FIN 3410 Test 1
Suppose you observe a spot euro-dollar exchange rate of $1.0500/€. If annual interest rates are 5% in the US and 3% in the euro zone, what is the no-arbitrage 1-year forward euro-dollar rate?
$1.0704/€ 1.05/1.03 x 1.05
Suppose you observe a spot exchange rate of $1.1108 pound. If interest rates are 3.9 percent per annum in the U.S. and 4.3 percent per annum in the U.K., what is the no arbitrage one-year forward rate?
$1.1065/pound F = 1.1108 x (1.39/1.43)
Suppose that the current exchange rate is €0.80 = $1.00. The direct quote, from the U.S. perspective is:
$1.25/€ 1/0.8 = 1.25
As of today, the spot exchange rate is €1.00 = $1.60 and the rates of inflation expected to prevail for the next year in the U.S. is 2 percent and 3 percent in the euro zone. What is the one-year forward rate that should prevail according to the Purchasing Power Parity?
$1.5845/€ F = $1.60/€ x (1 + 2%) / (1 + 3%) = $1.5845/€
The Singapore dollar-U.S. dollar (S$/US$) spot exchange rate is S$1.4338/US$, the Canadian dollar-U.S. dollar (C$/US$) spot rate is C$1.3715/US$ and the Singapore dollar-Canadian dollar (S$/C$) cross rate is S$1.0154/C$. Determine the triangular arbitrage profit that is possible if you have US$1,000,000.
$29,569 profit Buy C$ and Sell S$ $1,000,0000 x (1.4338 / (1.0154 x 1.3715)
Suppose the spot bid exchange rate is $1.1230/£ and the spot ask exchange rate is $1.1240/£. If you were to buy $10,000,000 worth of British pounds and then sell them one minute later, how much of your $10,000,000 would be "eaten" by the bid-ask spread?
$8,897 Sell $10m to buy pound: $10,000,000 /($1.124/£) = £8,896,797.15 Sell £8,896,797.15 to buy $: £8,896,797.15 x ($1.123/£) = $9,991,103.20 $10,000,000 - $9,991,103.20 = $8,896.80
A U.S.-based currency dealer has good credit and can borrow $1,000,000 or its equivalent in euros for one year. The one-year interest rate in the U.S. is i$ = 2% and in the euro zone the one-year interest rate is i€ = 6%. The spot exchange rate is $1.25/ € and the one-year forward exchange rate is $1.20/€1. Show how to realize a dollar profit via covered interest arbitrage.
(1+.06) x 1.20 / 1.25 = 1.0176 borrowing $1,000,000 / (1.25) = 800,000 x 1.06 = 848,000 sell 800,000 for 1,000,000 invest at 2% = 1,020,000 buy 848,000 x (1.20) = 1,017,600 Profit = 1,020,000 - 1,017,600 = $2,400
Assume one Canadian dollar is equal to US$.88 and one Peruvian nuevo sol is equal to US$.35. The value of one Peruvian nuevo sol is Canadian dollars is:
.35/.88 = .3977 About .3977 Canadian dollars
A Germany-based currency dealer has good credit and can borrow $1,000,000 or its equivalent in euros for one year. The one-year interest rate in the U.S. is i$ = 2% and in the euro zone the one-year interest rate is i€ = 6%. The spot exchange rate is $1.25/ € and the one-year forward exchange rate is $1.20/€1. Show how to realize a euro profit via covered interest arbitrage.
1.06 x 1.20 /1.25 =1.0176 Borrow $1,000,000 / (1.25) = 800,000 x (1.06) = 848,000 euro sell borrowed 800,000 euro for $1,000,000 invest at 2% = $1,020,000 Sell $1,020,000 then get 1,020,000 / (1.20) = 850,000 850,000 - 848,000 = 2,000 Euro
Interest Rate Parity (IRP) is best defined as:
A no-arbitrage, equilibrium condition that must hold when international finances
Generally unfavorable evidence on Purchasing Power Parity suggests that _____ .
