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:


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?)



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).

  • $\begingroup$ Thanks a lot :) $\endgroup$ – West Ray Apr 3 '19 at 8:50
  • $\begingroup$ No problem. Note that if you wish to annualize daily observations, you have to assume a fixed number of (business) days per year. Usually, the convention is multiply the standard deviation of the daily returns with $\sqrt{252}$. $\endgroup$ – AdB Apr 3 '19 at 9:01
  • $\begingroup$ Thanks a lot :) $\endgroup$ – West Ray Apr 3 '19 at 21:03

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