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LEHMAN BROTHERS' FOREIGN EXCHANGE TRAINING MANUAL
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LEHMAN BROTHERS
FOREIGN EXCHANGE
TRAINING MANUAL
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TABLE OF CONTENTS
CONTENTS ....................................................................................................................................... PAGE
FOREIGN EXCHANGE SPOT: INTRODUCTION ...................................................................... 1
FXSPOT:
AN INTRODUCTION TO FOREIGN EXCHANGE SPOT TRANSACTIONS ........... 2
INTRODUCTION ...................................................................................................................... 2
WJ-IAT IS AN OUTRIGHT? ..................................................................................................... 3
VALUE DATES ........................................................................................................................... 4
CREDIT AND SETTLEMENT RISKS .................................................................................. 6
EXCHANGE RATE QUOTATION TERMS ...................................................................... 7
RECIPROCAL QUOTATION TERMS (RATES) ............................................................. 10
EXCHANGE RATE MOVEMENTS ................................................................................... 11
SHORTCUT ................................................................................................................................ 14
BIDS AND OFFERS ................................................................................................................. 16
THE RULE OF THE LEFT BID -RIGHT OFFER ........................................................ 17
CROSS RATES ........................................................................................................................... 22
BID-OFFER FOR THE CROSS RATES OF CURRENCIES
ON SAME TERMS .................................................................................................................25
EXCHANGE RATE MOVEMENT REVISITED FOR CROSSES .............................. 26
BID-OFFER FOR CROSS RATES OF CURRENCIES ON
DIFFERENT TERMS ............................................................................................................ 27
SUMMARY .................................................................................................................................. 28
SHORTCUTS .............................................................................................................................. 31
TRADING CONVENTIONS AMONG MARKET MAKERS ...................................... 32
SUMMARY .................................................................................................................................. 33
REVIEW PROBLEMS .............................................................................................................. 35
FOREIGN EXCHANGE FORWARDS: INTRODUCTION ...................................................... 38
FXFORWARDS:
AN INTRODUCTION TO FOREIGN EXCHANGE FORWARDS ............................... 39
INTRODUCTION .................................................................................................................... 39
WJ-IAT ARE FORWARDS? ..................................................................................................... 39
CALCULATING THE FORWARD RATE ......................................................................... 40
HOW DO YOU CALCULATE FORWARD POINTS? ................................................... 43
PAY AND EARN POINTS ..................................................................................................... 43
SUMMARY .................................................................................................................................. 46
SAMPLE PROBLEMS .............................................................................................................. 46
PREMIUM VS. DISCOUNT POINTS .................................................................................. 51
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TABLE OF CONTENTS
(continued)
CONTENTS ....................................................................................................................................... PAGE
SAMPLE PROBLEMS .............................................................................................................. 52
FORWARD RATE CONVENTIONS .................................................................................. 54
SAMPLE PROBLEMS .............................................................................................................. 55
CALCULATING ODD DATES ............................................................................................ 53
TYPES OF TRANSACTIONS ................................................................................................ 59
HOW DO THE FORWARD POINTS CHANGE? ........................................................... 59
WHICH SIDE OF THE MARKET? ..................................................................................... 60
CURRENCY FUTURES........................................................................................................... 61
FUNDING .................................................................................................................................. 62
TRADE IDEAS AND HOW THEY ARE FORMED ...................................................... 62
TRADING EURODOLLAR FUTURES .............................................................................. 64
TRADING SPREADS INVOLVES ANALYZING YIELD CURVES ......................... 65
EXAMPLE OF A POSITIVE CARRY TRADE ................................................................. 66
FORWARDS REVIEWPROBLEMS .................................................................................... 67
FOREIGN EXCHANGE SWAPS: INTRODUCTION ................................................................. 69
WHAT IS A SWAP ............................................................................................................................ 70
VALUE DATES ......................................................................................................................... 71
BID-OFFER SPREADS ........................................................................................................... 77
CALCULATING SWAP POINTS ......................................................................................... 82
RULES OF THUMB ................................................................................................................. 84
PAY OR EARN THE POINTS .............................................................................................. 86
THE RATIONALE BEHIND THE CHART ..................................................................... 88
LEARNING POINTS ............................................................................................................... 92
SUMMARY .................................................................................................................................. 92
FOREIGN EXCHANGE OPTIONS: INTRODUCTION ........................................................... 94
FXOPTIONS:
AN INTRODUCTION TO FOREIGN EXCHANGE DERIVATIVES .......................... 95
INTRODUCTION .................................................................................................................... 95
VANILLA OPTIONS ............................................................................................................... 95
PAYOFF OF A LONG AND SHORT CALL OPTION .................................................. 96
PAYOFF OF A LONG AND SHORT PUT OPTION ..................................................... 96
THE GREEKS ............................................................................................................................ 97
DELTA RANGES FROM 0% (DEEP OTlvf) TO 100% (DEEP ITlvf) ......................... 99
TRADING GAMMA ON A LEHMAN CALL OPTION .............................................. 102
P&L ON GAMMA HEDGING EXAMPLE ..................................................................... 103
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TABLE OF CONTENTS
(continued)
CONTENTS ....................................................................................................................................... PAGE
SECOND ORDER GREEKS ............................................................................................... 106
FACTORS AND THEIR EFFECTS ON OPTION VALUE ........................................ 107
EXOTIC OPTIONS ................................................................................................................ 107
TRADING CONVENTIONS .............................................................................................. 110
TRADING STRATEGIES ..................................................................................................... 111
GLOSSARY ............................................................................................................................... 123
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FOREIGN EXCHANGE
SPOT
INTRODUCTION
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FX SPOT
AN INTRODUCTION TO FOREIGN EXCHANGE SPOT TRANSACTIONS
INTRODUCTION
Money has been around in one form or another since the days of the Pharaoh, replacing
former systems of bartering. But, as history progressed and scores of countries generated
their own individual monies, Middle Eastern money changers found a market exchanging
coins of one culture for those of another-the first foreign exchange 'market'. Over the ages,
the form of money changed from coin form to bill form, the latter flourishing in the Middle
Ages. But trading and speculation across foreign currencies began to increase after World
War I. This speculation was not looked upon favorably by world markets, giving rise to the
Bretton Woods Accord, a proposal undertaken towards the end World War II pegging major
currencies to the U.S. dollar. The dollar was in turn pegged to gold at $35 per ounce. This
accord allowed currencies to fluctuate by one percent on either side of the standard,
mandating that respective central banks intervene if the fluctuation was outside of those
limits. Although the Bretton Woods accord accomplished the goals of its charter tore-
establish economic stability in post-war Europe and Japan, it ultimately failed. Other similar
failed agreements were attempted in the following decades, but, ultimately in 1973, the
world defaulted to free-floating currencies. *
All major currencies now move independently of other currencies, being traded by anyone
who wishes. Now, hedge funds, banks, brokerage houses, corporations, and individuals all
participate in the foreign exchange market either on a speculative basis, to facilitate
transactions, or to hedge against currency risks associated with their core business.
