FRM Part II · FRM Exam Part II · VaR Mapping
A 1-year forward to buy EUR 1,000,000 at USD 1.10 is held by a US bank. Spot is USD 1.08 per EUR, the 1-year USD rate is 4.0% and the 1-year EUR rate is 2.0% (annual compounding). The present value of the EUR bond leg is closest to which USD amount?
The EUR leg is EUR 1,000,000 discounted at the EUR rate of 2% to EUR 980,392, then converted at spot 1.08 to about USD 1,058,824. Discounting at the USD rate would be wrong because the cash flow is denominated in euros.
- AUSD 1,058,824Correct
- BUSD 1,038,462
- CUSD 1,077,000
- DUSD 1,100,000
Explanation
Present value of EUR 1,000,000 in EUR is 1,000,000/1.02 = EUR 980,392. Converting at spot 1.08 gives USD 1,058,824. The domestic leg would be 1,100,000/1.04 = USD 1,057,692. Discounting at the USD rate instead gives 1,038,462, which is the wrong-rate error.
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