# How to calculate FX hedged bond yield?

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???

## 2 Answers

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

• I wonder how bond ETFs that are FX hedged (such as BNDX) handle this issue. When they publish a YTM of 0.84% etf.com/BNDX how is that number calculated. – noob2 Dec 6 '17 at 20:38
• noob2: They hedge with one month forwards, it's explained in the index methodology: End-of-Month Roll of Currency Hedging Positions bbhub.io/indices/sites/2/2017/03/… – Lliane Dec 7 '17 at 4:01