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# Reading 18: Currency Exchange Rates-LOS h习题精选

Session 4: Economics for Valuation

LOS h: Explain interest rate parity, and illustrate covered interest arbitrage.

Assume the 1 year USD:EUR forward rate is 0.89348, the German interest rate is 3.38 percent, and the U.S. interest rate is 1.90 percent. If interest rate parity (IRP) holds, the USD:EUR spot rate is approximately:

 A) 0.91204.
 B) 1.56670.
 C) 0.88069.

Interest rate parity is given by:

Forward FC C = Spot FC C × [(1 + rdomestic) / (1 + rforeign)], or alternatively
Spot FC C = Forward FC C × [(1 + rforeign) / (1 + rdomestic)] = 0.89348 × (1.0190 / 1.0338) = 0.88069

Note that in this question, the dollar is the foreign currency and the Euro is the domestic currency.

Assume that the domestic nominal rate of return is 4% and the foreign nominal rate of return is 5%. If the current exchange rate is FC C 0.400, the forward rate consistent with interest rate parity is:

 A) 0.396.
 B) 0.400.
 C) 0.318.

F/S= (1 + rD) / (1 + rF) where the currency is quoted as FC C
F = (1.04/1.05)(0.400) = 0.396

Given a forward exchange rate of 5 DC/FC, a spot rate of 5.102 DC/FC, domestic interest rates of 8%, and foreign rates of 10%, which of the following statements is CORRECT based on the approximation formula?

 A) Arbitrage opportunities exist.
 B) Borrow local currency and lend foreign currency.
 C) Arbitrage opportunities do not exist.

If (rD ? rF) is approximately equal to the forward premium, which is (Forward D/F) ? Spot(D/F) / Spot(D/F), then no arbitrage opportunities exist.

0.08 ? 0.10 ? (5 ? 5.102) / 5.102.

-0.02 ? -0.01999.

Suppose the Argentina peso is at a 1-year forward premium of 4% relative to the Brazilian real and that Argentina’s 1-year interest rate is 7%. If interest rate parity holds, then the Brazilian interest rate is closest to:

 A) 6.60%.
 B) 3.00%.
 C) 11.00%.

According to interest rate parity the currency with the lower interest rate is expected to appreciate so the Argentina rate of 7% is approximately 4% less than the Brazilian rate of 7 + 4 = 11%.

Given the following information, what is the forward exchange rate implied by interest rate parity?

• U.S. interest rate = 9%.
• North Korea interest rate = 10%.
• Spot rate = 1.65 KPW/\$.

 A) 1.665 KPW/\$.
 B) 0.612 KPW/\$.
 C) 1.635 KPW/\$.

Forward rate (DC/FC) = Spot Rate (DC/FC) × [(1 + domestic rate) / (1 + foreign rate)],
Forward rate = 1 / 1.65 (KPW/\$) × (1.09 / 1.10) = 0.60055 \$/KPW, or 1.665 KPW/\$.
Alternatively, forward rate = 1.65 (KPW/\$) × (1.10 / 1.09) = 1.665 (KPW/\$).

The domestic interest rate is 8% and the foreign interest rate is 6%. If the spot rate is 4 domestic units/foreign unit, what should the forward exchange rate be for interest rate parity to hold?

 A) 3.930.
 B) 4.075.
 C) 4.250.

Using the following interest rate parity equation:

ForwardDC/FC=SpotDC/FC × [(1 + rdomestic) / (1 + rforeign )]

Solving for the forward rate:  ForwardDC/FC = 4 × [(1 + 0.08) / (1 + 0.06)]

= 4(1.08) / (1.06)

= 4(1.01887)

= 4.07547

The domestic interest rate is 7% and the foreign interest rate is 9%. If the forward exchange rate is 5 domestic units per foreign unit, what spot exchange rate is consistent with interest rate parity (IRP)?

 A) 4.91.
 B) 5.09.
 C) 5.72.

Using the following IRP equation: ForwardFC C = SpotFC C × [(1 + rdomestic) / (1 + rforeign )]

Solving for the spot rate: SpotFC C = ForwardFC C × [(1 + rforeign) / (1 + rdomestic)]

= [(1 + 0.09) / (1 + 0.07)](5)

= (1.09 / 1.07)(5)

= 5.09

The domestic interest rate is 9% and the foreign interest rate is 7%. If the forward exchange rate is FC C 5.00, what spot exchange rate is consistent with interest rate parity?

 A) 4.83.
 B) 4.91.
 C) 5.09.

ForwardFC C / SpotFC C = (1 + rdomestic) / (1 + rforeign).

SpotFC C = ForwardFC C (1 + rforeign) / (1 + rdomestic) = (5.00)(1.07) / (1.09) = 4.908

One-year interest rates are 7.5% in the U.S. and 6.0% in New Zealand. The current spot exchange rate is NZD:USD 0.5500. If interest rate parity holds, today’s one-year forward rate (NZD:USD) must be closest to:

 A) NZD:USD 0.54233.
 B) NZD:USD 0.55778.
 C) NZD:USD 0.56675.

Interest rate parity is given by: ForwardFC C = 0.5500 × (1.075/1.06) = NZD:USD 0.55778

Lance Tuipuloto, CFA, is reviewing interest rate parity for a client meeting on a planned foreign investment. The domestic interest rate is 8% and the foreign interest rate is 6%. If the forward rate is 4.00 domestic units per foreign unit, what should the spot exchange rate be for interest rate parity to hold?

 A) 3.98.
 B) 4.08.
 C) 3.93.

F/S = (1 + rdomestic) / (1 + rforeign). Note in this equation exchange rates are quoted as Domestic/Foreign.

S = F (1 + rF) / (1 + rD) = (4.00)(1.06) / (1.08) = 3.93
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