Graphical Portfolio Analysis

This paper presents a new methodology for portfolio analysis based on the correspondence between the expression for the standard deviation of a two-asset portfolio and the magnitude of the sum of two complex numbers. This approach offers a geometric alternative to traditional portfolio analysis. The pedagogical advantages of the new framework are illustrated by rederiving many efficient set mathematics results. A previously unrecognized fact is uncovered using the graphical technique that the sum of the maximum and minimum betas for efficient portfolios is 1, so knowledge of one extreme beta implies knowledge of the other.