NATIONAL BUREAU OF ECONOMIC RESEARCH
NATIONAL BUREAU OF ECONOMIC RESEARCH

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

Gary Chamberlain, Michael Rothschild

NBER Working Paper No. 996 (Also Reprint No. r0446)
Issued in October 1982
NBER Program(s):   ME

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.

download in pdf format
   (442 K)

email paper

This paper is available as PDF (442 K) or via email.

Machine-readable bibliographic record - MARC, RIS, BibTeX

Document Object Identifier (DOI): 10.3386/w0996

Published: Chamberlain, Gary and Michael Rothschild. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets." Econometrica, Vol. 51, No. 5 (Sept. 1983), pp. 1281-1304. Also "Funds, Factors and Diversification in Arbitrage Pricing Models, by Gary Chamberlian, see above info.

Users who downloaded this paper also downloaded these:
Chamberlain and Rothschild t0015 Arbitrage and Mean-Variance Analysis on Large Asset Markets
Stock and Watson w11467 Implications of Dynamic Factor Models for VAR Analysis
Shleifer and Vishny w5167 The Limits of Arbitrage
Stock and Watson New Indexes of Coincident and Leading Economic Indicators
Quah and Sargent A Dynamic Index Model for Large Cross Sections
 
Publications
Activities
Meetings
Data
People
About

Support
National Bureau of Economic Research, 1050 Massachusetts Ave., Cambridge, MA 02138; 617-868-3900; email: info@nber.org

Contact Us