1. International Finance
The International
Financial
Environment
Foreign Exchange
Rates, Quotations
and Arbitrage
Zulfiqar Hasan
BBA(Hons.), MBA(Finance), London
Associate Professor
ZULFIQAR HASAN

2. Foreign Exchange Rate and Quotation
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:
$/ £: 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 currency per single unit of the second currency; and so $/£: 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: $/£: and ¥/£:
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3. Types of Foreign Exchange Quotation:
Foreign Exchange Quotation: A foreign Exchange quotation (or quote) is a statement of willingness to buy or sell at an announced rate.
01. European Quote: The foreign currency price of one dollar Example: BDT /$, read as BDT per dollar
02. American Quote: The dollar price of a unit of foreign currency
Example: $ /BDT, read as 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 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 = $ is an indirect quote in Bangladesh,
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4. 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
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5. Calculate Ps/ ¥ cross rate. Result: Ps/¥ = 0.0759.
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. Calculate ¥/Ps cross rate.
Japanese yen ¥121.13/$
Mexican peso Ps9.190/$
The Mexican importer can buy one US dollar for Ps9.190 and with that dollar buy ¥121.13; the ¥/Ps cross rate would be….
Calculate Ps/ ¥ cross rate.
Result: Ps/¥ =
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6. Calculate BDT/ $ cross rate Calculate $/BDT cross rate
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/ €:
$/ €:
Calculate BDT/ $ cross rate
Calculate $/BDT cross rate
Answer
BDT/ $ =
$/BDT =
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7. What is triangular arbitrage
What is triangular arbitrage? What is a condition that will give rise to a triangular arbitrage opportunity?
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.
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8. 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?
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9. a. The cross rate between Citibank and Barclays is: £ €
Example 02: Solutions ……
a. The cross rate between Citibank and Barclays is: €
b. How much Pound one can get from Barclays Bank if he has $100,000?
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10. Therefore, Profit = $ 101453.30 -$100,000 = $1453.30
Example 02: Solutions ……
c. How much Euro he can get if he sells the pound simultaneously to the Dresdner Bank? €
£ 1 = €
So, £ = € x = €
d. How much profit in Dollar he can make if he again sells the Euro in Citibank?
€ 1 = $0.9045
So, € = $ x = $
Therefore, Profit = $ $100,000 = $
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11. Triangular Arbitrage & Cross Rate Graphical Presentation
Citibank
Dresdner Bank
Barclays Bank
End with $1,014,533
Start with $1,000,000
Sell €1,121,651 to Citibank
at $0.9045/€
(6) Receive $1,014,533
Sell $1,000,000 to Barclays
Bank at $1.4443/£
(2) Receive £692,377
Sell £692,377 to Dresdner Bank
at €1.6200/£
(4) Receive €1,121,651
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12. 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?
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13. Show process of making a profit via triangular arbitrage
Practice 03
Given that, ¥ $/£
¥ 118/$, $1.81/£, ¥ 204/£. You have $100.
Show process of making a profit via triangular arbitrage
Solution:
01. Calculating Cross Rate: (¥ 118/$)/ ($1.81/£) = ¥213.58/£
02. Arbitrage Process
Convert $ to ¥ = ¥……
Convert ¥ …. to Pound = £……
Convert £…… to $ = $
Finding the Arbitrage Profit: New $ value – Old $ Value
= $ $100 = $ ……..
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14. Show process of making a profit via triangular arbitrage
Practice 03
Given that, ¥ $/£
¥ 118/$, $1.81/£, ¥ 204/£. You have $100.
Show process of making a profit via triangular arbitrage
Solution:
01. Calculating Cross Rate: (¥ 118/$)/ ($1.81/£) = ¥213.58/£
02. Arbitrage Process
Convert $100 to Yens = ¥11800
Convert ¥11800 to Pound = £
Convert £ to $ = $
Finding the Arbitrage Profit: New $ value – Old $ Value
= $ $100 = $
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15. Show process of making a profit via triangular arbitrage
Practice 04
Given that, ¥ $/£
¥ 122/$, $1.84/£, ¥ 208/£. You have $500.
