Arithmetic and Continuous Return Mean-Variance Efficient Frontiers

Abstract

The arithmetic mean-variance frontier shows that taking more risk is always rewarded with higher expected arithmetic return. This article shows that there is a danger from being too aggressive that is not reflected in the arithmetic return mean-variance frontier because expected arithmetic return is a poor indicator of long-term arithmetic return. Since long-term arithmetic return is equivalent to long-term average continuous return, the relevant mean-variance frontier replaces expected arithmetic return with expected continuous return. The article shows that, for the continuous return mean-variance frontier, expected return initially rises, then declines and becomes negative as risk increases.

Keywords: Modern Portfolio Theory