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Interpreting the Root Mean Square of Daily Returns as Volatility

Article Quant Q&A · Author: Řídící
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Summary

The document asks for a plain-language name for a measure formed by squaring daily asset returns, averaging them, and taking the square root. The response explains that, when return drift is assumed to be zero, this quantity can be treated as a measure of daily volatility. In statistical terms, it is the root mean square of returns, which corresponds to standard deviation when the mean is zero.

The exchange offers a concise interpretation rather than an extended naming discussion or empirical comparison. Its conclusion depends on the zero-drift assumption: if average returns are not zero, the root mean square also reflects that mean component and is not exactly the usual standard deviation. The measure is tied to the return sampling interval, so a daily input produces a daily-scale quantity; the document does not discuss annualization, estimation error, or alternative volatility estimators.

Key ideas

  • The measure is the square root of the average squared daily return.
  • With zero return drift, it can be interpreted as daily volatility.
  • The root mean square and standard deviation coincide when the return mean is zero.
  • A nonzero mean affects the root mean square, so the interpretation has an assumption.
  • The result retains the time scale of the returns used to calculate it.

Tags

StatisticsVolatility
Full text
# Does this volatility-like measure have a name?


# Does this volatility-like measure have a name?












So, basically I'm looking at `{=SQRT(AVERAGE((R1:R100)^2))}`, or in words: the square root of the average of squared daily returns.

Is there a nice simple term/name for this? (By simple term, I mean a word that I could use with non-statisticians and the like.)

## Answer by Kermittfrog (score 1)

https://quant.stackexchange.com/a/52937

If you assume a zero drift for our asset return, this formula is indeed simply a measure for (daily?) volatility.

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.