Foreign exchange is a business of exchanging one currency for another. This exchange can
take two basic forms: an outright or a swap. When two parties simply exchange one
currency for another the transaction is an outright. For example, if one party gives the other
dollars for Euros, they have completed an outrighttransaction. If this exchange takes place
for immediate delivery, it is called a spottransaction; if it takes place for forward delivery, it
is called a forward.
Two parties can also agree to exchange and re-exchange one currency for another. For
example, one party gives the other dollars for Euros for immediate delivery and
simultaneously agrees to re-exchange Euros for dollars at a specified rate at some time in the
future. These transactions are called swaps.
The first part of this workbook will focus on spot exchanges.
* Source: gftforex.com
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WHAT IS AN OUTRIGHT?
An outright currency transaction involves two parties exchanging one currency for another. The two
parties must agree on the two currencies, the amount of one currency, the settlement date, and the
exchange rate. The amount of the second currency will be derived from a calculation involving the
amount of the first currency and the exchange rate.
Outright rate ofexchange/spot: the amount of one unit of currency expressed in terms of
the other.
Outright Transaction: the exchange of one currency for the other at the outright
rate of exchange.
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VALUE DATES
The value date is the day the two parties actually exchange the two currencies. It is impractical, in
most circumstances, for the value date and the trade date to be the same. The forward value date is
usually required to allow both parties time to arrange for payments which often occur in different
time zones.
By market convention, foreign exchange trades settle two mutual business days (T + 2) after that
trade date unless otherwise specified. This is commonly referred to as value for spot. The spot
exchange rate is the benchmark price the market uses to express the underlying value of the currency.
Rates for dates other than the spot are always calculated relative to the spot rate.
Listed below are the various value dates available in the market-they are all determined relative to
the deal date. Assume the deal date is Monday, December 12.
Cash December 12 Deal Date
Value "Tomorrow Next"
Spot December 13 One Mutual Business Date
Forward Outright December 14 After Deal Date#
December 15 or Later
Two Mutual Business Days
After Deal Date++
Three Business Days or More
After Deal Date; Always
Longer Than Spot
# The Setdement Date May Not Fall on a Day That is a National Holiday in Either Country.
++ Exception: Spot for the Canadian Dollar Against the USD is One Business Day Later. Assuming Today is Monday,
December 12, Spot Would be December 13.
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QUESTIONS
Using the trader's calendar below, indicate the date on which each of these trades would settle.
Assume you are at a New York bank dealing in currencies against the US dollar.
Today is December 4th.
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1. You do a trade in CAD for cash settlement_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
2. You do a spot CAD trade_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
3. You do a GBP trade for value tomorrow_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
4. You do a spot GBP trade_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
5. You do a spot CHF trade_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
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ANSWERS
1) December 4
2) December 5
3) December 5
4) December 6
5) December 6
CREDIT AND SETTLEMENT RISKS
Foreign Exchange contracts represent a Credit Risk between Lehman and the client. The risk is equal
to the replacement cost of any deal in the event that the client cannot fulfill its obligations. For spot
transactions, the exposure is for only the two days between the trade date and the value date.
However, for forward contracts the exposure is greater because the time between the trade date and
the value date is greater. For example, if Lehman contracted to buy USD/sell EUR one year forward
at 1.0425 and the current forward rate is 1.0845, Lehman has a gain of over 4% of the face value of
the contract. If the client cannot fulfill the contract, Lehman must replace the forward at the rate
currently available and, therefore, stands to lose the 4% mark-to-market gain. Since the bank reports
mark-to-market gains as income, client nonperformance has bottom line implications.
Settlement Risk is another form of credit risk which can potentially be much greater. Each currency
deal actually involves two settlements, since each currency settles in its home country. Since the
exchange of currencies cannot be simultaneous due to time differences, each party is at risk for the
time period between the two settlements. For example, assume you have sold JPY against the USD.
The JPY will settle in Japan-your JPY account will be debited and the JPY delivered to the bank of
the buyer-hours before your dollar account in New York is credited. Your risk is that you deliver
JPY to the Japanese clearing, but the bank which owes you dollars in return for your JPY declares
bankruptcy by the opening of business in NY. You have paid out the JPY but will not receive your
dollars in exchange.
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EXCHANGE RATE QUOTATION TERMS
• The major currency pairs can be quoted in either European or Amen'can terms .
• Those that quote in number of US dollars per one unit of another currency is American. An
example of this is EUR/USD which is quoted as the number of USD per one Euro.
• A currency quoted as the number of units of a specific currency per one USD is quoted in
American terms. An example of this would be dollar-yen, which is quoted in yen per one USD.
\X!hen rates are spoken the base currency comes first. It is imperative that you remember these
conventions!
The arithmetic way to express these quotations will always have the base currency in the
denominator and the rates currency in the numerator. Do not allow this representation to confuse
you when actually saying the currency pairs. This is simply how they would look mathematically.
Examples are USD /EUR and JPY/USD being the nomenclature for arithmetic expression of
Dollars per Euro and JPY per USD, respectively. The following will illuminate this point.
Since two currencies are involved, one has to be quoted in terms of the other. \X!hen we say that the
exchange rate for the yen against the dollar is 123.50 yen, we are valuing the dollar in terms of the
yen-123.50 yen per dollar. The arithmetic expression tells you which currency is being quoted in
terms of the yen. In the case of the USD /EUR, the EUR is being quoted in terms of the USD.
