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I have intraday (30 min) data for a number of stocks, and I would like to calculate the covariance matrix of returns.

For the purpose of calculating the covariance matrix, is it better/more correct to calculate "one step" returns, i.e. 30 min returns intraday, with a single overnight return on each day, or to calculate daily returns at same time of the day, i.e. at 9:00 the return is calculated vs yesterday's price at 9:00, at 9:30 the return is calculated vs yesterday's price at 9:30 and so on?

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    $\begingroup$ The first method gives the covariance of 30 min returns. The second method gives something a little strange, the covariance of partially overlapping 1 day returns, it is difficult to imagine a use for it. What is the prupose of your calculation? $\endgroup$
    – nbbo2
    Commented Jun 13, 2023 at 22:11
  • $\begingroup$ I would like to perform PCA and analyze the eigen-portfolios. Maybe using intraday data is overkill... $\endgroup$
    – Enrico Detoma
    Commented Jun 14, 2023 at 4:45
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    $\begingroup$ If there's no primary reason for you to use intraday data, then leave this idea for the time being. Make your portfolio analysis on daily close-to-close data. Afterwards, you can try to reproduce your analysis with intraday data and compare the portfolio results of the daily data and the intraday data. This will highlight the benefits/drawbacks of using intraday data contrary to daily data. $\endgroup$
    – Pleb
    Commented Jun 14, 2023 at 12:14

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