Economics 【Reading 17】Sample nation, exchange, equivalent

invic

A U.S. importer wants to buy stuffed toys from the nation of South Apoa for a total cost of 6 million Apoas. The spot exchange rate is Apoa:USD 0.50. The USD equivalent cost is:

A) USD 12,000,000.

B) Apoa 3,000,000.

C) USD 3,000,000.

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$0.50 times 6,000,000 Apoa = USD 3,000,000.

bapswarrior

Mary Beth Morgan and Shaban Shoshi are currency traders for Mercury Forex Inc. They have compiled the following information concerning currencies in Sweden (SEK), New Zealand (NZD), and United States (USD).

	SEK/USD	USD/NZD
Spot bid rate	7.8927	$0.6994
Spot ask rate	7.9021	$0.7000
3-month forward bid rate	7.8780	$0.7010
3-month forward ask rate	7.8794	$0.7020

As they are reviewing the information in the currency quotes, Morgan states, “the Swedish Krona is trading at a forward premium, however that premium is less than 1%.” Shoshi replies, I’ll have to double check that, but it looks like the NZD is weak relative to the USD.”
With regard to their statements:

A) both are incorrect.

B) only Shoshi is correct.

C) only Morgan is correct.

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Remember that the forward premium or discount is always on the currency in the denominator of the quote.
Since bid/ask quotes are given, use the midpoints. The spot mid point = 7.8974 and the forward midpoint = 7.8787. Since Morgan’s statement is in terms of the Swedish Krona, we need to convert the currency quotes to USD/SEK.
Spot midpoint = (1 / 7.8974) = $0.1266 Forward midpoint = (1 / 7.8787) = $0.1269 USD/SEK premium/discount = [($0.1269 − $0.1266) / $0.1266](12 / 3) = 0.95% premium for the Swedish Krona. Morgan’s statement is correct.
To evaluate Shoshi’s statement, first find the midpoints.
Spot USD/NZD midpoint = $0.6997. Forward USD/NZD midpoint = $0.7015. USD/NZD premium/discount = [($0.7015 − $0.6997) / $0.6997](12 / 3) = 1.03% premium.
Since the NZD is trading at a forward premium, the NZD is strong relative to the USD. Shoshi’s statement is incorrect.

bapswarrior

A currency trader has compiled the following currency quotes:

	USD/EUR ($/€)	USD/GBP ($/£)	JPY/USD (¥)
Spot rate	$1.2139	$1.7730	115.674
6-month forward rate	$1.2067	$1.7894	114.867

Which of the following statements regarding currencies is CORRECT?

A) The euro is strong relative to the dollar and the yen is weak relative to the dollar.

B) The pound is strong relative to the dollar and the dollar is strong relative to the yen.

C) The euro is weak relative to the dollar and the yen is strong relative to the dollar.

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Remember that the forward premium or discount is always on the currency in the denominator of the quote.
USD/EUR premium/discount = [(1.2067 − 1.2139) / 1.2139](12 / 6) = -1.19%. Since the Euro is selling at a forward discount, the Euro is weak relative to the dollar and the dollar is strong relative to the Euro.
USD/GBP premium/discount = [(1.7894 − 1.7730) / 1.7730](12 / 6) = 1.85%. Since the Pound is selling at a forward premium, the Pound is strong relative to the dollar and the dollar is weak relative to the Pound.
JPY/USD premium/discount = [(114.867 − 115.674) / 115.674](12 / 6) = -1.40%. Since the dollar is selling at a forward discount, the dollar is weak relative to the yen and the yen is strong relative to the dollar.
Note that you did not necessarily need to calculate the amount of the discount or premium for this question.

bapswarrior

Doug Wyatt is a currency trader for Global Currency Exchange Inc. Wyatt has compiled the following information concerning the U.S. dollar ($) / Australian dollar (AUD) exchange rate.

• Spot bid rate: $0.745.
• Spot ask rate: $0.749.
• 3-month forward bid rate: $0.752.
• 3-month forward ask rate: $0.754.

Which of the following statements concerning the currencies is CORRECT?

