Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets
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.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
| Length: | |
| Date of creation: | Oct 1982 |
| Publication status: | published as 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. |
| Handle: | RePEc:nbr:nberwo:0996 |
| Note: | ME |
| Contact details of provider: | Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A. Phone: 617-868-3900 Web page: http://www.nber.org Email: More information through EDIRC
|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Ross, Stephen A., 1976.
"The arbitrage theory of capital asset pricing,"
Journal of Economic Theory,
Elsevier, vol. 13(3), pages 341-360, December.
- Stephen A. Ross, "undated". "The Arbitrage Theory of Capital Asset Pricing," Rodney L. White Center for Financial Research Working Papers 02-73, Wharton School Rodney L. White Center for Financial Research.
- Stephen A. Ross, "undated". "The Arbitrage Theory of Capital Asset Pricing," Rodney L. White Center for Financial Research Working Papers 2-73, Wharton School Rodney L. White Center for Financial Research.
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.
When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:0996. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ()
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.