The non-linear market impact of large trades: evidence from buy-side order flow

We perform an empirical study of a set of large institutional orders executed in the US equity market. Our results validate the hidden order arbitrage theory proposed by Farmer <italic>et al</italic>. [How efficiency shapes market impact, 2013] of the market impact of large institutional orders. We find that large trades are drawn from a distribution with tail exponent of roughly 3/2 and that market impact approximately increases as the square root of trade duration. We examine price reversion after the completion of a trade, finding that permanent impact is also a square root function of trade duration and that its ratio to the total impact observed at the last fill is roughly 2/3. Additionally, we confirm empirically that the post-trade price reverts to a level consistent with a fair pricing condition of Farmer <italic>et al</italic>. (2013). We study the relaxation dynamics of market impact and find that impact decay is a multi-regime process, approximated by a power law in the first few minutes after order completion and subsequently by exponential decay.