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Foreign Exchange Rate and QuotationForeign 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 possibleExchange Rates Explanation: Assume the quoted exchange rate is: $/ £: 2.0000. There are a number of points to be noted about this:1. The first of this pair of currencies is the $ and the second is £. This

distinction is important for definitions, rules etc.2. 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 $/£: 2.0000 means that the exchange rate is $2.0000= £1.

3. 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.

4. For example: $/£: 1.8525 and ¥/£: 225.40

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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 dollar02. American Quote: The dollar price of a unit of foreign currency

Example: $0.0.01329/BDT, read as 0.0.01329 dollars per BDT03. 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 currencyExample: $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,

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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

1. A spot transaction requires almost immediate delivery of foreign exchange

2. A forward transaction requires delivery of foreign exchange at some future date

3. A swap transaction is the simultaneous exchange of one foreign currency for another

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Example 01: Cross Rates

Japanese yen ¥121.13/$

Mexican peso Ps9.190/$

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.

$) (i.eCurrency Common in Bcurrency of value

$) (i.eCurrency Common in A currency of value

Bcurrency of unitsin

A currency ofunit 1 of Value

The Mexican importer can buy one US dollar for Ps9.190 and with that dollar buy ¥121.13; the ¥/Ps cross rate would be….

Ss

13.1806/P¥ 9.190/$P

121.13/$¥

dollar pesos/USMexican

dollar yen/US Japanes

Calculate Ps/ ¥ cross rate. Result: Ps/¥ = 0.0759.

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Practice 01: Cross Rates

BDT/ €: 105.3635

$/ €: 1.4215

A Bangladeshi importer needs US $ to pay for purchases in New York. Both the BDT and US $ are quoted in Euro (€).

Answer• BDT/ $ = 74.1214• $/BDT = 0.0135.

Currency Common in Bcurrency of value

Currency Common in A currency of value

Bcurrency of unitsin

A currency ofunit 1 of Value

1. Calculate BDT/ $ cross rate2. Calculate $/BDT cross rate

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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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Example 02: Intermarket Arbitrage

Assume that the following exchange rates are quoted.

Citibank $0.9045/€

Barclays Bank $1.4443/£

Dresdner Bank €1.6200/£

a. Calculate the cross rate between Citibank and Barclays

b. How much Pound one can get from Barclays Bank if he has $100,000?

c. How much Euro he can get if he sells the pound simultaneously to the Dresdner Bank?

d. How much profit in Dollar he can make if he again sells the Euro in Citibank?

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Example 02: Solutions ……

a. The cross rate between Citibank and Barclays is:

1.5968/ $0.9045/

$1.4443/ £

£ €

€

b. How much Pound one can get from Barclays Bank if he has $100,000?

£69237.69000,1001.4443

1 £$100,000 So,

1.4443

1 £ $1

1 £4443.1$

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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

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Triangular Arbitrage & Cross Rate Graphical Presentation

Citibank

Dresdner Bank Barclays Bank

End with $1,014,533 Start with $1,000,000

(3) Sell £692,377 to Dresdner Bank at €1.6200/£(4) Receive €1,121,651

(1) Sell $1,000,000 to Barclays Bank at $1.4443/£

(2) Receive £692,377(5) Sell €1,121,651 to Citibank at $0.9045/€

(6) Receive $1,014,533

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Practice 02: Intermarket Arbitrage

Assume that the following exchange rates are quoted.

Citibank $0.9145/€

Barclays Bank $1.3943/£

Dresdner Bank €1.6155/£

a. Calculate the cross rate between Citibank and Barclays

b. How much Pound one can get from Barclays Bank if he has $100,000?

c. How much Euro he can get if he sells the pound simultaneously to the Dresdner Bank?

d. How much profit in Dollar he can make if he again sells the Euro in Citibank?

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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

a. Convert $ to ¥ = ¥……b. Convert ¥ …. to Pound = £……c. Convert £…… to $ = $..........d. Finding the Arbitrage Profit: New $ value – Old $ Value

= $.........- $100 = $ ……..

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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

a. Convert $100 to Yens = ¥11800b. Convert ¥11800 to Pound = £57.8431c. Convert £57.8431 to $ = $104.6960d. Finding the Arbitrage Profit: New $ value – Old $ Value

= $104.6960- $100 = $ 4.6960

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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

a. Convert $ to ¥ = ¥……b. Convert ¥ …. to Pound = £……c. Convert £…… to $ = $..........d. Finding the Arbitrage Profit: New $ value – Old $ Value

= $.........- $500 = $ ……..

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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.

Hints:

Matterhorn – Fuji – Rushmore

Profit= SF 66666.67

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Practice 04 (Real Life): Riskless Profit from Arbitrage

Answer: EBL=>IBBL=>DBBL

Profit = BDT 563260.89- BDT 500000 = BDT 63260.89

DBBL BDT 83.6955/$

IBBL € 0.7258/$

EBL BDT 102.3636 / €

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.

The Following exchange rates are available to you.

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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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Understand bid/ask spreadSuppose 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.

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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

£2652.63122.52Tk

325000Tk

you toPound Sell

bank that meansIt

b. Now suppose that because of an emergency you cannot take the trip and you want reconvert the £2652.63 to back to Taka, just after purchasing the pounds. If the exchange rate has not changed, how much Taka you will receive?

