A test of speculative arbitrage: is the cross-section of volatility invariant?

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 circumvents the unobservable nature of “bets.” Utilizing a large sample of U.S. stocks post decimilization, we show that using realized volatilities rather than expected volatilities introduces noise that substantially biases the tests. This leads us to use estimates of normalized volatilities based on running 24 month windows. We find strong support for no speculative arbitrage at a moment in time, but not across time.