The authors propose a likelihood-ratio test of the hypothesis that the minimum-variance frontier of a set of K assets coincides with the frontier of this set and another set of N assets. They study the relation between this hypothesis, exact arbitrage pricing, and mutual fund separation. The exact distribution of the test statistic is available. The authors test the hypothesis that the frontier spanned by three size-sorted stock portfolios is the same as the frontier spanned by thirty-three size-sorted stock portfolios.

The authors propose a likelihood‐ratio test of the hypothesis that the minimum‐variance frontier of a set of K assets coincides with the frontier of this set and another set of N assets. They study the relation between this hypothesis, exact arbitrage pricing, and mutual fund separation. The exact distribution of the test statistic is available. The authors test the hypothesis that the frontier spanned by three size‐sorted stock portfolios is the same as the frontier spanned by thirty‐three size‐sorted stock portfolios.

We characterize the sets of mimicking positions with returns that can serve in place of factors in an exact K ‐factor arbitrage‐pricing relation for a set of N assets. All of the sets are K ‐dimensional nonsingular linear transformations of each other. We interpret three examples of such transformations and discuss empirical considerations. We provide conditions under which the mimicking positions can be expressed as portfolios, and we characterize the relation between mimicking portfolios and the minimum‐variance frontier.