Standard deviation is one common way of measuring an asset's volatility. One component in calculating the standard deviation is the mean of the samples, and in most of the examples I can find, people use the arithmetic mean for this purpose. But if you are averaging a set of year-over-year returns, (e.g. 1.01, 0.83, 1.12), would it be more sensible to use the geometric mean, since this number is more representative of the year-over-year return across all samples?
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You should use the arithmetic average. While it's true that the geometric average is more useful for calculating average compounded return over a period, the volatility is more of a mathematical measure than a financial one, and is typically defined as the standard deviation, which is based on the normal distribution and uses arithmetic mean.
There is a separate formula for Geometric Standard Deviation that would apply if you used the geometric mean, but when measuring volatility the arithmetic standard deviation (and thus arithmetic average) is always used.
D Stanley
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