Chapter 1 Forex is International Payments There is no sphere of human influence in which it is easier to show superficial cleverness and the appearance of superior wisdom as in matters of currency and exchange. (WINSTON CHURCHILL, speech in House of Commons, 1946) As for foreign exchange, it is almost as romantic as young love, and quite as resistant to formulae ( H L MENCKEN, The Dismal Science) Foreign exchange (shortened to forex or FX) is the consequence of the coexis- tence between the nationalism of currencies and the internationalism of trade. While nations zealously keep their identity with their own flags and curren- cies, the comparative and competitive advantages compel them to trade across borders. No country can produce all that it consumes, nor can it con- sume all that it produces (comparative advantage). Even if they were, it will not be effective and efficient (competitive advantage). We may say that what money does for goods and services within in a country (i.e. medium of exchange, store of value), forex does the same for dif-
Transcript
Chapter 1
Forex is International Payments
There is no sphere of human influence in which it is easier to show superficial
cleverness and the appearance of superior wisdom as in matters of currency
and exchange. (WINSTON CHURCHILL, speech in House of Commons, 1946)
As for foreign exchange, it is almost as romantic as young love, and quite as
resistant to formulae (H L MENCKEN, The Dismal Science)
Foreign exchange (shortened to forex or FX) is the consequence of the coexis-
tence between the nationalism of currencies and the internationalism of trade.
While nations zealously keep their identity with their own flags and curren-
cies, the comparative and competitive advantages compel them to trade
across borders. No country can produce all that it consumes, nor can it con-
sume all that it produces (comparative advantage). Even if they were, it will not
be effective and efficient (competitive advantage).
We may say that what money does for goods and services within in a
country (i.e. medium of exchange, store of value), forex does the same for dif-
Chapter 1
2
ferent brands of money (see Exhibit 1-1). If the world has a single currency or
trade does not cross national borders, the forex disappears.
EXHIBIT 1-1: Money versus Forex
Settlement of international trade requires two elements: international mon-
ey and an “adjustment” mechanism to correct trade imbalances among na-
tions. Experience shows that the first is less important and that the second has
been the source of much trouble. The evolution and the timeline of internation-
al payment systems are reviewed below.
1.1. Gold Standard: 1870–1914
Under Gold Standard, central banks issued paper money and held gold (or sil-
ver or both) in reserve to back the paper money. The international payments
system was built on the following features.
Export and import of gold was freely allowed
Currencies were valued in gold at a fixed rate (“mint par rate”)
Convertibility of currency to gold at mint par rate was guaranteed by
central banks
The mint par rates of a national currency determined its value against other
currencies. For example, if mint par rates of US dollar and Indian rupee were
$100 and Rs 4,000 per unit amount of gold, respectively, then dollar-rupee fo-
rex price would be: Rs 4,000 / $ 100 = Rs 40 per $. The forex price would be
fixed at this level, regardless of demand-supply for the currency. If it were not,
there would be an opportunity for arbitrage profit by converting currencies into
gold at mint par rates, and moving gold between the two countries. In practice,
the arbitrage rate level would be slightly off the mint par rate because of trans-
CHINA INDIA
noodles silk roti cotton
Analects Spring in a Small Town Arthashastra Mughal-e-Azam
yuan rupee forex
Forex as International Payments
3
action costs in shipping gold. Instead of one mint par rate, there was a range
defined by gold export point and import point.
The theory of the adjustment mechanism for trade imbalance under Gold
Standard involved the chain of events, including the movement of gold among
nations, shown in Exhibit 1-2.
EXHIBIT 1-2: Adjustment Mechanism under Gold Standard
The adjustment process was symmetrical in the sense that the country with
trade surplus shared the burden of the country with trade deficit. The forex
prices were fixed and stable, and the role of central bank was to freely buy and
sell gold at the mint par rate. The domestic policies (e.g. economic growth, un-
employment) were subordinate to external trade imbalances.
In practice, the changes in price level or unemployment and the movement
of gold was not to the extent warranted by the adjustment mechanism. This
was due to the skillful management of international clearing by the Bank of
England, which induced international capital flows in sterling pound by varying
the interest rates. Interest rate rose in countries with trade deficit and fell in
countries with trade surplus. The cornerstone of the Gold Standard remained
the full convertibility of sterling pound to gold at ₤1 s17 d10½ a troy ounce. The
Gold shipped out
Lower money stock
Deflation
TRADE SURPLUS
Less imports, more exports
More imports, less exports
Inflation
Higher money stock
Gold shipped in
TRADE DEFICIT
Chapter 1
4
beginning of the World War I put an end to the regime of fixed and stable ex-
change rates under Gold Standard.
1.2. First Floating Rate Regime: 1914–1925
Except Switzerland, most countries suspended the gold convertibility for resi-
dents during 1914–1917, and the pre-war fixed exchange rates were main-
tained by mopping up gold and foreign securities from the residents.
After the war, the currencies were allowed to float during 1918–1925 and
find their realistic financial strengths. The sterling pound fell from $4.86 to
$3.40. The floating rate regime was intended as an interim arrangement, and
the countries were to adopt such domestic policies as would restore the pre-
war exchange rates and gold standard.
1.3. Gold Exchange Standard: 1925–1931
Britain restored gold standard in 1925, and the pound-dollar rate was brought
to the pre-war rate of $4.86 to a pound. Over 30 other countries established
gold parities or fixed the exchange rate of their currencies with sterling pound.
The central banks held reserves predominantly in gold-convertible currencies
(mostly sterling pound) rather than gold. This was called gold exchange stan-
dard, which did not last beyond 1931 because many countries pursued domes-
tic policies that were unilateral and mercantilist, which did not fit in the auto-
matic and symmetric adjustment mechanism under Gold Standard. The Great
Depression of the late 1920s, too, aided the collapse of gold exchange stan-
dard. Many converted their sterling pound into gold, leading to a run on the
Bank of England‟s gold reserves.
1.4. Controlled Float: 1931 – 1939
Britain suspended gold-convertibility of sterling pound in 1931. By 1933, over
30 countries went off gold standard. Germany imposed exchange controls on
current account.
It was a period of chaos: there was the “sterling block” of Britain and her
colonies, struggling to prop up sterling; there was the “gold bloc” of Switzer-
land, Holland, France, Italy, Belgium, Luxembourg and Poland, struggling with
their overvalued currencies; there were central European countries struggling
with German recovery and rearmament; and there was the United States in
Forex as International Payments
5
economic isolation and lifting itself out of the Great Depression. In general, the
exchange rates were floating for the second time.
Unlike the floating in 1914 – 1925, however, the floating now was con-
trolled by national governments to protect their domestic policies. Mostly, the
control meant devaluation of currencies to achieve trade competitiveness. Out
of this chaos came Bretton Woods System.
1.5. Bretton Woods System: 1944 – 1971
Bretton Woods System was built on the gold-convertibility of US dollar. It was
officially described as “fixed rate regime with managed flexibility” and was po-
pularly called “adjustable peg.” The following were the features of the system.
All currencies were pegged to US dollar at fixed rate, and the dollar
was pegged to gold at $35 a troy ounce
The USA guaranteed the convertibility of dollar to gold, but only to the
central banks, and not to general public
Forex rates must be maintained within 1% of the fixed parity with
dollar, and intervention in market should occur on violation of this
band
Domestic economic policies (aimed at full employment) had primacy
over balance-of-payment (BOP) problem. This feature was the direct
opposite of the adjustment under Gold Standard.
In case of BOP problem, the following two-tier approach would apply:
o The problem is temporary: the country with deficit would
draw from the line of credit provided by International Mone-
tary Fund (IMF), which was set up as a part of the Bretton
Woods System
o Tthe problem is permanent: the country with deficit would
devalue its currency in consultation with the IMF
There should be no direct controls on trade account under the Gen-
eral Agreement on Trade and Tariffs (GATT), but the capital account
transactions could be controlled
In a way, the Bretton Woods System was like Gold Standard but without
the automatic adjustment mechanism because it gave domestic economic pol-
icy priority over external trade imbalances. Though there were large devalua-
tions of some currencies (notably that of sterling pound in 1949 and 1959), the
system worked well until 1965 with crisis-free economic growth. The US con-
Chapter 1
6
sciously ran trade deficit to enable other countries to build up reserves in dol-
lar, which was gold-convertible and hence “good as gold.”
During the second half of the 1960s, the US suffered Vietnam War, wor-
sened trade deficit, and inflation. To contain the inflation, dollar interest rate
was hiked, which attracted further capital into the US. In a way, the US was
importing goods and exporting inflation, which prompted the French President
to ask: what stops America from printing dollars and buying up France?
It had reached a stage where the US gold reserves were insufficient to
meet the gold-convertibility of dollar. Free market price of gold went above the
official price of $35 a troy ounce, and France converted their dollar reserves in-
to gold for political (and practical) reasons. Canada abandoned the adjustable
peg of Bretton Woods System and allowed its currency to float freely. And the
inevitable happened: the Nixon Administration of the US suspended the gold-
convertibility of US dollar, ending the Bretton Woods System.
1.6. Smithsonian Agreement: 1971 – 1973
The chaos in the aftermath of the collapse of Bretton Woods System brought
the top central banks together and resulted in Smithsonian Agreement, which
was a highly diluted version of the Bretton Woods System. The US President,
Richard Nixon, called it “the greatest monetary agreement in history.”
US dollar was devalued against gold from $35 to $38 a troy ounce, but the
gold-convertibility of dollar was not restored. Other currencies (notably German
deutschemark) were revalued against dollar. Currencies were allowed to move
within a wider band of 2.5% from the new fixed rates against dollar. Canada
continued to float its currency. The strains developed in the system as soon as
it was introduced. Britain left the system in 1972, followed by others so that by
March 1973, the “greatest monetary agreement” collapsed, having lived just 18
months.
1.7. Second Floating Rate Regime: From 1973
After the collapse of Smithsonian Agreement, diverse systems of forex rate
regimes came in existence. A brief review of them is given below.
Free Float: the forex rate is allowed to be determined by demand-supply forces
in the market. The central bank did not influence the forex rate but focused on
domestic monetary policy and inflation. The currencies that followed this sys-
Forex as International Payments
7
tem became the “hard currencies” and became an asset class alongside
bonds and equities.
Managed Float: the forex rate is allowed to be floated but controlled by the
central bank. In most cases, the control meant periodic, minor and discretio-
nary devaluation.
Gliding Parity: the changes in forex rate were linked to publicly-disclosed spe-
cific economic criteria.
Fixed Peg: the forex rate is pegged to the currency of the country‟s main trad-
ing partner or to a basket of currencies of trading partners.
1.8. Gold and Monetary System
The link between gold and currencies is more than 2,000 years old, and is still
intimate, though inexplicable. Because of this historical link, the forex depart-
ment in many banks deals with buying and selling of gold, too.
Gold had detractors and admirers. John Maynard Keynes, the famous Eng-
lish economist, mocked that it was a “barbaric relic of the past1.” Charles de
Gaulle, the famous French politician, praised it thus: “has no nationality … un-
iversally accepted as unalterable fiduciary value par excellence.”
Gold is unique because it is at once a commodity and monetary asset. As a
commodity, it is virtually indestructible, easily recoverable and recycled, highly
malleable and, of course, beautiful. As a monetary asset, it is an asset to its
holder but liability of none, and hence not vulnerable to distress of and repud-
iation by debtor or moratorium by sovereign debtor; uncorrelated with other fi-
nancial assets, providing the portfolio diversification. In times of crisis, financial
assets depreciate and become illiquid. In contrast, gold rises in (or holds its)
value, remains liquid, and is universally acceptable as a means of payment.
Gold coins acted as money, and gold reserves backed the paper money,
fully in the beginning and partly in the later years. Central to the Bretton Woods
system was the fixed parity between gold and US dollar. When IMF was
created under the Bretton Woods system, all members were given quotas,
which consisted of 75% of national currency and 25% gold; and the members
were obligated to buy or sell gold at the fixed parities. During the 1960s, the
1 Keynes comment, it must be said, was not on gold, but on the Gold Standard in inter-
national monetary system that prevailed during 1870-1914.
Chapter 1
8
central banks of the US and Western Europe formed “Gold Pool” to keep the
market price of gold at around the official price of US$ 35 a troy oz. The mar-
ket intervention was ineffective and central banks lost more than 12% of their
gold reserves, and the Pool was abolished in 1968. The central banks decided
not to intervene in the gold market but to deal only among themselves at the
official parity. As a result, a two-tier market developed for gold, one for official
transactions at fixed parity and the other for private transactions at market-
driven prices. The IMF planned Special Drawing Rights (SDR), a synthetic cur-
rency linked to a basket of national currencies, as a substitute for gold in its re-
serves.
The official reserve status of gold started disappearing from 1971 when the
US suspended dollar-gold convertibility at the fixed parity of US$ 35 a troy oz.
In 1978, the Second Amendment to the IMF Articles barred its members from
fixing their currency parities to gold, and it eliminated the obligation to buy or
sell gold at the fixed parities. With this, gold was officially eliminated from the
international monetary system. In 2000, Switzerland, the only country that had
official minimum gold backing for currency in circulation, abolished the link be-
tween Swiss franc and gold. With that, gold ceased to have any role in domes-
tic and international monetary systems―officially.
