A new approach to understanding the market impact of large trading orders ∗

Market impact is the change in price due to initiating a trade. In this paper we develop a new theory for average market impact based on properties of order flow, efficiency of price returns and other empirically testable assumptions. Our approach differs from previous efforts in that our results do not depend on assumptions about the functional form of utility or other ad hoc assumptions. We argue that the concave form of market impact is driven by market efficiency as follows: Large trading orders are executed incrementally, which imparts positive autocorrelations into order flow. To be compatible with efficiency the resulting predictability implies that returns must be asymmetric – returns of the same sign as the large order being executed must be smaller than those of the opposite sign. As the large order develops it becomes more and more predictable, which makes same-signed returns smaller and and thus makes the market impact concave. Under our theory the market impact depends on several factors, including the volume distribution of large orders, the information set used by market participants, and the way in which hidden orders couple to price volatility. In this paper we assume no coupling to volatility and show that depending on which of these assumptions is used it is possible to get linear, power law, or logarithmic impact functions. We present empirical results using data from the London Stock Exchange that are suggestive of logarithmic impact, but more data is needed to determine this with certainty.