Skip to content
All library documents

Choosing the Interest Rate Curve for a Foreign Government Bond

Article Quant Q&A · Author: lakshmen
Read the original

Summary

The document considers an Australian government bond issued in US dollars and asks which interest rate curve should measure its rate risk. The answers distinguish the bond's currency exposure from the issuer's country: because the payments are denominated in dollars, the interest rate component is associated with USD rates rather than the Australian dollar curve.

For risk measurement, the USD-denominated bond's yield can be viewed as a USD risk-free rate plus a credit spread reflecting the issuer's default risk. US Treasury yields or a USD swap curve can serve as the risk-free benchmark. The choice of hedge instruments depends on the desired decomposition: hedging USD rates while retaining spread exposure helps explain profit and loss in terms of rate moves and credit spread changes. The discussion gives a framework rather than a specific hedge calculation, and the observed bond yield includes both components.

Key ideas

  • A bond's interest rate exposure follows the currency of its payments, not simply the issuer's home country.
  • A USD-denominated foreign government bond yield combines USD risk-free rates and issuer credit spread.
  • Treasury or USD swap curves can be used to represent the risk-free USD component.
  • Hedge instrument choice can help isolate rate risk while retaining credit spread exposure.

Tags

Fixed incomeRisk management
Full text
# Which curve does the interest rate risk fall in?


# Which curve does the interest rate risk fall in?












For example, Australian government issues a bond denominated in USD currency? Which curve does the interest rate risk fall in? Australian Gov Curve or USD Gov Curve?

## Answer by VanillaCall (score 1)

https://quant.stackexchange.com/a/47204

It should be the USD curve because it was issued in USD currency and hence the yields should be benchmarked off the US Treasury curve.

## Answer by Dimitri Vulis (score 0)

https://quant.stackexchange.com/a/47205

You definitely don't have any exposure to any AUD curve. Looking at the risk to the USD-denominated Australian government curve is less than perfect because this curve is the sum of a USD default risk free curve and a credit spread to compensate the bondholders for the possibility that the bonds may default. For the risk free USD curve, you can use UST, or USD swap curve equally well. It's more convenient to choose the instruments that you would use to hedge your USD IR risk if you're looking to retain the credit spread exposure and not have a view on risk-free interest rates. With these risk measures, you should be able to explain your PL in terms of the USD rates and the credit spread.

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.