We derive testable implications of Kyle and Obizhaeva's (2016) notion of "bet invariance'' for the cross-section of trade-time volatilities. We jointly develop theoretical foundations of "no speculative arbitrage'' whose implications incorporate those of bet invariance. Our proposed test...

Dramatic microstructure changes in equity markets have made standard liquidity measures less accurate proxies of trading costs. We develop trade-time liquidity measures that reflect per-dollar price impacts of fixed-dollar volumes. Our measures (i) better capture institutional trading costs; and...

Amihud's (2002) stock (il)liquidity measure averages daily ratios of absolute close-to-close return to dollar volume, including overnight returns, while trading volumes come from regular hours. Our modified measure addresses this mismatch by using open-to-close returns. It is more strongly...

We document new intraday trading patterns indicative of the key roles of endogenous trading responses of investors to variations in imperfectly-competitive liquidity provision. When measured in trade times of fixed dollar values, price impacts and volatility fall sharply from open to close, and...

We develop measures of stock-specific trading activity based on durations of sequences of consecutive trades with fixed cumulative values. Trade sizes and signed-trade imbalances rise with activity, while price impacts generally fall, but not always, due to endogenous variation in liquidity...

We show that wholesalers internalize unbalanced amounts of retail order flow to provide liquidity to institutional investors. The Tick Size Pilot highlights how wholesaler incentives affect the magnitude and composition of internalized retail trade imbalances (Mroib, Boehmer et al.\ 2021). Large...