Chp 1Chp 1CurrencyCurrency Exchange Rates Exchange Rates

organization

Foreign exchange quotations Arbitrage Forward quotes

Currency Abbreviations Abbreviations are used to refer to the various

currencies. These abbreviations could be commonly used symbols or “official” three-letter codes.

Financial newspapers such as the Financial Times generally use symbols, while traders use three-letter codes. Symbols include $ (U.S. dollar), ¥ ( Japanese yen), € (euro), £ (British pound), A$ (Australian dollar), and Sfr (Swiss franc).

Three-letter codes for the same currencies are USD, JPY, EUR, GBP, AUD, and CHF.

We will alternatively use in this book (as done in the real world) the various currency abbreviations that are commonly encountered. For example, the Japanese yen can be referred to as ¥, JPY, or yen.

Foreign exchange quotations

A currency exchange rate is the rate used to exchange two currencies. An exchange rate states the price of one currency in terms of units of another currency.

Examples: $:€, €:$, ¥:$ Note: the notation in this new edition of

the text has changed relative to previous editions.（€ /£---- the number of euros per pound ）

Quote Convention used in this text

All quotes in this text will be presented as a:b = S

– where a is the quoted currency– b is the currency in which the price is expressed– S is the price of the quoted currency a in units of

currency b– For example, $:¥ = 130 means the U.S. dollar is

quoted at 130 Japanese yen (¥) per dollar. Or the U.S. dollar is priced at 130 yen.

Basic principles 1. All currencies are quoted against the U.S.

dollar, although there are such regional exceptions as the yen in Asia and the euro and pound in Europe.

Basic exchange rate

Cross exchange rateFrom the quotation of two currencies against the U.S. dollar, one can derive the cross-exchange rate between the two currencies

– For example, bank A gives the following quotations• €:$ = 1.3364• $:¥ = 123.52

– Calculate the euro in yen (€:¥) rate:

• (€:$) ($:¥) = 1.3364 123.52 = 165.07• The resulting quotation is: €:¥ = 165.07. One

euro is worth 165.07 yen.

– For example, bank B gives the following quotations for the Korean won and the Brazilian real:

• $: won = 928.350

• $: R$ = 1.9094

– Calculate the R$:won rate:

• ($:won) ÷ ($:R$) = 928.35/1.9094 = 486.20

• The resulting quotation is: R$:won = 486.20. One Brazilian Real is worth 486.50 won.

Fill in the missing exchange rates in the following table.

Euro US dollar Yen British pound

Euro 1 1.3 euro 0.013 euro 2 euro

US dollar        

Yen        

Britishpound

       

Euro US dollar

Yen British pound

Euro 1 1.3 euro 0.013 euro

2 euro

US dollar $0.77 1 $0.01 $1.54

Yen Yen 76.92

Yen 100 1 Yen 153.85

British pound

£0.5 £0.65 £0.0065 1

2. The Forex convention specifies rates for all currencies per dollar (as in $:¥) except for the pound and the euro.

Conclusions:

(a:b) ×(b:c) = a:c

(a:b) ÷(a:c) = c :b

More on quotation conventions direct exchange rate quotation are made in terms of the amount of local

or domestic currency(DC) required to purchase one unit of foreign currency(FC).

e.g. 100 yen per dollar

（ appreciation and depreciation） indirect exchange rate traders quote the amount of foreign currency

required to purchase one unit of home currency.

All exchange rate with dollar are usually given as direct rates, but there are two exception that give the indirect rates, The British pound and The euros.

On July 1, the British pound (£) is quoted as £:$ = 1.80. – Is this a direct or indirect quote from

the viewpoint of an American and a British investor?

– A month later, the exchange rate moved to £:$ = 1.90. Which currencies appreciated or depreciated?

American terms

the dollar price of one unit of the second currency is referred to as American terms, a direct quote in terms of U.S..

European terms

The amount of second currency per U.S. dollar is called European terms, an indirect quote from the U.S. perspective.

other conventions

quotation are given with 5 digits.

Forex quotes always include a BID PRICE and an ASK PRICE/OFFER PRICE, and there is no commission or fee added on a trade

Bid-ask(offer) quotes and spread

The Forex market is organized like an international Over- The-Counter market.

Bid price

Ask price

It is the price at which the dealer is willing to buy the quoted currency in exchange for the second currency

It is price at which the dealer is willing to sell the base currency in exchange for the second currency.

Midpoint price: (bid+ask)/2

The difference between the bid and ask price is called the spread.

Two principles– The a:b ask exchange rate is the reciprocal of

the b:a bid exchange rate.– The a:b bid exchange rate is the reciprocal of

the b:a ask exchange rate.

Quote in U.S. Bid Ask

Direct (€:$) $0.9836 $0.9839

Indirect ($:€) €1.0164 €1.0167

Indirect quotation = 1 Direct quotation

Bid-ask spread = ask price – bid priceask price

ExampleSuppose bid price for £ = $1.52, ask price = $1.60.

Spread = (1.60 – 1.52) = .05 or 5%1.60

A pip stands for “price interest point” and represents the smallest price fluctuation in the currency price. It is equivalent to the “tick” on stock markets.

