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.

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.