Geometric and Arithmetic Volatility
Journal of Insurance and Financial Management, 2022
Posted: 25 Oct 2011 Last revised: 21 Sep 2022
Date Written: October 24, 2011
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
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