Zulfiqar Hasan, Associate Professor
This is a Lecture Handout for the course of International Financial Management. The topic is "Foreign Exchange Rates, Quotations and Arbitrage".
Contents of the topic: Foreign Exchange, Foreign Exchange Rates, Types of FX rates, Types of Quotations, Direct Quotations, indirect quotations, American Quotations, European Quotations, Foreign exchange transaction, Arbitrage transaction, Exchange Rates and Export-Import Business
Foreign Exchange Rate
A foreign exchange rate is the price of one currency expected in terms of another currency.
Cross Rate: A cross rate is an exchange rate between two currencies, calculated from their common relationships with a third currency. When cross rates differ from the direct rates between two currencies, intermarket arbitrage is possible
Exchange Rates Explanation:
Assume the quoted exchange rate is:
$/ £: 2.0000. There are a number of points to be noted about this:
- The first of this pair of currencies is the $ and the second is £. This distinction is important for definitions, rules etc.
- Exchange rates are always given in terms of the number of units of the first currencyper single unit of the second currency; and so $/£: 2.0000 means that the exchange rate is $2.0000= £1.
- The final point to note is that exchange rates are normally given to four decimal places-but not necessarily. How many decimal places are used depends upon the size of the number before the decimal point.
For example: $/£: 1.8525 and ¥/£: 225.40
Types of Foreign Exchange Quotation:
Foreign Exchange Quotation: A foreign Exchange quotation (or quote) is a statement of willingness to buy or sell at an announced rate.
01. European Quote: The foreign currency price of one dollar
Example: BDT 75.2525/$, read as BDT 75.2525 per dollar
02. American Quote: The dollar price of a unit of foreign currency
Example: $0.0.01329/BDT, read as 0.0.01329 dollars per BDT
03. Direct Quote: A foreign exchange rate quoted as the domestic currency per unit of the foreign currency.
Direct quotation: 1 unit of foreign currency = x Number of home currency
Example: $1 = Tk 83.7535 is a direct quote in Bangladesh
04. Indirect Quote: A foreign exchange rate quoted as the foreign currency per unit of the domestic currency. In an indirect quote, the foreign currency is a variable amount and the domestic currency is fixed at one unit.
Indirect quotation: 1 unit of home currency = x Number of foreign currency units
For example: Tk 1 = $ 0.01193 is an indirect quote in Bangladesh,
Transaction in the Foreign Exchange Market
A foreign exchange transaction is an agreement between a buyer and a seller that a fixed amount of one currency will be delivered for some other currency at a specified rate. Transactions within this market can be executed on a spot, forward, or swap basis
- A spot transaction requires almost immediate delivery of foreign exchange
- A forward transaction requires delivery of foreign exchange at some future date
- A swap transaction is the simultaneous exchange of one foreign currency for another
Example 01: Cross Rates
A Mexican importer needs Japanese yen to pay for purchases in Tokyo. Both the Mexican peso (Ps) and Japanese yen (¥) are quoted in US dollars.
Japanese yen ¥121.13/$
Mexican peso Ps9.190/$
Calculate ¥/Ps cross rate.
Solutions:
Given Thant,
$1 = ¥121.13 and
$1 = Ps9.190
So,
¥121.13 = Ps9.190
¥1 = Ps9.190/121.13 = Ps 0.0759
Again, Ps9.190 =¥121.13
So, Ps 1 =¥121.13 /9.190 = ¥13.1806
Practice 01: Cross Rates
A Bangladeshi importer needs US$ to pay for purchases in New York. Both the BDT and US $ are quoted in Euro (€).
BDT/ €: 105.3635
$/ €: 1.4215
- Calculate BDT/ $ cross rate
- Calculate $/BDT cross rate র্
Answer:
- BDT/ $ = 74.1214
- $/BDT = 0.0135.
What is triangular arbitrage? What is a condition that will give rise to a triangular arbitrage opportunity?
Triangular arbitrage is the process of converting one currency to another, converting it again to a third currency and, finally, converting it back to the original currency within a short time span.
Triangular arbitrage is the process of trading out of the First currency into a second currency, then trading it for a third currency, which is in turn traded for first Currency.
The purpose is to earn an arbitrage profit via trading from the second to the third currency when the direct exchange between the two is not in alignment with the cross exchange rate.
Example 02: Intermarket Arbitrage
Assume that the following exchange rates are quoted.
| Citibank $0.9045/€ Barclays Bank $1.4443/£ Dresdner Bank €1.6200/£ |
- Calculate the cross rate between Citibank and Barclays
- How much Pound one can get from Barclays Bank if he has $100,000?
- How much Euro he can get if he sells the pound simultaneously to the Dresdner Bank?
- How much profit in Dollar he can make if he again sells the Euro in Citibank?
Example 02: Solutions
c. How much Euro he can get if he sells the pound simultaneously to the Dresdner Bank?
£ 1 = € 1.6200
So, £69237.69 = € 1.6200 x 69237.69 = € 112165.06
d. How much profit in Dollar he can make if he again sells the Euro in Citibank?
