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...

We document the intradaily patterns of return volatility and trading activity in trade times of fixed dollar volumes --- shorter trade times reflect higher trading activity. Unlike the U-shaped intraday seasonality in calendar-time volatility, trade-time volatility plunges by 40-60% over the...

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...