When Can Markets Crash Without News?

Abstract

In a resilient N-asset market with fixed fundamentals and paired-dollar execution, we prove that response elasticity e(S)=Sg'(S)/g(S) >= 2 excludes every positive systemic drawdown, whereas e(S) >= 1 excludes a simultaneous decline of all assets. The proof uses a response-adapted generalized price coordinate Phi(S) = integral from F to S of u/g(u) du, uniquely normalized so that an executed-dollar transfer produces an equal coordinate displacement. This reveals an additive trading conservation law and a recovery-driven stability barrier. Within the common family g_p(S)=eta(S/F)^p, the regimes p=2,1,0 respectively yield exclusion, inventory-bounded partial-coverage losses, and arbitrarily severe partial-coverage log losses under uniform finite turnover and inventory when pulses are permitted. We establish necessary dollar-turnover and share-inventory bounds. For constant per-share impact and bounded gross share rates, the maximal small-rate systemic loss is of quadratic order, with an attaining-order continuous construction. Rolling daily price limits constrain individual sessions but need not exclude multiday losses: a computer-assisted ten-asset path has nine assets reach their lower closing limits on two successive sessions, closes every executed-dollar ledger, and attains systemic log loss above 0.020. In this example the required gross-rate cap satisfies 0.044 < v_bar_* < 0.285. This preprint includes the English manuscript and separate supplementary material in the SIFIN review format. Reproducibility software, computational certificates and partial Lean formalization: https://github.com/Siyuan-chat/market-crash-reachability . This record does not claim journal publication or peer-review acceptance.