Concept
Geometric MA
Geometric MA is a Trend concept. The Library holds 3 implementations, each one a working definition you can pull into Quant.
Top Geometric MA indicators
3 total
What is a Geometric MA?
A geometric MA replaces the arithmetic mean inside a simple moving average with the geometric mean: multiply the last N prices together and take the Nth root. The equivalent, numerically safer construction is to average the logarithms of price and exponentiate the result, which makes the geometric MA an SMA computed in log space. By the AM-GM inequality it always sits at or below the arithmetic average of the same window, and the gap widens as dispersion inside the window grows.
The rationale is compounding: returns multiply rather than add, so averaging in log space matches how prices actually grow and pairs naturally with logarithmic chart scales. On short windows over typical price series the geometric and arithmetic lines are nearly indistinguishable; the distinction earns its keep on long horizons, volatile series, and percentage-based analysis.
How traders use it
- As a trend baseline on log-scaled or long-horizon charts, where log-space averaging keeps the line consistent with percentage moves rather than point moves.
- In compounded-growth work: geometric averaging underlies compound-return statistics, so geometric smoothing shows up in long-cycle growth bands and valuation-style curves.
- As a dispersion tell: since the shortfall below the SMA scales with variance, the spread between same-length arithmetic and geometric averages is a crude volatility read.
Related concepts · Moving-average lineage
Concept family
Trend
100 concepts mapped · 88 in the Library
Geometric MA FAQ
How different is a geometric moving average from an SMA?
On short, calm windows the two are nearly identical. The geometric version is always equal or slightly lower, and in log terms the shortfall is approximately half the variance of the window's log values, so the gap widens as volatility rises. For day-to-day smoothing the visual difference is negligible; it becomes meaningful on long windows, volatile series, and percentage-based work.
Why use a geometric mean for prices at all?
Because prices compound. A series that gains 10% and then loses 10% does not finish flat, and arithmetic averaging quietly ignores that asymmetry. The geometric mean is the average consistent with multiplicative growth, which is why compound-return statistics are built on it. As a plotted smoother the effect is subtle, but for return-based or log-scale analysis it is the coherent choice.
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