The way the two currencies are referred to verbally will usually tell you which one is the base, since
the base currency is usually stated first. For example, when the two currencies involved are the US
dollar and the yen, the relationship is called dollar-yen-meaning the number of yen per dollar. This
tells you that the dollar is the base and that the rate will be quoted in terms of yen per dollar.
Do not let the terminology confuse you; a "dollar-yen" rate is quoted as
Yen per USD.
##Also Known as the 'Loon'.
$ Sometitnes Known as the 'Fondue Franc'
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• The currency in the numerator always states how much of that currency is required for one unit of
the base currency.
U.S. terms: the dollar is in the numerator; for example, USD /GBP-- giving the
European Terms: units of dollar per pound.
the non-dollar currency is in the numerator; for example,
JPY/USD, giving the units of yen per dollar.
Numerator Terms Currency
Denominator Base Currenc
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QUESTIONS
• In many cases, you will see only the terms account; it is assumed you know the base. For
example, if you see JPY124.25 you know that this means 124.25 Yen per $1.
1. GBP 1.5541: base_ _ _ _ _ _ __ quoted in _ _ _ _ _ _ _ _ _ _ _ _t,erms.
2. CAD 1.5476: base_ _ _ _ _ _ __ quoted in _ _ _ _ _ _ _ _ _ _ _ terms.
3. AUD 0.5565: base_ _ _ _ _ _ __ quoted in____________terms.
4. EUR 1.0500: base_ _ _ _ _ _ __ quoted in_ _ _ _ _ _ _ _ _ _ _ _terms.
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ANSWERS
1. Sterling; US terms
2. USD; European terms
3. AUD; US terms
4. EUR; US terms
RECIPROCAL QUOTATION TERMS (RATES)
• The method of quotation can be changed from US to European terms, or vice versa, simply by
calculating the reciprocal of the rate. For example, Canadian dollars are usually quoted in
European terms, that is, the number of Canadian dollars per one US dollar.
CAD /USD = 1.5672
• However, at least for Canadian banks, you sometimes see it quoted in US terms. That is, the
number ofUSD per CAD.
To take the reciprocal:
1 I 1.5672 - 0.6381
0.6381 USD per 1 CAD
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EXCHANGE RATE MOVEMENTS
• The exchange rate is constantly changing, which means the value of one currency in terms of the
other is in constant flux. \X!hen this relationship changes, the market speaks of one currency as
strengthening or weakening vis-a-vis the second currency. For example, if the dollar strengthens,
by definition, the other currency must have weakened.
• \X!henever the base currency buys more of the terms currency or whenever there is an increase in
the numerator, the base currency has strengthened and the terms currency has weakened. For
example, if dollar-yen opened at 124.10 and closed at 124.60, you would say that the dollar
strengthened since one dollar buys more yen at the close than it did at the open. In this case, the
dollar closed higher or "up."
• Based on their outlook on a currency, traders will often take positions in that currency, buying it
if they think it will strengthen and selling it if they think it will weaken.
• Assume an FX trader bought one million dollar's worth of Swiss Francs at 1.4996 at
the open because she thought Francs would strengthen over that day. However, her
outlook for the day was wrong, and when she closed out her position by buying
back the dollars at 1.5040 she experienced a $2,925.53 (CHF4,400) loss.
CHF loss: -$1,000,000.00 +CHF1,499,600@ 1.4996
+$1.000.000.00 -CHF1.504.000@ 1.5040
-0- -CHF4,400
• The Swiss loss can then be converted into a dollar loss by dividing the Swiss loss by
the ending exchange rate.
CHF 4400 I 1.5040 = $2925.53
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QUESTIONS
• Based on the rates given below, decide which currency strengthened and which one weakened,
whether it closed up or down, and your profit/loss based on the position you took at the open.
&member: When the rate increases, the base strengthens, and the terms weakens.
1. Sterling opens at 1.5409 and closes at 1.5425.
The dollar and the pound . Therefore, the
Dollar closed (up/down) for the day, relative to the GBP. If you sold 1MM GBP and bought
USD at the open and the reversed the trade at the close, your (profit/loss) would be
_________(currency and amount).
2. Dollar-yen opens at 124.05 and closes at 123.50.
The Dollar and the yen . Therefore, the Yen
closed (up/down) for the day, relative to the USD. If you sold USD 1MM at the open and
reversed the position at the close, your (profit/loss) would
be_ _ _ _ _ _ _ _ _ _ _ _ _ ___
3. CHF/USD opens at 1.5030 and closes at 1.5035.
The USD and the Swiss Franc_ _ _ _ _ _ _ _ _ _ __
Therefore, the Dollar closed (up/down) for the day, relative to the CHF. If you sold CHF
10MM at the open and bought them back at the close, your (profit/loss) would be
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ANSWERS
1. The Dollar weakened and the Pound strengthened, since one Pound will buy more Dollars. The
Dollar closed down for the day. You had a loss of £1,037.28 or $1,600.
-£1,000,000 = +$1,540,900 @ 1.5409 -£1,000,000@ 1.5409 = +$1,540,900
+£1.000.000@ 1.5425 = -$1.542.500
+ £998.963 = - $1,540.900 @ 1.5425
0 - -$1,600
-£1,037 = 0
2. The Dollar weakened and the Yen strengthened, since one Dollar will buy fewer Yen. The Yen
closed up for the day. You had a profit of¥550,000 or $4,453.
- $1,000,000 = +¥124,050,000@ 124.05 -$1,000,000 @ 124.05 - +¥124,050,000
+ $1,004.453 = -¥124.050.000 @ 123.50 ...:....+.:L$1"-",0"-"0""-0,""-0"'-'00"--..>.:;:@~--=1=23"-!..5"'-'0"---------=¥-=.1=23=.5"-"0""-0,""-0~00
+$4,453 = 0 0 - +¥550,000
3. The dollar strengthened and the Swissie weakened since one Dollar will buy more Swissie. The
Dollar closed up for the day. You had a profit of CHF3,327 or $2,213.
