Is there a way to make a hedged portfolio using two bonds, one is in EUR, the other one is in USD and FX forward contract? Assume that FX rate follows geometric Brownian motion movement.
You can mitigate your fx exposure (hedge fx risk by engaging in an fixed/fixed fx swap. Let's setup an example:
You want to invest in two bonds, one EUR denominated and one USD denominated bond. Each bond pays semi-annual coupons (at the same dates for simplicity purposes) for the next two years. You are a US-based investor and thus want to earn returns on your investments in USD and not take exposure to fx fluctuations. You can trade an fx swap with the following cash flows:
Now, obviously there will either be a mismatch of notional amounts either at the beginning or maturity of the bonds. As mentioned we can walk through a numerical example but obviously you want to match the notional exchanges at maturity and rather engage in a simple fx spot cash trade at the beginning to match notional amounts between swap notionals and bond cash present value (market prices).
Please keep in mind that standard fx swaps only exchange cash flows at the initiation of the swap agreement and final settlement. But the swap can be structured, as above to exchange periodic cash flows in between. Also, note that you can trade forward-starting swaps in case you already own the bonds and want to have the swap cash flow dates match the bond coupon payment dates. Additionally, you may want to look at an un/mis-matched fx swaps, which basically allows you to exchange different notionals in the spot and forward transactions of the swap. Thus you can greatly customize the swap. But as with everything in life, the more you customize the more you will pay up to get the deal done with your counter party.