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I want to calculate monthly idiosyncratic volatility for the MDAX index which constitutes of 50 stocks. I use the Fama French 3 factor model for that. My dependent variable in the equation is the daily excess returns of individual stocks. I found that in many Fama French empirical studies, return on portfolio is used instead; however my sample size is so restricted which imposes me to use the returns on each stocks (Is my procedure correct???). I will regress my DV with the daily Fama French 3 factors that I will be myself calculating. I know that I have to multiply the standard deviation of daily residual by the square root of the number of trading days in the month to obtain monthly idiosyncratic volatility; however I'm so confused in this step ; how to obtain monthly IV for the whole index by multiplying each stock's daily residual by the square root of the number of trading days in month? It would be great if you can provide me with clarifications on what I've wrote above. Thank you in advance.

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