Show process of making a profit via triangular arbitrage
Solution:
01. Calculating Cross Rate: (¥ 118/$)/ ($1.81/£) = ¥213.58/£
02. Arbitrage Process
Convert $ to ¥ = ¥……
Convert ¥ …. to Pound = £……
Convert £…… to $ = $
Finding the Arbitrage Profit: New $ value – Old $ Value
= $ $500 = $ ……..
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16. Practice 03 (From Text): Riskless Profit From Arbitrage
Mt. Fuji Bank ¥120.00/$
Mt. Rushmore Bank SF1.6000/$
Matterhorn Bank ¥80.00/SF
The Following exchange rates are available to you.
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.
Hints:
Matterhorn – Fuji – Rushmore
Profit= SF
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17. Practice 04 (Real Life): Riskless Profit from Arbitrage
DBBL BDT /$
IBBL € /$
EBL BDT / €
The Following exchange rates are available to you.
Assume you have an initial BDT Can you make a profit via triangular arbitrage? If so, show steps and calculate the amount of profit in BDT.
Answer: EBL=>IBBL=>DBBL
Profit = BDT BDT = BDT
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18. 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
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19. Understand bid/ask spread
Suppose that you read the following quote in the newspaper: Tk/US$: –
Q1. What is the buying and selling rate for US $?
A1. The Bank’s buying rate for US $ is Taka and its selling rate is Taka
Or you buy US $ at Taka and sell US $ at Taka
Q2. What, therefore, are the bank’s buying and selling rates for Taka?
A2. The bank’s buying rate for Taka is 1/ = US $ / Tk and the selling rate is 1/ = US $ / Tk
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20. 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
How much pound you can get from the bank?
b. Now suppose that because of an emergency you cannot take the trip and you want reconvert the £ to back to Taka, just after purchasing the pounds. If the exchange rate has not changed, how much Taka you will receive?
= £ X (Banks bid rate of Tk per pound)
= Tk
Spread or Loss of Taka = Tk Tk = Tk
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21. Example 04: Bid-Ask Spread
Tk /$ - Tk /$ is the bid/ask for Bangladeshi Taka. Calculate the bid-ask spread for Bank if a customer wants to sell $1000 and then he wants to buy $1000.
Example: Tk /$ - Tk /$ is the bid/ask rate
The bank will buy Dollar at Tk per dollar, So if a customer wants to exchange $1000, he can get Tk $1000x = Tk
If a customer wants to purchase $ 1000, he should pay to the bank = 1000xTk =Tk
Spread or Profit = Tk Tk =Tk 2000
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22. Bid/Ask Spread Calculation
Currency
Bid
Ask
Spread
British Pound
$1.52
$1.60 5%
Japanese Yen
$0.0070
$0.0074
5.4%
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23. 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.
Currency
Buy
Sell
US Dollar
83.39
84.45
Euro
109.35
110.45
Pound
132.13
133.05
Australian Dollar
88.55
89.66
Japanese Yen
1.10
1.12
Canadian Dollar
84.14
84.51
Singapore Dollar
67.07
67.53
Saudi Real
22.11
22.80
Requirements ((from the individual viewpoint)
If you want to buy 1000 bugs of every currency, how much you have to spend for each currency?
If you then sell the currency you bought in part-01, how much you will receive from each currency?
What is your profit or loss from part-01 and part-02 in each currency?
Calculate the bid-ask spread in amount and in percentage for every currency.
Calculate the cross rate between –
US Dollar/Euro
Euro/Pound
Pound/US Dollar
Saudi Real/US Dollar
US Dollar/Singapore Dollar
Calculate the invert Rate from part-05.
Repeat 01,02, 03 and 04 from the bank view point.
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24. 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 –
USD/EUR –
Assuming no other fees, what are his proceeds from conversion?
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25. Example05: Solution
When he sells €250,000 he will trade with a dealer at the dealer’s bid price of $ per €:
USD/EUR –
€250,000 x
$1.4739
€1.00
=$368,475
When he sells £500,000 he will trade with a dealer at the dealer’s ask price of £ per $:
GBP/USD –
$1,353,502.58
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26. Example 05 (From Text): Ringgit appreciation or depreciation?
Before the Asian currency crisis the Malaysian ringgit traded at RM 2.700/$. It currently trades at RM /$. Did the Ringgit appreciate or depreciate, and by what percentage?