-CHF10,000,000 = +$6,653,360@ 1.5030 -CHF10,000,000@ 1.5030 =+$6,653,360@ 1.5030
+CHF10.003.327 = +$6.653.360@ 1.5035 +CHF10.000.000@ 1.5035 =+$6.651.147@ 1.5035
+CHF3,327 = 0 0 = +$2,213
In the problems above we saw thefollowing market moves:
• Dealers refer to small moves as pips. For example, in the case ofUSD/GBP, Sterling moved 16
pips whereas in the case of the USD /JPY, the market moved 55 pips. One hundred pips is a
"point" or a ''big figure." Note that pips or points can be a different decimal place depending on
the quoting convention of the market. In the Sterling market, one pip is 0.0001 but in the Yen
market, one pip is 0.01.
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SHORTCUT
On the preceding page, you calculated the profit and loss due to a change in the rates. There is a
shortcut method to calculating these gains and losses.
I Base currency gain/loss = % change * base amount
Where % change = (pip change/closing rate)
I Terms currency gain/loss = pip change* base amount
• Example: In the Sterling case, the opening rate was 1.5409, the closing rate was 1.5425, for a 16
pip change.
• Base gain/loss £1,037
• Terms gain/loss = $1,600
• Note: It is mathematically equivalent (and possibly more understandable) to fmd the Base
gain/loss by multiplying the pip change by the notional and dividing that figure by the closing
exchange rate [(0.0016 * 1,000,000) / 1.5425]. Since the exchange rate is measured in Dollar
terms, the pip change is the Dollar gain/loss. Multiply that dollar gain/loss by the notional to
get the total USD gain/loss. Divide that gain/loss by the closing rate to get the amount of
Sterling that equates to.
QUESTIONS
Using the shortcut method, re-calculate the following gains or losses.
1. JPY/USD opens at 124.11 and closes at 123.80; you bought one million dollar's worth of Yen
on the open and sold it on the close.
2. CHF/USD opens at 1.5000 and closes at 1.5035; you sold 1,000,000 USD at the open and
bought it back at the close.
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ANSWERS
1. Base currency gain = .31/123.80 * $1,000,000 = $2,504
Terms currency gain = .31 * $1,000,000 =JPY310,000
= .0035/1.5035 * $1,000,000 = ($2,328)
2. Base currency loss = .0035 * $1,000,000 = (CHF3,500)
Terms currency loss
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BIDS AND OFFERS
• \X!hen making a market in a currency, market-makers (traders) quote two rates:
Bid Rate at \X!hich Market Maker Will Buy the Base Currency
Offer Rate at \X!hich Market Maker Will Sell the Base Currenc
• The difference between the bid and the offer is called the spread.
USD/GBP = 1.5464/74, so the spread is 0.0010 USD/GBP.
JPY/USD = 123.50/123.60, so the spread is 0.10 JPY/USD.
The market may move 10 pips, with the new quote being 1.5474/84, but the spread remains the
same under normal market conditions.
Also, note that although the spread in both markets above is 10 pips, the value of 10 pips in the
USD /GBP is different from the value if the 10 pips in the JPY/USD market. However, in the
market, spreads are generally comparable between currencies on a percentage basis. In general,
greater uncertainty among traders is reflected in wider spreads in the market.
The size of the spread reflects:
o The liquidiry of that currency-the more liquid the currency, the narrower the
spread.
o The size of the deal-the bigger the transaction, the wider the spread because the
dealer is taking on more risk.
o The time of the day-spreads tend to be widest in the New York afternoon because
both Europe and Asia are closed or during the Asian lunchtime.
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THE RULE OF THE LEFT BID -RIGHT OFFER
• Market makers always trade the base currency. They buy the base currency on the left side of the
quote and sell the base currency on the right side of the quote.
Example I: If a market maker quotes Sterling at 1.5460/70, he will buy Sterling at $1.5460 per
pound and sell Sterling at $1.5670 per pound. This means you can buy Sterling at
1.5470 (offer) and sell it at 1.5460 (bid).
Example II: If a market-maker quotes the dollar against the CHF at 1.5044/50, he will buy the
dollars at 1.5044 CHF per dollar but sell them for 1.5050 CHF per dollar. This
meanyou can buy them at 1.5050 CHF per dollar and sell them at 1.5044.
• To be sure about what side of the market you are dealing on, alwqys think in terms of the base
currency. This means every transaction can be thought of in terms of these rules:
1. Determine what the market-maker is quoting as the base currency.
2. Determine what you need to do in terms of the base currency.
3. Remember that the market-maker buys the base on the left and sells it on the
right.
• In Example I, the market-maker is quoting the dollar as the base. You have the USD and need
the CHF, so you must sell the USD and buy the CHF. You deal on the market-maker's bid
Oeft).
• In Example II, the market-maker is quoting the Sterling as the base. You have the USD and
want the Sterling, so you must buy the Sterling. The market-maker will sell them to you at the
offered (right) side of the market.
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QUESTIONS
On which rate wouldyou deal in each ofthe problems below?
1. You have just received a 1,000,000 GBP payment. You want to convert these pounds into
dollars. You get a quote of 1.5457/61.
2. You have to buy Australian dollars to make a large payment. The quote is .5535/37.
3. You need to make a SEK payment. You get a quote of9.3854/9.3934.
4. You have received a large JPY denominated dividend which you want to convert into dollars.
The quote is 123.19/23.
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ANSWERS
1. 1.5457 USD/GBP
The base currency is GBP. You want to sell GBP and buy USD. You will deal on the bid
(left) side of the market; that is where the trader is buying the GBP from you.
2. .5537 USD/AUD
The base currency is the AUD. You want to buy AUD. You will deal on the offered (right)
side of the market; that is where the trader is selling the AUD to you.
3. 9.3854 SEK/USD
The base currency is the US$. You need to buy SEK to make the payment and sell USD.
You will deal on the bid (left) side of the market; that is there the trader is selling SEK and
buying USD from you.
4. 123.23 JPY/USD
The base currency is the USD. You want to sell JPY and buy USD. You will deal on the
offered (right) side of the market; that is where the trader is selling USD.
