Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets

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Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets

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Title: Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets
Author: Rothschild, Michael; Chamberlain, Gary

Note: Order does not necessarily reflect citation order of authors.

Citation: Chamberlain, Gary, and Michael J. Rothschild. 1982. Arbitrage, factor structure, and mean-variance analysis on large asset markets. NBER Working Paper 996.
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Abstract: We examine the implications of arbitrage in a market with many assets. The absence of arbitrage opportunities implies that the linear functionals that give the mean and cost of a portfolio are continuous; hence there exist unique portfolios that represent these functionals. These portfolios span the mean-variance efficient set. We resolve the question of when a market with many assets permits so much diversification that risk-free investment opportunities are available. Ross 112, 141 showed that if there is a factor structure, then the mean returns are approximately linear functions of factor loadings. We define an approximate factor structure and show that this weaker restriction is sufficient for Ross' result. If the covariance matrix of the asset returns has only K unbounded eigenvalues, then there is an approximate factor structure and it is unique. The corresponding K eigenvectors converge and play the role of factor loadings. Hence only a principal component analysis is needed in empirical work.
Published Version: http://www.nber.org/papers/w0996
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3230355

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  • FAS Scholarly Articles [7470]
    Peer reviewed scholarly articles from the Faculty of Arts and Sciences of Harvard University
 
 

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