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I have a minute-by-minute price series of a stock. I would like to calculate the daily volatility or standard deviation of the stock's returns.

One way to do so is to get the end-of-day prices (i.e. daily close prices), calculate daily returns, and then calculate the standard deviation of these daily returns.

The alternative method is to calculate the minute-by-minute returns, calculate the minutely standard deviation, and then convert this into a daily equivalent by multiplying by $\sqrt{1440}$ (i.e. the number of minutes in a day).

My questions are:

1- which method should I use, given that the minute-by-minute data is available to me?

2- Does using the daily returns result in loss of information?

3- Are there advantages/disadvantages of using one method over the other?

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  • $\begingroup$ 1. It would be better to use the realized variance estimator or alternative realized measures when estimating daily volatility using intraday observations. 2. Yes, using close-to-close returns only gives you the variability based on two data-points, while the realized variance estimator gives you the daily variability using 1440 datapoints (close-to-close). $\endgroup$
    – Pleb
    Jul 14, 2022 at 11:48
  • $\begingroup$ @Pleb what exactly is the difference between the realized variance estimator and what OP describes? Is it the use of returns (rather than price changes) and setting mean return = 0 when calculating the deciations? $\endgroup$ Jul 14, 2022 at 19:18
  • $\begingroup$ Also, @finstats the correct annualization factor here may be $\sqrt{390}$ (there are 390 minutes from 09:00 to 16:00, assuming NYSE hours). If you have a 24 hour product though then by all means carry on with $1440$ $\endgroup$ Jul 14, 2022 at 19:20
  • $\begingroup$ @rubikscube09 You set $\mu = 0$ because it's negligible intraday. I advocate for the use of RV estimator because the underlying theory naturally extends into measures that accounts for noise and/or jumps in prices. While there is not "much" difference between the RV and the scaling method OP describes, besides setting $\mu = 0$, the scaling method is just as prone to noise-contaminated prices as RV, and thus OP should be vary of extending the use-case of the scaling method to other financial products as the noise structure might be considerably different (eg. more noise at 1min frequency). $\endgroup$
    – Pleb
    Jul 16, 2022 at 11:16
  • $\begingroup$ Thanks @Pleb for the in depth explanation. I assume that if we have $\mu \neq 0$ the RV estimator loses some of its favorable probabilistic/statistical properties? $\endgroup$ Jul 25, 2022 at 15:54

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