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The Foreign Exchange Market. Explain how the foreign exchange rate reflects the demand and supply of goods, services, and assets, and the other flows that make up the balance of payments. Explain geographic arbitrage, triangular arbitrage, and intertemporal arbitrage.

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the foreign exchange market
The Foreign Exchange Market
  • Explain how the foreign exchange rate reflects the demand and supply of goods, services, and assets, and the other flows that make up the balance of payments.
  • Explain geographic arbitrage, triangular arbitrage, and intertemporal arbitrage.
  • Do the spot and forward foreign exchange markets and derive the interest parity condition.
  • Explain foreign exchange risk and how to hedge risk.
  • Describe effective exchange rates.

** -- next week

the foreign exchange market2
The Foreign Exchange Market
  • Most international transactions require the exchange of national currencies.
  • Foreign Exchange Markets are the markets where the many different national currencies are exchanged.
  • Changing foreign exchange rates add to the risk of many foreign transactions.
  • In markets where the forces of supply and demand are free to drive the prices of currencies, the exchange rates are said to float.
  • Some countries try to fix the value of their currencies at some target rate, often by by selling or buying currencies in the foreign exchange markets to neutralize shifts in supply and demand.
the evolution of the foreign exchange market
The Evolution of the Foreign Exchange Market
  • Markets for foreign exchange have operated for over two thousand years, ever since there have been distinct national moneys.
  • Early money changers carefully weighed and examined coins in order to determine their true gold or silver content.
  • The development of modern banking brought the exchange of bills rather than actual coins made of precious metals.
  • With the exchange of paper, money changers had to consider the reputation of the banks that issued the paper.
the evolution of the foreign exchange market4
The Evolution of the Foreign Exchange Market
  • The advent of paper or fiat money made the job of the money changer much more difficult and increased the risk of holding different national moneys.
  • The relative value of each fiat money depends on what it, and all other currencies, can buy currently and is expected to buy in terms of real goods and services in the future.
  • Expectations depend on a variety of information about current policies and about likely political and economic developments in the future.
  • Expectations are subject to constant revision as news about political and economic events becomes known. News is, by definition, unpredictable
  • Whenever expectations change, the exchange rate changes.
foreign exchange markets today
Foreign Exchange Markets Today
  • Nearly all of the trillion dollars worth of currencies that are exchanged every working day are traded in the over-the-counter market.
  • Worldwide, 2,772 dealer institutions reported that they were active in the foreign exchange markets in 2000.
  • According to the Federal Reserve Bank of New York, there were 93 major foreign exchange dealers operating in the United States in 1998, 82 of which were large commercial banks.
  • There were 213 major dealers in London, the most important center for foreign exchange transactions.
table 12 3 currencies involved in foreign exchange market trading
Table 12.3Currencies Involved in Foreign Exchange Market Trading

Currency Percent in: 1989 1992 1995 1998 2001

U.S. dollar 90% 82.0% 83.3% 87.3% 90.4% **

Deusche mark 27 39.6 36.1 30.1

Japanese yen 27 23.4 24.1 20.2 22.7

British pound 15 13.6 9.4 11.0 13.2

Swiss franc 10 8.4 7.3 7.1 6.1

French franc 2 3.8 7.9 5.1

Canadian dollar 1 3.3 3.4 3.6 4.5

Australian dollar 2 2.5 2.7 3.1 4.2

Euro - - - - 37.6

All others 26 23.4 25.8 32.5 21.3

Total 200% 200% 200% 200% 200%

Source: BIS (2001), Central Bank Survey of Foreign Exchange and Derivatives Market Activity, Basle: BIS

**Note the role of the $ as a “vehicle currency.”

table 12 5 global foreign exchange market turnover daily averages on april 1 us billions
Table 12.5Global Foreign Exchange Market Turnover(Daily Averages on April 1, $US billions)

1989 1992 1995 1998 2001

Spot Transactions 317 394 494 568 387

Forward Transactions 27 58 97 128 131

Foreign Exchange Swaps 190 190 324 546 734

Total Turnover1 590 820 1,190 1,490 1,210

1 Total is greater than sum of the three categories because of gaps in reporting.

Source: BIS (2001), Central Bank Survey of Foreign Exchange and Derivatives Market Activity, Basle: Bank for International Settlements

triangular arbitrage
Triangular Arbitrage
  • Triangular arbitrage involves a third currency and/or market.
  • Arbitrage opportunities exist if an observed rate in another market is not consistent with a cross-rate (ignoring transaction costs).
  • Again, profit opportunities are likely to be arbitraged away quickly, meaning that cross-rates are, for the most part, consistent with observed rates.
triangular arbitrage example
LONDON: The US dollar is trading for 1.7936 ($/£) and the Polish zloty (Z) for 6.5492 (Z/£).

