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Country X's national government purchases country Y's government-issued bonds. Would the bonds be issued in country Y's currency?

How does inflation (of either country's currency) factor into this, especially when the bonds mature, say, 10 years later?

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As usual on a marketplace - depends on the buyers and sellers. Any country would love its bonds to be denominated in its own currency. However, the bond buyers need to trust the currency the bonds issued in, otherwise they wouldn't invest.

Bond terms vary as well. Some have fixed interest, some variable, some promise inflation adjustments, some don't. Again - whatever the buyers and the sellers can agree upon.

In the US for example, the bonds are denominated in the US dollars, own currency. Some bonds have inflation protection (as mentioned by JB King). However, in Greece, the bonds are denominated in EUR, which is the currency used in Greece, but not controlled by Greece. In Russia, bonds are denominated in EUR or USD, neither is used nor controlled by the Russians. Similarly most of the world uses USD or EUR for international transactions with very rare exceptions. Thus the country's inflation doesn't affect the bond value (the US/EUR inflation does, though).

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Generally, I would suspect though I'm not sure that this is a certainty as I could imagine if a country wanted to appeal to another country that they may use a different denomination for the value of the bonds.

Generally, the inflation of each can be a factor as country X's inflation would impact how far the proceeds would go while country Y's inflation may impact the currency exchange rate that may also impact the return. There are also some bonds that may have features designed to mitigate inflation on one side. TIPS would be an example of a bond where the principal is adjusted based on inflation data and thus would impact the total return. Thus, for a TIPS bond the matured value would be adjusted by the US inflation figures. The other country's inflation would impact the purchasing power of the total return though this is something else to try to compute.

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