% change = (S1-S2)/(S2)
Assumptions
Values
Malaysian ringgit, before the crisis (RM/$)
Malaysian ringgit, after the crisis (RM/$)
Calculation percentage appreciation or depreciation
Percentage change in the ringgit
-28.95%
% chg = (S1-S2)/(S2)
Because the ringgit fell in value:
Depreciation
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27. Practice 05: Traveling with the Foreign Currencies
On your post graduation celebratory trip, you are leaving Copenhagen, Denmark, for St. Petersburg, Russia. Denmark’s currency is the Krone. You leave Copenhagen with 10,000 danish kroner still in your wallet. Wanting to exchange all of these for Russian rubles, you obtain the following quotes:
Dkr /$ R /$
a. What is the Danish krone/Russian Rubble cross rate?
b. How many rubles will you obtain for your kroner?
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28. Example 06: Traveling: Copenhagen to St. Petersburg
What is the cross-rate? What is left?
Assumptions
Values
Beginning your trip with Danish kroner
10,000.00
Spot rate (Dkr/$)
8.5515
Spot rate (Roubles/$)
30.962
a) Calculate the cross-rate
Cross-rate (Dkr/rouble)
0.2762
cross-rate = (Dkr/$) / (Rouble/$)
b) What would be the proceeds in Rubles?
Converting your Danish kroner into Rubles
36,206.51
Proceeds = Danish kroner / (Dkr/rouble)
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29. 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
Here
S = spot rate
F = forward rate
n = number of days until the forward contract becomes due
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30. 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.
Is it premium? or Discount?
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31. 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?
12.90%
Premium
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32. Factors that Affect Bid/Ask Spread
Order cost
Inventory cost
Competition
Volume
Currency risk
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33. 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:
Bid Ask
Outright spot: ¥ ¥118.37
Plus points (3 months)
Outright forward: ¥ ¥116.97
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34. 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
For direct quotes (i.e. quote expressed in home currency terms), the formula is
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35. Examples 08: Forward Quotations in Percentage Terms
Example: Indirect quote
Example: Direct quote
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36. Key Currency Cross Rates
Integrated Problem 01
Key Currency Cross Rates
Dollar
Euro
Pound
SFranc
Peso
Yen
CdnDlr
Canada
1.1377
1.4443
2.1133
0.9184
---
Japan
115.78
146.98
215.07
93.470
10.615
Mexico
20.262
8.8056
----
9.5877
Switzerland
1.2387
1.5725
2.3010
1.0888 UK
0.6834
0.4346
1.4633
USA
1.2695
1.8576
Take a look back at above Table to answer the following questions:
If you have $100, how many euros can you get?
How much is one euro worth?
If you have five million euros, how many dollars do you have?
Which is worth more, a New Zealand dollar or a Singapore dollar?
Which is worth more, a Mexican peso or a Chilean peso?
How many Swiss francs can you get for a euro? What do you call this rate?
Per unit, what is the most valuable currency of those listed? The least valuable?
Which would you rather have, $100 or ￡100? Why?
Which would you rather have, FF 100 or ￡100? Why?
What is the cross-rate for French francs in terms of British pounds? For British pounds in terms of French francs?
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37. Using the quotes from the table, we get: a. $100(€0.7877/$1) = €78.77
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. (P /$1)($1.2695/€1) = P /€
This is a cross rate.
g. Most valuable: Kuwait dinar = $3.4578
Least valuable: Columbian peso = $
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38. h. You would prefer £100, since: (£100)(£1/$.5383) = $185.760
Answer h-j
h. You would prefer £100, since:
(£100)(£1/$.5383) = $
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 ) = SF
j. Using the quotes in the book to find the SF/£ cross rate, we find:
($/SF )($1.8576/£1) = SF /£1
The £/SF exchange rate is the inverse of the SF/£ exchange rate, so:
£1/SF = £0.4346/SF 1
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39. 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.
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40. 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)
Here
S= spot rate
F = the forward rate
rf = foreign currency interest rates
rd = domestic currency interest rates
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41. 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 = 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.
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42. Example 09: Forward Exchange Rate Calculation
Let us look at an example: If the spot CAD/USD rate is 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.
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43. 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?
Here,
F = Forward Rate
P = Forward Premium
S = Spot Rate
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44. 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.
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