Annualizing Monthly and Quarterly Return Volatility

Summary

The document explains how to annualize the standard deviation of monthly or quarterly returns when the available history contains an arbitrary number of observations. For monthly returns, it says to multiply the standard deviation by the square root of twelve; for quarterly returns, use the square root of four. The annualizing factor depends on the observation interval, not on whether the sample spans a whole number of years.

It distinguishes annualization from sample size: more observations do not change the scaling factor, but they can narrow confidence intervals around the volatility estimate. The response does not discuss assumptions behind square-root-of-time scaling, such as return dependence or changing volatility, and it does not resolve whether to use a population or sample standard deviation. Its guidance is therefore a basic scaling rule rather than a full treatment of volatility estimation.

Key ideas

• Monthly return standard deviation is annualized by multiplying it by the square root of twelve.
• Quarterly return standard deviation is annualized by multiplying it by the square root of four.
• The number of observations does not determine the annualization factor.
• A larger sample can narrow confidence intervals without changing the scaling rule.

Tags

# Annualising standard deviation (monthly, quarterly data)


# Annualising standard deviation (monthly, quarterly data)












The question I have refers to annualised standard deviation.

For example, I have various funds monthly returns data for the period 1980-2019. Some of them report data for e.g. 13, 19, 43, 56 months and so on. Given that the particular fund is not straight 12, 24, 36 months and so on, can I still use the formula `= standard deviation (entire time series of a fund 1)*square root of 12`

Unless I should do a count of all available monthly returns and write the formula:

```
=stdev.p(range)*sqrt(counta(range))

i.e. (standard deviation * the square root of the count of monthly returns of a particular fund)
```

The 2nd question on the back of that is, what if the returns are quarterly, would the square root of 4 suffice (even if I have e.g. 5, 6, 7 and more quarters of data for a particular fund?)

Thanks

## Answer by AdB (score 1, accepted)

https://quant.stackexchange.com/a/44907

Yes, this is exactly the beauty of annualizing standard deviations!

If you have an arbitrary number of monthly (quarterly) returns, you simply multiply the standard deviation of those returns with $\sqrt{12}$ ($\sqrt{4}$) in order to obtain the standard deviation of the annualized returns. The number of observations does not count in this respect (apart from the fact that it narrows your confidence intervals to have more observations).

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.