# Impact is not just volatility

## TL;DR

This paper clarifies that market impact and volatility are distinct concepts, challenging the common square-root impact law and providing a scaling argument to better understand empirical observations.

## Contribution

It distinguishes impact from volatility and offers a new scaling framework that aligns with empirical data, clarifying misconceptions in market impact modeling.

## Key findings

- Impact and volatility are fundamentally different.
- The square-root impact law does not relate to price diffusion.
- A simple scaling argument explains empirical impact and volatility data.

## Abstract

The notion of market impact is subtle and sometimes misinterpreted. Here we argue that impact should not be misconstrued as volatility. In particular, the so-called ``square-root impact law'', which states that impact grows as the square-root of traded volume, has nothing to do with price diffusion, i.e. that typical price changes grow as the square-root of time. We rationalise empirical findings on impact and volatility by introducing a simple scaling argument and confronting it to data.