= £2652.63 X (Banks bid rate of Tk 121.52 per pound) = Tk 322347.60Spread or Loss of Taka = Tk 325000- Tk 322347.60 = Tk 2652.4

a. How much pound you can get from the bank?

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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

Tk 70.2525/$ - Tk 72.2525/$ 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.

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Bid/Ask Spread Calculation

$0.0074

$1.60

Ask

5.4%$0.0070Japanese Yen

5%$1.52British Pound

SpreadBidCurrency

= ask rate - bid rate

ask rate• Bid/Ask Spread

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Case Practice 01: Currency Rate QuotationFollowing foreign exchange quotation of Buying and selling rate of different currencies of a Bangladeshi Commercial Bank published in a Daily newspaper. Requirements ((from the individual viewpoint)

1. If you want to buy 1000 bugs of every currency, how much you have to spend for each currency?

2. If you then sell the currency you bought in part-01, how much you will receive from each currency?

3. What is your profit or loss from part-01 and part-02 in each currency?

4. Calculate the bid-ask spread in amount and in percentage for every currency.

5. Calculate the cross rate between –

i. US Dollar/Euro

ii. Euro/Pound

iii. Pound/US Dollar

iv. Saudi Real/US Dollar

v. US Dollar/Singapore Dollar

6. Calculate the invert Rate from part-05.

7. Repeat 01,02, 03 and 04 from the bank view point.

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

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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?

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Example05: Solution

When he sells €250,000 he will trade with a dealer at the dealer’s bid price of $1.4739 per €:

GBP/USD 0.5025 – 0.5076

When he sells £500,000 he will trade with a dealer at the dealer’s ask price of £0.5076 per $:

€250,000 x$1.4739

€1.00=$368,475

USD/EUR 1.4739 – 1.4744

$1,353,502.58

58.985027$£0.5076

$1.00£500000

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Example 05 (From Text): Ringgit appreciation or depreciation?

Assumptions Values

Malaysian ringgit, before the crisis (RM/$) 2.7000

Malaysian ringgit, after the crisis (RM/$) 3.8000

Calculation percentage appreciation or depreciation

Percentage change in the ringgit -28.95%

% chg = (S1-S2)/(S2)

Because the ringgit fell in value: Depreciation

Before the Asian currency crisis the Malaysian ringgit traded at RM 2.700/$. It currently trades at RM 3.8000/$. Did the Ringgit appreciate or depreciate, and by what percentage?

% change = (S1-S2)/(S2)

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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?

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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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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

100360/

nF

FSF dp

HereS = spot rateF = forward raten = number of days until the forward contract becomes due

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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.

7.14%

10090

360

112

112114

100360/

nF

FSf dp

Is it premium? or Discount?

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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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Factors that Affect Bid/Ask Spread

• Order cost• Inventory cost• Competition• Volume• Currency risk

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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 AskOutright spot: ¥118.27 ¥118.37

Outright forward: ¥116.84 ¥116.97

Plus points (3 months) -1.43 -1.40

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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

100 x days

360 x

Foward

Foward -Spot f FC

•For direct quotes (i.e. quote expressed in home currency terms), the formula is

100 x days

360 x

Spot

Spot - Forward f H

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Examples 08: Forward Quotations in Percentage Terms

• Example: Indirect quote

p.a. 2.32%

100x 90

360x

105.04

105.04 - 105.65 f ¥

p.a. 2.32%

100x 90

360x

50.00946521

50.00946521-30.00952018 f $

Example: Direct quote

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Integrated Problem 01Key Currency Cross Rates

Dollar Euro Pound SFranc Peso Yen CdnDlr

Canada 1.1377 1.4443 2.1133 0.9184 0.10430 0.00983 ---

Japan 115.78 146.98 215.07 93.470 10.615 --- 101.771

Mexico 10.9075 13.8471 20.262 8.8056 ---- 0.09421 9.5877

Switzerland 1.2387 1.5725 2.3010 --- 0.11356 0.01070 1.0888

UK 0.53830 0.6834 --- 0.4346 0.04935 0.00465 0.47319

Euro 0.78770 ---- 1.4633 0.63592 0.07222 0.00680 0.69240

USA --- 1.2695 1.8576 0.80730 0.09158 0.00864 0.87900

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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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

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Answer h-j

h. You would prefer £100, since:(£100)(£1/$.5383) = $185.760i. 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 230.1003j. Using the quotes in the book to find the SF/£ cross rate,

we find:($/SF 0.8073)($1.8576/£1) = SF 2.3010/£1The £/SF exchange rate is the inverse of the SF/£ exchange

rate, so:£1/SF 2.3010 = £0.4346/SF 1

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Interest Rate ParityInterest 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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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)

3601

3601

nr

nr

sF

f

d

HereS= spot rate F = the forward raterf = foreign currency interest rates rd = domestic currency interest

rates

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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.

CAD 1.0700360360

3.15%1

360360

3.64%11.0650F

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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.

1249.136090

%4.01

36090

%75.011239.1

F

3601

3601

nr

nr

sF

f

d

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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?

p)S(1F

5060$1.

2)0.0(1 $1.03

)%2(1 $1.03

p)S(1F

Here,F = Forward RateP = Forward PremiumS = Spot Rate

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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.

2.91%p So,

0.0291p

10.9709p

1$1.03

$1.00p

1S

Fp

p1S

F

p)S(1F