For five stock market crashes, we compare price declines with predictions from market microstructure invariance. During the 1987 crash and the 2008 sales by Société Générale, prices fell by magnitudes similar to predictions from invariance. Larger-than-predicted temporary price declines...

Finding a universal market impact formula remains one of the most fascinating puzzles in finance. This paper reviews two possible approaches for imposing restrictions on this formula. First, restrictions can be obtained from a system of economic equations using trading volume and volatility, as...