How Efficiency Shapes Market Impact

34 Pages Posted: 20 Mar 2013 Last revised: 27 Sep 2013

See all articles by J. Doyne Farmer

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School; Santa Fe Institute

Austin Gerig

U.S. Securities and Exchange Commission

Fabrizio Lillo

Università di Bologna

Henri Waelbroeck

Portware LLC

Date Written: March 19, 2013

Abstract

We develop a theory for the market impact of large trading orders, which we call metaorders because they are typically split into small pieces and executed incrementally. Market impact is empirically observed to be a concave function of metaorder size, i.e. the impact per share of large metaorders is smaller than that of small metaorders. We formulate a stylized model of an algorithmic execution service and derive a fair pricing condition, which says that the average transaction price of the metaorder is equal to the price after trading is completed. We show that at equilibrium the distribution of trading volume adjusts to reflect information, and dictates the shape of the impact function. The resulting theory makes empirically testable predictions for the functional form of both the temporary and permanent components of market impact. Based on the commonly observed asymptotic distribution for the volume of large trades, it says that market impact should increase asymptotically roughly as the square root of metaorder size, with average permanent impact relaxing to about two thirds of peak impact.

Keywords: market impact, metaorder

Suggested Citation

Farmer, J. Doyne and Gerig, Austin and Lillo, Fabrizio and Waelbroeck, Henri, How Efficiency Shapes Market Impact (March 19, 2013). Available at SSRN: https://ssrn.com/abstract=2235751 or http://dx.doi.org/10.2139/ssrn.2235751

J. Doyne Farmer

University of Oxford - Institute for New Economic Thinking at the Oxford Martin School ( email )

Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

HOME PAGE: http://www.inet.ox.ac.uk/people/view/4

Santa Fe Institute ( email )

1399 Hyde Park Road
Santa Fe, NM 87501
United States
505-984-8800 (Phone)
505-982-0565 (Fax)

HOME PAGE: http://www.santafe.edu/~jdf/

Austin Gerig (Contact Author)

U.S. Securities and Exchange Commission ( email )

United States Securities and Exchange Commission
100 F Street, NE
Washington, DC 20549
United States
202-551-4575 (Phone)

HOME PAGE: http://www.austingerig.com

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

Henri Waelbroeck

Portware LLC ( email )

233 Broadway, 24th Floor
New York, NY 10279
United States
212-370-8313 (Phone)

HOME PAGE: http://www.portware.com

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