Shmuel Kandel, Orthogonal Frontiers and Alternative Mean-Variance Efficiency Tests: Discussion, The Journal of Finance, Vol. 42, No. 3, Papers and Proceedings of the Forty-Fifth Annual Meeting of the American Finance Association, New Orleans, Louisiana, December 28-30, 1986 (Jul., 1987), pp. 620-622

A framework is presented for investigating the mean-variance efficiency of an unobservable portfolio based on its correlation with a proxy portfolio. A sensitivity analysis derives the highest correlation between the proxy and a portfolio that reverses the inference of a test of SHarpe-Lintner tangency. For example, the maximum correlation between the value-weighted NYSE-AMEX portfolio and a portfolio inferred tangent ranges from 0.76 to 0.48. We also test whether the correlation between the proxy and the tangent portfolio exceeds a given level. This hypothesis is often rejected for the NYSE-AMEX proxy at a correlation of 0.7.

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.

Tests of asset‐pricing models are developed that allow expected risk premiums and market betas to vary over time. These tests exploit the relation between expected excess returns and current market values. Using weekly data for 1963 through 1982 on ten common stock portfolios formed according to equity capitalization, a single‐risk‐premium model is not rejected if the expected premium is time varying and is not constrained to correspond to a market factor. Conditional mean‐variance efficiency of a value‐weighted stock index is rejected, and the rejection is insensitive to how much variability of expected risk premiums is assumed.