Despite official “demonetization” of gold, central banks still held about
30,000 tons of gold as reserves in 2006, a decline from about 36,000 tons in
1980. Except Chinese central bank, which bought about 200 tons from the
market since 2000, most other banks have been selling some of their gold re-
serves.
Exhibit 1-3 shows demand-supply for gold and the total above-ground
stock at 2008. There are three sources of supply (mining, recycling and central
bank sales) and three sources of demand (jewellery, investment and industri-
al). The total above-ground stock at 2008 was about 165,000 tons, about half
is held in the form of jewellery, and a less than a fifth as reserves by central
banks. Today, the private holdings of gold (by way of jewellery and invest-
ments) are four times more than the official holdings.
Three countries accounted for half of retail consumption in 2008: India
(27%), China (12%) and USA (10%). The voracious appetite of Indian house-
holds for gold is legendary. Estimates about Indian private gold holdings vary
between 10,000 and 20,000 tons (compared to 8,100 tons held by the US
Treasury).
Forex as International Payments
9
EXHIBIT 1-3: Gold: Demand, Supply and Total (above-ground) Stock
Souce: World Gold Council, 2008 and 2009
1.9. Balance of Payment and Currency Convertibility
The phrase “balance of payment” (BOP) is misleading. The word “balance” in
accounting terminology refers to the amount outstanding at a point of time, but
in BOP refers to the total amount over a period of time. According to Interna-
tional Monetary Fund, the BOP items are classified at seven levels, the first
three of which are as follows.
Chapter 1
10
1 Current Account 1.1 Goods and services 1.1.1 Goods 1.1.2 Services 1.2 Income 1.3 Current transfer
2 Capital and Financial Account 2.1 Capital Account 2.1.1 Capital transfers 2.1.2 Non-produced non-financial assets 2.2 Financial Account 2.2.1 Direct investment 2.2.2 Portfolio investment 2.2.3 Other investments 2.2.4 Reserve assets
The two accounts at the first level are current account and capital & finance
account. Goods (1.1.1) are those that have physical characteristics. This defi-
nition brings electricity and gas under this head. Services (1.1.2) differ from
goods in that they cannot be stored for future consumption. Income (1.2) dif-
fers from goods and services in that the latter are the output of production but
the former uses the two factors of production, namely, labor and capital. (The
third factor of production, land, is excluded from BOP.) The income from labor
is employee compensation and that from capital is investment income by way
of dividend and interest. Income from non-financial assets (e.g. royalties, li-
cense fee, rentals/charters of equipment, distribution rights, etc.) should come
under Services (1.1.2) rather than Income (1.2). Current transfers (1.3) are
those without quid pro quo (e.g. grants, aid, etc.). Workers‟ remittances to resi-
dents in another country will also come under this head, but remittances to
own account with a bank in another country will come under Financial Account
(2.2). This distinction is made because workers‟ remittances arise from labor.
All items other than goods under current account are collectively called “invi-
sibles” and the items under goods are called trade account.
Capital transfers (2.1.1) include debt forgiveness/write-off and migrants‟
transfer of personal effects and financial claims from the former to the new
country. Non-produced non-financial assets (2.1.2) are different from the in-
come they produce. Copyright to a work of art is non-produced non-financial
asset and its transfer should be reported under Capital transfer (2.1.1) but
royalty/licensing fee from it should be reported under Services (1.1.2). Finan-
cial account (2.2) records the transactions in financial assets and liabilities. If
the economy‟s savings exceed its investments, then there will be net financial
outflow from it (and vice versa). In turn, financial outflow will acquire non-
Forex as International Payments
11
financial resource in the other economy. Direct investments (2.2.1) are those in
which the acquirer takes an effective and lasting control. Portfolio investments
(2.2.2) are those in which the acquirer‟s interest is capital gains in financial as-
sets and are often easily shifted. Other investments (2.2.3) are residual cate-
gory consisting of loans, trade credits, bank deposits, etc. Reserve assets
(2.2.4) are instruments for the government to correct the payments imbalance
and include monetary gold, special drawing rights (SDR) in the IMF and central
bank‟s forex reserves.
For all heads except those under Financial Account (2.2), transactions are
recorded on gross basis: that is, debit and credit items separately. For those
under Financial Account, the items are posted on a net basis, except those re-
lated to long-term loans and trade credits.
The double-entry accounting should ensure that the sum of the two first-
level accounts (current and capital & finance) should be zero. In practice, how-
ever, this is rarely the case because of discrepancy in timing, coverage, valua-
tion, inaccurate estimation and clandestine capital flight. The balancing act is
performed by introducing the item “errors and omissions.” The negative sign
for this item implies overstatement of receipts and understatement of pay-
ments; and the positive sign, the opposite.
Let us now examine the concept of currency convertibility, which has
changed over time. Originally, it meant the convertibility of paper money to
gold at the fixed mint par rate. Today, gold is officially demonetized and re-
placed with foreign currencies as reserves; and no fixed parties exist among
major currencies. Therefore, convertibility today stands redefined as freedom
to convert national currency into foreign currencies at market prices.
To enable international trade, all currencies must be convertible on trade
account. To conserve reserves, governments may impose trade controls, par-
ticularly for services, to limit the convertibility on trade account. Convertibility
on capital account is generally restricted because capital flows are considered
the source of forex rate instability. Various methods were adopted to manage
capital account transactions. Belgium adopted two-tier (“dual”) forex rates, one
for commercial transaction and the other for financial transactions. The UK ex-
perimented with “external” convertibility: full convertibility on capital account
for non-residents but not for residents. Such distinction had been necessary
because, for historical reasons, the British pound was held by non-residents as
reserve currency, and restricting capital account convertibility would have re-
sulted in loss of confidence in the British currency.
Chapter 1
12
The forex regime today can be characterized by three features: forex rate
mechanism, reserve asset and capital account convertibility. Exhibit 1-4 shows
the different choices for each of these features.
EXHIBIT 1-4: Forex Regimes
Rate Mechanism Reserve Asset Capital A/c Convertibility
Free Float Convertible Currencies Free
Managed Float SDR Regulated
Gliding Peg Gold Dual
Fixed Peg Mix of the above
1.10. Which Regime is the Best?
There is no definitive answer. Every regime worked well for sometime under
some circumstances, and no system worked well for all times and in all cir-
cumstances. From the experience gained since 1973, we can make the follow-
ing general statements.
Adjustment mechanism is more important than the international reserve
money. When the adjustment mechanism is imperfect, there will be short-
age of reserve money
Balance-of-payment (BOP) problem is two-sided: if a country has trade def-
icit, then another has trade surplus. Both countries are to shoulder the bur-
den to correct it. However, in practice, the burden falls largely on the coun-
try with deficit. The debtor‟s problem is material and pressing while the
creditor‟s problem is largely moral and persuasive.
Left to itself, the BOP problem will correct itself, but causes a lot of pain. To
make the correction less painful, the governments intervene, with the fol-
lowing policy options for the country with deficit.
o Fund the deficit out of reserves. if the deficit is temporary and the
country has reserves
o Deflate the economy and face unemployment, if the deficit is fun-
damental and in current account
o Devalue the currency, if the deficit is fundamental and in current
account but deflation and unemployment are not acceptable
o Increase the interest rate, if the deficit is in capital account
o Apply exchange and trade controls (as a last resort)
For countries with free convertibility on capital account, the forex rate is in-
fluenced more by capital flows than the trade in goods and services.
13
Chapter 2
Forex Basics: the Literacy
Success is the natural consequence of applying the basic fundamentals. (JIM
ROBIN, American motivational speaker)
Once you have literacy, then you have a chance to bring in the new tools of
communications. (BILL GATES, founder of Microsoft Co)
Forex is one part literacy and ninety-nine parts numeracy. The one part literacy
is crucial and the foundation for the ninety-nine parts.
To be qualified as a forex trade, two criteria must be satisfied. First, there
must be two currencies in the trade: forex trade is always a currency pair.
Second, the rate of exchange between the two currencies must be fixed.
Consider the following two transactions: (1) a bank accepts a foreign cur-
rency time deposit from a customer at fixed rate of interest; and (2) a bank
opens a foreign currency import letter of credit (L/C) on behalf of its importer-
constituent in favor of a foreign supplier. Which of the two transactions is a fo-
rex transaction? None of them is.
Chapter 2
14
The first has only one currency and therefore is a money transaction. The
second transaction has two currencies― local and foreign currencies―but the
rate of exchange between them is not fixed as yet. We can say that the second
transaction will surely become a forex transaction in future (when the importer
makes the payment), but as of today, it has not entered the forex book of the
bank.
2.1. Currency Pair
Every forex transaction is a currency pair, and the forex price (or exchange
rate) is the price of one currency in terms of the other.
Exhibit 2-1 shows three types of exchange: barter, money and forex. In
barter, we exchange one goods (or services) for another. In money, we ex-
change goods (or services) for money. In forex, we exchange one brand of
money for another brand of money. Money branded is called currency.
EXHIBIT 2-1: Three Types of Exchanges
Type Exchange
Barter goods for goods
Money goods for money
Forex money for money
2.2. Base Currency and Quoting Currency
Of the two currencies in the pair, one is called the base currency (BC) and the
other, the quoting currency (QC).
Base currency is the currency that is priced: it is bought and sold like a
commodity (whence the name “commodity currency”) and ceases to act in the
traditional role of money. Quoting currency is the currency that prices the base
currency, and is thus acting in the role of money. What is quoted in the market
as forex price (or exchange rate) is the price of base currency in units of quot-
ing currency. This statement always holds in all “quotation styles” (see Section
2.8) and must be memorized.
Forex Price (or Exchange Rate) = Price of BC in QC
The amount of BC is fixed (usually at one unit) and the amount of QC va-
ries as the price of base currency varies over time. Accordingly, BC and QC
Forex Basics: the Literacy
15
are also called “constant/fixed amount currency” and “variable amount curren-
cy”, respectively.
2.3. ISO/SWIFT Codes
International Organization for Standardization (ISO) has given three-letter code
for every currency in their ISO 4217 standard. The first two letters are the
country code defined by ISO in their standard ISO 3166, and the third letter is
usually, but not always, the first letter of the currency name. Exhibit 2-2 lists
the ISO codes for some currencies, and the Annex I shows the complete list of
world currencies and their ISO codes.
EXHIBIT 2-2: ISO Codes for Major Currencies
Country Currency ISO Code
United Kingdom pound GBP
European Union euro EUR
United States dollar USD
Switzerland franc CHF
Japan yen JPY
India rupee INR
China renminbi CNY
South Africa rand ZAR
We can see that some codes deviate from the principles described above.
Box 2-1 gives an explanation for these apparent anomalies. The ISO codes
are adopted by the Society for Worldwide Interbank Financial Telecommunica-
tions (SWIFT), which is the communication and messaging network for banks
the world over. Only these standard ISO/SWIFT codes, and not the special
characters (e.g. $, €, ₤), must be used in any standard forex messaging.
The market practice for the notation of a currency pair is to write the BC
code first, followed by the QC code. For example,
Currency Pair BC QC Forex Price
EUR/USD EUR USD Price of EUR in USD
USD/JPY USD JPY Price of USD in JPY
In contrast to the above market practice, most academic text books and
certain parts of OTC derivatives documentation (e.g. 2005 Barrier Option Sup-
plement to 1998 FX and Currency Options Definitions) of International Swaps
Chapter 2
16
and Derivatives Association (ISDA) adopt the opposite approach: that is, they
write the QC code first, followed by the BC code. ISDA also introduced the
terms “denominator currency” and “numerator currency” for BC and QC, re-
spectively. In this book, we follow the current forex market practice of writing
BC first followed by QC to represent a currency pair.
BOX 2-1: Oddities in ISO Country/Currency Codes
United Kingdom (UK): ISO assigned GB as the country code to the United King-
dom (and reserved the code UK), which is unusual because Great Britain consists of
only England, Scotland and Wales while UK consists of GB and Northern Island. Eu-
ropean Commission (EC) and Internet Assigned Number Authority (IANA) generally
adopt ISO codes, but in the case of United Kingdom, they made an exception and
use “UK” instead of “GB.”
Switzerland (CH): the „CH‟ is from its official Latin name of Confoederatio Helvetica
(„Helvetica Confederation‟).
South Africa (ZA): the code of „ZA‟ is from its Dutch name of Zuid-Africa.
For the currency code, the third letter is usually the first letter of the currency
name. There are some exceptions to this general principle, as follows.
EU’s euro (EUR): Probably because „EUE‟ is hard on the tongue.
Chinese renminbi (CNY): The Chinese currency is yuan (whence the third letter Y
in its currency code), but in the communist China, everything is “people‟s”: people‟s
republic (as if there could be monarch‟s republic!), people‟s army, people‟s money
(“renminbi”), etc.
For precious metals that are traditionally associated with money, ISO‟s principle
is to start the code with the letter X and take the next two letters from the chemical
symbol of the metal. The chemical symbols are derived from their Latin names: au-
rum (AU) for gold (whence ISO code of XAU), argentums (AG) for silver (whence
the ISO code of XAG).
