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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

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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)
5.72.
C)
5.09.



Using the following IRP equation: ForwardFCC = SpotFCC × [(1 + rdomestic) / (1 + rforeign )]  
Solving for the spot rate: SpotFCC = ForwardFCC × [(1 + rforeign) / (1 + rdomestic)]  
                                    = [(1 + 0.09) / (1 + 0.07)](5)
                                    = (1.09 / 1.07)(5)
                                    = 5.09

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The domestic interest rate is 9% and the foreign interest rate is 7%. If the forward exchange rate is FCC 5.00, what spot exchange rate is consistent with interest rate parity?
A)
4.83.
B)
4.91.
C)
5.09.



ForwardFCC / SpotFCC = (1 + rdomestic) / (1 + rforeign).
SpotFCC = ForwardFCC (1 + rforeign) / (1 + rdomestic) = (5.00)(1.07) / (1.09) = 4.908

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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 0.55778.
B)

NZD:USD 0.54233.
C)

NZD:USD 0.56675.



Interest rate parity is given by:

ForwardFCC = 0.5500 × (1.075/1.06) = NZD:USD 0.55778

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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)
3.93.
B)
3.98.
C)
4.08.



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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The U.S. interest rate is 4%, the Jordan interest rate is 7% and the $/JOD spot rate is 2.0010. What is the $/JOD forward rate that satisfies interest rate parity?
A)

$0.5142 / JOD.
B)

$1.9450 / JOD.
C)

$1.0936 / JOD.



Forward(DC/FC) = Spot (DC/FC)[(1 + r domestic) / (1 + r foreign)]
(2.0010)(1.04/1.07)

(2.0010)(0.972)
= 1.9450

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A resident of China can invest in Chinese yuan at 5.5% or in Egyptian pounds at 6%. The current spot rate is 80 CY/EGP. What is the one-year forward rate expressed in CY/EGP?
A)

79.6226.
B)

80.3792.
C)

88.9876.



Forward (DC/FC) = Spot (DC/FC)[(1 + rdomestic) / (1 + rforeign)]
(80 CY/EGP)[(1 + 0.055) / (1 + 0.06)]

(80)(0.99528)
= 79.6226

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An investor can invest in Tunisian dinar at r = 6.25% or in Swiss francs at r = 5.15%. She is a resident of Tunisia and the current spot rate is CHF:TND 0.8105. What is the approximate one-year forward rate expressed in CHF:TND?
A)
0.8016.
B)
0.8194.
C)
0.8215.



The approximate forward premium/discount is given by the interest rate differential. This differential is: 6.25% − 5.15% = 1.10%. Since Tunisia has higher interest rates, its currency will be at a discount in the forward market. This discount equals: 0.011 × 0.8105 = 0.0089. Since the exchange rate is quoted in CHF:TND, as a depreciating currency, it will take more TND to buy one CHF. The forward rate is thus: 0.8105 + 0.0089 = CHF:TND 0.8194. In other words, the CHF is stronger in the forward market.

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Bob Bowman, CFA, is an analyst who has been recently assigned to the currency trading desk at Ridgeway Securities, a hedge fund management firm based in New York. Ridgeway’s stellar reputation as a top tier hedge fund manager has been built upon many years of its portfolio outperforming both the market and its peer group. Ridgeway’s portfolio is globally diversified, with less than 35% of its assets currently invested in U.S. securities. Ridgeway seeks to enhance its portfolio returns through the active use of currency futures that correspond to its investments. From time to time, Ridgeway will also take advantage of arbitrage opportunities that arise in the currency markets.In his new position, Bowman will be reporting to the head currency trader, Jane Anthony. Among Bowman’s new responsibilities, he will be performing an ongoing analysis of global currency rates. His analysis is expected to include projections of future exchange rates and a sensitivity analysis of exchange rates in a variety of interest rate scenarios. Using his projections as a starting point, he will then be expected to suggest possible trading strategies for Ridgeway. Bowman knows that his analysis will begin with the underlying principles of the five basic international parity relationships. However, he does realize that certain principles will be more useful than others when applied to a “real-world” situation. To test his knowledge of the subject, Anthony has asked Bowman to prepare a presentation on the interrelationships between exchange rates, interest rates, and inflation rates. For the presentation, Bowman will need to prepare a brief analysis of current market conditions and formulate some basic trading strategies based upon his projections. He also will need to demonstrate his ability to calculate predicted spot rates for currencies, given some basic inflation rate and interest rate assumptions.
Bowman begins his task by gathering the following current market statistics:
1 year U.S. Interest Rates = 8% 1 year U.K. Interest Rates = 10% 1 year $/₤ forward rate = 1.70 Current $/₤ spot rate = 1.85
Bowman knows that if the forward rate is lower than what interest rate parity indicates, the appropriate strategy would be to borrow:
A)
pounds, convert to dollars at the forward rate, and lend the dollars.
B)
pounds, convert to dollars at the spot rate, and lend the dollars.
C)
dollars, convert to pounds at the spot rate, and lend the pounds.



