How does one go about calculating a 10 year US treasury yield hedged back to EUR? I vaguely understand this but I think there's two methods
1) Calculate 3-month annualized hedging cost 2) Calculate the difference between 3-month USD libor and 3-month EUR and then add in the cross currency???
When you hedge 1 million in bonds, you do not enter into a 1 million forward, but a slightly larger number H, where H = 1 + estimated return on the bond in next 3 months. (I.e. you have to hedge now based on what the bond position will be worth 3 months from now). The bond return, in turn, is usually estimated from the bond yield. (If the bond yield is 2% then $H\approx 1+0.02/4=1.005$
The "carry from the hedge" i.e. essentially the cost of hedging is ex ante equal to $H*\frac{FWD-SPOT}{SPOT}$ where FWD and SPOT are the forward and spot rates now (at the beginning) of the quarter. The ex-post cost will also include an error term because the H you used will turn out to be not quite correct, so you had a small exposure to FX after all.
In any case a rough and ready estimate for the hedged yield can be had by subtracting $H*\frac{FWD-SPOT}{SPOT}$ from the yield of the bond, having care to convert between quarterly and annual figures.
If you don't have $FWD$ then you can calculate it as you mention from the difference of the two Libors plus the cross currency basis, but that is a more roundabout way.
An exact approach would be to calculate all the cash flows in USD, calculate their EUR equivalent using forward fx rates and then compute a yield from the EUR flows