All of the options are correct
You are a U.S.-based treasurer with $1,000,000 to invest. The dollar-euro exchange rate is quoted as $1.60 = €1.00 and the dollar-pound exchange rate is quoted at $2.00 = £1.00. If a bank quotes you a cross rate of £1.00 = €1.20 how can you make money?
Buy euro at $1.60/€, buy £ at €1.20/£, sell £ at $2/£ Calculate the actual cross rate. S(€/£) = S($/£) / S($/€) = (2 / 1.6) = €1.25. Thus, you now know that the pound is undervalued with respect to euro under the cross rate offered by the bank. To do "buy low, sell high," the direction of the trade should therefore be "sell € and buy £" with the bank quoting the cross rate. This means that starting from $, you should sell $ to buy € at $1.60/€, sell € to buy £ at €1.20/£, and sell £ to buy back $ at $2/£.
Suppose that the current exchange rate is c1.00 = $1.65. The indirect quote, from the U.S. perspective is ____.
C 0.6061 = $1.00
Suppose that the current exchange rate is c0.82 = $1.00. The direct quote, from the U.S. perspective is
C 1.00 = $1.22
Assume a Japanese firm invoices exports to the United States in U.S. dollars. Assume that the forward rate and spot rate of the Japanese yen are equal. If the Japanese firm expects the U.S. dollar to ____ against the yen, it would likely wish to hedge. It could hedge by ____ dollars forward.
Depreciate; selling
According to the Domestic and International Fisher Effects, if Venezuela has a much higher nominal rate than other countries, its inflation rate will likely be ____ than other countries, and its currency will ____
Higher; weaken
The current spot exchange rate is $1.1091/C and the three-month forward rate is $1.1547/C. You enter into a short position on c1,000. At a maturity, the spot exchange rate is $1.2127/C. How much have you made or lost?
Loss of 58 Long +(St - Ft) x contract size Short -(St - Ft) x contract size -(1.2127 - 1.1547) x C1000
You are a U.S.-based treasurer with $1,000,000 to invest. The dollar-euro exchange rate is quoted as $1.20 = €1.00 and the dollar-pound exchange rate is quoted at $1.80 = £1.00. If a bank quotes you a cross rate of £1.00 = €1.50, how much money can an astute trader make?
No arbitrage is possible. Implied cross rate = ($1.80 / £ ) / ($1.20 /€) = €1.50 / £. Since the implied cross rate and the quoted cross rate are the same, there is no arbitrage opportunity.
Given a home country and a foreign country, purchasing power parity suggests that:
None of the options are correct
If PPP holds for tradables and the relative prices between tradables and nontradable are maintained at a stable level, then:
PPP can hold in its relative version
A forward contract can be used to lock in the ____ of a specified currency at a future point in time.
Purchase price or sale price
Covered Interest Arbitrage (CIA) transactions will result in:
Restoring equilibrium prices
Joe Denver specializes in cross-rate arbitrage. He notices the following quotes: 1. Crédit Lyonnais: Yen / US dollar = JPY 107.0000 / USD 2. Barclays: US dollar / euro = USD 1.1100/ EUR 3. Crédit Agricole: Yen / EUR = JPY 120.0000 / EUR Ignoring transaction costs, compute how much Joe Denver can make a triangular arbitrage profit by trading at these prices. Assume that he has $1 million available to conduct the arbitrage.
Start with $1 million. Sell $1 million to Barclays for euro and receive: USD 1,000,000 / (USD 1.1100/ EUR) = EUR 900,900.90. Sell the EUR to Crédit Agricole for JPY and receive: EUR 900,900.90 ´ JPY 120.0000/EUR = JPY 108,108,108.11 Sell the JPY to Credit Lyonnais for USD and receive: JPY 108,108,108.11 / (JPY 107.0000/ USD) = USD 1,010,356.15 Arbitrage profit = $1,010,356.15 - $1,000,000 = $10,356.15 or a profit of 1.036%
If speculators expect the spot rate of the yen in 60 days to be ___ than the 60-day forward rate on the yen, they will ___ the yen forward and put ___ pressure on the yen's forward rate.
