Abstract

http://ssrn.com/abstract=303488
 
 

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


Gary Chamberlain


Harvard University - Department of Economics; National Bureau of Economic Research (NBER)

Michael Rothschild


Princeton University - Woodrow Wilson School of Public and International Affairs; University of California, Los Angeles (UCLA) - Department of Economics; National Bureau of Economic Research (NBER)

1984

NBER Working Paper No. w0996

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.

Number of Pages in PDF File: 46

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Date posted: March 15, 2004  

Suggested Citation

Chamberlain, Gary and Rothschild, Michael, Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets (1984). NBER Working Paper No. w0996. Available at SSRN: http://ssrn.com/abstract=303488

Contact Information

Gary Chamberlain (Contact Author)
Harvard University - Department of Economics ( email )
Littauer Center
Room 123
Cambridge, MA 02138
United States
617-495-1869 (Phone)
National Bureau of Economic Research (NBER)
1050 Massachusetts Avenue
Cambridge, MA 02138
United States
Michael Rothschild
Princeton University - Woodrow Wilson School of Public and International Affairs ( email )
Princeton, NJ 08544-1013
United States
609-258-0161 (Phone)
609-258-0922 (Fax)
University of California, Los Angeles (UCLA) - Department of Economics ( email )
Box 951477
Los Angeles, CA 90095-1477
United States
National Bureau of Economic Research (NBER) ( email )
1050 Massachusetts Avenue
Cambridge, MA 02138
United States
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