bapswarrior

The forward rate between the Mexican peso and the U.S. dollar is 556.75 MXN/USD and the spot rate is 581.23 MXN/USD. The Mexican interest rate is 5.89%, and the U.S. rate is 5.75%. If a person lives in Mexico and can borrow $10,000 or the equivalent in pesos, how much can she make if currency arbitrage opportunities exist?

A) $459.39.

B) Arbitrage opportunities do not exist.

C) $479.59.

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First determine if arbitrage opportunities exist by using the following equation:
if 1 + rD > [(1 + rF)(Forward rate)] / Spot rate, then borrow foreign (dollars).
1.0589 > [(1.0575)(556.75)] / 581.23
1.0589 > 588.763 / 581.23
1.0589 > 1.01296, therefore, borrow foreign (dollars).
Borrow $10,000 at 5.75%, interest = $575 due at the end of the year. Convert to pesos using the spot rate: ($10,000) × (581.23 MXN/USD) = 5,812,300 pesos.
Lend out at 5.89%: (5,812,300 pesos) × (1.0589) = 6,154,644.47 pesos. Convert to dollars: (6,154,644.47 MXN) × (USD/556.75 MXN) = $11,054.59. $11,054.59 − $10,000 (original amount borrowed) − $575 (interest) = $479.59 profit.

bapswarrior

The spot rate between the Canadian dollar and the British pound is 1.265 CAD/₤ and the forward rate is 1.193 CAD/₤. The interest rate in Canada and England are 6.13% and 6.01%, respectively. A person living in Toronto, Canada can borrow either Canadian dollars or pounds. If an arbitrage opportunity exists, which currency would they lend or borrow?

A) Lend pounds.

B) Borrow pounds.

C) Borrow Canadian dollars.

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Use the following formula to determine if an arbitrage opportunity exists and which currency to borrow.
if 1 + rD > [(1 + rF)(Forward rate)] / Spot rate, then borrow foreign.
1.0613 > [(1.0601)(1.193)] / 1.265
1.0613 > 1.265 / 1.265
1.0613 > 1 therefore borrow foreign (British pound) and lend domestic (Canadian dollar).

bapswarrior

If 1 + the domestic interest rate < (1 + the foreign interest rate × the forward rate) / spot rate, an investor seeking arbitrage profits should borrow:

A) foreign, convert to domestic, lend out domestic, and convert back to foreign.

B) domestic, convert to foreign, borrow foreign, and convert back to domestic.

C) domestic, lend out foreign, and convert back to domestic.

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If 1 + rD < (1 + rF)(forward rate) / spot rate, then borrow domestic, lend out foreign, and convert back to domestic.

bapswarrior

The forward rate between Swiss francs and U.S. dollars is 1.8 SF/$ and the current spot rate is 1.90 SF/$. The Swiss interest rate is 8.02% and the U.S. rate is 11.02%. Assume you can borrow francs or dollars and you live in Switzerland. If an arbitrage opportunity exists, how can you take advantage of it?

A) Borrow domestic currency.

B) Lend foreign currency.

C) Borrow foreign currency.

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Borrow foreign if 1 + rD> [(1 + rF)(forward rate)] / spot rate
1 + 0.0802 > [(1 + 0.1102)(1.8)] / 1.9
1.0802 > 1.99836 / 1.9
1.0802 > 1.0518 therefore borrow foreign (dollars) and lend domestic (francs).
Alternatively, U.S. rate is 11.02 − 8.02 = 3% higher and USD is at (1.8 − 1.9) / 1.9 = 5.3% discount since USD will fall more than the extra 3% interest, better to lend francs.

bapswarrior

The spot rate for the dollar is 0.1432 $/ADF. Andorran and U.S. interest rates are 6.6% and 7.2%, respectively. If the 1-year forward rate is 0.1430 $/ADF, a U.S. investor could earn an arbitrage dollar profit per ADF of:

A) $0.0011.

B) $0.0010.

C) $0.0075.

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Let us first check if an arbitrage opportunity exists. Applying the interest rate parity theorem, we have:

Forward rate = 0.1432 × 1.072/1.066 = 0.1440 $/ADF > 0.1430 $/ADF (quoted forward rate)

This implies that an arbitrage opportunity exists. The inequality implies that ADF is mispriced (weak) in the forward market or is underpriced relative to the dollar. We should buy ADF in the forward market and sell the dollar in the spot market. This requires that we borrow in Andorra and convert the francs into dollars at the spot rate. Invest the proceeds in U.S. securities @ 7.2%, and simultaneously enter into a forward transaction where we sell the dollars for ADF @ 0.1430 $/ADF. Assuming that we borrow 1 ADF today and convert it into dollars, we will have 0.1432 dollars to invest at 7.2% for one year. After one year we will have 0.1432 × 1.072 = 0.1535 dollars. At that point, we will owe an Andorran bank 1 × 1.066 or 1.066 ADF, including interest. We will need to convert enough dollars at the forward rate to pay off this loan. At the forward contract rate, we will need to convert 1.066 × 0.1430 = 0.1524 dollars into ADF to pay off our obligation. This will leave us with an arbitrage profit of 0.1535 − 0.1524 = 0.0011 dollars.

bapswarrior

Given currency quotes in FCC, if:  1 + rDC <	(1 +rFC)(forward rate)</SUB)	funds will:
	spot rate

A) flow out of the domestic country.

B) flow in and out of the domestic country.

C) flow into the domestic country.

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This equation is Interest Rate Parity rearranged! If the term on the left (1 + rDC), is less than the term on the right, it means that the domestic rate is low relative to the hedged foreign rate. Therefore, there is a profitable arbitrage from borrowing the domestic currency and lending at the foreign interest rate.
Because we lend in the foreign market, we say that the funds flow out of the domestic economy

bapswarrior

If (rD − rF) > Forward premium, which is (Forward D/F) − Spot(D/F) / Spot(D/F), then:

A) borrow domestic currency and lend out foreign currency.

B) arbitrage opportunities don't exist.

C) borrow foreign currency and lend out domestic currency.

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If (rD − rF) > Forward premium, which is (Forward D/F) − Spot(D/F) / Spot(D/F), then you would borrow foreign currency and lend out local currency. If the domestic rate is high relative to the hedged foreign rate, you would borrow foreign currency units and then sell them for domestic currency units at the spot rate, lend these domestic currency units at the domestic interest rate and simultaneously sell just enough domestic currency forward so that you can repay your foreign loan.

bapswarrior

Suppose that the current interest rates in the U.S. and the European Union are 13.665% and 8.500%, respectively. Also, the spot rate for the dollar is 1.1975 US$/euro, and the 1-year forward rate is 1.2545 US$/euro. If $100 is invested, what is the total arbitrage profit that a U.S. investor could earn?

A) No arbitrage profit can be made.

B) $5.7000.

C) $23.0670.

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Interest rate parity requires that:
(Forward/Spot) = [(1+rD)/(1+rF)]
(1.2545/1.1975) = [1.13665/1.085]
So, interest rate parity holds and no arbitrage opportunity exists.
Alternately:
(1 + 0.13665) = [(1 + 0.085)(1.2545) / 1.1975]

1.13665 = [(1.085)(1.2545) / 1.1975]

1.13665 = 1.36113 / 1.1975
1.13665 = 1.13665, therefore no arbitrage profit can be made.

bapswarrior

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.

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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%.

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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.

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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.

bapswarrior

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.

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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)

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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.

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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)

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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 $/₤.

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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)

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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)].

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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)

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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.

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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)

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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.

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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)