The Geometry of the Maximum Likelihood Estimator of the Zero-Beta Return
在均值-方差空间中探讨样本前沿、最大似然估计量及其他两种零贝塔收益率估计量之间的几何关系，并揭示抛物线族对投资组合空间的分割，为无风险资产下投资组合效率的似然比检验统计量提供新解释。
This paper explores geometric relations, in mean-variance space, among the sample frontier, the maximum likelihood estimator, and two other estimators of the zerobeta return. It is also demonstrated that a partition of the portfolio space is determined by a family of parabolas; the zeros of each parabola are the maximum likelihood estimators associated with all portfolios on the parabola. This observation is the basis for an additional interpretation of the statistic of the Likelihood Ratio Test of portfolio efficiency without a riskless asset.