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QUESTIONS
1. Decide where the client will deal:
Buy 5 GBP versus USD 1.5471/73
Sell10 USD versus JPY 125.06/12
Sell 7 NOK versus USD 7.5946/78
Buy 1 USD versus CAD 1.5626/32
Sell 5 EUR versus SEK 9.1268/9.1318
2. A corporation obtains the following quotes from a competition bank. Decide whom and at
which rate the client will deal at.
Buy 5 GBP versus USD 1.5471/73 1.5472/75
Sell10 USD versus JPY 125.06/12 125.01/05
Sell 7 NOK versus USD 7.5946/78 7.5950/80
Buy 1 USD versus CAD 1.5626/32 1.5620/25
Sell 5 EUR versus SEK 9.1268/9.1318 9.1260/9.1300
3. How much did the corporation save in each case (in$ or in foreign currency)?
GBP:
JPY:
NOK:
CAD:
EUR:
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ANSWERS
1. The corporation would deal at these rates:
GBP: 1.5473
JPY: 125.06
NOK: 7.5978
CAD: 1.5632
EUR/SEK: 9.1268
2. Given the competing rates, the corporation would deal at
GBP: 1.5473
JPY: 125.06
NOK: 7.5978
CAD: 1.5625
EUR/SEK: 9.1268
3. How much did the corporation save?
GBP: $500
JPY: ¥500,000
NOK: 24.25 NOK
CAD: 700 CAD
EUR/SEK: 4000 SEK
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CROSS RATES
So far, the exchange rates we have examined have involved the dollar as either the base or the terms
currency. However, the dollar is not always involved. \X!hen people talk about the price of one
foreign currency in terms of another and neither of the currencies is the dollar, it is called a cross rate.
• "Euro-yen" is a classic, widely traded cross-rate whose price movements reflect the market's
view on the Euro and the yen against various currencies. "Euro-yen" is a cross rate between the
EUR/JPY.
• Most commonly, traders derive cross rates using the two rates versus the USD because those
two rates are known. We will look first at how to derive them algebraically and then at a
shortcut rule. With cross rates, it is crucial to remember the base currency conventions.
Same terms (both are quoted in either US or European terms):
Example:
• Assume you want the CHF/JPY cross; that is, the number ofJPY for 1 CHF.
• 1.5029 CHF = 1 USD
• 125.22 JPY = 1 USD
• Therefore, CHF = 125.22 JPY
• 1 CHF = 125.22/1.5029
• 1CHF = 83.3189 JPY
• CHF/JPY = 83.3189
The shortcut rule is: If two currencies are quoted
against the $ on the same terms, divide the base
currency into the terms currency of the cross
currency pa1r.
Difforent terms (one currenry is quoted in US terms and the other in European terms). For example:
• Assume you want the GBP /JPY cross rate; i.e., the number ofJPY per 1 GBP .
• 125.06 JPY = 1 USD
• 1 GBP = 1.5467 USD
• Therefore, 1GBP = 125.06 GBP * $1.5467 = 193.4303
• GBP /JPY= 193.4303
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The short cut rule is: If two currencies are quoted
on diffirent terms, multipfy one rate by the other.
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QUESTIONS
Calculate the cross rates for the following currencies:
1. EUR/SEK
0.9772 EUR/USD
9.3622 USD/SEK
2. EUR/GBP
0.9772 EUR/USD
1.5465 USD/GBP
3. AUD/NZD
0.5535 USDI AUD
0.4841 USD /NZD
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ANSWERS
1. 9.1487 EUR/SEK
2. 0.6318 EUR/GBP
3. 1.1433 AUD/NZD
**Remember the shortcut rules:
If two currencies are quoted in the same terms,
divide the base currency of the cross currency pair
into the terms currency of the pair.
If two currencies are quoted in different terms,
multip!J one rate by the other.
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BID-OFFER FOR THE CROSS RATES OF CURRENCIES ON SAME
TERMS
So far we have ignored bid/offer spreads in calculating cross rates. The same rules apply--divide by
the base rate for currencies in the same terms and multiply the rates for those in different terms-but
now you have to figure out when to use the bid and when to use the offer of the first two currencies
to create the bid/offer of the cross.
Example:
• Assume you are the market-maker, and you want to derive the cross-rate market for CHF/JPY.
• First, always determine the base of the new cross. In this cross, the Swiss Franc is the base and
the yen is the terms currency. Now work with what you know. Since CHF is the base, you
know that 1) the currency being traded is the CHF, so 2) the bid and offer of the cross are for
CHF. You also know the value of CHF and JPY relative to the dollar. You will use this
information to derive the value of the CHF in terms of the JPY.
To get the bid side ofthe cross, bZ!J the base and sell the
terms ofthe cross.
• To get the JPY per CHF bid, you buy the CHF and sell JPY.
1. Buy CHF. As the market maker dealing in base currencies, to buy CHF you sell dollars on
your offer at 1.5031.
2. Sell JPY. Again as the trader, when sellingJPY, you buy dollars on your bid of125.06.
3. You want to know the value of 1 CHF in terms ofJPY. Since CHF and JPY are both in
European terms, you divide the base of the cross into the terms of the cross to get the cross
rate-CHF expressed in terms ofJPY.
The bid for JPY/CHF:
Sell Terms OPY) I Buy USD
Buy Base (CHF) I Sell USD
125.06 83.2013 JPY/CHF bid
1.5031
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• To get the offered side of the cross, sell the base and buy the terms .
1. Sell CHF. From your perspective, you buy USD on your bid of 1.5026.
2. Buy JPY. To buy JPY, you sell USD on the offer of 125.09.
3. You want to know the value of 1CHF in terms ofJPY.
The offer for JPYICHF:
BuyJPY I Sell USD
Sell CHF I Buy USD
125.09 83.2490 JPY I CHF offer
1.5026
• To simplify, always remember what to do with the base currency of the cross-then do the
opposite with the terms currency.
