A REVISED GEOMETRY OF MEAN-VARIANCE EFFICIENT PORTFOLIOS

A revised definition of efficiency compares portfolios with different net worths. One axiom rules out instantaneous riskless gains, the other asserts that it costs money to buy good portfolios. Unlimited short sales are allowed. Portfolios which cannot be improved at any price are called absolutely efficient. The geometry of the mean-standard deviation frontiers is governed by three “efficient set constants”. A few results regarding efficient portfolios must be modified, and a new version of the security line equation is proposed. Explicit formulas are given: no need to use different formulas for singular or non-singular covariance matrix.