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When Root Mean Square Estimates Intraday Return Volatility

Article Quant Q&A · Author: Ang Yiwei
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Summary

The document asks whether root mean square can estimate volatility from intraday feed returns, in place of the standard deviation. The answer gives the relationship between variance, the mean of squared observations, and the squared mean. When returns have a mean close to zero, the squared mean contributes little, so the square root of the mean squared return approximates standard deviation.

This approximation depends on the sample’s mean being negligible; RMS and standard deviation are not generally interchangeable when the mean is material. The discussion does not specify sampling intervals, return construction, or annualization, and provides no empirical comparison. It therefore gives a concise statistical condition for using RMS, rather than a full intraday volatility methodology.

Key ideas

  • The square root of mean squared returns equals standard deviation when the returns’ mean is zero.
  • When the mean is close to zero, RMS can approximate standard deviation.
  • A non-negligible mean makes RMS differ from standard deviation.
  • The post does not address sampling frequency, annualization, or empirical validation.

Tags

StatisticsVolatilityTechnical indicators
Full text
# Can I use root mean square(RMS) to calculate volatility of intraday feed data?


# Can I use root mean square(RMS) to calculate volatility of intraday feed data?












I've been using standard deviation as a direct/simple approach to calculate volatility of a given intraday feed data. My question is it logical/sensible that using root mean square (RMS), which is the square root of mean of squared return as an estimation of volatility?

## Answer by Mayeul sgc (score 2, accepted)

https://quant.stackexchange.com/a/48629

It can be used if your intra day data has a mean very close to 0. $$ \sigma=\sqrt{E(x^2)-E(x)^2} $$ if we have $$E(x) \approx 0 \Rightarrow E(x)^2 \approx 0$$ then $$ \sigma = \sqrt{E(x^2)}$$

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