Bid bZ!J base of the cross against the dollar
Offir sell base of the cross against the dollar
• Another way to simplify is to think of presenting the Bid-Ask spread in the most favorable terms
for the market maker. This is done by making the spread as wide as possible. So, If you are
calculating a spread of currencies on the same terms, i.e. dividing, you would make the widest
spread by dividing the larger number by the smaller number and the smaller number by the
larger number. Doing so makes minimizes the bid and maximizes the offer. In our example this
is done by dividing 125.06 by 1.5031 and 125.09 by 1.5026. Similarly, for currencies on different
terms, where one multiplies the currencies to get the cross rate, one minimizes the bid by
multiplying both of the smaller numbers against each other and both of the larger numbers
against each other. We will see this is the next example.
EXCHANGE RATE MOVEMENT REVISITED FOR CROSSES
Cross rates also move such that one currency strengthens or weakens vis-a-vis the other one. As
with dollar-based currencies, it is easier to conceptualize when you think of cross rate moves in terms
of the base. For example, if "Swiss-yen" moves from 83.24 to 83.50, the Swiss Franc has
strengthened since one Swiss Franc buys more yen. Similarly, a move from 83.24 to 83.00 is a
weaker CHFI stronger JPY rate.
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BID-OFFER FOR CROSS RATES OF CURRENCIES ON DIFFERENT
TERMS
• The procedure for finding cross rate bid-offer spread for currencies in different terms is exactly
the same except you multipfy the two rates rather than divide.
Example:
• Assume you want to determine the bid/offer cross rate ofEUR/CHF or "Euro-Swiss." Within
the cross, Euro is the base currency and the CHF is the terms currency.
USD/CHF
• Bid of the Cross: buy the base and sell the terms of the cross.
1. Buy EUR. As the trader you buy the EUR on your bid of .9791.
2. Sell CHF. As the trader you sell CHF and buy USD on your bid of 1.4984.
3. Multiply the two rates and get the cross-rate bid.
1 EUR = $0.9791 * 1.4984 CHF
EUR/CHF = 1.4671
• Offer of the Cross: sell the base and buy the terms .
1. Sell EUR. As the trader you sell the euro on your offer of .9796.
2. Buy CHF. As the trader you buy CHF and sell USD on your offer of 1.4991.
3. Multiply the two rates and get the cross-rate offer.
1 EUR = $0.9796 * 1.4991 CHF
EUR/CHF = 1.4685
Note: Unlike currencies on the same terms where you use the bid of the terms and the offer of the
base currency to get the bid of the cross, there is no "cross-over" for the currencies on
different terms:
Bid of base * bid of terms =bid of cross
Offer of base * offer of terms = offer of cross
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SUMMARY
DIFFERENT TERMS
Bid: buy the base currency and sell the terms, multip!J the two rates to get the cross.
Offer: sell the base currency and buy the terms, multip!J the two rates to get the cross.
SAME TERMS
Bid: buy the base and sell the terms, divide by the base of the cross.
Offer: sell the base and buy the terms, divide by the base of the cross.
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QUESTIONS
Determine the bid/offer cross rates.
1. What is the NOK/EUR cross?
2. What is the JPY/CAD rate?
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ANSWERS
1. 7.4222-7.4264 NOK/EUR
bid: buy EUR on your bid at .9785
sell NOK/buy USD on your bid at 7.5853
1 EUR = $0.9785 * 7.5853NOK
7.4222 NOK per one EUR
offer: sell EUR on your offer at .9789
buy NOK/sell USD on your offer at 7.5865
1 EUR = $0.9789 * 7.5865NOK
7.4264 NOK per one EUR
2. 79.76-79.85JPY/CAD
bid: buy CAD/sell USD on your offer at 1.5685
sell JPY/buy USD on you bid at 125.11
1 CAD= 125.11JPY / $1.5685
79.76 JPY per one CAD
offer: sell CAD/buy USD at the 1.5675
buy JPY/sell USD at 125.17
1 CAD= 125.17JPY/$1.5675
79.85 JPY per one CAD
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SHORTCUTS
Although it is essential to be able to derive the cross rates, there are times when you cannot take the
time to think-you have to be able to react immediately. These rules may help you:
• Currencies on same terms:
=• Offer base into bid terms bid cross
=• Bid base into offer terms offer cross
• Currencies on diffirent terms:
=• Bid base times bid terms bid cross
=• Offer base times offer terms offer cross
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TRADING CONVENTIONS AMONG MARKET MAKERS
An outright foreign exchange market is a two-sided foreign exchange quotation, consisting of two
rates: the rate at which an institution will buy the base currency and the rate at which the same
institution will sell the base currency. Market-makers, primarily major multinational commercial
banks, stand ready to buy and sell given currencies against the dollar. Most are also prepared to make
cross rate markets.
• With all market participants, market-makers:
• Generally quote a two-sided market (with wider spreads in volatile markets),
• Can change the quote up until the counterparty actually deals on the market
quoted, and
• Can be expected to hold the price for only three to four seconds.
• With other market-makers, they:
• Make reciprocal agreements on the currencies, standard amount of the
trade, and the size they will quote each other.
• Majors- EUR, USD, GBP, CHF,JPY
AUD, NZD, CAD
Penphery/ Commodiry - BRL, lvfXP, CLP, VEB
Emerging Markets, Latin Amen·ca - KRW, TWD, INR, THB
Emerging Markets, Asia - CZK, HUF, PLN
Emerging Markets, Europe -
• This list is not extensive. Lehman Brothers will deal in any currency where local authorities have
not placed restrictions on their currency.
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SUMMARY
• An outright transaction involves two parties exchanging one currency for another.
• Settlement conventions (value dates) for all currencies are:
• Cash = same date as deal date
• Value tomorrow= one business day after deal date
• Spot= two business days after deal date (except for CAD which is one day)
• Forward= any day after spot
• Spot is used as the benchmark price representing the underlying value of the currency. Unless
otherwise specified, a quoted exchange rate is assumed to be the spot rate.
• There is settlement risk in FX transactions because the deal involves two separate settlements-
one in each country-which do not take place simultaneously.
• \X!hen two currencies are involved, one currency must be expressed in terms of the other.
• The currency in the numerator = the terms currency
• The currency in the denominator = the base currency
• \X!henever it takes more of the terms currency to buy one unit of the base currency (whenever
the numerator gets bigger), the terms currency has weakened and the base currency has
strengthened.
