- CFA Exams
- CFA Exam: Level II 2021
- Study Session 14. Derivatives
- Reading 37. Pricing and Valuation of Forward Commitments
- Subject 6. Currency Forward and Futures Contracts

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**CFA Practice Question**

Suppose the domestic currency is the U.S. dollar and the foreign currency is the Canadian dollar.

- The spot exchange rate is $0.7321.
- The U.S. interest rate is 3.5%.
- The Canadian interest rate is 4.25%.
- Assume these interest rates are fixed and don't change over the life of the forward contract. They are based on annual compounding and are not quoted as LIBOR-type rates.
- Assume a currency forward contract has a maturity of 90 days.

What should be the forward price if you want to enter into a forward contract to long Canadian dollars in 90 days? What if interest is continuously compounded?

Correct Answer: 0.7308

F(0, T) = F(0, 90/365) = [0.7321/(1.0425)

F(0, T) = (0.7321 e

With discrete compounding:

F(0, T) = F(0, 90/365) = [0.7321/(1.0425)

^{90/365}] (1.035)^{90/365}= 0.7308With continuously compounding:

*r*= ln(1.035) = 3.44%, and*r(f)*= ln(1.0425) = 4.16%F(0, T) = (0.7321 e

^{-0.0416 (90/365)}) e^{0.0344 (90/365)}= 0.7308Note that the two rates are equal.

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**User Contributed Comments**
4

User |
Comment |
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danlan2 |
They are always equal. |

NIKKIZ |
Are they not equal just because of rounding? working to 5 decimals I got 0.73076 for discrete compounding and 0.73080 for continuous. Shouldn't continuous compounding increase the value compared to discrete? |

tushi123 |
@nikkiz- since the denominator is larger,continuous compounding will decrease the value |

mtsimone |
No, they're not always equal. The reason they are here is that we're at 4 decimal places (currency future convention) and it's only a 90 day contract. If the contract was 2 years you'd see a difference at 4 decimal places, in fact the difference at 4 places is .0004 and at 5 is .000404. If it were a 500M contract that's 201K+ difference and if it were my portfolio I'll take it. |