Comparing Bond Issuance Costs Across Currencies with Cross-Currency Swaps
Summary
The document explains how a corporate issuer can compare bond financing costs in two currencies when each bond is quoted against a different reference rate. The basic comparison is to calculate each bond’s all-in yield, then translate one set of cash flows through a cross-currency swap and compare the resulting equivalent funding spread with the alternative issuance. A swap quote can express the pickup between currency legs, while its valuation depends on the relevant reset curves and forward foreign exchange rates.
The discussion illustrates floating-rate legs and the present-value equivalence used to compare them. It also notes that financing cost alone omits liquidity, investor demand, counterparty exposure, legal and regulatory differences, and uncertainty in callable or amortising cash flows, which can create hedge mismatches. The simple subtraction formula in one answer is presented without enough convention detail to apply universally; actual comparisons require pricing the appropriate swap structure, tenor, and spread conventions. Different reset frequencies can also complicate the calculation.
Key ideas
- Compare all-in funding costs after converting one currency’s cash flows through a cross-currency swap.
- The swap pickup depends on currency reset curves, forward exchange rates, and the selected tenor.
- Equivalent swap legs have matching present values after conversion and discounting on the appropriate curves.
- Financing-cost comparisons omit liquidity, investor-base, legal, regulatory, and counterparty considerations.
- Uncertain bond cash flows can cause over-hedging or under-hedging and change the economics.
Tags
Full text
# Comparing debt issuance across currencies # Comparing debt issuance across currencies Imagine I’m a European corporate thinking of issuing a bond in either GBP or EUR. I have the spread above gilts for a GBP transaction and a spread above mid swaps for EUR. How do I see which one would be more ‘cheaper’? I know I need to swap the GBP one to a EUR equivalent but how do I do that step by step? ## Answer by Hans-Peter Schrei (score 3) https://quant.stackexchange.com/a/75382 In order to determine which bond issuance would be cheaper, you would need to compare the all-in costs of each option. This involves taking into account the bond's yield and any associated currency swap costs. Here is a step-by-step guide: - Obtain the GBP bond's spread above gilts and the EUR bond's spread above mid-swaps. - Calculate the all-in yield for each bond by adding the respective spreads to the reference rates (i.e., gilts for GBP bond and mid-swaps for EUR bond). - Determine the GBP/EUR cross-currency basis swap rate. This rate represents the cost of swapping GBP cash flows to EUR cash flows, or vice versa, over the life of the bond. The cross-currency basis swap rate can be calculated from the EUR swap rate, the GBP swap rate and the GBP/EUR cross-currency basis. - Convert the GBP bond's all-in yield to an equivalent EUR yield using the cross-currency basis swap rate. The formula to do this is: EUR-equivalent yield = GBP bond all-in yield - cross-currency basis swap rate - Compare the EUR-equivalent yield of the GBP bond to the all-in yield of the EUR bond. The bond with the lower all-in yield will be the cheaper option. Keep in mind that this analysis assumes that your main concern is the cost of financing, and it does not consider other factors such as liquidity, investor base, and potential market risks. ## Answer by Pythonista anonymous (score 1) https://quant.stackexchange.com/a/75384 I am not sure I understand the question fully. Do you mean that you can choose between issuing a bond in GBP and one in EUR, and you want to calculate which is cheaper? One way to think about it is to price a xccy (cross-currency) swap. This way you can calculate that, for a certain tenor and certain characteristics, a bond paying Euribor + 400 swaps to, say, GBP Sonia + 440. People typically refer to this saying there is a 40-bp pickup from GBP to EUR. So if, for whatever reason (e.g. the investor base being much larger in one currency than another, different appetite, etc) you can place your EUR bonds at Euribor + 400, but you can place your GBP bonds at Sonia + 450, it would be "cheaper" to issue in EUR, because GBP S + 450 swaps to Euribor + 410, which is more than Euribor + 400 A few clarifications: - this comparison looks at just the cost of financing; it ignores other factors like liquidity, the counterparty risk from the swap, the different legal and regulatory framework of issuing in one currency vs another, etc. - if the cashflows are certain, the comparison holds. The more elements of uncertainty there are, the harder it is to price the xccy, and the greater the chances that you may end up over-hedged or under-hedged. E.g. if the bond is callable, if the cashflows are uncertain (like in many ABS/RMBS bonds, where it's hard to forecast the exact amortisation), if partial prepayments are allowed under certain conditions, etc. What I mean is that the xccy pickup for a 5-year bond may be 20 bps, but maybe it is closer to zero for a shorter bond, so if you call it or prepay a lot the economics will be different. - there are some complications when comparing a daily rate like Sonia to a non-daily rate like Euribor Do you have access to Bloomberg? If you do, you can price a xccy swap with SWPM, specifically `SWPM -FLFL` for floating to floating, and `SWPM -FXFX` for fixed to fixed. Remember to set premium to zero and to solve for the spread. If you price a xccy swap, the 3 main curves which affect the result are: - the GBP reset rate - the EUR reset rate - the FWD fx In the case of floating to floating, what does it mean that EUR + 400 swaps to GBP + 440? Well, for each payment date: - The GBP leg receives reset rate + 440 - The EUR leg pays reset rate + 400 - The net payment in GBP =1-2 converted into GBP at the forward FX of the payment date The two legs are equivalent because: - if you take the EUR payment at 2, - convert it into GBP at the forward rate of the date, - then discount it using the GBP discount curve, - the present values of the two legs are the same
Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.