For supra-national currencies, ISO code starts with the letter X and the next two
letters are taken from currency name. Thus, XDR is for Special Drawing Rights of
IMF; XCD for East Caribbean dollar; XPF for CFP franc. Though euro is also a su-
pra-national currency, it was not given this coding convention, because euro‟s price
is determined by demand-supply while that of others is derived by indexing them to
the price of other currencies or pegging them to another currency.
Forex Basics: the Literacy
17
2.4. Hierarchy in the Currency Pair
Which currency should be the BC in a currency pair? The following is the order
of precedence among the major currencies: GBP, EUR, AUD, NZD, USD and
other currencies. Thus, whenever GBP is involved in the currency pair, it will
be the BC; whenever EUR is involved, it will be the BC unless the other cur-
rency is GBP; and so on. Accordingly, the following will be the BC-QC combi-
nations in different currency pairs, the first of the pair being the BC.
Notice that the above could have been quoted as 40.5000/50 without the
necessity for any decimal point in the abbreviated offer price. Matter-of-factly,
the reason for quoting zeroes after decimal point (which have no numeric val-
ue) is to indicate the number of decimal places in the offer side. For example,
the bid price of 40.5000 (with all zeros explicitly quoted) indicates that the offer
price will have four decimal places.
Key Concepts Introduced
Two requirements for a forex trade: (1) presence of two currencies; (2) the rate
of exchange between them is fixed.
Names of two currencies in the pair: base currency (BC) and quoting currency
(QC)
Three-letter ISO/SWIFT code for every currency
Numeraire currency is the one against which all other currencies are valued. It
makes the market of N currencies complete with just N – 1 currency pairs.
Two segments of forex market: interdealer and commercial. The numeraire in
the former is currently the USD; and in the latter, the local currency.
Two styles of quotation, direct and indirect, based on whether the numeraire is
BC or QC.
Chapter 2
26
Two-way quote: two sides of the quote, two parties, two market sides and two
currencies.
EXERCISES
The following are the two-way market quotes.
EUR/USD 0.9998/03
USD/CHF 0.9998/03
GBP/USD 1.0101/10
The market is the price-maker and you are the price-taker. Answer the follow-
ing.
1. On USD/CHF, at what price the market sells USD?
2. On EUR/USD, at what price the market buys EUR?
3. On GBP/USD, at what price the market buys USD?
4. On USD/CHF, at what price you can sell CHF?
5. On USD/CHF, at what price the market sells CHF?
6. On EUR/USD, at what price you can buy EUR?
7. On GBP/USD, at what price the market buys GBP?
8. On EUR/USD, at what price you can sell USD?
9. On GBP/USD, at what price you can buy GBP?
10. On USD/CHF, at what price the market buys CHF?
27
Chapter 3
Forex Settlement: Value Dates
… when the hours of operation of two payments systems do not overlap, it is
technically impossible to arrange for the simultaneous settlement of both sides
of a foreign exchange transaction. (Noel Report, BIS, 1993)
The vast size of daily FX trading, combined with the global interdependence of
FX market and payment systems participants, raises significant concerns re-
garding the risk … for settling FX trades. These concerns include the effects
on the safety and soundness of banks, the adequacy of market liquidity, mar-
ket efficiency and overall financial stability. (Allsopp Report, BIS, 1996)
What we call the settlement date in other markets is called the value date in fo-
rex market. Value date is to be distinguished from trade date: on trade date,
both parties agree on trade terms (i.e. currency pair, amount, price and value
date); and on value date, the two currencies are exchanged.
Value date is after the trade date by few days because the trade requires
processing work (e.g. confirmation, netting, etc, as explained in Chapter 9).
The gap between the two dates could be one (“T+1”) or two (“T+2”) business
days, where “T” stands for trade date and the numeral indicates the business
days thereafter (see Exhibit 3-1).
Chapter 3
28
EXHIBIT 3-1: Trade Date and Value Date
Settlement involves the exchange of two currencies, and is exposed to set-
tlement risk: the possibility that one party pays his obligation while the other
does not. One of the mechanisms to mitigate settlement risk is payment-
versus-payment3 (PvP) style of settlement under which the two obligations are
exchanged simultaneously. If one party fails, the other party withholds his obli-
gation.
3.1. Forex Settlement Risk
The unique feature of forex settlement is that it takes place at two different set-
tlement centers that are often located in different time zones. For example,
USD/JPY transaction is settled in Tokyo (for yen amount) and New York (for
dollar amount), and the two centers are 13 hours apart in time zone. As a re-
sult, one party pays the yen amount and receives the equivalent value in dollar
after a delay of 13 hours.
Because of the time zone differences, the PvP style of settlement is im-
possible in forex market, unless that payment mechanism is drastically mod-
ified. The non-simultaneous settlement of the two payments in a forex trade
enhances the settlement risk, leading in turn to credit risk, market risk, liquidity
risk and systemic risk. Credit risk is the loss of total amount; market risk is the
replacement cost of the failed trade; liquidity risk is the possibility of not secur-
3 Payment-versus-payment (PvP) in forex market is the same as delivery-versus-
payment (DvP) in equity and fixed-income securities markets. The word “delivery” is
used for financial security and the word “payment”, for money. The PvP/DvP reduces but does not eliminate settlement risk. Under PvP, if one party fails, the other party will with-hold the payment, and thus avoids the loss of full amount (credit risk). However, the non-
defaulting party will have to replace the failed transaction with a new one at the prevail-ing market price. The difference between the original price and the replacement price is the loss under PvP, which is called counterparty credit risk and equals market risk.
time
Trade Date (T) Value Date (T+1 or T+2)
Negotiation of
trade terms
Exchange of
currencies
FX Settlements: Value Dates
29
ing the additional funds required in replacement; and systemic risk is the do-
mino effect of parties failing to each other in succession. The elevated settle-
ment risk in forex is sometimes called Herstatt Risk (see Box 3-1) or cross-
currency settlement risk4.
Given the large volume of forex market, which is currently about USD 3.2
trillion a day (see Annex II), and its impact on domestic payments systems, a
4 It was so named in the Report of the Committee on Interbank Netting Schemes (popu-
larly called the Lamfalussy Report), Committee on Payments and Settlements Systems, Bank for International Settlements, 1990).
BOX 3-1: Bankhaus Herstatt
Bankhaus Herstatt was a Cologne-based German bank, small in size but active in
FX trading. Sharp increase in oil price in 1974 led to weaker US dollar (USD), and
Bankhaus Herstatt sold USD against deutschemark (DEM) in speculative trades. In
the settlement of USD/DEM transaction, Bankhaus Herstatt would receive DEM in
Frankfurt and pay USD in New York.
German regulators discovered fraud and concealment of large trading losses by
Bankhaus Herstatt. On June 26, 1974, the German authorities closed down Bank-
haus Herstatt after the close of interbank payments in Frankfurt. The time was
3:30pm in Frankfurt and 10:30am in New York. On receipt of this news, Herstatt‟s
dollar correspondent banks withheld the payments to be made on behalf of Herstatt
Bank.
As a result, Herstatt‟s counterparties lost the entire USD amount to be received
in New York (credit risk); had to arrange for emergency funding to make good the
loss of dollar amount from Herstatt (liquidity risk); and had to replace the original
transaction with a new transaction at the prevailing market price (market risk). At
least 12 counterparties faced these risks for a total amount of USD 200 million. To
make matters worse, the other banks suspended payments and credit lines to the
affected counterparties of Bankhaus Herstatt, unless they received confirmation that
the counter-payment had already been received, leading to a gridlock in the pay-
ments system (systemic risk).
It was the first time that the market participants and the regulators realized the
elevated risk in FX settlements.
Chapter 3
30
single failure can result in payments gridlock or even systemic failure. Encour-
aged by the regulators, the forex market has invented a global payments sys-
tem for forex transaction on PvP basis. It is called the continuous-linked set-
tlement (CLS) and discussed in Chapter 11.
3.2. Value Dates
All value dates in forex settlement are grouped into three: spot, forward and
short. Spot date is the most common value date and defined as the second
business day from trade date (but is not so simple, as we will explain shortly).
Any value date after spot date is called the forward date, and any value date
before the spot date is called the short date5. Exhibit 3-2 illustrates the relative
position in time of the three value dates.
EXHIBIT 3-2: Value Dates: Spot, Forward and Short
Spot Value Date
Spot value date, though commonly defined as the second business day from
trade date, is not always so. The following is the procedure to determine the
spot value date, depending on whether USD is one of the currencies.
Case A: USD is one of the currencies in the currency pair
Spot value date is the date that must be a second business day at non-dollar
center and a New York business day. It need not be a second business day at
New York. If New York is closed on what is a second business day at the other
center, then we move to the next business day on which both non-dollar center
and New York are simultaneously open.
5 In the ACI‟s The Model Code (2004), the term “short date” is used for any maturity of
less than one month, but in this book we restrict it to value dates before spot date.
time
Trade Date (T) 1 2
spot
forward short
FX Settlements: Value Dates
31
Case B: USD is not one of the currencies in the currency pair (i.e. cross rate)
Spot value date is the date that must be second business day at each settle-
ment center and a New York business day. Though not involved in settlement,
New York must be opened because the cross rates are ultimately derived by
crossing two USD-based rates (see Chapter 5). Therefore, New York will be
indirectly involved in settlement. If any of the settlement centers or New York is
closed on such date, we move to the next business day on which all the three
are open.
Because of above adjustments, the spot value date may fall on third or
fourth business day (or even later) after trade date. Exhibit 3-3 shows the algo-
rithm for determining spot value date.
EXHIBIT 3-3: Algorithm for Spot Value Date
Forward Value Date
Any value date after spot value date is forward value date (but see the footnote
on the previous page). Such dates are infinite, but are quoted only up to one
Is USD one of the currencies?
This is the Spot Value Date
Go to the second business day at
each settlement center
Is New York open on this date?
Go to the next business
day at each settle center
YES NO
YES NO
Go to the second business day at
non-USD center
Is New York open on this date?
Go to the next business
day at non-USD center
YES NO
Chapter 3
32
year for most currency pairs. For hedging forex exposures beyond one year,
the market practice is to use other derivatives (e.g. currency swap, currency fu-
tures, currency option) rather than currency forwards. Even up to one year,
only few periods, called “standard tenors”, are quoted, which are:
Classification as above is the first step in any valuation. Our focus is not fi-
nancial valuation but analysis of forex cash flows from the perspective of risk
and profit/loss calculations. To redefine the concepts of exposure and mis-
match in terms of cash flows, we will construct a cash flows table, which is a
very valuable tool in financial engineering. The design of the table is such that
the columns display the cash flow amount and the rows display the cash flow
timing. Different columns are used for cash flows in different currencies. We il-
lustrate the cash flow table for the following forex swap.
Bought USD 100 on USD/INR @ 40.10 value date spot (near leg)
Sold USD 100 on USD/INR @ 40.15 value date 3-month (far leg)
The cash flow table must have separate columns for each currency and
separate rows for each value date. Exhibit 4-5 shows the cash flows for the fo-
rex swap above. The buy trade results in cash inflow (shown with positive sign)
and sell trade results in cash outflow (shown with negative sign).
EXHIBIT 4-5: Cash Flows Table
USD INR Remark
Spot +100 4,010 Cash flows from near leg
Total +100 4,010 Day total
3-month 100 +4,015 Cash flows from far leg
Total +100 +4,015 Day total
G Total 0 +5
Note that buy-sell trades result in a pair of cash flows in the same row of
different columns; and borrow-lend trades result in a pair of cash flows in the
same column of different rows. We can redefine exposure and mismatch in
terms of cash flows as follows: exposure is the grand total of all cash flows in
Chapter 4
48
the currency; and mismatch is the daily total of all cash flows in a currency for
a value date.
If the grand total of all cash flows in a currency is zero, there is no expo-
sure; if positive, the exposure is overbought (or long); and if negative, the ex-
posure is oversold (or short). Similarly, if the daily total of cash flows in a cur-
rency for a value date is zero, there is no mismatch; if positive, the mismatch is
surplus; and if negative, the mismatch is deficit. Since the sum of cash flows at
all value dates is simply the grand total of all cash flows, it follows that the sum
of mismatches is the exposure.
In the example above, the mismatch in USD cash flows is +100 (surplus)
on spot value date and 100 on 3-month value date; and the sum of mis-
matches is zero or square. For INR cash flows, the mismatch is 4,010 on spot
value date and +4,015 on 3-month value date; and their sum of +5, which
would seem an overbought exposure but is not. By definition, exposure must
arise in two currencies in a complementary way. The net cash flow in one cur-
rency alone is the profit/loss: profit if the cash flow is positive; and loss, if it is
negative. In our example, there is a profit of INR 5. However, it is not the net
profit. If it were, everyone in the market will do this forex swap and profit from
it. Consider now the mismatch. We have surplus cash in USD from spot to 3-
month value dates; and deficit in INR for the same period. They are corrected
by simultaneously lending USD and borrowing INR from spot to 3-month value
date. The net difference in two interest amounts (USD receivable, INR paya-
ble) will exactly offset the profit of INR 5 in the FX swap. We will examine the
link between forex swap and the two interest rates in Chapter 6. What remains
after eliminating exposure and mismatch is the net profit/loss. Let us summar-
ize the two concepts of exposure and mismatch.
