Mean-Variance Analysis

The mean‐variance frontier is characterized with and without a risk‐free asset. The global minimum variance portfolio and tangency portfolio are defined, and two‐fund spanning is explained. The frontier is characterized in terms of the return defined from the SDF that is in the span of the assets. This is related to the Hansen‐Jagannathan bound. There is an SDF that is an affine function of a return if and only if the return is on the mean‐variance frontier. Separating distributions are defined and shown to imply two‐fund separation and mean‐variance efficiency of the market portfolio.