Risk free rate and equity risk premium selection

Hi guys,

I need your help in clarifying once for all how to select the risk free rate and the equity risk premium in the CAPM context.

1) For risk free rate, I understand that is practically used the government bond coupon (or YTM) (with the duration correlated to the time horizon of our investment) of the same currency as the target company reports its cash flows (e.g., 10-year T-bond for US companies).

But based on the logic of the model, why should I have to assume different risk free rates based on the currency of the target company? I mean, investors have no limitations in where to put their money so there should be a unique risk free rate - am I wrong on this? Then of course we should factor it the country risk

2) Once selected the risk free rate, then the equity risk premium should be correlated: If I choose a 10-year US Tbond then I would calculate the equity risk premium on US stock market (S&P 500 as proxy), if I choose a German bond rate then I would use the German stock market as a proxy - Am I right non this?

But also here it applies the same logic as above: as an investor I can put my money both in American, German or whatever country equities so why there are different equity risk premiums? There should be an unique aggregated average figure for the overall global stock market.

Can someone shed some light on this please and clarify the logics and practical assumptions?

Thanks,

Emanuele