CFA Practice Question

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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

With discrete compounding:
F(0, T) = F(0, 90/365) = [0.7321/(1.0425)90/365] (1.035)90/365 = 0.7308

With 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) = 0.7308

Note that the two rates are equal.

User Contributed Comments 4

User Comment
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.
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