# Instantaneous Arbitrage and the CAPM

By Lars Tyge Nielsen

May 2006

### Abstract

This paper studies the concept of instantaneous arbitrage in continuous time and its relation to the instantaneous CAPM. Absence of instantaneous arbitrage is equivalent to the existence of a trading strategy which satisfies the CAPM beta pricing relation in place of the market. Thus the difference between the arbitrage argument and the CAPM argument in Black and Scholes [1973] is this: the arbitrage argument assumes that there exists some portfolio satisfying the CAPM equation, whereas the CAPM argument assumes, in addition, that this portfolio is the market portfolio.

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