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Is inflation included in risk free rate when using CAPM?

 It seems that inflation should be add into interest rate to form nominal interest rate, isn't it?

norminal rate = real rate * (1+inf rate)

 

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 so, when we calculate cost of equity, if inflation rate is given, do we need to use nominal rate?

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 psuh~~~~~~~~~

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the RFR in CAPM is a nominal rate, so we need to use inflation rate and real risk free rate to derive the nominal rate

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