If the forward rate is lower than what the interest rate parity indicates, the appropriate strategy would be: borrow pounds, convert to dollars at the spot rate, and lend dollars. (Study Session 4, LOS 17.h)

Bowman also knows that if the forward rate is higher than what interest rate parity indicates, the appropriate strategy would be to borrow:
A)
dollars, convert to pounds at the spot rate, and lend the pounds.
B)
dollars, convert to pounds at the forward rate, and lend the pounds.
C)
pounds, convert to dollars at the spot rate, and lend the dollars.



If the forward rate is higher than what interest rate parity indicates, the appropriate strategy would be: borrow dollars, convert to pounds at the spot rate, and lend the pounds. (Study Session 4, LOS 17.h)

Based on the information above, Bowman would like to calculate the forward rate implied by interest rate parity. The answer is:
A)
1.82 $/₤.
B)
1.88 $/₤.
C)
1.67 $/₤.



Given the above relationship, interest rate parity does not hold.
(If interest parity held, 1.70 = 1.85 × (1.08 / 1.10), but 1.85 × (1.08 / 1.10) = 1.82).
Therefore, an arbitrage opportunity exists.
To determine whether to borrow dollars or pounds, express the foreign rate in hedged US$ terms (by manipulating the equation for IRP). We get:
(1.70 / 1.85) × 1.10 = 1.0108, which is less than 1.08 (U.S. rate), so we should start by borrowing British pounds and lending U.S. dollars.
Arbitrage Example:
  • Today:
    • borrow 5,000 GBP @ 10%
    • buy $9,250 with the proceeds of the loan (5,000 GBP × 1.85).
    • lend $9,250 @ 8%
    • buy 5,500 GBP one year in the future @ 1.70 $/£. This guarantees your loan repayment of 5,000 GBP × 1.1 = 5,500 GBP.
  • One year later, close out your position:
    • collect the proceeds of your loan: $9,990 = $9,250 × 1.08
    • buy 5,500 GBP with your forward contract → cost = 5,500 GBP × 1.70 = $9,350
    • pay off your loan of 5,500 GBP
    • reap your profits: $9,990 − $9,350 = $640
    • Alternately, you could say that the arbitrage profit is 376.47 GBP. Bob Bowman is a US investor so we left his profits in USD. 640 USD = 1.70 × 376.47 GBP.

(Study Session 4, LOS 17.h)


A junior colleague asks Bowman for the mathematical equation that describes interest rate parity. Which of the following equations most accurately describes interest rate parity? (S0 is the spot exchange rate expressed in dollars per unit of foreign currency, F0,T is the forward exchange rate, and rUS and rFX are the risk-free rates in the U.S. and foreign country.)
A)
S1 = F0,t [(1+rUS) / (1+rFX)].
B)
F0,t = S0 [(1+rFX) / (1+rUS)].
C)
F0,t = S0 [(1+rUS) / (1+rFX)].