Exposure (also known as Position or Exchange Position)
It refers to forex price risk and is of two types: long (or overbought) and short (or oversold)
It is computed as the grand total of cash flows in a currency. If the to-tal is positive, it is long position; and if negative, short position.
It arises in two currencies in a complementary way: long in one cur-rency and short in the other for equivalent amount. Exposure in one currency alone is gross P/L.
Exposure creates mismatch
Outright trades create new exposure or eliminate existing exposure
Forex Deals: Classification and Risk
49
Mismatch (also known as Gap or Cash Position)
It refers to cash balances and is of two types: surplus and deficit
It is computed as the total of cash flows in a currency for a particular value date. If the total is positive, it is surplus; and if negative, deficit.
The surplus (or deficit) in a currency on a value date is accompanied by deficit (or surplus) in the same currency on another value date. In other words, surplus or deficit is for a period between the two value dates. Further, mismatch arises in two currencies in a complementary way: surplus in one currency for a period and deficit in another cur-rency for the same period
Surplus/deficit for a period in one currency alone is not mismatch but liquidity problem; and surplus/deficit in one currency alone and on a value date alone is the net P/L.
Forex swap trades create mismatch without creating exposure
4.6. Deal Blotter, Position and Gap Statements
As soon as a trade is executed by the trader, it is immediately entered into
deal blotter, which records the economic details of the trade: time stamp, cur-
rency pair, deal type, market side (i.e. buy or sell), deal currency and amount,
price, and value date. The blotter is maintained for each trader and for each
session (which is typically a day). Exhibit 4-6 shows a specimen of deal blotter.
EXHIBIT 4-6: Deal Blotter
Date: May 22, 2008 Trader: ACR (amount in millions)
Time Currency Pair
Deal Type
Market Side
Deal Amount
Price Value Date
9:30:15 EURUSD outright Buy EUR 5 1.5765 spot
9:30:25 USDJPY outright Sell USD 5 104.39 spot
9:30:55 EURUSD outright Sell EUR 5 1.5795 spot
9:31:05 EURUSD outright Sell EUR 3 1.5805 spot
9:31:15 USDJPY outright Buy USD 2 104.05 cash
9:31:30 EURUSD outright Sell EUR 2 1.5785 spot
9:35:15 EURUSD outright Sell USD 5 1.5742 1-mon
9:40:00 USDJPY swap Sell USD 2 104.16 cash
9:40:00 USDJPY swap Buy USD 2 104.11 spot
9:40:10 EURUSD swap Sell USD 5 1.5745 spot
9:40:10 EURUSD swap Buy USD 5 1.5738 1-mon
Chapter 4
50
From the deal blotter, every trade is processed further in real-time for its ef-
fect on position and gap. Exhibit 4-7 shows the typical format of position and
gap statements for the deals in Exhibit 4-6.
EXHIBIT 4-7: Position and Gap Statement
Position Date: May 22, 2008 Trader: ACR (amount in millions)
Time Purchase Sale Position EUR
9:30:15 5.000000 5 OB 9:30:55 5.000000 0 Square 9:31:05 3.000000 3 OS
9:31:30 2.000000 5 OS
9:35:15 3.176216 1.823784 OS
9:40:10 3.175611 1.351827 OB 9:40:10 3.177024 1.825197 OS
USD
9:30:15 7.8825 7.8825 OS
9:30:25 5.0000 12.8825 OS 9:30:55 7.8975 4.9850 OS 9:31:05 4.7415 0.2435 OS 9:31:15 2.0000 1.7565 OB 9:31:30 3.1570 4.9135 OB 9:35:15 5.0000 0.0865 OS 9:40:00 2.0000 2.0865 OS 9:40:00 2.0000 0.0865 OS 9:40:10 5.0000 5.0865 OS 9:40:10 5.0000 0.0865 OS
JPY
9:30:25 521.95 521.95 OB 9:31:15 208.10 313.85 OB 9:40:00 208.32 522.17 OB 9:40:00 208.22 313.95 OB
Position Summary (OB = overbought; OS = oversold) EUR: 1.825197(OS); USD: 5.0865 (OS); JPY: 313.95 (OB)
Gap Date: May 22, 2008 Trader: ACR (amount in millions)
Value Purchase Sale Gap
EUR
spot 8.175611 10.000000 1.824389 Deficit
1-mon 3.176216 3.177024 0.000808 Deficit
Total 11.351837 13.177024 1.825197
USD
cash 2.0000 2.0000 0 square
spot 17.7960 17.8825 0.0865 Deficit
1-mon 5.0000 5.0000 0 square
Total 24.7960 24.8825 0.0865
JPY
cash 208.32 208.10 0.22 surplus
spot 521.95 208.22 313.73 surplus
Total 730.27 416.32 313.95
Forex Deals: Classification and Risk
51
Notice that, for each currency, the sum of gaps should be equal to the posi-
tion. If they do not, then there is a mistake in the accounting for cash flows.
4.7. Limits on Position, Gap and Others
Bank controls the forex operations by placing limits on position, gap, counter-
party exposure, stop-loss, etc. Of them, the most important is that on position.
The position limit has two variants: daylight limit and overnight limit. The
daylight limit is the limit during the day while the overnight limit is the limit at
the close of business each day. The overnight limit is also used to compute
capital adequacy for trading operations under Basel II regulatory regime. The
international norm for computing the position limit is the “short hand” rule, ac-
cording to which the limit for capital adequacy is computed as follows.
Segregate currencies into those with overbought and oversold posi-
tions
Translate the position into home currency equivalent
Separately sum the overbought and oversold positions
The higher of the aggregate overbought and aggregate oversold posi-
tions is considered the “net open position.”
The reason for the short hand rule is the currency diversification effect. In
the forex market, in terms of price changes, it is a see-saw between US dollar
and all other currencies. If dollar rises against a currency, it rises against all
other; and vice versa. Most banks are now adopting advanced techniques like
value-at-risk (VaR) to measure forex price risk. Basel II regulations allow VaR
model to compute capital adequacy as an alternative to the short-hand rule.
4.8. Forex Swap versus Currency Swap
Though sounding similar in name, they are structurally and functionally differ-
ent. Forex swap is a cash management tool: currency swap is a risk manage-
ment tool. Under the accounting standards of FASB 133 and IAS 39, forex
swap is not a derivative but currency swap is.
Forex swap, being a cash management tool, must necessarily exchange
the principal amounts in two currencies. Like in money market instruments, the
period of forex swap is one year or less and there is only one interest payment,
Chapter 4
52
which is merged with the principal re-exchange. The near leg is the exchange
of principal and the far leg price is the re-exchange of principal and interest
combined. The structure and pricing of forex swap is discussed in Chapter 7.
Currency swap, being a risk management tool, need not exchange of prin-
cipal amounts in two currencies. It exchanges two currency interest amounts
and the forex price change during the period. It may or may not exchange
principal amounts. The swap period is more than one year and can extend up
to 10 – 20 years with interest payments typically at quarterly or half yearly in-
tervals. Exhibit 4-8 summarizes the similarities and differences between two
swaps.
EXHIBIT 4-8: FX Swap versus Currency Swap
Feature FX Swap Currency Swap
Purpose Cash management Risk management
Swap period One year or less More than one year
Principal Always exchanged May nor may not be ex-changed
Interest Always exchanged and combined with principal re-exchange at the end
Always exchanged and there will be a series of such exchanges
Key Concepts
Two currencies in a trade: deal currency and derived currency, each of which
can be the base currency or the quoting currency.
Two types of deals: outright and forex swap. Forex swap is different from cur-
rency swap: the former is cash management tool and the latter is risk man-
agement tool.
Two concepts: exposure (a.k.a. position or exchange position) and mismatch
(a.k.a. gap or cash position).
Two types of exposure: overbought (a.k.a. long) and oversold (a.k.a. short)
Two types of mismatch: surplus and deficit
Forex Deals: Classification and Risk
53
Exposure is the grand total of all cash flows in a currency, and will arise in two
currencies in a complementary way. Exposure in only one currency is the
gross profit/loss
Mismatch is the daily total of cash flows in a currency on a value date. The
surplus or deficit runs for a period marked by two value dates. Mismatch arises
in two currencies in a complementary way (i.e. surplus in one and deficit in
another for the same period). Mismatch in one currency alone is funding prob-
lem; and mismatch in one currency alone and only on one value date (rather
than a period) is net profit/loss.
EXERCISES
Taking into account the following deals, update the position and gap state-
ments, in the format shown in Exhibit 4-7. Instead of deal time, use the serial
number of the deal as its substitute. All amounts are indicated in millions. Note
that for JPY/INR currency pair, the price is for 100 units of JPY.
1. (USD/INR, outright): Bought USD 3 @ 40.61 value date spot
2. (EUR/USD, outright): Sold EUR 3 @ 1.5737 value date spot
3. (JPY/INR, outright): Bought JPY 500 @ 39.01 value date 1-mon
4. (USD/JPY, outright): Bought USD 5 @ 104.33 value date spot
5. (USD/INR, outright): Bought 2 @ 40.62 value date spot
6. (EUR/USD, outright): Sold EUR 2 @ 1.5729 value date spot
7. (GBP/INR, outright): Sold GBP 1.2 @ 80.27 value date cash
8. (GBP/USD, outright): Bought GBP 1 @ 1.9763 value date cash
9. (USD/INR, outright): Bought USD 2 @ 40.60 value date spot
10. (USD/JPY, swap): SB USD 5 @ 104.38/104.00 value date spot/1-mon
11. (USD/INR, swap): BS USD 5 @ 40.65/45.67 value date spot/1-mon
12. (GBP/USD, swap): SB USD 2 @ 1.9755/1.9751 value date cash/spot
13. (USD/INR, outright): Sold USD 9.7 @ 40.66 value date cash
14. (USD/INR, outright): Bought USD 10 @ 40.65 value date spot
15. (USD/INR, swap): BS USD 12 @ 40.65/40.66 value date cash/spot
Chapter 4
54
16. (EUR/USD, outright): Bought EUR 7 @ 1.5717 value date spot
17. (GBP/USD, outright): Bought GBP 0.2 @ 1.9749 value date spot
18. (EUR/USD, outright): Sold EUR 2 @ 1.5721 value date spot
55
Chapter 5
Cross Rate Arithmetic
God does arithmetic. (KARL FRIEDRICH GAUSS, German mathematician)
I continued to do arithmetic with my father, passing proudly through fractions
and decimals. I eventually arrived at the point where so many cows ate so
much grass and tanks filled with water in so many hours I found it quite enth-
ralling. (AGATHA CHRISTIE, An Autobiography)
As stated in Chapter 2, forex is one part literacy and ninety-nine parts numera-
cy. Forex arithmetic, however, is simple and involves only the four operators:
addition, subtraction, multiplication and division. It does not involve complex
calculations like differentiation and integration, unlike option pricing.
We have made a reference to cross rates in Section 2.7. They are currency
pairs without the interbank numeraire currency (which is currently USD). Cross
rates are not quoted directly in the market, but are derived by „crossing‟ two
numeraire-based rates. The „crossing‟ means either multiplication or division,
and is the subject matter of this chapter.
Chapter 5
56
5.1. Chain Rule
One apple is INR 15 and one banana is INR 3. One apple is worth how many
bananas? We say instantly that one apple is worth five bananas because the
solution is intuitive. Let us consider similar situation. Three roses are INR 5
and seven lotuses are INR 25. One rose is worth how many lotuses? The solu-
tion does not strike immediately because it is not very intuitive. When intuition
fails, we apply logic. Chain rule is that logic and the principle of cross rate
arithmetic.
Chain rule consists of four steps: define the cross rate in the proper format;
identify the two underlying rates; arrange the underlying rates to form a chain;
and multiply and divide. We will explain the four steps with the following exam-
ple of EUR/INR cross rate.
Define the cross rate
What we mean by „definition‟ is to state the problem: one (or some other fixed
quantity) unit of base currency is how many units of quoting currency. In ex-
pressing the problem, we write the base currency on the left hand side and
quoting currency on the right hand side. The definition for our example is thus:
EUR 1 = INR?
Identify the underlying rates
The underlying rates are each currency of cross rate against the numeraire
USD. The underlying rates for our example are EUR/USD and USD/INR and
let their prices be
EUR/USD = 1.5775 (EUR 1 = USD 1.5775)
USD/INR = 40.31 (USD 1 = INR 40.31)
Arrange the underlying rates to form a chain
Select the underlying rate containing the quoting currency of the cross rate. In
our example, it is USD/INR. Arrange the price of this underlying rate in such
way that INR goes to the other side of the equation, as follows.
EUR 1 = INR ?
INR 40.31 = USD 1
Cross Rate Arithmetic
57
In the first currency pair, INR is on the right hand side; and in the second,
on the left hand side. It thus forms a chain. Repeat the process for the second
underlying rate in such a way that USD is placed on the left hand side.
EUR 1 = INR ?
