Great Moments in Financial Economics: IV. The Fundamental Theorem (Part I)

Abstract

This is the fourth in a series of articles in this Journal examining the historical origins of key ideas in the history of financial economics. The fundamental theorem asserts: there are no arbitrage opportunities if and only if state-prices exist. Like Newton's laws of motion, though highly abstract, it underlies the most important results in financial economics. The paper starts with some necessary background, explaining the related trio of ideas, subjective probabilities, risk-neutral probabilities and state-prices. Our search for the origins of the concept of state-prices will take us back several centuries to some work of Edmund Halley and Christiaan Huygens, who were financial economists on the side. In a Great Moment in the history of financial economics in 1953, the first clear and general application of state-prices to economics appears in the work of Kenneth Arrow. Less well known is some early important commentary by the economist Jacques Dreze. In the middle 1970's Mark Rubinstein and Stephen Ross may have been the first financial economists to appreciate the link between arbitrage and state-prices in incomplete markets, with the first completely clear statement and proof of the theorem provided by Ross. I then show how starting with the theorem, the important results of asset price theory (in particular, the CAPM) can be derived.

An extension of the fundamental theorem which anticipates modern option pricing will be discussed in Part II of this article which will appear in the next issue of the Journal.

Keywords: Probability, state-prices, arbitrage, complete markets

JEL Classification: G00