Geometric and Arithmetic Volatility

Abstract

Volatility as a risk measure has been criticized and dismissed on various grounds. Yet, volatility is the dominating risk measure in the investment management industry. Volatility is typically calculated as the arithmetic standard deviation of returns. At the same time, it is industry practice to use discrete returns, chain-linked annualized discrete returns and geometric average discrete returns in investment reporting. Unfortunately, mixing arithmetic and geometric calculations potentially distort risk and return comparisons. In this research note, we derive geometric and arithmetic versions of volatility. We discuss how they relate and their proper context.

Keywords: volatility, discrete, continuous, compounding, arithmetic, geometric, return