Skip to content
All library documents

Decomposing a Cross-Currency Bond Investment into Swap Cash Flows

Article Quant Q&A · Author: Dr Brownian
Read the original

Summary

The document sketches how a foreign investor might translate a bond investment into domestic-currency cash flows using a cross-currency swap, then interest rate swaps. Its example has a US investor acquiring euros through a swap, purchasing a euro-denominated corporate bond, and using rate swaps to convert floating legs into fixed exposures. The resulting cash flows combine the bond coupon, the euro swap and basis spread, and a dollar fixed-rate receipt.

The explanation highlights residual risks: floating-rate payments may need separate hedging, and principal or coupon amounts may not align perfectly with a mark-to-market cross-currency swap, leaving some foreign exchange exposure. The author describes the response as unfinished and acknowledges that it does not directly calculate the requested cross-currency yield, basis pickup, or PV01 treatment. It is therefore a cash-flow decomposition illustration, not a complete arbitrage valuation method or quantitative demonstration.

Key ideas

  • A cross-currency swap can fund a foreign bond purchase while exchanging principal and currency cash flows.
  • Interest rate swaps can convert the floating legs into fixed-rate exposures.
  • The bond coupon, swap basis, and domestic fixed-rate leg determine the combined cash-flow profile.
  • Principal and coupon mismatches can leave residual foreign exchange exposure.
  • The example is explicitly incomplete and does not calculate yield pickup or PV01.

Tags

Fixed incomeForexArbitrageDerivatives pricing
Full text
# Cross Currency swap - Bond Yields arbitrage


# Cross Currency swap - Bond Yields arbitrage












Could somebody explain me step-by-step how can I compute the cross-currency yield of a bond bought by a foreign investor and x-ccy swapped back into his domestic currency? I basically would like to see the arbitrage/pickup adding the basis.

Should I add the PV01 to my calculation or should I just just add/subtract the basis?

Thank you very much in advance.

## Answer by Attack68 (score 1)

https://quant.stackexchange.com/a/46910

> Say a US investor with 1mm USD wants to buy a 10Y Volkswagen bond in EUR priced at 100 EUR with a 5% coupon.

First that investor needs to acquire EUR for purchase without exposing themselves to FX risk. To do this they execute a cross-currency swap.

The investor will pay 1mm USD and receive say 1.1mm EUR with the agreed cashflows: he will receive USD 3M LIBOR and pay EUR 3M EURIOR + $X$ bps (in this case suppose $X$ is -15).

Now the investor buys the bond in EUR and receives a 5% coupon for 10Y.

There are two residual concerns:

- The floating IBOR payments in either currency.

- The slight discrepancy of repayment amount of EUR is not consistent with a mark-to-market cross-currency swap, and the coupons may be FX risk exposed (only a minor problem often ignored).

To get around the first concern the investor may trade interest rate swaps. He swaps floating rates for fixed rates in each currency. Suppose he receives fixed on a 10Y USD IRS at 2%, and pays fixed on a 10Y EUR IRS at 0.5%.

Now the resultant cashflows for the investor are:

> Receive a 5% EUR bond coupon. Pay a 0.5% EUR fixed rate. Receive 3M EURIBOR. Pay 3M EURIOR -15bps. Receive USD 3M LIOR. Pay USD 3M LIBOR. Receive 2% USD fixed rate.

Netting everything above the cashflows are:

> Receive 4.5% - 15bps EUR Receive 2% USD fixed rate.

This answer is a draft (I don't have time to finish it currently) since it doesnt directly answer your question but is hopefully informative...

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.