Speaker: Julius Bonart
Title: On the origin of nonlinear market impact: Statistical conditioning and artefactual concavity
Abstract: We reexamine the empirical “square-root law” of market impact, which describes a concave relationship between size of institutional orders and average price response. I argue that this pattern can arise as a statistical artefact rather than a structural feature of price formation. Under minimal assumptions—mean-reverting trading signal, rational expectations pricing, and statistical independence between order duration and participation rate—the conditional drift of prices during execution follows a square-root scaling as a consequence of the Doob h-transform. This result holds across alternative economic interpretations, including informational (Kyle-type) and mechanical (order-flow anticipation) frameworks, both of which yield linear price-formation equations. The analysis suggests that the observed concavity of market impact may reflect conditioning bias rather than genuine nonlinearity. This reinterpretation has implications for transaction cost analysis, causal inference in market microstructure, and challenges the empirical foundation of recent claims that markets are intrinsically unstable or self-organized near criticality.