Daily Volatility: When to Use Standard Deviation and Annualization

Summary

The document asks whether daily log returns can be presented directly as daily variation when the goal is not to report risk over a longer horizon. It distinguishes an individual return observation from a volatility estimate: one return shows a realized move, while standard deviation across returns gives a more robust measure of variation. The answer therefore favors standard deviation when a less noisy estimate is needed.

Annualization depends on the question being answered. It is not required for every use: a one-day risk calculation, such as daily value at risk, calls for a daily return measure. The discussion does not specify a volatility estimator, sampling window, or assumptions for scaling volatility across horizons. Its guidance is limited to matching the return horizon to the intended analysis and not treating one observed return as a stable estimate of volatility.

Key ideas

• A single return records one realized move and is not a robust volatility estimate.
• Standard deviation across returns provides a more robust measure of daily variation.
• Annualization is unnecessary when the analysis concerns a daily risk horizon.
• Choose a return or volatility horizon that matches the risk question being asked.

Tags

# Do I have to annualize daily volatility?


# Do I have to annualize daily volatility?












I computed daily returns via $\ln(P_t)-\ln(P_{t-1})$ in order to get the volatility. But I do not want to present my results over a certain period of time (whether it's a week, a month or a year). I just want to see the daily variations. Is that meaningful?

Also, in that case, should I still compute the standard deviation? Or is it enough if I present the returns as the volatility?

## Answer by Aksakal almost surely binary (score 1, accepted)

https://quant.stackexchange.com/a/54624

A single observation of a return (magnitude) is not a very robust estimate of the volatility. If you're ok with it not being robust then yes, you can use it. Otherwise, the standard deviation is a more robust measure of volatility.

No, you don't need to annualize returns in every situation. For instance, if you're calculating 1-day VaR, the daily return (not annualized) is the relevant metric.

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