Interest Rate Parity
Interest rates between countries and their exchange rates (spot and futures) must be in equilibrium at all times or else there will be arbitrage opportunities. Interest rate parity says that:
F0,t = S0 [(1+rUS) / (1+rFX)]
Where:
S0 =the current exchange rate in the spot market
F0,t =the current exchange rate in the forward of futures market
rUS=the risk-free interest rate in the U.S.
rFX=the risk-free interest rate in the foreign market

Note: the above currency quotes are expressed in $/FX. (Study Session 4, LOS 17.h)


Now, suppose Bowman has the following information available to him: the current spot exchange rate for Indian Rupees is $0.02046. Inflation over the next 5 years is expected to be 3% in the U.S. and 5% in India. Bowman must calculate the U.S. Dollar/Indian Rupee expected future spot exchange rate in 5 years implied by purchasing power parity (PPP). The answer is:
A)
$0.02250.
B)
$0.01858.
C)
$0.02010.



The PPP assumption is that the future spot exchange rate will change exactly as the inflation rates affect the values of each currency. For the computation, raise the U.S. inflation rate to the 5th power (because of 5 years) and divide it by the Indian inflation rate raised to the 5th power. Then multiply the result by the spot exchange rate. ((1.03)5 / (1.05)5) × 0.02046 = $0.01858. (Study Session 4, LOS 17.h)

Bowman routinely calculates the expected spot rate for the Japanese Yen per U.S. dollar. He knows that the current spot exchange rate is 189.76 Yen/USD. He is also aware that the interest rates in Japan, Great Britain, and the U.S. are 8%, 4%, and 5% respectively. Calculate the expected spot rate for Yen/USD in a one year period.
A)
187.95 Yen/USD.
B)
184.49 Yen/USD.
C)
195.18 Yen/USD.


The exact methodology of the covered interest rate parity (IRP) is: expected spot rate in one period (FC/DC) = spot rate today (FC/DC) × [(1 + RFC) / (1 + RDC)].
Setting up this equation gives us E(S1) = 189.76 Yen/USD × (1.08 / 1.05) = 195.18 Yen/USD. (Study Session 4, LOS 17.h)

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Jennifer Nance has recently been hired as an analyst at the Central City Bank in the currency trading department. Nance, who recently graduated with a degree in economics, will be working with other analysts to determine if there are profit opportunities in the foreign exchange market.Nance has the following information available on currency spot exchange rates:
  • Euros are trading at $0.9905 in New York.
  • Euros are trading at 9.8674 Mexican Pesos (MXN) in Berne.
  • U.S. Dollars are trading at 9.75 Mexican Pesos in Mexico City.

Nance is asked to determine if a profitable arbitrage opportunity exists, and if so, to determine the amount of profit in percent.
A)
Yes, a 1.3% arbitrage profit is available.
B)
Yes, a 1.2% arbitrage profit is available.
C)
Yes, a 2.18% arbitrage profit is available.



Typically, we assume that the rates versus the $ are “correct” and calculate the implied cross rate: MXN:USD 0.9905 × 9.75 = USD:MXN 9.657. Since 9.657 < 9.8674, the euro is overvalued in Berne, relative to the Mexican peso. Hence, you want to sell euros for pesos in Berne. A $100 U.S. investment would buy 100.96 euros in New York. Taking 100.96 euros to Berne, one could acquire 996.21 Mexican Pesos. Buying U.S. Dollars with 996.21 Mexican Pesos would yield $102.18. Percent profit: (102.18 / 100) − 1 = 0.0218 or 2.18%.


Now suppose that the 12 month forward rate between Japanese Yen and U.S. Dollars is YEN:USD 0.007690. The current spot exchange rate is YEN:USD 0.007556. The U.S. interest rate is 6.03%. Japan’s interest rate is 5.60%.
Which of the following is closest to the amount Nance could earn on a $1,000 principal?
A)
$231 profit by borrowing dollars and lending yen.
B)
$14 profit by borrowing dollars and lending yen.
C)
$227 profit by borrowing yen and lending dollars.



Nance should proceed as follows: borrow $1,000 at 6.03%. (After 12 months, repay the loan for $1,060.30.) Convert the borrowed $1,000 into ($1,000 / 0.007556) = 132,345.16 Yen. Lend the Yen in Japan for 12 months at 5.60% interest. At the end of the year, receive 139,756.48 Yen. Using the forward contract, convert the yen back to dollars at the forward rate of 0.007690. Receive (139,756.48 Yen × 0.007690 = $1,074.73, pay back the dollar loan of $1,060.30 and realize a profit of $14.43.

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