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.


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.

  • 2
    $\begingroup$ (+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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