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Abstract

We show that the cost of market orders and the profit of infinitesimal market-making or -taking strategies can be expressed in terms of directly observable quantities, namely the spread and the lag-dependent impact function. Imposing that any market taking or liquidity providing strategies is at best marginally profitable, we obtain a linear relation between the bid-ask spread and the instantaneous impact of market orders, in good agreement with our empirical observations on electronic markets. We then use this relation to justify a strong, and hitherto unnoticed, empirical correlation between the spread and the volatility_per trade_, with R^2s exceeding 0.9. This correlation suggests both that the main determinant of the bid-ask spread is adverse selection, and that most of the volatilitycomes from trade impact. We argue that the role of the time-horizon appearing in the definition of costs is crucial and that long-range correlations in the order flow, overlooked in previous studies, must be carefully factored in. We find that the spread is significantly larger on the nyse, a liquid market with specialists, where monopoly rents appear to be present.

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Paper provided by arXiv.org in its series Papers with number physics/0603084.

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Date of creation: Mar 2006
Date of revision: Mar 2007
Handle: RePEc:arx:papers:physics/0603084

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1. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor and Francis Journals, vol. 3(6), pages 481-514.
   
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Cited by:

1. Challet, Damien, 2008. "Feedback and efficiency in limit order markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3831-3836.
   
   • Damien Challet, 2007. "Feedback and efficiency in limit order markets," Papers 0709.3005, arXiv.org, revised Sep 2007.
2. Takero Ibuki & Jun-ichi Inoue, 2011. "Response of double-auction markets to instantaneous Selling–Buying signals with stochastic Bid–Ask spread," Journal of Economic Interaction and Coordination, Springer, vol. 6(2), pages 93-120, November.
3. Gilles Zumbach, 2007. "Time reversal invariance in finance," Papers 0708.4022, arXiv.org.
4. Geoff Willis, 2011. "Why Money Trickles Up - Wealth & Income Distributions," Papers 1105.2122, arXiv.org, revised May 2011.
   
   • Willis, Geoff, 2011. "Why money trickles up – wealth & income distributions," MPRA Paper 30851, University Library of Munich, Germany.
5. Philippe Moutot, 2011. "Systemic risk and financial development in a monetary model," Working Paper Series 1352, European Central Bank.
6. G.-F. Gu & W. Chen & W.-X. Zhou, 2007. "Quantifying bid-ask spreads in the Chinese stock market using limit-order book data," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 57(1), pages 81-87, 05.

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