A) The AUD is selling at a forward premium of 3.21%.

B) The AUD is selling at a forward discount of 4.83%.

C) The AUD is selling at a forward premium of 4.83%.

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Remember that the forward premium or discount is always on the currency in the denominator of the quote. In this case, the premium or discount is on the AUD. The forward premium or discount is calculated as [(forward rate − spot rate) / spot rate](12 / number of months forward).
Since bid/ask quotes are given, use the midpoints. The spot midpoint = $0.747 and the forward midpoint is $0.753.
Forward premium/discount = [($0.753 - $0.747) / $0.747][12 / 3] = 0.008032 × 4 = 0.0321.
The AUD is selling at a forward premium of 3.21%.

bapswarrior

Professor Imada Suzaken made the following statement to his economics class: “If you can earn 8% on A-rated bonds in the U.S. but only 6% on similar bonds in Canada, Canadian investors may want to buy those bonds in the U.S. for the excess return. However, after collecting the extra dollars, the investors would lose those profits when they converted their gains into their home currency.”
Suzaken is describing:

A) exchange-rate parity.

B) purchasing-power parity.

C) interest-rate parity.

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Interest-rate parity is the concept that exchange rates must change so that the return on investments with identical risk will be the same in any currency. Suzaken’s statement reflects interest rate parity.

bapswarrior

Terrance Burnhart, a junior analyst at Wertheim Investments Inc., was discussing the concepts of purchasing power parity (PPP) and interest rate parity (IRP) with his colleague, Francis Ferngood. During the conversation Burnhart made the following statements:

Statement 1: Absolute PPP is based on a number of unrealistic assumptions that limits its real-world usefulness. These assumptions are: that all goods and services can be transported among countries at no cost; all countries use the same basket of goods and services to measure their price levels; and all countries measure their rates of inflation the same way.

Statement 2: IRP rests on the idea of equal real interest rates across international borders. Real interest rate differentials would result in capital flows to the higher real interest rate country, equalizing the rates over time. Another way to say this is that differences in interest rates are equal to differences in expected changes in exchange rates.

With respect to these statements:

A) both are correct.

B) only statement 1 is correct.

C) only statement 2 is correct.

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IRP means that interest rates and exchange rates will adjust so the risk adjusted return on assets between any two countries and their associated currencies will be the same. PPP is based on the idea that a given basket of goods should cost the same in different countries after taking into account the changes in exchange rates. PPP does not hold due to transportation costs and other factors.

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 data available:

	US Dollar ($)	UK Pound (£)	Euro (€)
Expected inflation rate	6.0%	3.0%	7.0%
One-year nominal interest rate	10.0%	6.0%	9.0%

Market Spot Rates
	US Dollar ($)	UK Pound (£)	Euro (€)
US Dollar ($)	$1.0000	$1.6000	$0.8000
UK Pound (£)	0.6250	1.0000	2.0000
Euro (€)	1.2500	0.5000	1.0000

Market 1-year Forward Rates
	US Dollar ($)	UK Pound (£)	Euro (€)
US Dollar ($)	$1.0000	$1.6400	$0.8082
UK Pound (£)	0.6098	1.0000	2.0292
Euro (€)	1.2373	0.4928	1.0000

Assume borrowing and lending rates are equal and bid-ask spreads are zero in the spot and forward markets. Using the data above, Nance is asked to calculate the profits in pounds from covered interest arbitrage between the United Kingdom and the United States, assuming an investor starts by borrowing ₤500,000. The answer is:

A) ₤6,750.00.

B) ₤36,585.37.

C) ₤6,585.37.

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In this example, covered interest arbitrage involves borrowing pounds at the U.K. interest rate, converting to dollars at the spot rate, investing the dollars at the U.S. interest rate, converting the dollar investment proceeds back to pounds at the forward rate, and repaying the pound loan. Arbitrage profits are the difference between the proceeds from the forward contract and the amount repaid on the loan.
We start by borrowing 500,000. At a borrowing rate of 6.0%, we will have to repay 500,000(1.06) = 530,000 at the end of the year.
We convert the 500,000 pounds to dollars at the spot rate of $1.6000, which gives us 500,000 × 1.6000 = $800,000.
We invest $800,000 for one year at 10.0%, and at the end of the year we receive $800,000(1.10) = $880,000.
This means that initially we must enter into a forward contract at $1.6400 and then at the end of the year convert $880,000 into ($880,000 / $1.6400) = 536,585.37.
We pay back the 530,000 loan balance and our arbitrage profits are 536,585.37 − 530,000 = 6,585.37.