NEW YORK: The zloty (Z) is trading for 3.7826 (Z/$) in New York.

The cross-rate in London is:

=(Z/£)/(S/£) = Z/£ *£/S = (Z/S)= 6.5492/1.7936 =

3.6514 (Z/$) in London Versus 3.7826 (Z/$) in New York.

Hence, an arbitrage opportunity exists, i.e. profitable

Triangular Arbitrage: Example
triangular arbitrage the trip
Triangular Arbitrage –The Trip!

Buy $1.7936 with £1

Start with £1

Buy Z6.7845 with $s

Purchase £s in London using Zs

Purchase Zs in New York

END: Purchase £1.0359 in London using Z6.7845 purchased in New York

Profit = £1.0359 - £1.00 = £0.0359

the process of arbitrage
The Process of Arbitrage
  • Arbitrage effectively combines isolated markets into a single integrated market because profit-seeking arbitrageurs buy where prices are low (SF) and sell where prices are high (NY.)
  • Suppose the two isolated markets for violins are as shown by the supply and demand curves in Figure 12.4.

Spatial Arbitrage refers to buying a currency in one market and selling it in another.

  • Price differences arise from geographical (spatial) dispersed markets.
  • Due to the low-cost rapid-information nature of the foreign exchange market, these prices differences are arbitraged away quickly.
the process of arbitrage12
The Process of Arbitrage
  • Arbitrage by consumers reduces demand for violins in New York and increases demand in San Francisco.
  • If there are no costs to moving violins from San Francisco to New York, then prices will equalize at a single national price of pUSwhere PSF <PUS< PNY
an example the market for mexican pesos
An Example: The Market for Mexican Pesos

Note:e =$/MXP: a ↑e ≈ depreciation of the $ (appreciation of the MXP)

  • The demand curve intersects the supply curve at the price $.10.
  • That is, one peso costs ten U.S. cents or 10 pesos =$1
  • We use the letter e to represent the foreign exchange rate, so that the equilibrium can be written as e = $.10 or its inverse, 1/e = 10 pesos/$
  • The exchange rate between 2 currencies can be stated in 2 ways:

(a) Price of foreign currency in units of domestic currency, $/MXP =e OR

(b) price of domestic currency in terms of foreign currency, MXP/$ =1/e

an example an increase in demand for pesos
An Example: An Increase in Demand for Pesos
  • If holders of dollars want to engage in more foreign transactions that require Mexican pesos, the demand for pesos will increase.
  • Such an increase in demand for pesos will cause the dollar to depreciate (from $0.10 to $0.1250) and the exchange rate e to rise, all other things equal. In the example shown, e rises from $.10 to $.125 OR the MXP appreciates from $1= 10MXP to $1=8MXP
the foreign exchange market the mexican perspective
The Foreign Exchange Market: The Mexican Perspective
  • The supply curve for dollars is seen as the demand curve for pesos from the Mexican perspective.
  • Similarly, the U.S. demand curve for dollars is the viewed in Mexico as the supply curve of pesos.
  • Thus, the equilibrium exchange rate from the Mexican perspective is 1/e = 1/.10 = 10 pesos.
the foreign exchange market a shift in the supply of pesos
The Foreign Exchange Market: A Shift in the Supply of Pesos

Mexicans supply more pesos because they demand dollars

  • The shift in demand for dollars from the U.S. perspective is a shift in supply of pesos from the Mexican perspective.
  • The shift in supply causes the exchange rate to decline from 10 pesos, or 1/e = 1/$.10, to 1/e = 1/$.125 = 8 pesos.
  • 37.5 million dollars are exchanged for 300 million (8x37.5) pesos.
how many foreign exchange rates are there
How Many Foreign Exchange Rates Are There?
  • There were 216 currencies in the world at the start of 2002.
  • This seems to suggest that there are 216 x 216 = 46,656 different exchange rates.
  • There are actually fewer than 46,656 exchange rates.
  • In general, for n different currencies, there are

[n(n – 1)]/2 different foreign exchange markets.

