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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.

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what do you try to hedge? if fx exposure then yes a strip of fx forwards or fx swap –  Matt Wolf Dec 10 '12 at 12:32
    
Could you give me a hint how to do it? –  user3378 Dec 10 '12 at 14:34
    
are you looking for a mathematical approach or like to know how market practitioners hedge fx exposure? What is your base currency? Which exposure do you try to hedge? Please elaborate before I can help further –  Matt Wolf Dec 10 '12 at 23:55
    
I am asking because a lot different risks exist in your portfolio (interest rate risk, credit risk (in case of corporate bonds), sovereign risk (in case of sovereign bonds), prepayment risk (in case of prepayment features embedded in the bonds), and new credit risk arises when implementing an fx swap. I need to know what exactly you try to hedge here... –  Matt Wolf Dec 11 '12 at 0:33
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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:

  • At initiation you provide USD based funding to your swap counter party in exchange for EUR based funding which you use to purchase the EUR bond (I do not go into the details of the exact amounts, if desired, we can go through the detailed math later).
  • During the life time of the swap, every 6 months on the bond coupon payment settlement dates you receive a fixed payment denominated in USD and surrender a fixed (known) payment in euros to your counterparty. The euro amount equals the amount you receive as coupon payment from your eur bond investment.
  • At maturity you receive back the USD swap notional and return the EUR notional you received at the outset of the swap agreement. This EUR notional is the amount you receive from the repayment of par of your EUR bond investment.

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.

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Thanks for the deatiled answer, now I understand you question from the begining. My question was to hedge against exposure to geometric Brownian motion, using only these two bonds, FX forward and possbile zero interest rate savings account. Thank you! –  user3378 Dec 11 '12 at 17:00
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