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Now I'm updating typical equity premium of CAPM and Fama French 3 factors. As you know, some of interest rates are already in negative. To calculate market factors, not so hard to apply them as risk free rate practically. however i wonder if it is no matter that negative risk free rates are applied from the academic perspective. Are there any white papers about this topic? i wanna check the discussion about negative risk free rate.

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The capm doesn't care whether the risk free rate is positive or negative. In fact I'm not aware of any financial theory that is rendered invalid by negative rates. The only thing that's special about zero rate level is the fact that you can attain zero rate by holding physical cash. However it's impractical to hold large amounts of physical cash, so thats of limited relevance.

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