€ 1 = $0.9045
So, € 112165.06 = $ 0.9045 x 112165.06 = $ 101453.30
Therefore, Profit = $ 101453.30 -$100,000 = $1453.30
Triangular Arbitrage & Cross Rate Graphical Presentation
Practice 02: Intermarket Arbitrage
Assume that the following exchange rates are quoted.
| Citibank $0.9145/€ Barclays Bank $1.3943/£ Dresdner Bank €1.6155/£ |
- Calculate the cross rate between Citibank and Barclays
- How much Pound one can get from Barclays Bank if he has $100,000?
- How much Euro he can get if he sells the pound simultaneously to the Dresdner Bank?
- How much profit in Dollar he can make if he again sells the Euro in Citibank?
Practice 03
Given that, ¥ $/£
¥ 118/$, $1.81/£, ¥ 204/£. You have $100.
Show process of making a profit via triangular arbitrage
Solution Format
01. Calculating Cross Rate: (¥ 118/$)/ ($1.81/£) = ¥213.58/£
02. Arbitrage Process
Convert $ to ¥ = ¥……
Convert ¥ …. to Pound = £……
Convert £…… to $ = $..........
Finding the Arbitrage Profit: New $ value – Old $ Value
= $.........- $100 = $ ……..
Solution:
01. Calculating Cross Rate: (¥ 118/$)/ ($1.81/£) = ¥213.58/£
02. Arbitrage Process
Convert $100 to Yens = ¥11800
Convert ¥11800 to Pound = £57.8431
Convert £57.8431 to $ = $104.6960
Finding the Arbitrage Profit: New $ value – Old $ Value
= $104.6960- $100 = $ 4.6960
|
Practice 04 Given that, ¥ $/£ ¥ 122/$, $1.84/£, ¥ 208/£. You have $500. Show process of making a profit via triangular arbitrage |
Practice 03 (From Text): Riskless Profit From Arbitrage
The Following exchange rates are available to you.
Mt. Fuji Bank ¥120.00/$
Mt. Rushmore Bank SF1.6000/$
Matterhorn Bank ¥80.00/SF
Assume you have an initial SF10,000,000. Can you make a profit via triangular arbitrage? If so, show steps and calculate the amount of profit in Swiss Francs.
Solution Hints: Matterhorn => Fuji =>Rushmore
Result: Profit= SF 66666.67
|
Practice 04 (Real Life): Riskless Profit from Arbitrage DBBL BDT 83.6955/$ Assume you have an initial BDT 500000. Can you make a profit via triangular arbitrage? If so, show steps and calculate the amount of profit in BDT. |
Hints: EBL=>IBBL=>DBBL
Answer: Profit = BDT 563260.89- BDT 500000 = BDT 63260.89
Bid- Ask Spread
Bid Rate: The rate at which the bank will buy a currency from you is called the Bid-rate.
Ask Rate: the rate at which the bank will sell a currency to you is the ask rate.
Stated differently, you buy at the ask rate, and you sell at the bid rate.
Bid/ask spread: Bid/ask spread is the difference between buying and selling prices
Understand bid/ask spread
Suppose that you read the following quote in the newspaper: Tk/US$: 81.5225 – 82.5535
Q1. What is the buying and selling rate for US $?
A1. The Bank’s buying rate for US $ is Taka 81.5225 and its selling rate is Taka 82.5535
Or you buy US $ at Taka 82.5535 and sell US $ at Taka 81.5225
Q2. What, therefore, are the bank’s buying and selling rates for Taka?
A2. The bank’s buying rate for Taka is 1/82.5535 = US $ / Tk 0.0121 and the selling rate is 1/81.5225 = US $ / Tk 0.0123.
Example 03: Understand bid/ask spread
Assume you have TK 325,000 and plan to travel from Bangladesh to the United Kingdom. Assume further that the Banks Bid-Ask rate for Taka/ £ is 121.52-122.52
Example 04: Bid-Ask Spread
Example: Tk 70.2525/$ - Tk 72.2525/$ is the bid/ask rate
The bank will buy Dollar at Tk 70.2525 per dollar, So if a customer wants to exchange $1000, he can get Tk $1000x70.2525 = Tk 70252.50
If a customer wants to purchase $ 1000, he should pay to the bank = 1000xTk 72.2525 =Tk 72252.50
Spread or Profit = Tk 72252.50- Tk 70252.50 =Tk 2000
Bid/Ask Spread Calculation
Case Practice 01: Currency Rate Quotation
Following foreign exchange quotation of Buying and selling rate of different currencies of a Bangladeshi Commercial Bank published in a Daily newspaper.
Example 05: Bid-Ask Transaction
A businessman has just completed transactions in Italy and England. He is now holding €250,000 and £500,000 and wants to convert to U.S. dollars.
His currency dealer provides this quotation:
GBP/USD 0.5025 – 0.5076
USD/EUR 1.4739 – 1.4744
Assuming no other fees, what are his proceeds from conversion?
Example 05: Solution
When he sells €250,000 he will trade with a dealer at the dealer’s bid price of $1.4739 per €:
Example 05 (From Text): Ringgit appreciation or depreciation?
