Market efficiency and the long-memory of supply and demand: Is price
impact variable and permanent or fixed and temporary?

In this comment we discuss the problem of reconciling the linear efficiency
of price returns with the long-memory of supply and demand. We present new
evidence that shows that efficiency is maintained by a liquidity imbalance that
co-moves with the imbalance of buyer vs. seller initiated transactions. For
example, during a period where there is an excess of buyer initiated
transactions, there is also more liquidity for buy orders than sell orders, so
that buy orders generate smaller and less frequent price responses than sell
orders. At the moment a buy order is placed the transaction sign imbalance
tends to dominate, generating a price impact. However, the liquidity imbalance
rapidly increases with time, so that after a small number of time steps it
cancels all the inefficiency caused by the transaction sign imbalance, bounding
the price impact. While the view presented by Bouchaud et al. of a fixed and
temporary bare price impact is self-consistent and formally correct, we argue
that viewing this in terms of a variable but permanent price impact provides a
simpler and more natural view. This is in the spirit of the original conjecture
of Lillo and Farmer, but generalized to allow for finite time lags in the build
up of the liquidity imbalance after a transaction. We discuss the possible
strategic motivations that give rise to the liquidity imbalance and offer an
alternative hypothesis. We also present some results that call into question
the statistical significance of large swings in expected price impact at long
times.