  How and why stock prices move is a centuries-old question still not answered
conclusively. More recently, attention shifted to higher frequencies, where
trades are processed piecewise across different timescales. Here we reveal that
price impact has a universal non-linear shape for trades aggregated on any
intra-day scale. Its shape varies little across instruments, but drastically
different master curves are obtained for order-volume and -sign impact. The
scaling is largely determined by the relevant Hurst exponents. We further show
that extreme order flow imbalance is not associated with large returns. To the
contrary, it is observed when the price is "pinned" to a particular level.
Prices move only when there is sufficient balance in the local order flow. In
fact, the probability that a trade changes the mid-price falls to zero with
increasing (absolute) order-sign bias along an arc-shaped curve for all
intra-day scales. Our findings challenge the widespread assumption of linear
aggregate impact. They imply that market dynamics on all intra-day timescales
are shaped by correlations and bilateral adaptation in the flows of liquidity
provision and taking.
