We present a version of the APT based on an asset index set of an arbitrary infinite cardinality. Under assumptions due to Ross and Chamberlain-Rothschild, we shhow that in the absence of gains from asymptotic arbitrage, the square of the deviations of the individual rates of return from a factor-pricing formula sum to a finite number ; and that this absence, while sufficient, is not necessary for the formula to hold. We relate these results to recent work, and explain, in particular, how a version of the APT exhibits several inconsistencies when the index set is the Lebesgue unit interval.
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Find related papers by JEL classification: G12 - Financial Economics - - General Financial Markets - - - Asset Pricing C60 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - General
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