  • In the real world of 216 countries and moneys, there are therefore [216(215)]/2 = 23,220 foreign exchange rates.
forward exchange markets
Forward Exchange Markets
  • Forward exchange markets are where future foreign exchange transactions are contracted today.
  • The forward exchange rate is the price of one currency in terms of another currency for an exchange that is contractually agreed on today but will not be carried out until some future date.
  • Over half of all transactions on the world’s foreign exchange markets are forward transactions.
  • The forward markets are operated by the same dealers who operate the spot markets.
intertemporal arbitrage
Intertemporal Arbitrage
  • Suppose that you can store your wealth of $100 in assets denominated in U.S. dollars or British pounds.
  • If you purchase dollar-denominated assets in the U.S., the $100 ($wt ) will earn a return of rUS, which means that over the period of one year (intertemporal from Ch.10) your wealth would grow to

$wt+1 = $100(1 + rUS ) =$100 +$100* rUS

given that rUS is the return on U.S. assets.

Decision to Invest at Home or Abroad

  • To decide where to invest your $100, you will have to compare the U.S. returns to what you would end up with after one year if you invested the $100 in Britain.
  • The British investment is somewhat more complex because you will have to pay attention not only to the British rate of return (rUK), but also the spot (e) and future exchange rates (ftt+1).
intertemporal arbitrage20
Intertemporal Arbitrage
  • If you invest in the U.K., you must first convert $’s to £’s.
  • Your wealth in terms of pounds is £wt = $100/et, where et is the spot exchange rate.
  • If rUK is the rate of return on British assets, then after one year your wealth in British pounds will grow to be:

£wt+1 = ($100/et)(1 + rUK).

  • Before you can compare the value of your British investment to the U.S. investment, you must convert the pound value of your investment back to your home currency, dollars, at next year’s exchange rate, et+1. This is either (a) approximated by the forward rate (ftt+1) where possible or (b) approximated by forecasting it to be (Et (et+1) )where Etis expected – based on market participants.
  • If you use the forward market to contract the sale of your pounds one year from now at the forward exchange rate ftt+1, then the dollar value of British investment is:

£wt+1 = £wt+1(ftt+1) = ($100/et)(1 + rUK )(ftt+1 ).

intertemporal arbitrage21
Intertemporal Arbitrage

Now you can compare this dollar value of the British investment to the

dollar value of the U.S. investment:

US → $100(1 + rUS )versus($100/et)(1 + rUK)(ftt+1) ←[UK].

Suppose $100(1 + ↑rUS)< ↓[($100/ ↑et)(1 + ↓rUK)(↓ftt+1)]. With unrestricted

international asset trade, there will be international investment

arbitrage until the inequality becomes an equality, or when

$100(1 + rUS) = ($100/et)(1 + rUK)(ftt+1) ****

Adjustment: (a) UK investors stay home & US investors supply $s to the

US money market and demand £s . The effect is to increase e ($depreciation,

£ appreciation). (b) US investors need to sell £s forward next year and

demand $ (increase in £s; increase demand for $s) – cause ↓ftt+1). Both (a)

and (b) reduce the RHS until **** is established. Note that the interest rates

are affected too (↑rUS as less funds are available in the US money market,

while ↓rUK as more funds are available in the UK money market).

Idea: 4 markets are involved in the adjustment process; UK & US money markets (↑rUS & ↓rUK); Forward & Spot Markets (↓ftt+1 & ↑et)

the interest parity condition
The Interest Parity Condition

The relationship $100(1 + rUS) = ($100/et)(1 + rUK)(ftt+1) can

be rearranged to yield the interest parity condition. Dividing

each side by $100 gives us: (1 + r) = (1/et)(1 + r*)(ftt+1).

