Section 1 Foreign Exchange Markets · Capital Markets The FOREX Markets Μ. Anthropelos, Ph.D. 4....

Πανεπιστήμιο Πειραιώς,

Τμήμα Τραπεζικής και Χρηματοοικονομικής Διοικητικής

Μεταπτυχιακό Πρόγραμμα

«Χρηματοοικονομική και Τραπεζική Χρηματοδοτήσεις και Επενδύσεις»

Capital & Money Markets

Section 1

Foreign Exchange Markets

Michail Anthropelos, Ph.D.

[email protected]

http://bankfin.unipi.gr/faculty/anthropelos/

1Capital Markets The FOREX Markets Μ. Anthropelos, Ph.D.

mailto:[email protected]

The Market for Foreign Exchange

The Market of Foreign Exchange (FX or FOREX) is the largestfinancial market in the world.

Source: Bank of International Settlements

The FOREX market encompasses: the conversion of purchasing power from one currencyinto another, the bank deposits of foreign currencies, the extension of credit denominated ina foreign currency, the foreign trade financing and the trading in foreign currencyderivative contracts.

Capital Markets The FOREX Markets Μ. Anthropelos, Ph.D. 2

0,01 0,06 0,26 0,65 0,82

1,19 1,50

1,20

1,88

3,21 3,60

5,30 5,10

6,59

0,00

1,00

2,00

3,00

4,00

5,00

6,00

7,00

1973 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010 2013 2016 2019

Daily Global FOREX trading Volume in Trillions $

Function and structure of the FOREX Market

The spot and the forward foreign exchange markets are mainly anover-the-counter (OTC) (there is no central marketplace where buyersand sellers congregate). Rather, all market participants are connectedvia a network (the largest communication system in the world).

• The FOREX market participants can be categorized in the followinggroups: reporting dealers (42%), non-financial customers (7%) andother financial institutions (such as non-reporting banks, funds,insurance companies & central banks, 51%).

• The FOREX market (regarding the volume) can be discriminated as:

A. Wholesale market or interbank market: where banks, brokers andnonbank announce the exchange rates at which they are willing to selland buy (it accounts for 95%).

B. Retail market: where every individual can buy or sell small amountsof foreign currencies in a given exchange rates.


Spot, Forward and Swap FX transactions

• A transaction in a FX market can be in spot rate (τρέχουσα ισοτιμία),in forward rate (προθεσμιακή ισοτιμία) or as a part of currency swap.

• According to 2019 BIS statistics, 30% of the global FX markettransactions were settled in spot rate, 16% in currency forwardcontracts, 51% were part of currency swap contracts and rest wasassociated with options and other derivative products.

1. Spot transaction involves (almost) the immediate purchase or saleof foreign exchange (usually 2 trading days).

2. Forward transaction involves the delivery of the foreign currencyon a certain future date (after 30, 60, 90, 180…days), at a exchangerate which is determined today. For example, currency forwards(προθεσμιακά συμβόλαια σε συνάλλαγμα) and currency futures(συμβόλαια μελλοντικής εκπλήρωσης σε συνάλλαγμα).

3. A swap is the transaction that combines a spot rate and at least oneforward rate transaction in the opposite direction.


The Spot Rate

• Spot rate currency quotations can be stated in direct or indirect

terms.

• The direct quotation (άμεση αναφορά) gives the price of one unit of

a foreign currency priced in domestic currency. For example, in Europe

the US$ is referred in € i.e., $1= €0.8971 and for British pound £1=

€1.1476 (spot rates on 04/03/20).

• Similarly, the indirect quotation (έμμεση αναφορά) gives the price of

one unit of the domestic currency priced in a foreign currency. For

example, €1= $1.1147 and €1= £0.8714.

Notation

S(j/k) refers to the spot rate of

one unit of currency k in terms of currency j.

i.e., S(€/$) = 0.8971. Note that S(€/$)=1/S($/€).


The Cross-Exchange Rate Quotations, cont’d


Spot Rates on 03/03/2020

Source: ft.com

The Bid-Ask Spread

Each international bank that gets involved in the FX markets announcestwo spot rates:

1. the rate at which it is willing to buy a foreign currency: the bid price.

2. the rate at which it is willing to sell a foreign currency: the ask price.

Spread = ask price – bid price or

Percentage spread = (ask price – bid price)/ask price x 100

What does determine the size of the spread at a currency?

1) The spread reflects the depth and the liquidity of the specific currencymarket.

2) The uncertainty about the currency value (its volatility).

3) The deposit of the specific currency that a particular bank has.

✓ The quotes in the financial press refer to the interbank market fortransaction exceeding $1mil.

