# Instantaneous Arbitrage and the CAPM

## TL;DR

This paper explores the relationship between instantaneous arbitrage and the CAPM in continuous time, showing that absence of arbitrage implies the existence of a CAPM-compliant trading strategy, with implications for asset pricing models.

## Contribution

It establishes the equivalence between no instantaneous arbitrage and the existence of a CAPM-based trading strategy, clarifying differences in arbitrage and CAPM arguments.

## Key findings

- Absence of instantaneous arbitrage implies a CAPM-compliant trading strategy.
- The difference between arbitrage and CAPM arguments lies in the portfolio assumptions.
- The paper clarifies the conditions under which CAPM holds in continuous time.

## 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.