By J. Doyne Farmer, Austin Gerig, Fabrizio Lillo, Henri Waelbroeck
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. Within a framework in which informed traders are competitive we 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 a commonly observed asymptotic distribution for the volume of large trades, it says that market impact should increase asymptotically roughly as the square root of size, with average permanent impact relaxing to about two thirds of peak impact.
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