For a market with an atomless continuum of assets, we formulate the intuitive idea of a ''well-diversified'' portfolio, and present a notion of ''exact arbitrage'', strictly weaker than the more conventional notion of ''asymptotic...
moreFor a market with an atomless continuum of assets, we formulate the intuitive idea of a ''well-diversified'' portfolio, and present a notion of ''exact arbitrage'', strictly weaker than the more conventional notion of ''asymptotic arbitrage'', and necessary and sufficient for the validity of an APT pricing formula. Our formula involves ''essential'' risk, one based on a specific index portfolio constructed from factors and factor loadings that are endogenously extracted to satisfy an optimality property involving a finite number of factors. We illustrate how our results can be translated to markets with a large but finite number of assets. r , pp. 173-197] for a discussion of naive and efficient diversification. We note here that there is no uniform terminology in the literature. For example, the terms non-diversifiable risk and diversifiable risk used here for the CAPM are also called systematic risk and unsystematic risk in . On the other hand, systematic risk and unsystematic risk used here for the APT model are also referred to as non-diversifiable and diversifiable risk in, for example, [37,38, pp. 116-120].