Stronger; buy; upward
The current spot exchange rate is $1.55/€ and the three-month forward rate is $1.50/€. Based on your analysis of the exchange rate, you are confident that the spot exchange rate will be $1.52/€ in three months. Assume that you would like to buy or sell €1,000,000. What actions do you need to take to speculate in the forward market?
Take a long position in a forward contract on €1,000,000 at $1.50/€.
The current spot exchange rate is $1.45/€ and the 3-month forward rate is $1.55/€. Based upon your economic forecast, you are pretty confident that the spot exchange rate will be $1.50/€ in three months. Assume that you would like to buy or sell €100,000. What actions would you take to speculate in the forward market? How much will you make if your prediction is correct?
Take a short position in a forward contract on euro. If you are right, you will make $5,000. You strongly believe that the euro's forward rate is over-priced. You should short the euro in the forward market. If you are right in 3 months time, you can buy euro at S3 = $1.50/€ and deliver it at F3 = $1.55/€. Your profit will be: €100,000 x (F3 - S3) = €100,000 x ($1.55/€ - $1.50/€) = $5,000
Consider the following spot and forward rate questions for the Swiss franc. S0($/SFr) .85 F1($/SFr) .86 F2($/SFr) .87I F3($/SFr) .88 Which of the following is true?
The Swiss franc is trading at a forward premium
Arbitrage is best defined as:
The act of simultaneously buying and selling the same or equivalent assets or commodities for the purpose of making certain guaranteed profits.
The SF/$ spot exchange rate is SF 1.2511/$ and the 90-day forward exchange rate SF 1.2727/$. The forward premium (discount) on annualized basis is ____.
The dollar trading at an 7% premium to the Swiss franc. (F-S) / S ((1.2727-1.2511)/1.2511) x (365/90) = 7.0%
Uncovered interest rate parity usually does not hold, and yield-seeking speculators tend to borrow low interest rate currencies to invest in high interest rate currencies without hedging. If the interest rate in the U.S. is i$ = 5 percent for the next year and interest rate in the U.K. is ipound = 8 percent for the next year, the failure of uncovered IRP to hold would suggest that:
The pound is expected to appreciate against the dollar
Consider a trader who takes a long position in a six-month forward contract on the euro. The forward rate is $1.75 = €1.00; the contract size is €62,500. At the maturity of the contract the spot exchange rate is $1.65 = €1.00.
The trader has lost $6,250. = (S-F) x Size of contract = ($1.65/€ - $1.75/€) x €62,500 = - $6,250 (i.e., loss of $6,250)
The bid/ask spread on an exchange rate can be used directly to determine:
The transaction cost of foreign exchange
Suppose that the one-year interest rate is 5.0% in the United States and 3.5% in Germany, and that the spot exchange rate is $1.12/€ and the one-year forward exchange rate, is $1.16/€. Assume that an arbitrageur can borrow up to $1,000,000.
This is an example of an arbitrage opportunity by borrowing $ and investing in €; interest rate parity does not hold. (1 + i$) = 1.05 < (1 + i€) x F / S = 1.035 x 1.16 / 1.12 = 1.072 IRP is not holding. The arbitrageur should borrow $ to do a covered interest arbitrage.
According to the International Fisher Effect and/or Interest Rate Parity, if an investor purchases a five-year U.S. bond that has an annual interest rate of 5% rather than a comparable British bond that has an annual interest rate of 6%, then the investor must be expecting the ________ to ________ at a rate of at least 1% per year over the next 5 years.
U.S. dollar; appreciate
Assume that British interest rates are higher than U.S. interest rates, and that the spot rate equals the forward rate. Covered interest arbitrage puts ____ pressure on the pound's spot rate, and ____ pressure on the pound's forward rate.