Dividing each side by (1 + rUS) and multiplying each side by et

results in:

et = [(1 + rUK)/(1 + rUS)](ftt+1). Let [(1 + rUK)/(1 + rUS)] =μ

Thus, et = μ ftt+1. This states that the relationship of today’s

exchange rate (et) to the forward rate (ftt+1) is a factor μwhich is

a ratio of respective interest rates (or rates of return). This is

known as CIP or CIA because investors can hedge against

future changes in et by using the forward rate ftt+1. It is

“covered” because the use of the forward market eliminates

exchange risk. In the absence of forward market rates, hedging

is not possible. Our best estimate of the future value of the

spot rate uses the expected (Et ) rate, Et(et+1).

the interest parity condition23
The Interest Parity Condition

When there is no forward exchange market, investors must compare

returns across countries using their expectations of the spot rate one year

from now, denoted as Et(et+1). The choice is thus:

US → $100(1 + rUS )versus($100/et)(1 + rUK)(Et (et+1)) ←[UK].

Suppose $100(1 + ↑rUS)< ↓[($100/ ↑et)(1 + ↓rUK)(↓ftt+1)]. Intertemporal

arbitrage will still occur if the difference between the right-hand and left-

hand sides of the relationship is big enough to overcome exchange rate risk.

Arbitrage will occur until the inequality becomes an equality, or when

$100(1 + rUS) ≈ ($100/et)(1 + rUK)(Et (et+1)) ****

Simplifying as before yields:

et = [(1 + rUK)/(1 + rUS)] (Et (et+1)). This is known as the uncovered

Interest parity condition (UIP) or UNCIA or simply as the interest parity

condition. Let [(1 + rUK)/(1 + rUS)] =μ

Thus, et = μ Et (et+1).

This states that unlike before (when we had the forward rate), now the

future exchange rate in the face of our ignorance, depends on expectations

of every investor engaged in buying or selling financial assets and currencies! In a global economy, different cultures, different political

conditions etc and any other idiotic stuff impacts the exchange rate!

a simplified version of the interest parity condition
A Simplified Version of the Interest Parity Condition

(rUS – rUK ) ≈ (Et (et+1) – et)/et = Et(Δe)/et [**)

where the Δ stands for “the change in.”

  • That is, the proportional change expected in the exchange rate is roughly equal to the difference in the interest rates of the two countries.
  • Thus, when arbitrage has equalized the overall returns for domestic and foreign assets, the difference between the rates of return on the assets in the two countries is exactly offset by the expected percentage change in the exchange rate over the period that investors expect to hold the assets. Example:

If Et(Δe)/et >0, there is expected appreciation of the foreign currency (depreciation of the home currency):

Et(Δe)/et =$1.80/£ -$1.60/£]/$1.60/£ *100 = +12.5%. The £ has appreciated by 12.5% against the $. Thus, it pays to invest Abroad.

2. If Et(Δe)/et<0, there is expected depreciation of the foreign currency

Et(Δe)/et=$1.60/£ -$1.80/£]/$1.80/£ *100 =-12.5%. The £ has depreciated by 12.5% against the $. It doesn’t pay to invest abroad.

Numerical Example [**]

Suppose that the interest rate in the United States is higher at 12%

per year (rUS) than the interest rate on British assets at 7% (rUK ).

Suppose also that economic conditions and policies in the two

countries lead investors to expect that the exchange rate will be

$2 dollars = £1, one year from now, so that Et (et+1 )= $2/£1=2.

a numerical example
A Numerical Example

Applying the simplified equation,

(rUS – rUK ) ≈ (Et (et+1) – et)/et = Et(Δe)/et

where Δe =(et+1- et)

  • An interest differential of 5 percent (0.12 - 0.07 = .05)

implies that the dollar is expected to fall by 5 percent over the

coming year.

  • In the case of perfect intertemporal arbitrage, if the spot rate is expected to be $2.00 one year from now, a depreciation of 5

percent implies that the current spot rate must be about

($2.00 x0.05) = 10 cents) so ($2.00- 0.10cents)= $1.90.

there are many future exchange rates
There Are Many Future Exchange Rates

Intertemporal arbitrage links all future exchange rates according

to the interest parity condition.

