Newest papers

On Bonart's interpretation of the Square-Root Impact Law

J. -P. Bouchaud, Iacopo Mastromatteo, B. Toth · 2026 · arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.10053 · cited by 0 works (OpenAlex) · open-access PDF

Chinese

该任务是分离的步骤干净冲击法(SRIL), $I = Ysqrt{Q/V}$,正确 ---一个单一机制必须同时解释的两个事实:一个形式(冲击比例于交易量Q$的平方根)和一个宽度($Y=O(1)$,独立于参与率 $φ$),Bonart最近提出了一种优雅的解决方案:如果实现和反事实价格是分散的,信息中立冲击模型必须有白色增量,而Sril不随其后。

Machine translation (Meta M2M100); the English original follows.

Abstract

The square-root impact law (SRIL), $I = Yσ\sqrt{Q/V}$, bundles two facts that a single mechanism must explain at once: a shape (impact proportional to square-root of traded volume $Q$) and an amplitude ($Y=O(1)$, independent of the participation rate $φ$). Bonart has recently proposed an elegant solution: if realized and counterfactual prices are both diffusive, information-neutral impact must have white increments and the SRIL follows without the wart. We reformulate and simplify his argument, and foreground the ingredient he himself regards as essential --- that the market whitens the stationary stream of each participant's metaorders, not any isolated one. The Lillo--Mike--Farmer model satisfies his premises, yet gives an isolated metaorder the super-square-root impact $φ^{(1-γ)/2}Q^{(1+γ)/2}$, $γ\in(0,1)$, because single metaorders (i.e. not part of a stream) are statistically invisible and thus priced mechanically. We then construct an explicit multi-agent propagator that realizes Bonart's whitening, and show it reproduces the clean SRIL precisely when the market can attribute trades to their issuer. But correct re-attribution of anonymous trades is a formidable task, which requires markets to behave as implausibly efficient signal processing machines. The stream hypothesis makes a sharp, falsifiable prediction --- isolated metaorders, well separated in time, should not obey the SRIL --- that does not seem agree with empirical data known to us. Independently, a volume-conservation argument singles out the square-root law and lays bare the step the diffusivity route must assume: diffusivity fixes the variance of impact --- an additive, stationary, age-blind quantity --- whereas the SRIL is a law for the mean impact, which marginally decays as $1/\sqrt{\text{age}}$ and therefore demands an origin of time.

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Topics: Counterfactual thinking, Economics, Variance (accounting), Argument (complex analysis), Interpretation (philosophy), Econometrics

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