A non-probabilistic approach to efficient portfolios

The notion of efficient portfolios is restated employing a novel approach to asset uncertainty, in which an uncertainty set conveys all information on asset returns. Based on the idea that a portfolio is a function mapping the asset returns to the portfolio return, the width of the image of the uncertainty set is used as a risk measure. The statement of the separation theorem is inherited. Furthermore, non-positive Value at Risk with 100% confidence is found in a class of efficient portfolios.

Automated summary

This article restates the concept of efficient portfolios using a novel approach to asset uncertainty, where an uncertainty set conveys all information on asset returns. By considering a portfolio as a function mapping asset returns to the portfolio return, the width of the image of the uncertainty set is utilized as a risk measure. The separation theorem statement is inherited, and non-positive Value at Risk with 100% confidence is found in a class of efficient portfolios.