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I want to calculate monthly idiosyncratic volatility for the DAX index comprising 30 stocks. I will use the Fama french 3 model. My question is whether I have to calculate these factors for each stock or there is any database which will provide me with this data. I am a beginner in this model and wish I CAN HAVE A clear answer for this. It will save my life. Thanks in advance.

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Ken French's data library has all the factors here. You should probably use their calculated factors for Europe rather than their regular factors computed from U.S. markets.

Let $R_t$ denote the return of the DAX from $t-1$ to $t$. You want to run a monthly, time-series regression of returns in excess of the risk free rate on the three factors:

$$ R_{t} - R_{ft} = \alpha + \beta_1 \mathit{SMB}_{t} + \beta_2 \mathit{HML} + \beta_3 \mathit{RMRF}_t + \epsilon_{t}$$

It's important to get the timing to match up exactly. Eg. the June return is from May 31 to June 30. There's a somewhat subjective question of how long a time-series regression to run. The upside of a longer time-series regression is utilizing more data the downside is that betas aren't stable over time.

You may want to carefully read French's data website and the Fama-French international factors paper to see exactly what they're using for the market index. Since the DAX is itself rather market indexy, idiosyncratic volatility relative to whatever market index Fama-French use for their European factors may not be that great.

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    $\begingroup$ (+1) for the precise answer. I would like to add that any data from Kenneth French‘s website is denoted in US-Dollar. As OP is analyzing german stocks, these return-serieses should be converted into US-Dollar prior to the regression. Results are therefore from the view of a typical US-investor. If a local view is preferred, some sites like here provide national Fama/French factors for Germany denoted in Euro. $\endgroup$ – skoestlmeier Jan 9 at 17:37

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