For example, if the rates of return in the United States and

Britain are expected to be rUS and rUK , respectively, for the

next two periods, then in the case of perfect arbitrage, the

following two-period interest parity condition will hold:

$100(1 + r)2 = ($100/et)(1 + r*)2 Et (et+2)

The spot rate is thus a function of the expected exchange rate

two periods from now:

et = Et (et+2)[(1 + rUK)/(1 + rUS)]2.

In general, for n periods into the future:

et = Et (et+n)[(1 + rUK)/(1 + rUS)]n

there are many future exchange rates27
There Are Many Future Exchange Rates

Note: ↑e – depreciation of $

↓e – appreciation of the £

  • If the exchange rate is expected to depreciate in the future, perhaps because the domestic rate of return is higher than the foreign rate of return, intertemporal arbitrage will tend to generate a time path of expected exchange rates over the next five periods that looks like the upward-sloping green curve.
  • If the exchange rate is expected to appreciate, then the exchange rate will follow a downward sloping path like the red curve.
predicting exchange rate changes
Predicting Exchange Rate Changes
  • The multi-period interest parity condition predicts that a country’s exchange rate will either appreciate or depreciate as time passes, depending on whether rUK > rUS or rUS > rUK,
  • Suppose rUK > rUS then et >Et(et+1), expect the home currency to eventually appreciate.
  • Exchange rates actually fluctuate much more than interest rate differences across countries suggest.
  • Only fundamental shifts in long-run expectations, which imply shifts in the whole long-run time path of exchange rates, can explain the large changes in spot exchange rates that we often observe.
  • Predictions of exchange rate changes therefore must predict changes in long-run expectations, which is an impossible task!
predicting exchange rate changes29
Predicting Exchange Rate Changes

If people set their expectations rationally they will make

use of all relevant information to set their expectations,

which consists of:

  • Their understanding of how foreign exchange rates are determined, that is, their model of exchange rate determination;
  • All available information that helps to put values on the variables in their model of exchange rate determination.

Economists define items 1 and 2 as the information set.

predicting exchange rate changes30
Predicting Exchange Rate Changes

The expected exchange rate at time t + n (n years in the

future), given the current information set Ωt is written as:

Et (et+n | Ωt ).

The information set Ωt of course keeps changing as time passes

as news arrives. The expected exchange rate for the period

t + n at time t will generally not be the same as the expected

exchange rate for period t + n at t +1 because Ωt ≠ Ωt+1.

That is, in general: Et [(et+n)* Ωt ] ≠ Et+1[(et+n)* Ωt+1].

The spot rate will deviate from its long-run time path whenever news

arrives. News is, by definition, unpredictable

Thus, the logical conclusion is that:

In general, when expectations are rationally set and the interest parity

condition holds (international investment is not restricted), future changes

in the exchange rates are unpredictable.

effective exchange rates
Effective Exchange Rates

The exchange rate between just two currencies tells a firm little

about an economy’s competitive position in the global

economy.

Many government agencies and private financial firms compile

broader exchange rate measures that attempt to capture the

overall value of a country’s currency vis-a-vis many countries.

Effective exchange rates are weighted averages of sets of foreign exchange rates.

The U.S. Federal Reserve Bank compiles several effective

exchange rates, including the Broad Dollar Index, the Major

Currencies Dollar Index, and the Other Important Trading Partners Dollar Index.

table 12 12 trade weights for u s dollar effective exchange rate indexes 1997
Table 12.12Trade Weights for U.S. Dollar Effective Exchange Rate Indexes, 1997

Broad Major Other Trading

Currencies Partners

Canada 17.3 30.3 -

Euro Area 16.4 28.7 -

Japan 14.6 25.6 -

Mexico 8.6 - 19.9

China 6.6 - 15.3

U.K. 4.6 8.0 -

Taiwan 3.9 - 9.1

Korea 3.7 - 8.6

Singapore 3.1 - 7.2

Hong Kong 2.8 - 6.6

Malaysia 2.4 - 5.5

Brazil 1.9 - 4.4

Switzerland 1.8 - -

Other 12.3 4.2 23.4

effective exchange rates33
Effective Exchange Rates
  • Each of the Fed’s three effective exchange rates behaved very differently over the past 25 years.
  • The Figure also shows how volatile exchange rates have been over the past 25 years.
  • Notice that even the effective exchange rates of the United States dollar have fluctuated widely, changing by more than 10 percent in many years.