INR 40.31 = USD 1
USD 1.5775 = EUR 1
Multiply and divide
Take the product of left hand side and divide it by the product of right hand
side. It should be clear now why we formed a chain of currencies: to cancel all
of them except those of the cross rate. The result of this arithmetic operation is
the solution to the problem stated in the first step. Thus, for our example,
Sale 1.2504 + 0.0010 = 1.2514 1.2501 0.0010 = 1.2491
For some purchases, the customer may present to the bank a negotiable
instrument (e.g. check, draft, etc) payable in the foreign country. In such cas-
es, there will be no prior credit in the nostro account, and the transaction can-
not be treated as TT buying. There are two ways to process such transactions.
First, the bank may send the instrument on collection basis to its nostro agent,
who will present it in the local clearing. After the proceeds are realized, the no-
stro agent will credit the amount to the nostro account under advice to the
bank. The bank will then put through the transaction as TT buying, paying the
local currency to the customer at the market rates prevailing on that date.
Second, the bank may at its discretion discount9 the instrument and settle
the local currency immediately with the customer, send the instrument to no-
stro agent and wait until the foreign currency amount is cleared and credited to
its nostro account. In this transaction, the bank is parting away with local cur-
rency amount before it receives the equivalent foreign currency amount. Effec-
tively, the bank has lent the local currency amount to the customer, for which
interest would be charged separately upfront. The bank will assume a transit
time, which varies from country to country, and is about a week, for which in-
terest would be charged. Since the foreign currency would be paid after the
transit time (of a week), the forex price to the transaction should be 1W forward
price. The following USD/INR example illustrates the transaction price and in-
9 In banking, the term purchase or demand purchase is used for financing “sight” instru-
ment (i.e. instrument payable at sight or on demand after presenting it); and the term discount is used for “usance” or time instrument (i.e. instrument payable after a specified
period from the date of presentation). Since we have used the word “purchase” in the first-level classification of commercial transaction, we will use the word discount for fi-
nancing of both sight and usance bills to avoid the confusion whether the “purchase” is related to the market side of the transaction or financing of sight bill.
Chapter 8
112
terest amount for discounting of clean instrument for USD 10,000. We will as-
sume a margin of 0.15 units of quoting currency; transit time of one week; and
INR interest rate of 10% pa
USD/INR spot price 50.48 / 50.49
Swap: S/1W 1 / 2 (to be converted into decimal form)
The elevated settlement risk in forex (“Herstatt risk”) is introduced in Sec-
tion 3.1. The forex settlements were disrupted by the failures of Bank Herstatt
(1974), Drexel Burnham Lambert (1989), Bank for Credit and Commerce Inter-
national (1991) and Barings Bank (1995). The Committee on Payments and
Settlements Systems (CPSS) of Bank for International Settlements (BIS) has
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170
been regularly examining the safety and efficiency of payment systems, which
resulted in various reports: Angell Report (1989), Lamfalussy Report (1990),
Noel Report (1993) and Allsopp Report (1996).
11.1. Settlement Risk in Forex
Allsopp Report focused specially on the settlement risk in forex transactions. It
provided, for the first time, a measure for settlement exposure and linked it to
the five categories of settlement status, as follows.
Status Description Exposure
Revocable (R) Payment instruction for sold currency is not issued or, if issued, cancellable
None
Irrevocable (I) Cancellation of payment instruction for sold currency is not possible; and the payment from the counterparty for bought currency is not yet due
Bought currency amount
Uncertain (U) Payment from the counterparty for bought currency is due but no infor-mation about the finality of its receipt
Bought currency amount
Fail (F) Payment of bought currency is not received from counterparty
Bought currency amount
Settled (S) Payment of bought currency is re-ceived with finality
None
Exhibit 11-1 shows the timeline for various settlement statuses of the trade.
The “payment” is for the sold currency amount and the “receipt” is for the
bought currency amount.
EXHIBIT 11-1: Timeline and Duration of Settlement Status for Trade
The duration of each status depends on the currency pair and the market
side (i.e. bought or sold). The following table shows the average duration (in
hours) for the three most actively traded currencies against USD.
Trade
Date
Deadline for cancellation of
payment instruction
Identify final or
failed receipt
Receipt of amount
due
R I U F or S
Continuous Linked Settlement
171
Currency USD sold USD bought
I U I U
EUR 9 13 22 8
GBP 9 15 24 8
JPY 5 20 33 8
Source: Progress in Reducing FX Settlement Risk, BIS, May 2008
In reality, there are more risks to settlement, namely, counterparty credit
risk, liquidity risk and systemic risk. Counterparty credit risk (formerly called
pre-settlement risk) arises during the Status R period (i.e. between the trade
date and the time the payment instruction for sold currency becomes irrevoca-
ble). It arises because, if the counterparty fails during this period, we need to
replace the original contract with a new contract at the prevailing market price.
The difference between the prevailing market price and the original contract
price is the replacement cost and the size of counterparty credit risk. When the
settlement status is F, we need to arrange for additional funding, which is the
liquidity risk. If the settlement fails are widespread, there is a possibility that the
entire settlement process might come to halt because of domino effect, which
is the systemic risk.
Allsopp Report recommended a three-pronged strategy to reduce settle-
ment risk in forex: (1) action by individual banks to improve their risk controls
and operational practices; (2) action by industry groups to adopt risk-reducing
settlement services such as multi-currency and multilateral netting; and (3) ac-
tion by central banks to induce the industry pursuing the required strategies by
improving the national payments systems.
11.2. Evolution of Continuous Linked Settlement
The industry responded with various initiatives. FXNET, Valuenet and SWIFT
Accord pursued bilateral netting arrangements under standardized agreements
(e.g. IFEMA). Exchange Clearing House (ECHO) and Multinet pursued multila-
teral netting. In 1997, a group of 20 banks (“G20”) from eight countries formed
the company, CLS Services Ltd (CLSS), to provide PvP services by means of
“continuous linked settlement”.
The “continuous” means that the settlement runs continuously in the speci-
fied time-window until all the currency time zones are covered; and the “linked”
means that the payment made for sold currency is linked to the payment to be
received for bought currency. Either both of them are settled or none of them is
settled. Continuous linked settlement is different from trade guarantee. In the
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172
latter, the settlement is guaranteed; in the former, the principal amount is
guaranteed, but not the settlement. If the settlement fails, the non-defaulting
party will not lose the principal but has to replace the trade at the prevailing
market price, which is subject to the loss of replacement cost.
The jurisdiction for incorporating CLSS was narrowed to US or UK, based
on the enforceability of settlement finality and security interest. The concern
about the possibility of the Office of Foreign Asset Control (OFAC) in the US
blocking the foreign banks‟ funds with CLSS for political reasons led to the UK
as the choice for incorporating CLSS. To implement PvP settlement, CLSS
must maintain accounts with central banks to access the real-time gross set-
tlement (RTGS) system for each currency. In many countries, banking status is
required to maintain accounts with the central bank. Therefore, CLSS formed
two subsidiaries in 1999: CLS Bank International (CLSB), which is incorpo-
rated in New York as a special purpose multi-currency bank subject to the reg-
ulatory oversight by the Federal Reserve; and CLS Operations in the UK to
provide operational support and IT infrastructure. For tax reasons, there was a
corporate restructuring in 2000 under which a new holding company, CLS
Group Holdings AG, was incorporated in Switzerland, which was regulated by
the Federal Reserve as a bank holding company. CLSS became a shell com-
pany and its name changed to CLS UK Holdings Ltd, which operated through
two subsidiaries: CLS Bank International, a special purpose bank in the US;
and CLS Services Ltd (formerly CLS Operations Ltd), in the UK to provide op-
erational support. Exhibit 11-2 shows the corporate structure.
EXHIBIT 11-2: CLS Corporate Structure
The acronym “CLS” is a registered trademark and may be used only with
CLS Bank International (CLSB) or CLS Services (CLSS) Ltd. The phrase “con-
tinuous linked settlement” is not a registered trade mark, however.
CLS Group Holdings (Switzerland)
CLS UK Holdings (UK) (shell company)
CLS Bank Intl. (US) CLS Services (UK)
Continuous Linked Settlement
173
11.3. Operations
After time and cost overruns of 25 months and 130%, respectively, CLSB
started operations in September 2002 with seven currencies, which were in-
creased to 17 currencies over time, as follows.
Sep 2002 AUD, CAD, CHF, EUR, GBP, JPY and USD
Sep 2003 DKK, NOK, SEK and SGD
Dec 2004 HKD, KRW, NZD and ZAR
May 2008 ILS and MXN
Currently, six instruments are settled in each CLS currency: FX spot, FX
forward, FX swap, FX option premium and exercise, non-deliverable forward
(NDF) and credit derivatives. The first three involve settlement in two curren-
cies on PvP basis. The last three involve payment in a single currency, which
does not require PvP requirement, but CLSB provides value-added services
(e.g. automated confirmation/exercise notice) in the instruments. In each of the
CLS currencies, CLSB makes and receives payment with its members in the
RTGS system through its accounts with central banks. CLSB has two types of
members: settlement member and user member.
Settlement Members: they maintain a single multi-currency account with CLSB
and assume responsibility for settlement risk and providing liquidity. For this
reason, only large financial institutions can be settlement members, and CLSB
has prescribed certain qualifying criteria.
User Members: they maintain a single multi-currency account with a settlement
member, but can submit settlement instructions directly to CLSB, which are
settled by the settlement member with CLSB. User member does not assume
responsibility for settlement risk or liquidity support.
Both settlement member and user member must be shareholders of CLS
Group, but the converse is not true. As at the end of March 2009, there are 70
shareholders but only 60 members. Members access the CLSB systems
through SWIFTNet InterAct, which is an automated and interactive messaging
system of SWIFT. There are two more parties in the CLS operations: third par-
ties and nostro agent. Third parties are users of the CLS, but not its members.
They settle transactions through either user members or settlement members.
As of March 2009, there are 4,686 third parties, consisting of 411 banks and
4,275 investment funds. Nostro agents are neither users nor members of the
CLS: they are facilitators. Since CLSB makes and receives payments only
through RTGS systems, settlement members, too, must have access to them.
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174
If they do not have direct access to RTGS systems, then a nostro agent will es-
tablish the connectivity between the CLSB and settlement members. In gener-
al, most settlement members have direct access to the RTGS system. Exhibit
11-3 shows the relations between various parties.
EXHIBIT 11-3: Linkages in CLSB Operations
Submission of Settlement Instructions
Settlement instructions are submitted by settlement members and user mem-
bers to CLSS via SWIFTNet. They can be submitted as soon as the trade is
executed and up to 06:30 CET on value date. However, the best practice is not
to submit the instruction after 00:00 CET on value date. In other words, cash
value date trades are settled outside the CLS system.
Matching
After comparing the settlement instructions from both the parties, CLSS will
assign the following trade status, which is made available to the members in
real time.
Status Description
REJECTED Possible duplication
INVALID Not a CLS currency or a business day
SUSPENDED Trade does not pass risk management tests
UNMATCHED Settlement instruction not received from counterparty
MATCHED Eligible for settlement
User Member
CLS Bank
Settlement Member
Third Party Nostro Agent Third Party
Central
Bank
RTGS
Payment instruction
and settlement
Payment instruction
only
Continuous Linked Settlement
175
Matched instructions can be cancelled or modified up to 00:30 CET on val-
ue date unilaterally and up to 06:30 CET on value date bilaterally.
Settlement and Funding
CLSS makes a distinction between settlement and funding. Settlement refers
to the book entries in the settlement member‟s account with CLSB and is on
gross basis. Funding is the pay-in in central bank RTGS funds and is on net
basis. The following example illustrates the settlement and funding for three
transactions in EUR/USD as follows. (Sale = Debit; Purchase = Credit).
SETTLEMENT (in the settlement member‟s account with CLSB)
EUR USD
Debit Credit Debit Credit
100 125
200 245
150 185
Total 250 200 245 310
Settlement member pays EUR 250 and receives EUR 200; and pays USD
245 and receives USD 310. It is on gross basis.
FUNDING (between CLSB and settlement member in RTGS funds)
EUR USD
Debit Credit Debit Credit
50 65
Settlement member pays EUR 50 and receives USD 65. It is on net basis.
The multi-lateral netting before pay-in results in, on an average, the reduc-
tion of 95% in funding and 99.75% in the number of transactions, which im-
proves liquidity management and lowers transaction costs. The following is the
timeline for various activities, which are summarized in Exhibit 11-4.
00:00 CET: Initial pay-in schedule (IPIS) after multilateral netting is issued; this
is also the deadline for unilateral cancellation or amendment.
06:30 CET: Revised pay-in schedule (RPIS); this is also the deadline for bila-
teral cancellation or amendment.
07:0012:00 CET: This is the five-hour settlement cycle time window, during
which settlement will be completed in the first two hours while the funding
takes place continuously.
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176
09:00 CET: Settlement completion target time (SCTT)
10:00 CET: Funding completion target time for Asia-Pacific currencies (FCTT1)
12:00 CET: Funding completion target time for other currencies (FCTT2)
EXHIBIT 11-4: Timeline for CLS Process
The funding takes place in the CLSB‟s accounts with various central banks,
whose RTGS systems and their operating hours are as follows.
