Stats › Intraday and market microstructure › Square root impact law
The square root law of market impact has an r squared of 0.0035
| Study and sample | Exponent | Standard error | Prefactor |
|---|---|---|---|
| 6.9 m US metaorders, 2007 to 2009 | 0.47 | 0.01 | 0.15 |
| The same, impact surface fit | 0.52 | 0.01 | 0.207 |
| 399 k European metaorders, 2010 | 0.449 | none reported | not reported |
| Proprietary futures, 2007 to 2010, small tick | about 0.5 | none reported | of order unity |
| The same, large tick | about 0.6 | none reported | of order unity |
| 1 m Bitcoin metaorders, 2011 to 2013 | about 0.5 | none reported | about 0.9 |
Published estimates of the exponent in the relation between metaorder size and price impact, from studies whose full text was opened. Only one of the six reports standard errors on its exponent. The prefactor spread is the practical problem: 0.15 on the largest sample against about 1 in the paper that is usually cited.
Fitted on nearly eight million metaorders, the square root impact law's own coefficient of determination is 0.0035. It describes conditional averages, not individual trades, and the one paper that prints that number does not discuss it.
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