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Nance is asked to calculate the one-year forward EUR:USD rate that would preclude profits from covered interest arbitrage between the U.S. dollar and the Euro?

A) EUR:USD 0.7925.

B) EUR:USD 0.8082.

C) EUR:USD 0.8073.

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Interest rate parity implies that, in order to prevent covered interest arbitrage, the one-year forward EUR:USD rate should be equal to $0.8000(1.10) / (1.09) = $0.8073.

bapswarrior

The interest rates in the U.S. and Great Britain are 7.23% and 6.94% respectively. The forward rate is 1.70$/₤ and the spot rate is 1.73$/₤. Which currency would an investor borrow, if any, to make an arbitrage profit?

A) Lending pounds.

B) Borrow dollars.

C) Borrow pounds.

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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.
1.0723 > [(1.0694)(1.70)] / 1.73
1.0723 > 1.81798 / 1.73
1.0723 > 1.0509, therefore borrow foreign (pounds).
Alternatively, the dollar is appreciating. [(1.73 − 1.70) / 1.70] = 1.76% and the $U.S. interest rate is higher. Clearly, investing in $U.S. (and borrowing pounds) is the way to go.

bapswarrior

The annual interest rate is 8.02% in Mexico and 7.45% in Canada. The spot peso-dollar exchange rate is 569.87 MXN/CAD, and the one-year forward rate is 526.78 MXN/CAD. If an arbitrage opportunity exists, how much would a person living in Mexico make borrowing 15,000,000 pesos or the equivalent in Canadian dollars?

A) 1,292,410 pesos.

B) 1,284,230 pesos.

C) 1,304,207 pesos.

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Note that peso is at a forward premium (less pesos per CAD in the future) and that peso interest rate is higher. Therefore it is clear there are arbitrage profits from lending in pesos and borrowing CAD.
First convert to Canadian dollars to determine the amount of interest due at the end of the year. (15,000,000 MXN) × (CAD/569.87 MXN) = 26,321.79 CAD.
26,321.79 CAD × 0.0745 = 1,960.97 CAD interest due at the end of the year.
Lend out pesos 15,000,000 pesos × 1.0802 = 16,203,000 pesos received at the end of the year.
Convert to Canadian dollars (16,203,000 MXN) × (CAD/526.78 MXN) = 30,758.57 CAD.
Subtract the original loan amount and interest: 30,758.57 − 26,321.79 (original loan) − 1,960.97 (interest) = 2,475.81 CAD profit.
Convert the remainder back to pesos: (2,475.81 CAD) × (526.78 MXN/CAD) = 1,304,207.19 peso profit.

bapswarrior

The annual interest rates in England and New Zealand are 6.54% and 7.03%, respectively. The one-year forward exchange rate between the British pound and the New Zealand dollar is 0.45 GBP/NZD and the spot rate is 0.41 GBP/NZD. If a person living in London can borrow 10,000 pounds or the equivalent amount in New Zealand dollars, how much arbitrage profit, if any, can he make?

A) 1,043.61 GBP.

B) 1,093.20 GBP.

C) 1,124.88 GBP.

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Borrow 10,000 GBP at 6.54% = 654 GBP interest due at the end of the year.
Convert to NZD: (10,000 GBP) × (1 NZD/0.41 GBP) = 24,390 NZD.
Lend out NZD at 7.03% interest: (24,390 NZD) × (1.0703) = 26,104.88 NZD.
Convert back to GBP: (26,104.88 NZD) × (0.45 GBP/NZD) = 11,747.20 GBP.
11,747.20 GBP − 10,000 GBP (original amount borrowed) − 654 GBP interest = 1,093.20 GBP profit.