Arithmetic and Continuous Return Mean-Variance Efficient Frontiers
Posted: 10 Jan 2011
Date Written: January 15, 2008
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
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