Upward; downward
Relative to the spot price, the forward price is
Usually less than or more than the spot price more often than it is equal to the spot price.
Interest Rate Parity (IRP) is best defined as
a "no arbitrage" equilibrium condition that must hold when international financial markets are in equilibrium.
Intervention in the foreign exchange market is the process of
a central bank buying or selling its currency in order to influence its value.
The (domestic) Fisher effect states that _____ .
an increase (decrease) in the expected inflation rate in a country will cause a proportionate increase (decrease) in the interest rate in the country
Covered Interest Arbitrage (CIA) activities will result in
restoring equilibrium prices eventually.
The difference between a broker and a dealer is
brokers bring together buyers and sellers, but carry no inventory; dealers stand ready to buy and sell from their inventory.
A dealer in pounds who thinks that the exchange rate is about to increase in volatility
may want to widen his bid-ask spread.
Bank dealers in conversations among themselves use a shorthand notation to quote bid and ask forward prices in terms of forward points. This is convenient because _____ ,
forward points may remain constant for long periods of time, even if the spot rates change frequently, and in swap transactions where the trader is attempting to minimize currency exposure, the actual spot and outright forward rates are often of no consequence
Foreign exchange swap transactions_____ .
involve the simultaneous sale (or purchase) of spot foreign exchange against a forward purchase (or sale) of approximately an equal amount of the foreign currency
The forward market _________.
involves contracting today for the future purchase of sale of foreign exchange at a price agreed upon today
The spot market _____ .
involves the almost-immediate purchase or sale of foreign exchange
In view of the fact that Purchasing Power Parity is the manifestation of the law of one price applied to a standard commodity basket,
it will hold only if the prices of the constituent commodities are equalized across countries in a given currency or if the composition of the consumption basket is the same across countries.
If a foreign county experiences rapid inflation,
its currency will tend to depreciate against those of countries with stable prices.
A dealer in British pounds who thinks that the pound is about to depreciate
may want to lower both his bid price and his ask price.
An arbitrage is best defined as
the act of simultaneously buying and selling the same or equivalent assets or commodities for the purpose of (ideally) making certain guaranteed profits.
For a U.S. trader working in American quotes (say, $/€), if the forward price is higher than the spot price _____ .
the currency (say, the €) is trading at a premium in the forward market.
The EUR-USD spot exchange rate is $1.50/€ and the 120-day forward exchange rate is $1.45/€. Assume 360 days in a year. The forward premium (discount) is:
the dollar trading at a 10% discount to the euro for delivery in 120 days. (F-S)/S x 360/120 = (1.45-1.50)/1.50 x 360/120 = -10%
Purchasing Power Parity (PPP) theory states that _____ .
the exchange rate between currencies of two countries should be equal to the ratio of the countries' price levels, and as the purchasing power of a currency sharply declines (due to hyperinflation) that currency will depreciate against stable currencies
When a currency (say, €) trades at a premium in the forward market
the forward rate (say, $/€) is more than the spot rate.
The (approximate) International Fisher Effect suggests that _____ .
the nominal interest rate differential reflects the expected change in the exchange rate
If the interest rate in the U.S. is i$ = 2 percent for the next year and interest rate in the U.K. is i£ = 3 percent for the next year, uncovered IRP suggests that
the pound is expected to depreciate against the dollar by about 1 percent and the dollar is expected to appreciate against the pound by about 1 percent
When Interest Rate Parity does not hold,
there are opportunities for covered interest arbitrage.
Relative to the spot price, the forward price is
usually less than or more than the spot price more often than it is equal to the spot price.
One important reason to study the Purchasing Power Parity (PPP) theory is because ________.
when inflation rates differ across international borders, PPP provides a baseline forecast of future exchange rates
If one has agreed to buy a foreign currency forward, _____ .
you have a long position in the forward contract
Suppose that the current exchange rate is $1.1178/€. The indirect quote, from the U.S. perspective is
€0.8946/ $ 1/1.1178 = 0.8946
