# how negative rates (mr and rf) affect CAPM

I don't understand how the negative rates factor into this and what it means in the market

Beta= .73
rf= (-) 0.0032
mr= (-)0.0264

CAPM =  [(-)0.0032 + [(-) 0.0264 – (-) 0.0032]0.73 = ???


Although Rf can be negative (but not too negative), Rm cannot be less than Rf as in your example. It is a non-equilibrium situation, no one would invest in risky securities if they have an expectation lower than risk-free securities. So Rm > Rf is a necessary assumption of the CAPM, whether rates are positive or negative. Also, algebra is algebra and the CAPM is the CAPM, there is no CAPM2.

• Or in another lingo, simply that if you have a market risk premium $E[R_M - r_f] < 0$ that is negative, you have here a risky bet (i.e. the market) that yields an expected return less than a for-sure bet (i.e. the risk free asset). This isn't an equilibrium. The necessity of the CAPM to have strictly positive risk premia is indeed critical. Of course, however, you could build a model whereby this is still preferred by a representative agent (i.e. frictions to financial market access, etc) where this is possible. But such a world is beyond the classical CAPM assumptions. – user32416 Oct 1 '15 at 20:37

The risk free rate can be viewed as the opportunity cost to hold an investment i.e. Every risky investment should at least pay out the risk free rate. This is why you subtract the Rf from the Rm

When yields are negative you would have to add the Rf to Rm meaning you should expect to earn a much lower return [everything else held constant]:

CAPM1= negative interest rates
CAPM2= positive interest rates

Beta= .73
rf= (-) 0.0032
mr= (-)0.0264

CAPM1=  [(-)0.0032 + [(-) 0.0264 – (-) 0.0032]0.73 = -2.0136%

CAPM2=  [0.0032 + [(-) 0.0264 – 0.0032]0.73 = -1.8408%


Remember that CAPM is the expected return on the investment