Geometric and Arithmetic Volatility

7 Pages Posted: 25 Oct 2011

Date Written: October 24, 2011


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

Suggested Citation

Steiner, Andreas, Geometric and Arithmetic Volatility (October 24, 2011). Available at SSRN: or

Andreas Steiner (Contact Author)

Andreas Steiner Consulting GmbH ( email )

Walderstrasse 43c
Hinwil, 8340

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