# 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.

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.