Explain why coherent metaorder impact has an order-one variance share

Establish a microscopic mechanism showing why coherent metaorder impact retains an order-one, participation-independent share of daily price variance rather than becoming variance-subdominant as the number of contemporaneously executed metaorders increases.

Background

The paper develops a volume-conservation variance budget in which the square-root exponent is selected if coherent metaorder impact contributes an order-one share of daily variance and that share does not scale with the number of metaorders executed simultaneously. Under these assumptions, the impact prefactor satisfies Y² = 1 − b², where b² represents the complementary contribution of trade-level noise or exogenous shocks.

The unresolved issue is the microscopic justification for the premise that coherent impact has an order-one variance share. Without such a mechanism, the system may instead approach the b → 1 regime, in which coherent impact contributes negligibly to daily variance and participation-dependent, under-concave impact such as that produced by the Lillo–Mike–Farmer model can arise.

References

What we still lack is a microscopic reason for the premise itself --- for why coherent metaorder impact should retain an $O(1)$, $M$-independent share of daily variance rather than diluting to the variance-subdominant $b\to1$ world.

— On Bonart's interpretation of the Square-Root Impact Law  (2610.10053 - Bouchaud et al., 7 Oct 2026) in Section 6, paragraph “What remains open”