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Fama and French (1993) three factors are available in Kenneth French's data library. Some papers use them as they are provided there and others calculate them again. If Fama and French (1993) used some different data screening, for example by excluding more or less stocks, this would produce different factors.

My question is: is using these factors data screening dependent? In estimating multi-factor models, do I have to use exactly the same data screening as they do? Moreover, if I form industry portfolios, (calculating the industry portfolio excess return instead of the stock excess return) can I use the same factors or should I create new ones and why?

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In general, it is always better to determine how the FF93 risk exposures are for your data. FF93 use a very comprehensive (read expensive) dataset, therefore it is very likely that your investable universe is different.

In the case you're investigating a large stock universe such as the SP500 I would feel comfortable using the FF factors on Ken French's website. If this is not the case, say you also examine small stocks or other countries then the US I would determine the risk exposures for your dataset.

The risk premiums of the FF factors tend to be stronger among small stocks, thus indeed filtering and determining a minimum size does matter. For example, the UK (FTSE 1000) exhibits a large portion of small stock. I believe that FF08 exclude companies with a value of market equity less than $12.5 dollar. Best way to overcome this is to use proper break-points (equivalent of the NYSE breakpoint used by FF) and to employ value weighting instead of equal weighting.

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The fama and french database is updated monthly relative to the asset universe available in the market at that point in time. The asset universe used in 1973 will not be the same as the one used in December of last year.

I would recommend using the five factor model FF(2014)

since portfolio theory assumes a linear positive relationship between CAPM beta of any stock and the market the answer to your question is no, it is not dependent. Keep in mind that the factor variables available are for US stocks only and will not work effectively for others.

If you wish to analyze the EU markets you can form regional based portfolios by using the average return of the largest EU indexes as the market portfolio, then long small cap and short large cap for SMB and long high B/M and short low B/M for the HML factor.

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