If we are running monthly cross sectional regressional, where we regress excess stock returns on...

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Accounting

If we are running monthly cross sectional regressional, where we regress excess stock returns on their the stock characteristics like market capitalization, B/M plus a new factor for example "twitter factor", for all companies in a given month. Then we fetch monthly betas for twitter factor, and we use that twitter factor beta and regress that on fama french factors and get significant alpha - to me this means additional premium associated with the Twitter factor that is not explained by the allready existing factors.
Question: If we now want to analyse if this twitter factor is compensation for some risk, for example default risk which we represent as the atlman z score, what appraoch we can use ?
Use Altman Z score for each company, for each month as control variable in regression 1, and then again fetch monthly betas for twitter factor and regress on existing factors to see if alpha is still significant.
Or Use Altman Z score for each company, for each month as control variable in regression 1, and then again fetch monthly betas for twitter factor and regress on existing factors but also include agregate Altman Z score for all firms in regression 2 as well to see if alpha is still significant.
Thank you

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