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EWMA Volatility Estimates Conditional Risk, Not One Series-Wide Spread

Article Quant Q&A · Author: bronson
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Summary

The note distinguishes two calculations that can sound similar: taking the standard deviation of a smoothed data series and estimating volatility with an exponentially weighted moving average (EWMA). The first produces one sample standard deviation for the observations considered. EWMA volatility instead updates over time, giving a conditional volatility estimate for each period. The distinction matters when analysis requires a changing risk estimate rather than a single description of overall dispersion.

The document gives a conceptual answer but no equations, worked example, or empirical comparison. It does not specify EWMA parameters, the input series, or assumptions about the data, so it cannot guide model calibration or establish which volatility measure is appropriate for a particular trading task. Its main lesson is about the different quantities the two procedures estimate; they should not be treated as interchangeable.

Key ideas

  • The standard deviation of a smoothed series summarizes dispersion with one sample estimate.
  • EWMA volatility provides a conditional estimate that can change from period to period.
  • The two calculations answer different questions and are not equivalent.

Tags

VolatilityStatistics
Full text
# EWMA Volatility vs Volatility of EWMA


# EWMA Volatility vs Volatility of EWMA












Is taking the standard deviation of a EWMA smoothed series equivalent to getting the EWMA volatility for that series?

## Answer by RA334 (score 3, accepted)

https://quant.stackexchange.com/a/40719

Short answer: No. if you take the standard deviation of a (smoothed) series you’ll be estimating a single sample standard deviation for the entire series. In contrast, the EWMA volatility estimates a conditional volatility for each period in the sample.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.