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I have rolling 3-year returns for an asset and a benchmark.

I want to compare the covariance of the asset and benchmark, should I use the covariance of the rolling 3-year returns or the covariance of the data at the weekly frequency (the underlying data)?

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  • $\begingroup$ What are you trying to do, i.e. what is your research question? Typically, the co-variance is measured by the underlying data. $\endgroup$
    – skoestlmeier
    Commented Aug 23, 2019 at 15:36
  • $\begingroup$ As part of CAPM, to calculate Beta (by doing cov/var) and multiply this amount by the returns of the benchmark (minus the Rf). Should the returns be cumulative or simple? If cumulative, is the covariance calculated on these rolling cumulative returns or on the underlying monthly returns? $\endgroup$
    – santorch
    Commented Aug 23, 2019 at 15:46
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    $\begingroup$ You are able to calculate market-beta with your stated formula whether you believe the CAPM holds or not. However, your input data are just simple returns, i.e. daily total returns (including dividend payments, adjusted for corporate actions like stock splits, etc.) $\endgroup$
    – skoestlmeier
    Commented Aug 26, 2019 at 7:33
  • $\begingroup$ Is there anything stating the log returns are more appropriate to use? $\endgroup$
    – santorch
    Commented Aug 26, 2019 at 10:38
  • $\begingroup$ Take at look at this answer. $\endgroup$
    – skoestlmeier
    Commented Aug 26, 2019 at 13:19

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