Time, Arbitrage, and the Law of One Price: The Case for a Paradigm Shift

Abstract

:Consider a Competitive, Efficient, and Frictionless Economy (CEFE) where resources are scarce at any date, and hence money as a valid claim against scarce resources is also scarce. In this economy, there is always price competition, which can at any date generate an unlimited number of arbitrage opportunities. For example, at any date, opportunities can exist to buy and sell each one of the contracts for delivery of the same good or asset at multiple prices currently as well as on an infinite number of future dates. I prove all arbitrage transactions, including “spot” transactions, tie up arbitrageurs’ capital representing money, good or asset such that this capital cannot be used for any other purpose for a non-zero quantity of time. This makes it impossible to exploit all arbitrage opportunities with the scarce capital available at any date and leads to an infinite number of unexploited opportunities and a non-negligible opportunity cost of the capital tied-up in arbitrage transactions, represented by each arbitrageur’s best missed arbitrage opportunity, if no better opportunity exits, hence the breakdown of the law of one price in its standard sense. This helps construct a new paradigm of CEFE which resolves long-standing theoretical, empirical, and experimental puzzles.