The Efficient Market Hypothesis when Time Travel is Possible

Abstract

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, infinitelylived 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, singletimeline 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-traveling 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 alternative theories of time travel and the challenges of empirically identifying time-travelling traders.

Keywords: time travel, efficient market hypothesis, single timeline, no-arbitrage condition, preemption