• The opposite is also true. \X!henever the base currency can buy more of the terms currency, the
base has strengthened, the terms has weakened.
• Assuming one of the currencies involved is the USD, when the USD is in the numerator, the
currency is quoted in USD terms; when the dollar is not in the numerator, the currency is quoted
in European terms.
• US terms: USD/GBP
• European terms: CHF/USD
• \X!hen speaking of one currency in terms of another, the base currency is usualfy stated first.
• ''Dollar-Swiss"
• "Sterling-dollar"
• Traders always think in terms of buying/selling the base currency.
• Traders buy the base currency on their bid and sell the base currency on
their offer.
• Traders buy the base currency on their left and sell the base on their right.
• Traders will always sell to you at a higher rate than they will buy from you.
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• \X!hen asking for a rate, always think in the base currency from the
customer's perspective.
• A cross rate is the price of one currency in terms of the other when neither one is the dollar.
• To get the bid of the cross, you buy the base currency of the cross and sell
the terms currency.
• To get the offer of the cross, you sell the base currency of the cross and buy
the terms currency.
• If two currencies are quoted in the same terms, divide by the base currency
to get the cross rate.
• If two currencies are quoted in the different terms, multiply the rates to get
the cross rate.
• To get the bid/offir on cross rates:
• Same terms:
• Offer of base currency into bid of terms currency = bid of
cross
• Bid of the base currency into offer of terms currency=
offer of cross
• Different terms:
• Offer of base currency times bid of terms = bid of cross
• Offer of base times offer of terms = offer of cross
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REVIEW PROBLEMS
1. Assuming the client had called Lehman for the above quotes, at what rate would you deal?
a) You want to buy GBP _ _ _ _ _ __
b) You want to sell CHF _ _ _ _ _ _ __
c) You want to buy JPY _ _ _ _ _ _ __
d) You want to sell NZD_ _ _ _ _ _ __
2. Using the same rates as above, determine the following bid/offer cross rates.
a) GBP/CHF
b) NZD/JPY
c) GBP/NZD
3. Today is Tuesday, October 22, 2002.
a) You do a ''Dollar-yen" trade. What date will it settle?_ _ _ _ _ _ _ _ _ _ __
b) You do a "Sterling-dollar" trade for cash. What date will it settle?_ _ _ _ _ _ __
c) You do a "Dollar-CAD" trade. What date will it settle?_ _ _ _ _ _ _ _ _ _ __
4. You have just become the new Yen trader at Lehman Brothers. The old Yen trader left for
Monaco with a square position. You do the following:
a) Citi calls for a JPY quote. You quote 123.97/124.00. Citi buys USD SMM.
1. At what rate is the deal done? _ _ _ _ _ _ _ _ _ _ _ _ _ __
2. What is your position in JPY? _ _ _ _ _ _ _ _ _ _ _ _ _ __
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3. What is you position in USD? _ _ _ _ _ _ _ _ _ _ _ _ _ __
b) You know that the dollar is going higher. Another bank quotes you 124.10/124.25.
1. Is the dollar higher? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
2. What trade would you do? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
3. What are your positions now? _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
4. What is your profit/loss? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ __
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ANSWERS
1. As a dealer, you transact at the following rates:
Buy GBP I sell USD: 1.5475
Sell CHF I buy USD: 1.5025
Buy JPY I sell USD: 125.20
Sell NZDI buy USD: 0.4837
2.
3. a) October 24, 2002
b) October 22,2002
c) October 23, 2002
4. a) 1. Deal is done at the offer of 124.00
2. You are long¥ 620,000,000.
3. You are short 5MM dollars.
b) 1. Yes
2. Buy 5 dollars.
3. You are square dollars, short¥ 1,250,000.
4. $10,073 loss
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FOREIGN EXCHANGE
FORWARDS
INTRODUCTION
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FX FORWARDS
AN INTRODUCTION TO FOREIGN EXCHANGE FORWARDS
INTRODUCTION
Investors in currencies have diverse needs and interests in the market. Much of those needs
are met in the spot market, where a significant volume (about $600 billion per day) occurs.
But, a significant portion of the market (around 60% or $900 billion per day) needs currency
trades that mature past the spot date. Forward transactions are defined by a settlement date
beyond the standard two-day spot settlement. Forward settlement can range anywhere from
3 days to three years.
WHAT ARE FORWARDS?
• Forwards are an agreement between two counterparties to exchange currencies at a
pre-determined rate on some future date.
• Since any foreign exchange transaction automatically involves two currencies, two
interest rates are necessary, the dominant interest rate and the secondary interest
rate. Examples of the dominant /secondary interest rates would include EUR vs.
USD or USD vs. JPY.
• Forwards can include outrights and swaps.
• An outright is a spot transaction for a future date (past the spot date). It is a
derivative product consisting of a spot transaction combined with a forward spread.
The spot portion of the transaction is more volatile than the forward portion, so
most of the price action will occur in that portion of the outright.
• A swap is a simultaneous buying and selling of the same currency with a
counterparty with each leg maturing on a different date. The near leg of a swap can
be either for spot settlement (a traditional swap) or for forward settlement (a
forward/forward). A swap is a combination of a spot deal and a forward outright.
• To arrive at a forward rate at which to deal, forward points are applied to the spot
rate. Forward points may be either positive or negative, and are a function of the
interest rate differential between the two currencies in which you are dealing and the
maturity of the trade. Forward points do not represent an expectation of the
direction of a currency, but rather the interest rate differential.
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CALCULATING THE FORWARD RATE
In the first section, we discussed outright exchanges of one currency for another for spot settlement.
Now we will focus on the pricing of outright exchanges for forward dates, or dates other than spot.
The rate of exchange for any date other than spot is a function of spot and the relative interest rates in
each currency, because the assumption is that any funds you have will be invested in a time deposit
of that currency. The forward rate is the rate which neutralizes the effoct ofdiffirences in the Eurocurrenry interest
rates. If this were not the case, investors and speculators would always buy and invest in the high
interest rate currency, eliminating their exchange rate risk with the forward contract. An example will
illustrate this.
