### CFA Practice Question

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### CFA Practice Question

Consider a one-year currency swap with semi-annual payments. The two currencies are the US\$ and the euro. When the two parties entered the swap, the exchange rate was \$0.75/euro, and the term structure was as follows: The annualized fixed rates in dollars and euros are 7.84% and 6.48%, respectively.

Ninety days after the swap, the term structure is as follows: If the current exchange rate is 0.7, what is the market value of the swap to pay dollar-fixed and receive euro-fixed?
A. -0.0712
B. -0.0661
C. 0.0698
Explanation: First we compute the dollar discount factors:
B90(180) = 1 / (1 + 0.071 x 90/360) = 0.9826
B90(360) = 1 / (1 + 0.074 x 270/360) = 0.9474

Fixed dollar payments:
The present value of the fixed dollar payments of 0.0392 (0.0784/2), including the hypothetical notional principal, is 0.0392 x (0.9826 + 0.9474) + 1 x 0.9474 = \$1.0231.

Floating dollar payments:
The 180-day dollar rate at the start of the swap was 7.2%, so the first floating dollar payment would be 0.036. The present value of the floating payments plus the hypothetical notional principal of \$1 is 1.036 x 0.9826 = \$1.0180.

Then we compute the euro discount factors:
B90euro(90) = 1 / (1 + 0.055 x 90/360) = 0.9864
B90euro(270) = 1 / (1 + 0.06 x 270/360) = 0.9569

Fixed euro payments:
The present value of the fixed payments plus the hypothetical 1 euro notional principal is 0.0324 x (0.9864 + 0.9569) + 1 (0.9569) = 1.0199 euro.

Floating euro payments:
The 180-day euro rate at the start of the swap was 6%, so the first floating euro payment would be 0.03. The present value of the floating payments plus the hypothetical notional principal of 1 euro is 1.03 x 0.9864 = 1.0160 euro.

The euro notional principal, established at the start of the swap, is 1/0.75 = 1.3333 euro.

Now we obtain the following values for the four swaps:
• Pay dollar fixed, receive euro fixed = -\$1.0231 + euro 1.3333 x \$0.7 x 1.0199 = -\$0.0712
• Pay dollar fixed, receive euro floating = -\$1.0231 + euro 1.3333 x \$0.7 x 1.0160 = -\$0.0749
• Pay dollar floating, receive euro fixed = -\$1.0180 + euro 1.3333 x \$0.7 x 1.0199 = -\$0.0661
• Pay dollar floating, receive euro floating = -\$1.0180 + euro 1.3333 x \$0.7 x 1.0160 = -\$0.0698