Country & Currency RTGS Local Time CET
Switzerland CHF SIC 17:00a – 15:00 17:00
a – 15:00
New Zealand NZD ESAS 09:00 – 08:30b 23:00
a – 22:00
Canada CAS LVTS 06:00 – 18:00 00:00 – 12:00
Mexico MXN SPEI 08:30 – 17:00 01:00 – 12:30
Australia AUD RITS 09:15 – 18:30 01:15 – 10:30
Japan JPY BOJ-NET 09:00 – 19:00 02:00 – 12:00
S Korea KRW BOK-Wire 09:30 – 17:00 02:30 – 10:00
Hong Kong HKD CHATS 09:00 – 17:30 03:00 – 11:30
US USD Fedwire 21:00a – 18:00 03:00 – 02:00
b
Singapore SGD MEPS+ 09:00 – 19:00 03:00 – 13:00
Norway NOK NBO 05:40 – 16:30 05:40 – 16:30
Denmark DKK KRONOS 07:00 – 15:30 07:00 – 15:30
EU EUR TARGET 07:00 – 17:00 07:00 – 17:00
UK GBP CHAPS 06:00 – 16:00 07:00 – 17:00
Sweden SEK K-RIX 07:00 – 17:00 07:00 – 17:00
S Africa ZAR SAMOS 07:00 – 16:00 07:00 – 16:00
Israel ILS ZAHAV 07:00 – 14:15 07:00 – 14:15 aOne day before value date (V1);
bOne day after value date (V+1) (Source:
Progress in Reducing Foreign Exchange Settlement Risk, BIS, May 2008)
The 07:00–12:00 CET time window is chosen because the RTGS systems
of 17 currencies are simultaneously open during this period (see Exhibit 11-5).
Time (CET) 00:00
IPIS
06:30
RPIS
07:00
start
09:00
SCTT
10:00
FCTT1
12:00
FCTT2
settlement and funding time
Continuous Linked Settlement
177
Chapter 11
178
Funding for Asia-Pacific currencies (AUD, HKD, JPY, KRW, NZD and
SGD) occurs during the three-hour period of 07:00 – 10:00 CET during which
their RTGS systems are open. For other currencies, funding continues in the
full five-hour period of 07:00 – 12:00 CET.
Processing Queue
Before the pay-in schedule is issued, settlement instructions are filtered based
on certain risk management criteria (discussed in the next section). Since the
funding takes place continuously, a large payment amount in the early stages
may block all other payments and result in a total pay-in failure. To prevent
such a situation, large amounts are split into smaller amounts to facilitate early
pay-ins. After the pay-in occurs in the RTGS funds, CLSB completes the cor-
responding pay-out to the settlement member or its nostro agent. The unset-
tled trades at 12:00 CET are removed from the queue, and the counterparties
will decide whether to settle them in CLS on the next day or settle it outside
CLS on the same day.
11.4. Risk Management
Each trade in the processing queue is subjected to three risk management
tests: positive adjusted balance, short position limit and aggregate short posi-
tion limit. Only after passing these tests, the payment instruction is processed.
Positive Adjusted Balance
CLSB converts the balances in all currencies, both long and short, in the set-
tlement member‟s account into USD-equivalent at the prevailing market prices
(supplied by Reuters) and add them up. The aggregate USD-equivalent is the
positive adjustment balance. Before converting them into USD-equivalent, the
balances are subjected to haircut, which reduces the long balances and in-
creases the short balances. The haircut is usually set at the price change over
6-day period at four standard deviations. For a payment instruction to be
processed, positive adjusted balance must be greater than zero.
Short Position Limit
CLSB assigns a currency-wise short position limit for each settlement member
and reviews it periodically. This is a liquidity facility, which enables the settle-
ment to occur even if the CLSB has not received the other currency amount.
Note that the short position limit does not create any credit risk to the CLSB
because the positive adjusted balance (the first test) is greater than zero.
Continuous Linked Settlement
179
Aggregate Short Position Limit
It is a limit on the settlement member‟s total short positions in all currencies.
Like positive adjusted balance, it is computed in USD-equivalent after applying
the haircuts. The limit is reviewed from time to time.
The following example illustrates the aggregate short position limit and pos-
itive adjusted balance, assuming that the settlement member has the following
positions in its accounts with the CLSB. All the amounts are in USD equivalent
and after adjusting for haircuts.
Currency Dr/Short Cr/Long
EUR 125
GBP 250
JPY 100
Total 225 250
The aggregate short position is USD 225 and the adjusted positive balance
is USD 25, which is the difference between total positions and total long posi-
tions. For a payment instruction to be processed, the following tests must be
passed: (1) positive adjusted balance must be greater than zero, which is the
case indeed; (2) short position of USD 125 in EUR and USD 100 in JPY must
be less than the limits set for each currency; and (3) aggregate short position
of USD 225 must be less than the limit specified for this test.
11.5. Liquidity Facilities
The pay-in in CLS is extremely time critical and differs substantially from other
payment systems. For Asia-Pacific currencies, domestic clearing is completed
before CLS clearing begins; for European currencies, domestic clearing and
CLS clearing are roughly coterminous; and for North American currencies,
CLS clearing is completed before domestic clearing starts.
The time difference between CLS and domestic clearings has significant
impact on liquidity management. For example, for Asia-Pacific currencies, a
bank expecting a large receipt in CLS will build up a large debit position in do-
mestic clearing. Similarly, for North American currencies, making a large pay-in
in CLS is exposed to cost and credit risk because the covering funds are re-
ceived later in the domestic clearing. Consider a bank that executed an over-
night sell-buy forex swap in EUR against USD, and invested the overnight
USD funds in USD money market. In the settlement of far leg, the bank will pay
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180
USD in CLS before it receives the covering funds in CHIPS. To improve the li-
quidity management and to ensure successful completion of pay-in in CLS,
there are three tools: inside/outside (I/O) swap, top-up and contingency swap
(TUCS) and liquidity providers.
Inside/Outside (I/O) Swap
Consider the situation in which Bank A has a large short position in EUR and a
large long position in USD; and Bank B has a complementary position of large
long position in EUR and large short position in USD. Both of them can enter
into the following intra-day swap.
Bank A buys EUR (and sells USD) from Bank B value cash (“inside leg”) Bank A sells EUR (and buys USD) to Bank B value cash (“outside leg”)
The first leg is called inside leg because it is settled within CLS; and the
second leg is called outside leg because it is settled outside CLS and in the
domestic clearing of the two currencies. The inside leg ensures that the pay-in
for EUR is completed early. Though I/O swap enables a smooth pay-in in CLS
despite large short position for a member, it introduces to one party (in the
above example, to Bank B) the Herstatt risk, which defeats the very purpose of
CLS. The introduction of Herstatt risk here is considered tolerable in view of
significant improvement in the liquidity of CLS pay-in.
After the initial pay-in schedule is issued at 00:00 CET, CLSS will identify
the potential I/O swaps between various members and publish them by 00:30
CET. The I/O swap advice from CLSS is subject to the counterparty limits that
the members have established for each other, maximum trade size for each
currency, etc. The members interested in executing the I/O swaps must bilate-
rally negotiate and confirm the I/O swap to the CLS. The inside leg must be
matched by 03:30 CET so that it can be incorporated in the final pay-in sche-
dule at 06:00 CET. Overall, I/O swaps have not been popular.
Top-up Contingency Swap (TUCS)
Some settlement members privately formed a group to execute I/O swaps on a
bilateral basis. However, the process is highly manual and hence lost its relev-
ance.
Liquidity Providers
If a settlement member‟s short position in a currency is extended and continu-
ing, it does not create credit risk to the CLSB because there is an equivalent
Continuous Linked Settlement
181
long position in another currency (under the first test). However, the CLSB
cannot make the pay-out in the short currency in the circumstances.
To enable CLSB complete the pay-out, there is a liquidity facility committed
by certain settlement members (“liquidity providers”) for each currency. Under
this facility, CLSB enters into an overnight forex swap with liquidity providers,
Under the swap, CLSB receives funds in the short currency (with which it com-
pletes the pay-out) and pays funds in long currency (which would otherwise
have been credited to the failing settlement member‟s account). On the next
day, one of the following will take place. First, the failing member makes good
the short currency funds, which settles the second leg of swap. Second, if the
failing member does not make good the short currency, CLSB will enter into an
outright transaction to complete the second leg of forex swap. The hair cut built
into the failing member‟s long position should be adequate to withstand the
price changes overnight. If the outright transaction is not possible (because of
lack of quotes), the overnight forex swap is rolled over for a maximum of four
business days, after which CLSB computes the loss and allocates it pro rata to
those settlement members that had traded with the failing member such that
the loss to a member is capped at the bilateral net amount with the failing
member. In the unlikely event of CLSB not able to raise enough funds to cover
the short fall amount, there will be general loss allocation to all surviving mem-
bers. The general loss allocation is subject to a cap of USD 30 million.
11.6. Operations Milestones
Despite the initial cost and time overruns, CLS made significant progress after
it commenced operations in September 2002. The following are the milestones
in its operations.
Date Milestone
Feb 2003 Daily value of settlements exceed USD 1 trillion
Jan 2004 Daily value of settlements exceed USD 2 trillion
Dec 2004 Daily value of settlements exceed USD 3 trillion
Sep 2005 Daily value of settlements exceed USD 4 trillion
May 2006 Daily payment instructions exceed 0.5 million
Jun 2006 Daily value of settlements exceed USD 5 trillion
Dec 2006 Daily value of settlements exceed USD 6 trillion
Jun 2007 Daily value of settlements exceed USD 7 trillion
Sep 2007 Daily value of settlements exceed USD 8 trillion
Nov 2007 Daily payment instructions exceed 1 million
Mar 2008 Daily value of settlements exceed USD 10 trillion
Sep 2008 Daily payment instructions exceed 1.5 million
Chapter 11
182
On the negative side, there were just two jarring notes. The first occurred
within first six months of operations. On March 25, 2003, database program-
ming errors by IBM resulted in 30% of the settlements being wrongly rejected.
The CLSS staff was slow to respond, and the RTGS systems of Asia-Pacific
currencies had to be extended to complete the settlement.
The second problem occurred on May 27, 2003, just two months after the
first problem. Due to errors by the CLSS staff, pay-out occurred before pay-in!
However, the problem was solved immediately.
183
Chapter 12
Front Office: Trading and Hedging
Currency trading is unnecessary, unproductive and totally immoral. It should
be stopped. It should be made illegal. We don‟t need currency trading. (MOHA-
MAD MAHATHIR, Prime Minister of Malaysia, at a meeting of IMF in Hong Kong
on September 20, 1997. The context was the sharp fall of Malaysian ringgit in
FX market. )
Hedging is the tai chi of trading. (JIM KHAROUF, Futures, October 1996)
Trading (also called speculation) is taking risk, which results in either profit or
loss. Hedging is eliminating risk, which results in neither profit nor loss. To-
gether, they constitute the main activity of front office.
12.1. FX-speak
FX traders have their own lingo which, like airline pilot‟s language, is precise
with a vocabulary of about two dozen words. The deal conversation takes
hardly about 5-10 seconds. Exhibit 12-1 lists alphabetically the commonly used
words and phrases and their meaning.
Chapter 12
184
EXHIBIT 12-1: FX Trader’s Lingo
BIO Billion, which is always the American billion (i.e. a thousand millions) and not a British billion (i.e. a million millions). The British use the word milliard for American billion, but it is no longer in use. It is also called YARD (q.v.)
CABLE GBP/USD. It is so called because the London closing price of this rate used to be sent to New York by cable; and the New York traders, would ask: “Has the cable arrived?”, “What is the cable (price)”?
CBL Short for CABLE (q.v.)
CH Short for CHANGE (q.v.)
CHANGE Said by the by the price quoter/maker and means that the price quoted earlier has changed and does not hold now.
CHECK Another way of saying CHANGE (q.v.)
CHK Short for CHECK (q.v.)
CHOICE Used after the price (“1.2555 choice”) by the price quo-ter/maker and means that the price asker/taker can buy or sell at the same price. In other words, the bid-offer spread is zero.
COPEY Nickname Danish krone (DKK)
FIGURE Pronunciation for “00” (e.g. “figure five” for 00/05)
LEVEL Used after the price (“1.2525/30 level”) by the price quo-ter/maker and means that the price is for indication only and not for dealing.
LVL Short for LEVEL (q.v.)
MINE Said by the price asker/taker and means “I bought” (base cur-rency in outright) or “I received” (swap points in FX swap)
MIO Short for million
MY RISK Said by the asker/price-taker and means that the quoter hold the price for a while and any change in price during the hold-ing period will be at the risk of asker. If the asker wants to deal, he would check the latest price by saying “How now?” Typically used when the asker is executing a matching trade with another simultaneously.
OFF Another way of saying CHANGE (q.v.)
OZZY Nickname for Australian dollar (AUD)
SMALL Trade amount will be about USD 0.25 MIO equivalent
STOCKY Nickname for Swedish krona (SEK)
TINY Trade amount will be about USD 0.1 MIO equivalent
URS Short for YOURS (q.v.)
VALUE Short for value date
YARD American billion. From the last syllable of the equivalent but archaic British word “milliard”. It is also called BIO (q.v.)
YOURS Said by the price asker/taker and means “you bought” (base currency in outright) or “you received” (swap points in FX swap)
Front Office: Trading and Hedging
185
12.2. Market Practices in Interdealer Market
The market has some uniform global practices defined by ACI12
Model Code of
Conduct. In addition, the local chapter of ACI or the local regulator may have
recommended additional practices applicable to the local market. And most
important, there are certain informal rules, unwritten yet powerful, among deal-
ers, which govern the dealing practices. The following are some of them.
