# FX Hedging costs when using 3m FX Fowards vs XCCY swaps for an IG Bond

Suppose I want to hedge the FX exposure of an USD Corp Bond(held to maturity) to GBP and I can choose between rolling 3m FX Forwards and XCCY swaps. How can I estimate the difference in the hedging costs of these two approaches in terms of their impact on the Z-Spread ?

My understanding is that I need to forecast the behaviour of the 3m currency basis over the lifetime of the bond and compare it with the basis that I'd lock in the xccy swap. Could you point me me towards som research that would help me answer this question ?

ps. let's assume that the rates exposure is hedged separately using IRS

To get an accurate answer you probably won't be able to get around using a proper pricer and comparing the two methods. To contrast the two approaches:

1. FX Forwards: convert all cashflows from CCY1 to CCY2 using the interpolated FX forwards, then discount all payments at a single $$YTM_{CCY2}$$.
2. XCCY: create a cross currency swap where the paying CCY1 leg features the bond's coupon payments and receiving CCY2 leg the target coupon rate. To account for the richness/cheapness of the bond, choose the premia of swap to be $$100-P_{bond}$$. You could also enter this on a matched-maturity (rather than par-par) basis where you strike at the mid market rate (zero NPV). Finally, solve for the fixed rate $$R_{CCY2}$$ on the CCY2 leg.

The main risks will indeed be the forward points for method 1 and the XCCY basis for method 2. However, depending on the payment frequency of the bond, you might need to factor in several other curves as well, e.g. 3s6s or 3s12s basis or OIS curves. You don't need to forecast the 3m XCCY basis per se since you a have a full XCCY basis curve up to 30 years or so. This is what your pricer will rely on.

The hedge cost differential would then just be the difference $$c = YTM_{CCY2} - R_{CCY2}$$. You could also compare the implied basis from covered interest rate parity versus the quoted XCCY basis. Generally the two should align relatively well though.

If you want to do a comparison in spread terms then you could use method 2 and swap into a floating interest rate instead which would give you a XCCY ASW (asset swap spread). This can be directly compared to the local currency ASW (which is close enough to the Z-Spread). For the first method, I've never seen an FX implied Z-Spread being used (although it's mathematically possibly of course).

There are many books that cover these topics in detail but perhaps a bank primer such as this one is sufficient.

• Thanks for the answer! About the way you described the FX Forwards approach, you are basically using FX Forwards to hedge every cashflow, does this mean that you assume that the 3m forward points will move in line with the "forward 3m forward points" implied in the FX Forward Points curve? – Gigi B Apr 28 at 9:12
• Yes, FX swaps (forward forwards) and FX forwards are held together by no-arbitrage conditions, similarly to IRS. For example, the 3m forward 3m EUR USD points will be obtained from the spot 3m and 6m points. The FX swap points are then just the difference between the far leg points and near leg points. So if you swap a USD denominated bond into EUR and EURUSD strengthens (forwards go up) your $YTM_{EUR}$ goes down since your USD is now valued less. – oronimbus Apr 28 at 9:59
• Just to make sure that I totally understand it: spot 3m forwards points moving in line with forward 3m forward points is just an assumption which may or may not hold in reality and what this approach does is to use the current FX curve to forecast the future path of the 3m FX Forward points. Is my understanding correct? – Gigi B Apr 28 at 11:20
• Correct. Two examples: 1) 3m forward stays constant, 6m forwards go up => 3m3m forward points increase. 2) 3m forward goes up, 6m forward stays constant => 3m3m points decrease. This is a mathematical relationship and should in practice be manifested by the "no arbitrage" principle (FX liquidity runs deep). The FX forward curve not only gives you the 3m (forward or FX swap) rate but any rate really: O/N, T/N, 2 weeks,...., 9 months. – oronimbus Apr 28 at 11:56