➢ Why such a spread exists?


The Cross-Exchange Rate Quotations

Usually, in the interbank transactions all the currencies are quoted against the

American $. The cross rate (σταυρωτή ισοτιμία) is given by the combination of

the spot rates of two currencies against $.

Example: Suppose that a (European) bank announces the following spot rates:

€1= $1.1146-8 and 1€ = £0.8713-5

This means that:

• S($/€b)= 1.1146, S($/€a)= 1.1148 and

S(€/$b)=1/S($/€a)=0.8970, S(€/$a)=1/S($/€b)= 0.8972

• S(£/€b)= 0.8713, S(£/€a)= 0.8715 and

S(€ /£b)=1/S(£/€a)=1.1474, S(€/£a)=1/S(£/€b)= 1.1477.

Suppose that the firm CM has $100 and wants to exchange them to £.

1. CM sells $100 to the bank at S(€/$b) and gets €89.70.

2. Then, CM sells the euros at S(£/€b)= 0.8713 and gets £78.16.

This means that the bank uses S(£/$b)=0.7816.

Similarly, S(£/$a)=S(€/$a) x S(£/€a)= 0.8972 x 0.8715 =0.7819, i.e.,

1£=$0.7816-9.



More generally, we have that:

where the above spot rates are equal in the case of no spread.

Note that given N currencies, one can calculate a triangular matrix of

N(N-1)/2 cross exchange rates.


),/()/()/(

)/()/(

and )/()/()/(

)/()/(

bb

a

bb

aa

b

aa

klSljSlkS

ljSkjS

klSljSlkS

ljSkjS

==

==

A Typical Exchange Rate Quotations

10

Rates on 04/03/2020

Source: www.oanda.com



We have that:

• S(€/$b)= 0.89769, S(€/$a)= 0.89782

• S($/£b) = 1.28136 and S($/£a) = 1.28151.

From those data, we should have

Note that S(€/$a) x S($/£a) = 1.15057 ≈ S(€/£a) and

S(€/$b) x S($/£b) = 1.15026 ≈ S(€/£b)

Triangular Arbitrage

If there are some direct quotes which are not consistent with the cross-rate spread, a possibility of certain profit (profit without risk) is emerged.

This situation is defined as triangular arbitrage in FX markets. In otherwords, triangular arbitrage (or currency arbitrage) involves buying acurrency in one market and selling it in another.

Example:

Suppose that:

a) a London bank offers £ at S(£/€b) = 0.8579,

b) a European bank in Frankfurt offers € at S(€/$b) = 0.8783 and

c) on that day a bank in NY buys £ at S($/£b) = 1.4500 (very high).

An arbitrageur would sell dollars for euros in Frankfurt, use the euros toacquire pounds in London and sell the pounds for dollars in NY.


Triangular Arbitrage cont’d

More precisely, if the arbitrageur has available (say) $1 mil.:

1. He gets €878,300 in Frankfurt.

2. He sells theses euros for £753,469 = 878,300 x 0.8579 in London.

3. He resells theses pounds in NY for $1,092,566= 753,469 x 1.45.

The riskless immediate profit is $92,566.

This arbitrage is created because: .

• The above situation would tend to cause the euro appreciation against

US dollar, which will be canceled by the depreciation of euro against

the pound. At the same time, pound will tend to fall in NY against dollar.

• The currency arbitrage opportunities are very rare nowadays (due to

extensive network, high-speed information, quotes against a specific

currency). Minimal deviations may exist due to additional transaction

costs.Capital Markets The FOREX Markets Μ. Anthropelos, Ph.D. 13

𝑆($/£b) > 𝑆(Eurob/$) × 𝑆(£/Eurob)

The Forward Rate

A currency forward or futures contract is an agreement between

two parties (two banks or one bank and one of its clients) for the

delivery of a certain amount of a foreign currency on a certain

future date, at a certain exchange rate (agreed at the starting of the

contract).

Capital Markets The FOREX Markets Μ. Anthropelos, Ph.D.14

Two parties:

• Long position: The buyer of the foreign currency.

• Short position: The seller of the foreign currency.

Why trade at forward contracts?

1. Hedging (reduction of risk exposure).

2. Speculation (undertaking more risk and more expected profit).

3. Arbitrage (certain profit without undertaking more risk).

Note: The outcome of a forward contract is a zero-sum game.

The Forward Rate (cont’d)

Forward rates for USD/EUR on 04/03/20

Source: www.cmegroup.com

✓ Of course, there is a spread in forward rates too, which is actually higher than the

corresponding spread in spot market (why?) 15

The Forward Rate (cont’d)

Notation:

refers to the price of one unit of currency k in terms of

currency j, for delivery in N months.