E.g. €:$ = 1.3015 – 1.3019. The spread equals 4 pips.

spread

The difference is the spread (gain)

The difference is the spread (gain)

The following factors will affect spread

Trade volume Market condition

Arbitrage Cross-rate calculations with Bid-Ask spreads

(FC2 ： FC1)ask=(DC ： FC1)ask * (FC2 ： DC)ask

(FC2 ： FC1)bid=(DC ： FC1)bid * (FC2 ： DC)bid

Direct ask (FC ： DC) = 1 / Indirect bid (DC ：FC)

Direct bid (FC ： DC) = 1 / Indirect ask (DC ：FC)– Notation: DC=domestic currency, FC=foreign

currency

Two check to be made correctly

Look at the symbolsMake sure that you maximize the bid-ask

spread

An arbitrage could be created if it were profitable to buy from one bank and sell to another bank.

Arbitrage aligns exchange rate quotations throughout the world– For example, the $:€ rate must be the same, at

a given instant, in Frankfurt, Paris and New York.

There are two types of arbitrage with exchange rate

Bilateral arbitrage

Triangular arbitrage

Bilateral arbitrage

The law of one price

Equivalent assets sell for the same price,

exchange rate quotes in two countries should be same within a transaction cost band.

the bid-ask spread in one country should be aligned with the bid-ask spread in the other. If not, a bilateral arbitrage opportunity exists.

Suppose

London 　 ￡ 1=US$ 1.4815 ~ 1.4825

NewYork 　　 ￡ l =US$ 1.4845 ~ 1.4855

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Arbitrage Example Consider the following three banks each providing

a $:¥ quote :

Bank A Bank B Bank C

122.25-35 122.40-45 122.25-45

Does an arbitrage opportunity exist?

One could buy dollars from Bank A for 122.35 yen per dollar and simultaneously sell them to Bank B for 122.40 yen per dollar. A small gain, but it is riskless and does not require any invested capital.

Triangular arbitrage

It occurs if the quoted exchange rate between the two currencies is higher or lower than the cross-rate implied by the exchange rate of the two currencies against the third currency.

You observe these rates:– Tokyo $ ： ¥ 120.00– NYC $: SFr 1.6000– Zurich SFr: ¥ 80.00

Transaction costs

Triangular arbitrage involves 3 stepsPick the cross rate currencyDetermine whether the cross-rate bid-ask quotes are in

line with the direct quotes by determining whether it is cheaper to buy foreign currency directly or indirectly

If not, an arbitrage opportunities exists.

If transaction costs are ignored Check whether (FC1:DC)*(DC:FC2) *(FC2:FC1) =1

Check whether quoted and cross-rate bid-ask spreads overlap for any currency out of our three currencies. If you have rate 1 [bid1, ask1] and rate 2 [bid2, ask2] such that ask2<bid1, buy at ask2 and sell at bid1.

Triangular Arbitrage Example You observe these quotes below. Is any currency arbitrage possible?

bid ask bid ask bid askEUR：USD 0.9836 0.9839 GBP：EUR 1.5373 1.5380 USD：GBP 0.6566 0.6571USD：EUR 1.0164 1.0167 EUR：GBP 0.6502 0.6505 GBP：USD 1.5219 1.5231

bid ask bid askEUR：USD 0.9836 0.9839 0.9895 0.9908GBP：EUR 1.5373 1.5380 1.5469 1.5485USD：GBP 0.6566 0.6571 0.6609 0.6614

Frankfurt London New York

QUOTED CROSS-RATES

Calculate cross-rates and compare with the quoted rates

Forward quotes Spot exchange rates are quoted for delivery two

business days after the transaction is concluded Forward exchange rate foreign exchange

traders quote exchange rates for delivery further than two days in the future.

in other words, contract a commitment is irrevocable made on the transaction date, but delivery take places later, on a date set in the contract.

Forward exchange rates are often quoted as a premium or discount

Forward premium– Nominal value in the forward exchange market is

higher than in the spot exchange market

Forward discount– Nominal value in the forward exchange market is

lower than in the spot exchange market

Given an exchange rate of y ： x, the annualized forward premium on y

Forward rate - Spot rate 12

Spot rate No.months forward

You observe the following: Spot USD/EUR=1.4570-76, and 6-months forward USD/EUR=1.4408-34. Is EUR trading at a premium or discount relative to the USD? Compute the annualized forward discount/premium.

Interest rate parity: The forward discount and the interest rate differential

Interest rate parity

it is a relationship linking spot exchange rate, forward exchange rate and interest rate.

for two currencies, FC and DC, the IRP is that the forward discount equals the discounted interest rate differential between the two currencies.

（ FFC ： DC - S ） / S = (rDC - rFC)/(1+rFC)

Riskless Arbitrage: Covered Interest Parity Spot: $: € = 0.8000 One year interest rate ($): 10% One year interest rate (€): 14%

Time 0Borrow at 10%

U.S.D

Time 1

Euros

Lend at 14%

Spot $: € ?

Buying a forward contract

F $: € =0.8080

1+r$ = S /F (1+r€)

F / S = (1+r€) / (1+r $)

a

ba

r1rr

rateSpotrateSpotrateForward

(F- S) / S = (r€ - r $) / (1+ r $)

Spot exchange rate = S a: b

On the Forex market, you notice the following quotes:

Spot: $:¥ = 105.00 – 105.50

One year interest rate ($): 3 ½ – 4%

One year interest rate (¥): ½ - 1%

What should be the quote for the one year forward exchange rate $:¥?

Forward Quotations with Bid-Ask Spreads - Example

1 - 35

Solution:

Thus, the forward quotation is $:¥: 107.60 – 109.174

6.10701.1

035.100.105

174.109005.1

04.150.105

BID

ASK

F

F