CAPM and Fama–French Models with Negative Risk-Free Rates

Summary

The note addresses whether negative risk-free rates invalidate the CAPM or the use of a risk-free rate when calculating market excess returns in the CAPM and Fama–French three-factor model. Its answer is that the CAPM does not require the risk-free rate to be positive, and the respondent knows of no financial theory made invalid simply by negative rates.

The only special feature of a zero rate identified is that physical cash can nominally earn zero, creating a practical lower bound consideration. The answer qualifies that point: storing large amounts of cash is impractical, so it has limited relevance. This is a brief conceptual response rather than a literature review; it provides no papers, derivation, empirical analysis, or detailed treatment of how negative rates affect factor construction.

Key ideas

• The CAPM can use a negative risk-free rate without invalidating the model.
• Negative rates can be applied when constructing market excess returns in factor models.
• Zero is distinctive because physical cash can nominally earn no interest.
• The cash alternative is limited in practice because holding large amounts is impractical.

Tags

# Discussion about negative interest rate


# Discussion about negative interest rate












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.

## Answer by dm63 (score 1)

https://quant.stackexchange.com/a/28430

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.