I suggest you consider the methodologies found in: 1. Stehle (1977) An empirical test of the alternative hypotheses of national and international pricing of risk assets in the Journal of Finance, 2. Engel andRodrigues (1989) Tests of international CAPM with time-varying covariances in the Journal of Applied Econometrics, 3. Bodurtha and Mark (1991) Testing the CAPM with rime-varying risks and returns in the Journal of Finance, and 4. Ng (2004) The international CAPM when expected returns are time varying in the Journal of International Money and Finance.
After the review of the suggested literature above.
Please choose the appropriate risk free (Rf) instrument, i.e. Government Bond and whether this variable (the constant or intercept in the CAPM model) will affect the return of a given financial asset (Ri - Rf) or be part of the estimation per se (Rf +(ErMkt-Rf)*β).
Make sure you use the same frequency on data: daily (suggested) or monthly. If you employ daily frequency for company and market returns you may use LN returns, bond yields are usually expressed as EAR, therefore don’t forget to transform them into daily returns.