Exact Arbitrage Pricing and the Minimum-Variance Frontier

Authors

  • JONATHAN TIEMANN

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    • Graduate School of Business Administration, Harvard University. I would like to thank Richard Green and Stephen Ross for several helpful conversations. Eric Denardo and Kurt Anstreicher helped me clarify ideas regarding the role of duality. I am also grateful to an anonymous referee for many thoughtful comments.

ABSTRACT

The author examines the relationship between the Arbitrage Pricing Theory of Ross and mean-variance analysis. In particular, conditions are derived on the vector of the factor risk premia that are equivalent to the existence of a strictly positively weighted portfolio on the minimum-variance frontier. Also, a sufficient condition is given under which the existence of a positive minimum-variance portfolio of all the assets in the economy will imply the existence of a positive minimum-variance portfolio on a subset. This means that rejection of the hypothesis of the existence of a positive minimum-variance portfolio on a subset satisfying this condition implies rejection for the whole set.

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