Arithmetic and Continuous Return Mean-Variance Efficient Frontiers

Abstract

The arithmetic mean-variance efficient frontier shows that taking more risk is always rewarded with higher expected arithmetic return. However, expected arithmetic return is a poor indicator of long-term arithmetic return, which corresponds to expected continuous return. For the continuous return mean-variance efficient frontier, expected continuous return initially rises, then declines and becomes negative without limit as risk increases. Too much aggressiveness can lead to disaster, even without borrowing.

Keywords: Mean-Variance Frontier, Long-Term Return, Leverage

JEL Classification: G10, G11, G14