The Linear Structure of Capital Asset Pricing Models

Abstract

Arbitrage Theory has turned out to be a fundamental tool in analysing financial markets and financial decisions. Financial decision making benefits from Arbitrage Theory by the concept of valuation by arbitrage. Loosely speaking, valuation by arbitrage enables us to reveal existing riskless arbitrage opportunities in cases a choice has to be made among two or more financial decision alternatives. The underlying concept will be explained at a later stage. Arbitrage Theory itself is concerned with the analysis of financial markets and theories thereof. It can be seen as a theoretical basis of any reasonable theory of financial asset prices. The following introduction is to show that all the capital asset pricing models advanced in the literature — we will, of course, consider a sample only — share a common structural property. At a later stage we will see that this common property can be deduced from a very simple model of those financial markets which do not provide risk-free arbitrage opportunities.