The efficient market hypothesis when time travel is possible

This paper extends the Efficient Markets Hypothesis (EMH) into a novel setting in which traders can travel back in time to exploit future information. We consider a fully specified trading model with risk-neutral, rational investors and a single, infinitely-lived asset. Agents can, at a fixed cost, build time machines, travel to the past, and trade using knowledge of future dividends and prices. Under a self-consistent, single-timeline theory of time travel, we show that no arbitrage opportunities can persist. In equilibrium, the asset price fully reflects not only all current and past information but also all future information that could have been acted upon by backward-travelling arbitrageurs. We state and prove an Extended Efficient Markets Hypothesis (EEMH), showing that time travel does not undermine but rather reinforces the no-arbitrage conditions at the heart of the EMH. We conclude by discussing the relevance of known constraints on the EMH, alternative theories of time travel and the challenges of empirically identifying time-travelling traders. Journal of Economic Literature Codes: G14, Z10. • Shows that time travel does not undermine the Efficient Markets Hypothesis (EMH) but rather reinforces, as any arbitrage opportunities would have already been exploited and eliminated. • Develops a formal trading model where agents can build time machines at fixed cost to exploit future information. • Shows prices reflect all information – past, present and future – that could ever be used for arbitrage. • Demonstrates how self-consistency constraints and rational expectations ensure market efficiency. • Argues that evidence of time travel cannot be found in financial data since time travellers’ actions would be indistinguishable from normal price movements in an efficient market.