Example: On 02/09/16 the $/€ rates were:

S($/€)=1.11381

F1($/€)= 1.11585

F3($/€)= 1.1186

F12($/€)= 1.1290

In this case, we say that € is trading at a premium to $.

Similarly, we say that $ is trading at a discount to €.

• Generally, a foreign currency is said to be at a forward premium if

the forward rate expressed in units of the domestic currency is higher

than the spot rate. Otherwise, the foreign currency is at a forward

discount.


)/( kjFN

The Forward Premium/Discount

• It is common to express the premium or the discount of a forward

rate as an annualized percentage deviation from the spot rate (it is

more convenient for comparisons).

More precisely, the forward premium or discount is given as:

Example: On 04/03/20, it holds that:

We say that € is trading vs $ at a 1.72% premium, for delivery in three

months.

✓ What do you think determines whether we have discount or premium?


NkjS

kjSkjFkjf N

N

12

)/(

)/()/()/(

−=

%.)/($

)/($)/($)/($ 1780

3

1233 =

−=

EuroS

EuroSEuroFEurof

The Forward Premium/Discount

An example of Dollar/Euro exchange rate:

✓ On March 19, S($/€)=1.137 and F12($/€) was around $1.174 (the later was

not a prediction for the exchange today).


The Exchange Rates as Equilibria

The exchange rates (spot/forward) are market clearing prices that

equilibrate supplies and demands in foreign exchange market.

$/€ example:

Demand for euros = American demand for Euroland goods, services

and euro-denominated financial assets.

Demand for dollars = European demand for American goods, services

and American-denominated financial assets.

Demand for euros = Supply of dollars

✓ Why does this equilibrium on goods and assets fluctuate so much?


Factors that Affect the Exchange Rate Equilibria

Some of the factors that influence currency supply and demand:

1. Relative inflation rates: In general, a nation running a relative high

rate of inflation will find its currency declining in value relative to the

currencies with lower inflation rate. (why?)

2. Relative (real) interest rates: A rise in domestic real interest rate

(ceteris paribus) will increase the demand of the domestic securities

and will result a currency appreciation.

3. Relative economic growth: Relative stronger economic growth

implies currency appreciation.

4. Political and economic risk: Less stability implies currency

depreciation.

Note: What affects the changes in exchange rates is mostly the market’s

expectations on the above factors.


The Interest Rate Parity (IRP)

Suppose that an investor in Athens has €1. He has two alternative ways

to invest this euro in riskless (default-free) positions for a year.

1. Invest in euro (risk-free) interest rate r€ :

2. Invest in dollar (risk-free) interest rate r$ :

First convert €1 in $S($/€) and

Finally, convert the outcome in euros:


€1 In one year €(1+r€ )

The Interest Rate Parity, IRP, (διεθνής ισοδυναμία επιτοκίων) is anarbitrage condition that must hold when international financial markets arein equilibrium (equilibrium in the sense that there is no arbitrageopportunity in the exchange market).

$S($/€) In one year $S($/€)*(1+r$)

($/Euro)F

)r(S($/Euro) $

12

1+

The Interest Rate Parity (IRP) cont’d

Hence, if there is no arbitrage in the euro/dollar exchange market, it

should hold:

which is the formal statement of the IRP.

More generally we have:

where, N is the number of months, rj and rk are the annual risk-free

interest rates at currency j and k respectively. Hence if IRP holds,


)1()(

)(1

12

$euro r$/EuroF

$/EuroSr +=+

12/12/ )1)1( N

j

N

N

k r((j/k)F

S(j/k)r +=+

.jkN rr(j/k)FS(j/k)

The Interest Rate Parity (IRP) cont’d

The IRP is equivalent to:

which is sometimes approximated by:

The last equation provides a link between interest rates in two differentcountries and the corresponding spot and forward exchange rates.

✓ It is important to have in mind that difference of interest rates does NOTmean that spot future in the future will change accordingly.

and are different quantities (the later is stochastic).

When the IRP is violated, one can get a risk-free profit by exploiting thegap. This situation is called covered interest rate arbitrage.


($/Eu)F

($/Eu)FS($/Eu)

($/Eu)F

S($/Eu)rr $eu

12

12

12

−=−

($/Eu)F

($/Eu)FS($/Eu)rr $eu

12

12−=−

𝐹12($/𝐸𝑢) 𝑆12($/𝐸𝑢)

Covered Interest Arbitrage (CIA)

Example: Suppose that

r$ = 5% and r£ = 8%, S($/£) = 1.5 and F12($/£) = 1.48

Assume that an investor in NY up to $1 mil.

