Exact arbitrage, well-diversified portfolios and asset pricing in large markets |
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| Authors: | M Ali Khan Yeneng Sun |
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| Institution: | a Department of Economics, The Johns Hopkins University, Baltimore, MD 21218, USA;b Institute for Mathematical Sciences, National University of Singapore, 3 Prince George's Park, Singapore 118402, Singapore;c Department of Mathematics and Center for Financial Engineering, National University of Singapore, Singapore |
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| Abstract: | 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 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. |
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| Keywords: | Exact arbitrage Asymptotic arbitrage Exact law of large numbers Well-diversified portfolio Essential risk Arbitrage pricing theory Loeb measure space |
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