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I have a time series dataset and to model CAPM, I also need a risk free rate of return. I wanted to use the daily US 10-year bond yields as the risk-free rate. My data spans over 7 years.

I have calculated the daily returns of the stock indices of interest by taking the first difference of the logs. This also gives me a stationary series.

However, the US bond yields seem to be non-stationary at 1% and 5% confidence levels but not at 10%. Hence, should I log differencing the yields too before I run the CAPM regression?

I am unsure of this as I think differencing the yields would give me the daily yield volatility which cannot be used in CAPM as far as I am aware.

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