Price Quotes
A dealer is not bound to quote a price when asked for quotation. He may indi-
cate his lack of interest by replying “not in the market.”
Price quoter/maker should usually quote both bid and offer except in excep-
tional circumstances. During market closing hours, for illiquid currency pairs or
in volatile price conditions, the price quoter/maker may request the price ask-
er/taker to disclose the market side (i.e. buy or sell) and the deal amount. The
asker need not disclose them and approach another price quoter.
All price quotes are firm and tradable for “standard” amount (explained below)
unless indicated otherwise. If the price is for indication only, the quoter should
indicate so (e.g. “1.2525/30 level”, “1.2525/30 for info only”).
Price quoter/maker should not engage in “spoofing”: quoting an off-market
price and withdrawing it immediately with a view to misguiding others about the
current market level or conditions.
The price quoted must be traded (“hit”) immediately by the price asker saying
“mine”, “yours” or “thanks, nothing”. If the asker requires the price to be held
for few seconds more, he should say “my risk” and when he decides to hit the
price, he should say “how now?” or “are you there?”. The price quoter/maker
may give a new price or indicate that the old price is good for dealing. If the
asker does not say “my risk”, the quoter himself may say “your risk”, indicating
that the price is held at the asker‟s risk and the asker should ask for the price
12 ACI is the abbreviation for the Paris-based Association Cambiste International. Origi-
nally, it was an informal club of forex traders with the motto “Once a dealer, always a
dealer” and an old style telephone receiver as its logo, and was popularly known as “Forex Club” in tune with its informal style. It has national chapters in most countries un-der the name “Forex Association”. In the later years, ACI extended its scope to money
market and money derivatives (which was wholly unnecessary), became formal (and even academic) in its functioning, and renamed itself as “ACI The Financial Markets As-sociation.” Their website is www.aciforex.com.
Chapter 12
186
again. For swap quotations, the quoter may indicate the price is good for a
specified period (e.g. “25/26 good for an hour”) because the swap points are
not volatile like spot price.
Price asker/taker is not bound to trade on the price given to him. He may ask
for price and not deal; he may ask for price for the second time and not deal;
and so on ad infinitum. However, ad infinitum should not be ad nauseam.
There should be no reason to ask the price for the third time. Asking for the
second time is acceptable because the first price may have been “trended”
(see Section 12.4), which was against the asker.
If the price quoter/maker gives the choice price (which will be naturally within
the bid-offer range of market price), the price asker/taker is not bound to trade,
but courtesy demand that he should. Similarly, if the price asker/taker requests
for a second quote with a narrow spread and the price quoter/maker obliges,
the price asker/taker is not bound to deal on the second quote, but courtesy
demands that he should.
Deal Amounts
All prices quoted are for standard (“market lot”) amounts. How much is a mar-
ket lot depends on the business center and the currency pair, and is informally
set by the traders in each local market. The following is an indicative list.
Business center Currency Pair Market Lot
Tokyo USD/JPY USD 1 – 3 MIO
Others active pairs USD 1 – 2 MIO
London Top five currency pairs USD 1 – 5 MIO
New York Top five currency pairs USD 1 – 3 MIO
India
USD/INR (spot) USD 0.5 – 1 MIO
USD/INR (FX swap) USD 0.5 – 2 MIO
Other active pairs (spot) USD 0.5 – 2 MIO
If the amount is other than the market amount, the price asker/taker must indi-
cate it in advance (e.g. “cable for small please?”, “spot yen for tiny please”, eu-
ro for ten please?”). In the last request, the word “ten” means ten million. All
quantity indicators are assumed to be in millions. If the asker has not specified
his non-standard amount in advance, the price quoter/maker has the right to
reject the deal concluded. When non-standard amount is indicated in advance,
the price quoter is not bound to quote the price or he may insist on knowing
the market side (i.e. buy or sell) of the price asker. When the price quoter asks
for the market side of the asker, the asker may refuse to divulge it and ap-
proach another price quoter for the price.
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Position Parking
Position parking is the dangerous practice of transferring a position to another
dealer with a commitment to reverse it next day at the same price. Such prac-
tice is used to hide the excessive trading beyond the sanctioned limit by the
party parking the position. Position parking is prohibited.
Value Dates
Since the procedure to determine value dates differs for currency pairs and
business centers, it is desirable that the parties clearly specify the value date
in terms of month and date rather than generic terms like “spot”, “tom”, etc.
Further, it is desirable that the month is spelt rather than specified by a numer-
al since different conventions are prevalent (e.g. DD/MM, MM/DD).
Brokers
Advances in information technology are replacing services of voice brokers,
who may be a thing of the past very soon in the inter-dealer market. Some of
the practices with respect to the inter-dealer brokers are as follows.
Broker must not disclose the name of the principal until the deal is concluded.
Broker must not quote firm price to a principal unless the broker has received it
firm from another principal; and the broker should not maintain any position on
his own, even for a very short period. For spot trades, the broker must give the
name of the counterparty to each principal on conclusion of trade. Position
parking is prohibited.
For forex swap trades, the broker may fix different principals for near leg and
far leg, which should be accepted by the principal, unless it is agreed in ad-
vance that the principal should be the same for both legs of the swap.
Management of “stuffing”: stuffing is the exceptional situation when the broker
is hit on the quote by the asker-principal while the quoter-principal withdraws it,
both occurring simultaneously. As a result, the broker is stuck on one side: he
is said to be “stuffed.” In such cases, the asker-principal may use his discretion
to relieve the broker from the trade (provided the broker explains the situation
immediately and satisfactorily) or hold the broker to the trade. In the latter
case, the broker will have to conclude another trade immediately with another
principal at the next available price. The asker-principal should not insist on the
original price but accept the replacement price, and collect the difference be-
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tween them from the broker. All cases of stuffing must be informed immediate-
ly to the managements of broker and the principal.
Points-parking is an undesirable activity and associated with stuffing. Instead
of settling the price difference on the stuck deal, the broker maintains a run-
ning account with the principal for parking the price difference (“points”) on
stuck deals to be offset over a period of time. Points-parking is prohibited.
Ethics
Difficulty arises when ethics are incorporated in the code of conduct. Two facts
need to be recognized. First, ethics are practiced out of personal conviction
and cannot be enforcedalways. Second, what is ethical and what is not dif-
fers from culture to culture. Some of the ethics incorporated in the code of
conduct are as follows.
“Management should watch for signs of the abuse of drugs including alcohol
and abused substances.” (Note the exclusion of tobacco. By the way, no an-
nual meeting of ACI is complete without liberal dose of alcoholic drinks, as do
the meetings of local chapters.)
“Gifts and entertainment should not be excessive or frequent.”
“Entertainment should neither be offered nor attended when it is underwritten
but not attended by the host.” (The drink and dinner at ACI conferences are
hosted by different sponsors. Neither the host is visible nor the attendees look
for him.)
“Gambling and betting among market participants should be discouraged.”
(Note that they are not prohibited but discouraged. And what is the difference
between gambling, betting and trading?)
“Dealing for personal account is allowed but the management should ensure
safeguards against insider trading and front running.” (Safeguards against
front running are certainly required. Insider trading may be relevant in equity
market, but its applicability in forex market is doubtful.)
12.3. Sample Deal Conversations
Few sample conversations are shown in this section. They illustrate the trad-
er‟s language, vocabulary and the market practices. In the specimens below,
“A” is the asker of price and “Q” is the quoter of price.
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Conversation #1
Script Remark
A: Hi, IOB, chn, spot euro pls? Asker identifies himself as Indian Over-seas Bank, Chennai (“IOB, chn”) and asks for EUR/USD spot price.
Q: Hi, there, 1.25 35/39 Quoter gives the price
A: At 39, we buy two euro At 1.2539, the asker buys two million eu-ro (“two euro”). All amounts are unders-tood to be in millions
Q: Agreed. Val Jan 25 Quoter confirms that spot value date (“val”) is Jan 25.
A: Tks n bye Closing line
Conversation #2
Script Remark
A: Hi, IOB, chn, spot cbl for small pls?
Asker identifies himself, asks for GBP/USD (“cbl”) spot price and indicat-ing that the amount will be about USD 0.25 MIO (“small”)
Q: 55/57 Quoter gives the price; only small figure is quoted and the big figure is omitted
A: At 57, we sell 0.25 MIO dlr At the 57, asker can buy GBP or sell USD. Since the deal currency is USD (“dlr”), the asker must explicitly specify it
Q: Tks. I buy dlr 0.25 MIO at 1.4557 val Jan 25. TGIF
Quoter confirms all the details and ex-claims “thank God it‟s Friday” (TGIF)
Conversation #3 (very precise, brief and terse)
Script Remark
A: yen pls? USD/JPY price: unless otherwise speci-fied, the other currency is always USD, Value date is always spot unless other-wise specified
Q: 98/03 Only small figure is quoted
A: At 98, five Asker sold 5 MIO USD. The deal cur-rency is base currency unless otherwise specified. At 98, asker can only sell USD
Q: Agreed Quoter confirms the trade
A: At 103.98, v sell USD 5 MIO val Jan 25. Done n confirmed
Asker confirms the full details of the trade
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Conversation #4 (with a broker, who is the asker, A, in the following)
Script Remark
A: spot rupee, Sir? Broker asking for USD/INR spot price
Q: 50.00/01 Bank gives the price
A: Tks, ntg. I deal 0000/50 Broker offers his own price with a nar-row spread and his offer (at 50.0050) is better than the bank‟s offer of 50.01
Q: Mine one Bank bought USD 1 MIO at 50.0050
A: You bought from ABC dlr one @ 50.0050 value Jan 25
Broker provides the seller‟s name and gives the other details
A: Some good selling coming, big fig now 99
Broker supplying info on market, and in-dicating that the big figure (“big fig”) now is 49.99 (“99”).
Q: How you deal? Bank asks for a dealing price
A: 49.99/50.00 sry wide sprd Broker is quoting the full price for both bid and offer because he does not risk any misunderstanding on the big figure. He is apologetic that the spread is wide now compared to his earlier quote
Q: Tks, ntg. I deal parity Quoter shows no interest on the broker‟s quote, and says that his price is the same, too (“parity”)
A: Ticcy, my risk Broker requests the bank to hold the price for a while (“ticcy”) and he will as-sume the risk of price change for the de-lay (“my risk”)
A: R U there at 99/00 Broker asking whether the dealing price is still 49.99/50.00 (“99/00”)
Q: SS Bank confirms (“SS”) it is
A: Urs half at 49.99. XYZ sold. Val 25/1
Brokers sell USD 0.5 MIO (“half”) on be-half of XYZ to the Quoter. Price and val-ue date confirmed.
A: can give u another half at 9950
Broker indicates he can sell (“give”) USD 0.5 MIO more at 49.9950. It is an indication and not a firm quote
Q: Show me firm Bank asks the broker to give firm quote
A: I sell half at 9950 firm Broker confirms that he sells at 9950
Q: Taken Bank buys(“taken”) USD 0.5 MIO at 49.9950
A: ABC sold at 49.9950. Val Jan 25. Done n cnfmd. Lvl now is 99/00.
Broker confirms the deal with other de-tails, and indicates that the current price if 49.99/50.00 for information only (“lvl”).
Q: Tks, no interest there Bank indicates no interest at that level
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12.4. Trending
From the sample conversations in the previous section, readers may have no-
ticed that there will be different two-way quotes from different dealers prevail at
the same time, Yet, they do not provide any arbitrage profit opportunity be-
cause they do not cross the bid-offer spread. Such quotes are called “trended”
quotes, which provide valuable information about the price quoter‟s intention.
Suppose that the current market price is 1.2550 /55. You are a dealer in
the market and your intention is to buy the base currency. You have two alter-
natives: first, go another dealer in the market and buy at his offer price, which
is 1.2555; and second, make your own quote and place it in the market so that
you can buy at your bid price. In the second case, your quote must be different
from the current market quote: it should be a “trended” quote. How different
should it be, should it be higher or lower than the current market price?
One might think that since the intention is to buy and since buying at lower
price is better, the quote should be trended lower (or “left”) to, say, 1.2549/54.
This is incorrect and reflects greed, and greed is dangerous. Consider what
happens if your quote is 1.2549/54. It is attractive to the buyer, not seller: you
sell at 1.2554 and the market sells at 1.2555. Therefore, if you quote this price,
you attract a buyer and sell to him, which is the opposite of what you want to
do. Since you have sold on this quote, you must immediately cover by buying
at the market‟s offer price of 1.2555, making a loss of one „pip.‟ And your origi-
nal intention of buying remains unfulfilled.
