This article introduces the concept of a statistical arbitrage opportunity (SAO). In a finite-horizon economy, a SAO is a zero-cost trading strategy for which (i) the expected payoff is positive, and (ii) the conditional expected payoff in each final state of the economy is nonnegative. Unlike a pure arbitrage opportunity, a SAO can have negative payoffs provided that the average payoff in each final state is nonnegative. If the pricing kernel in the economy is path independent, then no SAOs can exist. Furthermore, ruling out SAOs imposes a novel martingale-type restriction on the dynamics of securities prices. The important properties of the restriction are that it (1) is model-free, in the sense that it requires no parametric assumptions about the true equilibrium model, (2) can be tested in samples affected by selection biases, such as the peso problem, and (3) continues to hold when investors' beliefs are mistaken. The article argues that one can use the new restriction to empirically resolve the joint hypothesis problem present in the traditional tests of the efficient market hypothesis.

We study how the market return depends on the time of the day using E-mini S&P 500 futures actively traded around the clock. Strikingly, 4 hours around European open account for the entire average market return. This period’s returns have a 1.6 Sharpe ratio and remain high after transaction costs. Average returns are a noisy zero during the remaining 20 hours. High returns are consistent with European investors processing information accumulated overnight and thus resolving uncertainty. Indeed, uncertainty reflected by VIX futures prices rises overnight and falls around European open. The results are stronger during the 2020 COVID crisis.

Some fundamental questions regarding equity-index return dynamics are difficult to address due to the latent character of spot volatility. We exploit tick-by-tick option quotes to compute a novel “Corridor Volatility” index which may serve as an observable proxy for short-term volatility. Exploiting this index, we find that equity-index volatility jumps are common, symmetrically distributed, and cojump with the underlying returns. Moreover, the return-volatility asymmetry is more pronounced than is generally recognized and is in force for both diffusive and jump innovations in volatility. Finally, the index performs admirably during turbulent market conditions, constituting a useful real-time gauge of market stress.