Working Papers, The Johns Hopkins University, Department of Economics 483
For 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. One formula involves essential risk 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.
exact arbitrage asymptotic arbitrage exact law of large numbers well-diversified portfolio essential risk arbitrage pricing theory Loeb measure space.