Assume you are a dollar-based investor who has $1,000,000 to invest for one year in Sterling-
denominated stock. Your investment parameters do not permit you to be exposed to exchange rate
risk, so you must set the rate at which you will re-convert the Sterling into dollars at the time you
enter into the investment. There is a 3% interest rate differential between the dollar and Sterling
market, since you can earn 2% if you invest in the Eurodollar market for the year or 5% if you invest
in Euro Sterling. In an arbitrage-free market, the forward rate will eliminate the 3% interest rate
differential between the dollar and Sterling. To determine what forward rate would eliminate the
benefit of being invested in Sterling:
1. determine how much you would earn if you invested in dollars;
2. buy one million dollars' worth of GBP spot against the dollar (currently 1.55 $1[)
3. determine how many pounds you will have at the end of the investment period; and
4. determine what forward exchange rate will convert your pound return into a dollar
amount equal to what you would have earned had you invested in dollars.
=• $1,QQQ,QQQ.QQ X 1.0202777781 $1,020,277.78
• $1,000,000 I 1.55 = £645,161.29
• £645,161.29 X 1.0511 = £677,419.35
• The rate which equates these two cash flows is 1.4762 $I£
$1,020,277.78 =X* £677,419.35
• X= $1,020,277.781 £677,419.35
• X= $1.5061
1 Use exact days over the correct day-count convention (360-day year for most currencies except
Sterling which uses a 365-day year): [$1,000,000 * (1+0.02 * (3651360))] and [£667,419.35 * (1 + .05
* 3651365)].
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By buying£ at 1.5500 and selling it at the forward rate of 1.5061, the benefit of the 3 %interest
rate differential is completely eliminated. At a forward rate of 1.5061 $/£,you would be totally
indifferent as to which currency you invest in. This rate is also the equilibrium rate between the
spot and forward markets; at 1.5061 $/£,you would be no better off if you bought the currency
forward or if you bought the currency spot today and invested it for the year before you needed
it.
We now know that 1.5061 is the equilibrium forward rate. At any other rate, there is an arbitrage
opportunity between the forward market and the Eurocurrency market. If the rate were higher,
say 1.53, you could arbitrage (take advantage of) the discrepancy between the FX market and the
time deposit market. To do so, you would buy£ spot today@ 1.55, invest in a Sterling time
deposit for the year at 5%, and then sell the£ (repatriate the dollars) at the pre-agreed forward
rate of 1.53. Since you sell£ at the higher exchange rate of 1.53, the forward rate does not
totally eliminate the interest rate differential and you would come out ahead. Since these are
highly liquid, closely watched markets, arbitrage is extremely rare.
It is important to note that the forward rate reflects the current interest rate, and it assumes that
you invest at that rate. If the interest rate differential changes between the time you do the
forward and the time you invest your funds, you would experience a gain or a loss. For example,
assume you do a forward in Canadian dollars with a 1% interest rate differential priced into the
contract. The instant after you do the forward, the Canadian rate drops 10 basis points. Now
you will have fewer CAD at the end of one year than you "should" have, so you will experience a
loss vis-a-vis what you would have earned had you remained in dollars. Ifyou do not earn the interest
rate difforential implied in the forward rate, you will expen.ence a loss or a gain.
In the swaps section of this workbook we will review hedging, arbitrage, and how to position
yourself at current rates in order to "bet" on a relative move in interest rates.
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CONFIDENTIAL TREATMENT REQUESTED BY BARCLAYS SOURCE: LEHMAN LIVE
Rather than using the aforementioned cash flow analysis technique, it is more common to think of
the forward rate in terms of how much it differs from the spot rate. Normally, you will know the
spot rate and the forward points (discussed momentarily), and given these two pieces of information
you can derive the forward rate. The difference between the forward rate and spot is referred to as
forward points.
GBP: Spot Forward Points Forward Rate
1.5500 0.0439 1.5061
JPY: 122.50 0.2287 122.2713
AUD: 0.5575 0.0048 0.5527
The difference between the spot and the forward rate is the forward points. In the example we have
just seen:
GBP: Spot Forward Rate Forward Points
1.5500 1.5061 0.0439
JPY: 122.50 122.2713 0.2287
AUD: 0.5575 0.5527 0.0048
The forward rate neutralizes the interest rate differential, making you indifferent as to whether you
buy a currency spot or forward.
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CONFIDENTIAL TREATMENT REQUESTED BY BARCLAYS SOURCE: LEHMAN LIVE
Although you are normally given forward points, it is a useful exercise to know how to calculate
them.
HOW DO YOU CALCULATE FORWARD POINTS?
S =Spot Rate
E1 = Dominant Interest Rate
E2 = Secondary Interest Rate
T = Number of Days to Maturity
• Example:
• What are the 1 year Forward Points for EUR/USD?
Spot = 1.0110
1 YR EUR Interest rate= 2.97
1 YR USD Interest rate = 1.52
T = 365
Points= 1.0110 * (1.52-2.97) * (365/360) * 100
1-Year EUR/USD is -148.6
PAY AND EARN POINTS
Remember, the forward rate neutralizes the interest rate differential, making you indifferent as to
whether you buy or sell a currency spot or forward.
• If you benefit from the differential by having an interest-bearing
deposit in the higher interest rate currency from the period
between today and the forward date, you will pay for it in the
forward points.
• If you do not benefit from the differential, you will earn the
forward points.
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Confidential Treatment Requested By Lehman Brothers Holdings, Inc.
CONFIDENTIAL TREATMENT REQUESTED BY BARCLAYS SOURCE: LEHMAN LIVE
Since the information you normally have is spot and the forward points not the forward rate, you
must decide (a) whether you should pay or earn the points and (b) whether to add or subtract the
points to get the forward rate. Let's see how this works in the following examples:
Let's say that you-the client-want to buy GBP forward against the USD. We will assume that
when you buy Sterling forward against dollars, you will have a dollar deposit for the period from
today to the forward date. In our example, dollar interest rates are lower than Sterling interest rates,
so you will not earn the differential during that period. Therefore, you will earn the forward points.
In the case of Sterling, that means you will buy the£ at a lower, more advantageous rate (that is, pay
fewer dollars per pound) in the future, so you subtract the points to get the rate. The points are 439
points:
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