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I noticed when I regress the return of a portfolio on the Fama French 3 factor model that the value and the statistical significance of the coefficients vary when I use daily versus monthly portfolio returns. I would like to know what is the best frequency to estimate these coefficients?

For my purpose I do need to use higher frequency data (daily)

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In this context, I refer to the book on Empirical Asset Pricing by Bali, Engle and Murray (2016). They state on page 124 that

A minimum number of data points are usually required to ensure the quality of the values estimated by the regression. In the case of daily data over a one-year period, a reasonable requirement may be that the regression be fit using at least 200 data points. While using one year’s worth of daily data to calculate beta is common, other estimation period lengths and data frequencies are also used. Another common approach is to use monthly excess return data from the past five years.

Its basically a regression and usual regression thumb rules are applicable.

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