  Constant price impact functions, much used in financial literature, are shown
to give rise to paradoxical outcomes since they do not allow for proper
predictability removal: for instance the exploitation of a single large trade
whose size and time of execution are known in advance to some insider leaves
the arbitrage opportunity unchanged, which allows arbitrage exploitation
multiple times. We argue that chain arbitrage exploitation should not exist,
which provides an a contrario consistency criterion. Remarkably, all the stocks
investigated in Paris Stock Exchange have dynamically consistent price impact
functions. Both the bid-ask spread and the feedback of sequential same-side
market orders onto both sides of the order book are essential to ensure
consistency at the smallest time scale.