Consider now the trending in the opposite way: higher (or “right”) to, say,
1.2551/56. Compared to the market price of 1.2550/55, it is attractive to the
seller: you buy at 1.2551 and the market buys at 1.2550. Therefore, you attract
the seller and buys from him at your bid price of 1.2551. You have done what
you intended (i.e. to buy) in this correctly trended price, but to whom the trend-
ing benefit, counterparty or yourself? The answer is both. That the counterpar-
ty benefited by selling at a higher price is obvious. Your benefit in the trending
is not as obvious. You have two ways of buying: go to the market and buy at
1.2555; or correctly trend the price and buy at 1.2551. The latter is better than
the former. In other words, Consider now another unlikely but possible situa-
tion. You have trended correctly to 1.2551/56, but the counterparty foolishly
bought from you at 1.2556. You ended up selling at 1.2556 instead of buying
at 1.2551. To cover the sale, you immediately buy from the market at 1.2555
and it results in profit of one pip!
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To sump up, if you trend with benefit to you alone, your trending is wrong,
you attract the wrong party and you make a small loss in reversing the un-
wanted trade. If you trend with befit to the counterparty, your trending is right,
you attract the right party and the trending benefits you, too; and if you are hit
on the wrong side of the correctly trended quote, you make a small profit in re-
versing the unwanted trade.
12.5. Trading Operations
Money, bond, equity and forex markets constitute the four underlying markets
or asset classes. Trading in forex market is different from that in the other
three. The table below shows the stylized facts on risk/return profile of the four
asset classes, with the following instruments as the proxies for each.
Money: three-month Treasury bill or certificate of deposit
Bond: five-year sovereign or AAA-rated corporate bond
Equity: large-cap index stock
Forex: reserve currencies (EUR, GBP, JPY, CHF) against USD
Money Bond Equity Forex
Daily returna 0 0 – 1% 0 – 10% 0 – 0.5%
Weekly returna 0 – 0.10% 0 – 2% 2 – 30% 1 – 2%
Annual returna
Of which: Yield/Dividend Capital gain/loss
1 – 5% 1 – 5% 0
3 – 12% 2 – 6% 0 – 6%
10 – 70% 0.1 – 0.5% 10 – 70%
4 – 15% 2 – 5% 2 – 10%
Riskb 0 0 – 10% 10 – 70% 4 – 12%
Leverage in cash market
c
None None (usually)
2 10 – 50
Transaction cost 0.1% 0.1% 0.25% 0.01% a Could be positive or negative
b Standard deviation (“volatility”) of returns
c Ratio of investment value to owned funds
Money and bond markets are used for fixed return investment with buy-
and-hold strategy. If they are held until maturity, there would be no capital
gain/loss and therefore no risk. It is true that the instrument may change its
value during its life because of changes in interest rate, resulting in capital
gain/loss. However, such capital gain/loss will disappear at maturity because
of the “pull-to-par” effect in the price of money and bond instruments. Further,
there is no leverage in these markets: you do not borrow and invest, but invest
only to the extent of own funds. We must note here that we are discussing the
underlying markets (i.e. cash or spot) and not derivative markets. In derivative
Front Office: Trading and Hedging
193
markets, leverage is available for all four asset classes. Matter-of-factly, leve-
rage is one of the qualifying features for derivatives.
Equity and forex markets, on the other hand, provide capital gain/loss
(which is the source of risk) and leverage. The extent of capital gain/loss and
leverage is different in each market. Before examining the differences and their
implications for trading, let us look at the nature of price changes in equity and
forex markets shown in Exhibit 12-2.
EXHIBIT 12-2: Daily Prices Changes in Forex and Equity Markets
Each vertical bar represents the daily range of price change. We can con-
clude the following stylized facts from the exhibit.
In forex market, the price changes regularly but only by about 0.5% a
day, and the trend is immediately reversed substantially within 34
days, because of which the net change over a week is only about
12% and over a year about 415%. In equity market, on the other
hand, the price moves in jerks, and the trend is persisting, because of
which the weekly change is almost equal to the sum of daily changes.
The price changes are smooth in forex market but have “gaps” (shown
as circles in the exhibit) in equity market. The “gap” is the break be-
tween the ranges of price changes over consecutive days.
EQUITY market FOREX market Price
change
Time
1%
3%
5%
7%
Chapter 12
194
Let us explain the reason for these differences. Because the daily price
changes are very small, forex market provides leverage of up to 1050 times.
This, coupled with the very low transaction costs and 24-hour trading, results
in smaller holding periods (of few hours to few days) and quick turnaround,
which results in immediate and substantial trend reversal within a week. In
other words, forex trading is short-term levered speculation. The equity market,
in contrast, has lower leverage, higher transaction cost, large price changes al-
ternating with negligible changes, and persistent trend. This forces the strategy
to be buy-and-hold for long term with little or no leverage. As for price “gaps”,
the price changes because of the arrival of new information and news. Since
the forex market is open 24 hours days, it translates the news instantly as it
happens into price changes, resulting in small and continuous changes at the
same rate as the news arrival. The equity market works only for 8–10 hours a
day and when it opens next day, it translates the accumulated news over the
last 14–16 hours into price action in one shot, resulting in sudden and large
changes at market opening, leading to price “gaps.”
Levered Speculation and Stop-loss Limit
Levered speculation requires adherence to the stop-loss limit: to exit the trade
at a pre-defined level of loss if the market moves against. The stop-loss limit is
a form of insurance against ruin.
Consider a trade with 10 times leverage. If the market moves against as by
10%, it results in loss of entire investment amount, leading to ruin. To prevent
such a contingency, we keep a stop-loss limit of, say 2%, so that the first loss
still leaves enough money to play another four trades.
Let us now compare the two strategies: buy-and-hold without leverage and
levered speculation with stop-loss limit. They are implemented on an asset
whose current market price is 100 and the outlook is bullish. Immediately after
we buy the asset, the market price falls to 95, which is quite common because
of short-term noise and countertrend in the price changes. In the buy-and-hold
strategy, we ignore the short-term countertrend and continue to hold on to the
trade. In fact, some investors average the holding price by buying more at low-
er price, which is called dollar cost averaging (DCA) and popular in mutual
fund industry. In the second strategy (10 times leverage, 2% stop-loss), the
price dip forces us to exit with a loss. Immediately thereafter, the price rallies to
110. The first strategy would result in a profit of 10% while the second had al-
ready exited at a loss of 20%. It is obvious that, in buy-and-hold strategy, we
need to be right on the trend to make profit; but in the levered speculation with
stop-loss, we need to be right on the trend as well as on the market timing.
Front Office: Trading and Hedging
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The success depends, not on where the price reached, but the path it took to
reach there. Economists call this as the “path dependence” of the strategy.
One might think that it is the stop-loss that exposes us to the problem of
market timing and that the removal of stop-loss will ensure profit if we are right
on the trend. This is downright wrong. Loss on account of market timing will
only weaken the trader but makes him survive another day to fight. Removing
stop-loss, on the other hand, is like removing the protective armor: it results in
total ruin. This brings us to the topic of “money management”.
Money Management
The “money management” here is different from cash (or liquidity) manage-
ment in finance. Money management, as applied to gambling, deals with se-
lecting the right game of chance and the right amount of money to be staked
on each play of the game selected.
Let us review the probability math for the games of chance. In particular,
we need to define and establish the relation between probability, odds, payoff,
payoff odds, expectation and edge.
Probability (p) of an outcome is the ratio of the number of times the out-
come can occur to the total number of all outcomes; and its value will be be-
tween 0 and 1. Odds (o) of an outcome are the ratio of the probability of its oc-
currence to the probability of it not occurring.
p = (chances for an outcome / total number of outcomes) o = (probability of an outcome / probability of it not occurring)
For example, in a 52-card deck, there are four aces. The probability of pick-
ing up an ace is 4/52 or 1/13 (“1 in 13”); and the odds for it, 4/48 or 1/12 (“1 to
12”). The odds are more commonly expressed as “against” rather than “for”.
Thus, if the odds for are 1-to-12, it is the same as the odds against of 12-to-1.
Since the total of probability of occurrence and non-occurrence is unity, the fol-
lowing is the relationship between the probability and the odds.
o = p / (1 p)
p = o / (1 + o) and (1 p) = 1 / (1 + o)
Payoff is the amount won or lost in a game of chance, and the mathemati-
cal expectation (or simply the expectation) of the game is the weighted aver-
age of profit and loss amounts, the weights being their probabilities. Thus, if
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196
the profit is x with a probability of p and the loss is y with a probability of (1p),
then the expectation is:
expectation = (x p) + (y (1p))
Expectation holds only on an average over a large number of plays. For
example, consider the coin toss game that pays one unit on head and loses
one unit on tail. Since the chance of each outcome is even (i.e. p = 0.5), the
expectation is zero. However, on a single outcome, there is either profit or loss
of one unit. If we play it many times, then the average payoff will be zero.
It is more convenient to express the profit amount relative to the loss
amount because the loss is the amount of investment. The ratio of profit-to-
loss will indicate how much an unit of investment has grown. Expressed in this
fashion, it is called payoff odds (b). Thus, if the game pays profit of 3 units and
loss of 2 units, the payoff odds (for) are 3-to-2. If the expectation is computed
with payoff odds (b), it is called “edge” (E), which is also called “advantage.”
E = (b p) (1p) = (b + 1)p 1
With payoff expressed as payoff odds, the edge now represents the pro-
portional return on investment (where investment is the loss amount, of
course). Consider now the following five games of chance.
#1 #2 #3 #4 #5
Profit (x) 1 2 3 9 21
Loss (y) 1 3 2 16 4
Prob. of x (p) 0.5 0.50 0.50 0.80 0.20
Prob. of y (1p) 0.5 0.50 0.50 0.20 0.40
Payoff odds (b) 1 0.67 1.50 0.5625 5.25
Edge (E) 0 0.1667 0.25 0.25 0.25
Game #1 has zero edge (“fair bet”): you cannot make profit in this game
and therefore should not play it. Game #2 has negative edge (“bad bet”): you
will lose playing this game and therefore should not play it. Games #3 through
#5 have positive edge (“good bet”): you win in these games and may play
them. The positive edge corresponds to some valuable information that you
know and others do not. We may note that if the market were efficient, the pos-
itive edge disappears by adjusting either the probabilities or the payoff odds.
Recall that the edge is the return on investment and that investment is loss
amount. Thus, in Game #2, the player will lose 16.67% of 3; in Game #3, the
player will gain 25% of 2; in Game #4, the gain will be 25% of 16; and so on.
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197
We must note that the edge works only on an average over many plays of
the game, and does not hold for a single play. For example, if we play the
Game #1 five times, it is possible that we may win all the five times, but the
probability of that will be very small at: 0.55 = 0.03125 (or 3.125%). Let us de-
fine the following.
N = Total number of plays
A = Total amount staked or invested over N number of plays (al-
so called “action”) and is computed as (N y)
TE = Total expectation over N number of plays, which is computed
as (A y)
TP = Total actual payoff over N number of plays
We can make the following conclusions from the statistical theory:
To be significant, N should be at least 20. In other words, we must
play the game at least 20 times.
The deviation of total actual payoff (TP) from the total expectation
(TE) will be within y N (square root of N) of TE for 68% of the cas-
es; and within 2y N of TE for 96% of the cases. For example, if we
play Game #2 for 100 times, then N = 100; N = 10; A = (100 3) =
300; TE = (300 0.1667) = 50. The actual total payoff (TP) will
have the follo wing range.
50 (3 10) = 80 to 20 in 68% of the cases
50 (2 3 10) = 110 to +10 in 96% of the cases
The absolute size of the deviation, N, increases with N but tends to-
wards zero as a proportion of A, which implies that the difference be-
tween TE and TP becomes larger with N but the fraction TE/A will
tends to be the same as the fraction TP/A.
Thus, playing a positive sum game does not guarantee profit if the game is
played for just few times. We need to play at least 20 times for the edge to be
statistically meaningful. The next question is which of the three good bets do
we play? We can play any of them, and the question should be how much of
the capital should be staked in each play of the game.
If we stake the entire capital, the ruin is guaranteed, regardless of the
probability and the payoff. To illustrate the point, consider the Game #5, in
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198
which the edge is 0.25 (or 25%) and the game is played five times. The proba-
bility of winning all the five is 0.255 = 0.000977 (or 0.0977%) and the probabili-
ty of just one loss is 1 0.255 = 0.9990 (or 99.9%). Since we are betting the
entire stake, the probability of ruin is 99.9% over the five games. As we in-
crease the number of games, the probability of a single loss becomes almost a
certainty. Staking too little of the capital, on the other hand, will make the prob-
ability of ruin close to zero, but also makes the return on investment so ridicu-
lously small that we would be better off investing the capital in fixed-income
securities rather than speculate in a game of chance. The optimal amount to
be staked on each play was derived by a mathematician, J L Kelly, and is ex-
pressed as a fraction of the capital available at any point of time. It is called
Kelly’s fraction (f*) and is given by
f* = [(b + 1)p 1] / b
The numerator is the edge and the denominator is the payoff odds. For this
reason, Kelly‟s fraction is often defined as “edge / odds” where the odds
should be understood as payoff odds and not probability odds. For even bets
(i.e. those in which profit and loss amounts are the same so that b = 1), the
Kelly‟s fraction is simplified to:
f* = 2p 1.
Kelly‟s fraction should be computed only when the edge is positive. Since
the stake amount is fraction of the available capital, the probability of ruin is
close to zero, and the probability of losing x% of capital is 100 x. Thus, the
chance of losing 10% of initial capital is 90% and that of losing 90% is 10%.
The differences in probability and payoffs are factored into the fraction. For the