Practice 05: Traveling with the Foreign Currencies
On your post graduation celebratory trip, you are leaving Copenhagen, Denmark, for St. Petersburg, Russia. Denmark’s currency is the Krone. You leave Copenhagen with 10,000 danish kroner still in your wallet. Wanting to exchange all of these for Russian rubles, you obtain the following quotes:
Dkr 8.5515/$ R 30.962/$
a. What is the Danish krone/Russian Rubble cross rate?
b. How many rubles will you obtain for your kroner?
Example 06: Traveling: Copenhagen to St. Petersburg
Forward Premium or Discount
Forward premium or discount is the percentage difference between the spot and forward exchange rate.
If the difference is positive, it is Premium
If the difference is negative, it is Discount
Example 07: Premium or Discount
Given that Spot rate of ¥/$:114 and 90-day forward rate is ¥/$:112, find out the forward premium or discount rate.
Practice 06: Premium or Discount
Assume that it is August 01, 2006 and today’s spot rate is €0.9804/$ and the 180-day forward rate is €0.9210/$. What is the forward premium or discount on Euro?
Factors that Affect Bid/Ask Spread
- cost
- Inventory cost
- Competition
- Volume
- Currency risk
Expressing Forward Quotations on a Points Basis..
The yen is quoted only to two decimal points
A forward quotation is not a foreign exchange rate, rather the difference between the spot and forward rates
¤ Example:
Forward Quotations in Percentage Terms
¤ Forward quotations may also be expressed as the percent-per-annum deviation from the spot rate
¤ The important thing to remember is which currency is being used as the home or base currency
For indirect quotes (i.e. quote expressed in foreign currency terms), the formula is
Examples 08: Forward Quotations in Percentage Terms
• Example: Indirect quote
Integrated Problem 01
Answer a-g
Using the quotes from the table, we get:
a. $100(€0.7877/$1) = €78.77
b. $1.2695
c. €5M($1.2695/€) = $6,347,594
d. Singapore dollar
e. Mexican peso
f. (P10.9075/$1)($1.2695/€1) = P13.8473/€
This is a cross rate.
g. Most valuable: Kuwait dinar = $3.4578
Least valuable: Columbian peso = $0.0004088
Answer h-j
h. You would prefer £100, since:
(£100)(£1/$.5383) = $185.760
i. You would still prefer £100. Using the $/£ exchange rate and the SF/£ exchange rate to find the amount of Swiss francs £100 will buy, we get:
(£100)($1.8576/£1)($/SF 0.8073) = SF 230.1003
j. Using the quotes in the book to find the SF/£ cross rate, we find:
($/SF 0.8073)($1.8576/£1) = SF 2.3010/£1
The £/SF exchange rate is the inverse of the SF/£ exchange rate, so:
£1/SF 2.3010 = £0.4346/SF 1
Interest Rate Parity
Interest Rate Parity refers to the fundamental equation that governs the relationship between interest rates and currency exchange rates. It describes the relationship between forward exchange rates, spot exchange rates, and interest rates between two countries.
There are two versions of interest rate parity:
Covered Interest Rate Parity: Under covered parity, there is no incentive to borrow money from, say, the United States, convert it to Canadian dollars while entering a forward exchange agreement, then loan it to Canadians at higher interest rates because the difference between the forward and spot rates would be the same as the difference between the two interest rates.
Uncovered Interest Rate Parity: Uncovered parity does not use forward exchange rates, but rather the expected change in spot rates. For there to be potential for profit, the interest rates must be higher than the expected change in profits. Uncovered parity uses estimates rather than actual contract prices, so exploiting the lack of it is riskier.
Forward Exchange Rate Calculation
• Therefore, the forward exchange rate is just a function of the relative interest rates of two currencies.
• In fact, forward rates can be calculated from spot rates and interest rates
• Forward Rate = Spot Rate X (1 + Interest Rate of Overseas country)/
(1 + Interest Rate of Domestic country)
Example 09: Forward Rate
Consider U.S. and Canadian rates as an illustration. Suppose that the spot rate for the Canadian dollar is presently 1 USD = 1.0650 CAD (ignoring bid-ask spreads for the moment). One-year interest rates are at 3.15% for the U.S. dollar and 3.64% for the Canadian dollar.
Example 09: Forward Exchange Rate Calculation
Let us look at an example: If the spot CAD/USD rate is 1.1239 and the three month interest rates on CAD and USD are 0.75% and 0.4% annually respectively, then calculate the 3 month CAD/USD forward rate.
Example 10: Forward Rate Calculation
If the euros spot rate is $1.03 and its one-year forward rate has a premium of 2%, what will be the one-year forward rate?
Example 11: Forward Premium
If the euro’s one-year forward rate is quoted as $1.00 and the euro’s spot rate is quoted at $1.03, calculate the euro’s forward premium.
Contributor: Zulfiqar Hasan is a university teacher working as Associate Professor (Finance). He has completed his MBA from London School of Commerce, London, UK.
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