Arbitrage and Mean-Variance Analysis on Large Asset Markets

Gary Chamberlain and Michael Rothschild ()

No 15, NBER Technical Working Papers from National Bureau of Economic Research, Inc

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. The mean variance efficient set is a cone generated by these portfolios. Ross [16, 18J showed that if there is a factor structure, then the distance between the vector or mean returns and the space spanned by the factor loadings is bounded as the number of assets increases. We show that if the covariance matrix of asset returns has only K unbounded eigenvalues, then the corresponding K eigenvectors converge and play the role of factor loadings in Ross' result. Hence only a principal components analysis is needed to test the arbitrage pricing theory. Our eigenvalue conditional can hold even though conventional measures of the approximation error in a K factor model are unbounded. We also resolve the question of when a market with many assets permits so much diversification that risk-free investment opportunities are available.

Date: 1981-07
Note: ME
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Published as Chamberlain, Gary and Michael Rothschild. "Arbitrage, Factor Structure, And Mean-Variance Analysis On Large Asset Markets," Econometrica, 1983, v51(5), 1281-1304.

Downloads: (external link)
http://www.nber.org/papers/t0015.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:nbr:nberte:0015

Ordering information: This working paper can be ordered from
http://www.nber.org/papers/t0015

Access Statistics for this paper

More papers in NBER Technical Working Papers from National Bureau of Economic Research, Inc National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.. Contact information at EDIRC.
Bibliographic data for series maintained by ().