1. First we note that the IRP does not hold:

(F12/S)x(1+r£) = 1.0656 > (1+r$) = 1.05.

2. Borrow $1 mil. at r$.

3. Buy £666,667 in London and invest them at r£.

After a year:

1. Get £720,000=666,667(1.08).

2. Sell the pounds forward in exchange for $1,065,600= £720,000xF12.

3. Return in NY bank $1,050,000.

Risk-free profit = $1,065,600 - $1,050,000 = $15,600.


Facts about IRP

➢ The IRP is one of the best-documented relationships in international

finance.

➢ The CIA does not last for long. As soon as investors get informed

about this opportunity the gap in IRP will immediate close.

➢ The IRP may not hold (precisely) all the time due to two basic

reasons:

1. Transaction costs (there is a spread in borrowing and lending

interest rates and in the spot and forward exchange rates).

2. Capital controls or threat of them, (governments’ restriction rules,

e.g. taxes, bans).

3. Control of risks (default risk may be a reason for not exploiting the

CIA). If default risk is significant, CIA is not a real arbitrage. In

fact, CIA is a way to speculate on the creditability of borrowers.

Could IRP be used to forecast spot exchange rates in the future?


Purchasing Power Parity (PPP)

The Purchasing Power Parity, PPP, (ισοδυναμία της αγοραστικήςδύναμης) states that the exchange rate between the domestic and aforeign currency will adjust to reflect changes in the price levels of thetwo countries.


k

j

Ni

ikjSkjS

+

+=

1

1)/()/(

The (relative) version of the PPP is given in the following equation:

where, SN(j/k) is the spot exchange rate after N months and ij and ik arethe rates of inflation for the two currencies for N months.

The PPP is sometimes written in the following equivalent form:

where, eN stands for the change rate in the exchange rate in N months.k

kj

Ni

iie

+

−=

1

Facts about PPP

➢ PPP states that the exchange rate changes may indicate nothingmore than the difference in the inflation rates between countries.

➢ If PPP holds, the differential inflation rates between countries areexactly offset by exchange rate changes. Hence, the counties’competitive positions in the world export market will not besystematically affected by the exchange rate changes.

➢ If PPP doesn’t hold, fluctuations in the exchange rates change thereal exchange rate.

The real exchange rate can be defined as follows:

It measures the deviations of the PPP.

qN different than 1 implies changes in the counties’ competitiveness.

➢ In reality PPP is usually violated. Why?

➢ Even if PPP may not hold, it still very useful (used as benchmark forcurrency valuations and for comparisons).


)1(

)1(

)/(

)/(

)1)(1(

1

k

j

NkN

j

Ni

i

kjS

kjS

ie

iq

+

+=

++

+=

The Fisher Effects

The Fisher Effect states that an increase (decrease) in the expected

inflation rate in a country will cause a proportionate increase (decrease)

in the interest rate in the country.


More precisely, the Fisher Effect (FE) states that the interest rate in acountry (currency) r is made up two components:

or equivalently:

where, ρ is the real (required) rate of return and E[i] is the expectedinflation rate.

➢ In the generalized version of the Fisher effect, among the countriesbetween which there is no capital restrictions and risk differences, thereal interest rate should be the equal: ρj = ρk.

➢ Currencies with high inflation should bear high nominal interest rates.

])[111 iE(ρ)(r ++=+

][][][ iEρiEρiEρr +++=

The Fisher Effects cont’d

ρj = ρk implies that:

i.e. currencies with high rates of inflation should bear higher interest

rates than currencies with lower rates of inflation (and similar

creditability).

29

][][ jkjk iEiErr −−

When we apply the above equation into the PPP we get the following

approximation:

The above relationship is called the International Fisher Effect (IFE).

12/

1

1)/()]/([

N

k

j

Nr

rkjSkjSE

+

+

➢ Combination of IFE and IRP implies that FN can be seen as an estimation of SN.

➢ Empirical evidence shows that IFE holds in long run (currencies with high interest

rates tend to depreciate).

➢ Deviation of the IFE may be caused by capital movements of investors that take

advantage of the interest rate differentials (the carry trade strategy for instance).

Bibliography

• C. Eun & B.G. Resnick: ‘International Financial Management’, 5th

ed., Chapters 4, 5 and 13.

• A.C. Shapiro: ‘Multinational Financial Management’, 10th ed.,

Chapters 2, 4, 7 and 10.


Section 1 Foreign Exchange Markets · Capital Markets The FOREX Markets Μ. Anthropelos, Ph.D. 4....

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