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

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

dc.contributor.author	Rothschild, Michael
dc.contributor.author	Chamberlain, Gary
dc.date.accessioned	2009-09-02T18:48:43Z
dc.date.issued	1982
dc.identifier.citation	Chamberlain, Gary, and Michael J. Rothschild. 1982. Arbitrage, factor structure, and mean-variance analysis on large asset markets. NBER Working Paper 996.	en
dc.identifier.issn	0898-2937	en
dc.identifier.uri	http://nrs.harvard.edu/urn-3:HUL.InstRepos:3230355
dc.description.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 <i>approximate factor structure</i> 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.	en
dc.description.sponsorship	Economics	en
dc.language.iso	en_US	en
dc.publisher	National Bureau of Economic Research	en
dc.relation.isversionof	http://www.nber.org/papers/w0996	en
dash.license	LAA
dc.title	Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets	en
dc.relation.journal	Working paper series (National Bureau of Economic Research)	en
dash.depositing.author	Chamberlain, Gary
dc.date.available	2009-09-02T18:48:43Z