Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets
AbstractWe 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.
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Bibliographic InfoPaper provided by Harvard University Department of Economics in its series Scholarly Articles with number 3230355.
Date of creation: 1982
Date of revision:
Publication status: Published in Working paper series (National Bureau of Economic Research)
Other versions of this item:
- Chamberlain, Gary & Rothschild, Michael, 1983. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," Econometrica, Econometric Society, vol. 51(5), pages 1281-304, September.
- Gary Chamberlain & Michael Rothschild, 1984. "Arbitrage, Factor Structure, and Mean-Variance Analysis on Large Asset Markets," NBER Working Papers 0996, National Bureau of Economic Research, Inc.
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- Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
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