Factor Structures and Arbitrage Pricing in Large Asset Markets

Nabil I. Al-Najjar

No 1140, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: The paper develops a new modeling framework to study factor structures and Arbitrage Pricing Theory in large asset markets. The asset economy in this framework consists of a continuum of assets. Finite subsets of assets are interpreted as random draws from the underlying economy. I show that the absence of arbitrage opportunities (or equilvalently, the continuity of the pricing function) implies, under the traditional assumptions, exact factor-pricing for a full measure of assets. In particular, with probability one, in a typical finite subset of assets, all assets are exactly factor-priced. I further show that approximate factor structures exist in general, and that they can be chosedn efficiently according to a measure of explanatory power in the spirit of R(squared) in Econometrics. The definition of approximate factor structures here is less stringent than in Chamberlain and Rothchild (1983), yet still sufficiently strong to imply approximate factor pricing for most assets. Factor structures in the present model are also robust to using proxies to replace the true factors. None of these results hold in the traditional modeling approach in which the large asset economy is represented by an infinite sequence of assets. I provide examples explaining the reasons for the sharp differences between the implications of the two modeling approaches.

Date: 1994-05
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