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Calculating FX Delta for a Foreign-Currency Bond Position

Article Quant Q&A · Author: godimedia
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Summary

The document explains that a bond denominated in a foreign currency creates foreign-exchange delta for an investor reporting in USD. To estimate the exposure, it considers the amount that would be received by unwinding the position at settlement: notional multiplied by clean price plus accrued coupon, with proceeds expressed in the bond’s currency.

Converting those proceeds at the spot exchange rate gives the USD mark-to-market value. Holding other factors constant, a change in the exchange rate changes the USD value of the proceeds, creating FX sensitivity. If delta is defined as exposure to a 100% move in the exchange rate, it equals the current unwind proceeds under this convention. The explanation assumes clean price excludes accrued interest and notes that bookkeeping may separate principal from accrued coupon; it does not address hedging, settlement-specific conventions, or other bond risks.

Key ideas

  • A foreign-currency bond creates FX delta when the portfolio is reported in another currency.
  • Estimate unwind proceeds using notional, clean price, and accrued coupon through settlement.
  • Convert the proceeds at spot to obtain the position’s USD mark-to-market value.
  • Under a 100% exposure convention, FX delta equals the current unwind proceeds.
  • The calculation isolates currency sensitivity and does not cover the bond’s other risk factors.

Tags

Fixed incomeForexRisk management
Full text
# Can a Bond have FX Delta Risk?


# Can a Bond have FX Delta Risk?












Given we know the

- Notional

- Trade Price

- Currency in which the Bond Pays Coupons

- FX Rate from Bond Currency to USD

Trying to understand if a Bond can have FX Delta Risk and how it should be computed?

## Answer by Dimitri Vulis (score 2, accepted)

https://quant.stackexchange.com/a/71429

Yes.

Assuming your reporting is in USD.

Assume that by "trade price" you mean "clean price", ex accrued. Most coupon bonds are quoted like that.

If you unwind the bond position today, settling T + some n, like 2 days, then the proceeds will be notional * (clean price + accrued coupon until the settlement date) in the currency of the bond on the settlement date. You can convert these foreign currency proceeds into USD in a separate transaction, using the spot exchange rate. Logically, this should just be the USD mark to market, but you may need some arbitrary bookkeeping to separate the principal from the accrued.

If, ceteris paribus, the exchange rate moves: the currency of the bond appreciates / depreciates versus USD, then the USD proceeds increases / decreases. This sensitivity is where the FX delta comes from.

If you conveniently define the FX delta to be the exposure scaled to 100%, then the FX delta is exactly the proceeds if you unwind now.

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.