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I have trouble understanding what type of maturity to use when calculating CAPM. My professor uses the 3-Month risk-free rate to backtest a portfolio strategy that uses a lookback period of 1 year daily returns. Another professor uses the 10-year risk-free rate? Shouldn't one use the maturity that corresponds to the holding period as it best describes the opportunity forfeited? Is the risk-free rate chosen out of preference? wouldn't this just under/overstate CAPM?

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Could you provide more information on how they use these risk free rate ? My guess is that they choose the risk free rate accordingly to the time-step used in the considered method. –  lmorin Aug 16 at 0:49
    
@Imorin Sure, the professor that used the 3-month risk-free rate took an actual time series of returns and subtracted the 3-mo risk free rate time series (found in FRED) to find the market risk-premium. The other professor simply uses the 10-yr rate and subtracts it from the cumulative return of the strategy/returns in that given time frame. –  Jason Guevara Aug 16 at 1:16

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I think the best strategy is to follow Ken French who posted all of the Fama-French factors on his website a while ago, including the risk-free rate.

The latter is updated at the same frequency as the portolio returns, e.g. you can't use a 3-month - based rate if you work with monthly equity returns.

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