1. Chp 1 Currency Exchange Rates

2. organization
Foreign exchange quotations
Arbitrage
Forward quotes

3. 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.

4. 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 ）

5. 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.

6. 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
From the quotation of two currencies against the U.S. dollar, one can derive the cross-exchange rate between the two currencies
Cross exchange rate

7. For example, bank A gives the following quotations
€:$ =
$:¥ =
Calculate the euro in yen (€:¥) rate:
(€:$)  ($:¥) =  =
The resulting quotation is: €:¥ = One euro is worth yen.
For example, bank B gives the following quotations for the Korean won and the Brazilian real:
$: won =
$: R$ =
Calculate the R$:won rate:
($:won) ÷ ($:R$) = / =
The resulting quotation is: R$:won = One Brazilian Real is worth won.

8. Fill in the missing exchange rates in the following table.
Euro
US dollar
Yen
British pound 1
1.3 euro
0.013 euro
2 euro
British
pound

9. Euro
US dollar
Yen
British pound 1
1.3 euro
0.013 euro
2 euro
$0.77
$0.01
$1.54
Yen 76.92
Yen 100
Yen
£0.5
£0.65
£0.0065

10. Conclusions:
(a:b) ×(b:c) = a:c
(a:b) ÷(a:c) = c :b
2. The Forex convention specifies rates for all currencies per dollar (as in $:¥) except for the pound and the euro.

11. 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.

12. 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 £:$ = Which currencies appreciated or depreciated?

14. 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

15. Bid-ask(offer) quotes and spread
The Forex market is organized like an international Over- The-Counter market.
It is the price at which the dealer is willing to buy the quoted currency in exchange for the second currency
Bid price
Ask price
It is price at which the dealer is willing to sell the base currency in exchange for the second currency.
The difference between the bid and ask price is called the spread.
Midpoint price: (bid+ask)/2

16. Two principles Indirect quotation = 1 Direct quotation Quote in U.S.
Bid
Ask
Direct (€:$)
$0.9836
$0.9839
Indirect ($:€)
€1.0164
€1.0167
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.
Indirect quotation =
Direct quotation

17. Bid-ask spread = ask price – bid price ask price Example
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. €:$ = – The spread equals 4 pips.
spread
Bid-ask spread = ask price – bid price
ask price
Example
Suppose bid price for £ = $1.52,
ask price = $1.60.
Spread = (1.60 – 1.52) = .05 or 5%
1.60

18. The difference is the spread (gain)

19. The following factors will affect spread
Trade volume
Market condition

20. 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

21. Two check to be made correctly
Look at the symbols
Make sure that you maximize the bid-ask spread

22. Arbitrage aligns exchange rate quotations throughout the world
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

23. Equivalent assets sell for the same price,
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$ ~
NewYork　　 ￡l =US$ ~

24. Arbitrage Example
Consider the following three banks each providing a $:¥ quote :
Bank A Bank B Bank C
Does an arbitrage opportunity exist?
One could buy dollars from Bank A for yen per dollar and simultaneously sell them to Bank B for yen per dollar. A small gain, but it is riskless and does not require any invested capital.

25. 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 $：¥
NYC $: SFr
Zurich SFr: ¥

26. Triangular arbitrage involves 3 steps
Pick the cross rate currency
Determine 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
Transaction costs
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.

27. Triangular Arbitrage Example
You observe these quotes below. Is any currency arbitrage possible?
Calculate cross-rates and compare with the quoted rates

28. 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.

29. Forward premium Forward discount
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

30. You observe the following: Spot USD/EUR=1
You observe the following: Spot USD/EUR= , and 6-months forward USD/EUR= Is EUR trading at a premium or discount relative to the USD? Compute the annualized forward discount/premium.

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

32. Riskless Arbitrage: Covered Interest Parity
Spot: $: € =
One year interest rate ($): 10%
One year interest rate (€): 14%
Borrow at 10%
U.S.D
Time 0
Time 1
Buying a forward contract
Spot $: € ?
Euros
F $: € =0.8080
Lend at 14%

33. (F- S) / S = (r€ - r $) / (1+ r $)
1+r$ = S /F (1+r€)
F / S = (1+r€) / (1+r $)
(F- S) / S = (r€ - r $) / (1+ r $)
Spot exchange rate = S a: b

34. Forward Quotations with Bid-Ask Spreads - Example
On the Forex market, you notice the following quotes:
Spot: $:¥ = –
One year interest rate ($): 3 ½ – 4%
One year interest rate (¥): ½ - 1%
What should be the quote for the one year forward exchange rate $:¥?

35. Solution:
Thus, the forward quotation is $:¥: –