı¨t-Sahalia, Mykland, and Zhang exploit their information and place market orders. (2006) show that, controlling for trade reversals, the Therefore, in high volatility assets, recent transaction remaining component of microstructure noise displays prices are more informative (compared to bid and ask positive autocorrelation for stocks such as Microsoft and quotes) about the true value of the asset, and thus Intel. Bandi, Moise, and Russell (2006) show that innova- about future prices, than in low volatility assets. tions in microstructure volatility may be a priced factor. Depth in the limit order book is also informative about To estimate microstructure noise, Engle and Sun the true value of the asset. However, depth at and away (2007) use reduced form statistical models. Diebold and from the quotes has different effects. Thus, selling Strasser (2007) base their estimates on the insights from pressure (depth at the ask) tends to lead to lower static microstructure models. Such models have no role prices, whereas dispersion on the sell side (depth away for the history contained in a limit order book, and its use from the ask) tends to lead to higher prices. in determining the expected value of the asset. In contrast, ARTICLE IN PRESS R.L. Goettler et al. / Journal of Financial Economics 93 (2009) 67–87 69 our model is dynamic and shows the informativeness of before it becomes stale due to an exogenous change in the the limit order book in predicting future price changes.
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