Chapter 4
Foreign Exchange, Eurocurrencies,
and Currency Risk Management
The Eurocurrency Market
The Foreign Exchange Market
Foreign Exchange Rates and Quotations
Exposure to Currency Risk
Hedging Transaction Exposure
with Forward Contracts
The Empirical Behavior of Exchange Rates
Summary
Symbols
Upper Case Symbols = Prices
lower case symbols = changes in a price
Ptd = price of an asset at time t in currency d
itd = nominal interest rate in currency d during period t
td = real interest rate in currency d during period t
ptd = inflation in currency d during period t
Std/f = spot exchange rate at time t between d and f
std/f = change in the spot rate during period t
Ftd/f = forward exchange rate between d and f
The Fisher equation
(1+i) = (1+)(1+p)
For domestic (d) and foreign (f) currencies
id and if = nominal interest rates in the domestic and foreign currencies
pd and pf = inflation rates in the domestic and foreign currencies
d and f = real interest rates in domestic and foreign currencies
Foreign exchange (fx) markets
Markets
Spot market
Trade in cash with delivery in two business days
Forward market
Trade at a pre-specified price and on a pre-specified future date
Volume
$ trillion average daily volume during 2001
75% of trade is in the interbank market
Global foreign exchange turnover
(Average daily central bank volume during April)
Source: Bank for International Settlements (BIS) triennial survey of central banks.
FX turnover by currency
Source: Bank for International Settlements (), March 2002.
Percentages sum to 200 because two currencies are involved in each transaction.
Major fx trading centers
Source: Bank for International Settlements (), March 2002.
Participants in the fx market
Wholesale market
Dealers (or market makers)
Buy and sell at quoted bid and offer prices
Brokers
Serve as matchmakers, without putting their own money at risk
Retail market
Governments
Corporations
Smaller financial institutions
Individuals
FX turnover by counterparty
Source: Bank for International Settlements (), March 2002.
Two rules for multinational finance
Rule #1 Keep track of your units
Rule #2 Always buy or sell the currency in the denominator of a foreign exchange quote
Rule #1 Keep track of your units
A bottle of Georges de Bouef merlot
Buy 1 bottle of wine P€ = €40/btl
Spot exchange rate S$/€ = $
Û S€/$ = 1/S$/€ = €
How much is this in dollars?
P$ = P€S$/€ = (€40/btl) ($ = $32/btl
= P€/S€/$ = (€40/btl) / (€ = $32/btl
Rule #1 Keep track of your units
A bottle of Georges de Bouef merlot
Buy 1 bottle of wine P€ = €40/btl
Spot exchange rate S$/€ = $
Û S€/$ = 1/S$/€ = €
How much is this in dollars?
P$ = P€ S€/$ = (€40/btl) (€
= €250 / (btl-$) ???
Keep track of your currency units!
Rule #2 Think of buying or selling
the asset in the denominator
Buying and selling a bottle of wine
Buy a bottle at €40/btl and sell at €50/btl
Þ €10/btl profit
Buying and selling euros
Buy €s at $ and sell at $
Buy €s at $ º Sell $s at €
Sell €s at $ º Buy $s at €
Þ $ profit Þ € profit
An example of what can go wrong
Buy $s at $ and sell $s at $
But, if you are buying dollars you are selling euros…
Buy $s at $ º Sell €s at €
Sell $s at $ º Buy €s at €
Þ $ loss Þ € loss
Always think of buying or selling
the currency in the denominator!
FX quotation conventions
(or, variations of Rule #2)
European/American quotes for the $
European quotes are convenient for a European because they place the foreign currency (the $) in the denominator
. €
American quotes are convenient for an American because they place the foreign currency (the €) in the denominator
. $
FX quotation conventions
(or, variations of Rule #2)
Direct/indirect quotes for foreign currency f
Direct quotes are convenient for a domestic resident because they place the foreign currency in the denominator (d/f);
. ¥ for a resident of Japan
Indirect quotes are inconvenient for a domestic resident because they place the foreign currency in the numerator (f/d);
. ¥ for a resident of Europe
Percentage forward
premiums or discounts
= (F1d/f - S0d/f ) / S0d/f
Forward premium
Nominal value in the forward exchange market is higher than in the spot exchange market
Forward discount
Nominal value in the forward exchange market is lower than in the spot exchange market
An example of a
forward premium
Suppose
S0$/DKr = $ and F1$/DKr = $
Danish kroner forward premium
= ($ -$
= +25%
so the Danish krone is selling at a
25% forward premium
An example of a
forward discount
Alternatively
S0DKr/$ = Û S0$/DKr = $
F1DKr/$ = Û F1$/DKr = $
Dollar forward premium
= (DKr4/$-DKr5/$)/(DKr5/$)
= -20%
so the dollar is selling at a
20% forward discount
Exposure to currency risk
Currency risk
The risk of unexpected changes in foreign exchange rates
Exposure to currency risk
The MNC has an exposure to fx risk when the value of assets or liabilities can change with unexpected changes in fx rates
Percentage changes in fx rates
Percentage change in the value of a foreign currency
= (S1d/f - S0d/f ) / S0d/f
= s1d/f
An example of change in a fx rate
Percentage change in the Danish kroner
S0$/DKr = $
S1$/DKr = $
s$/DKr = percentage change in the kroner
= (S1$/DKr-S0$/DKr ) / S0$/DKr
= ($ / ($
= +25%
An example of change in a fx rate
Percentage change in the . dollar
S0$/DKr = $ Û S0DKr/$ = DKr5/$
S1$/DKr = $ Û S1DKr/$ = DKr4/$
sDKr/$ = percentage change in the dollar
= (S1DKr/$-S0DKr/$ ) / S0DKr/$
= (DKr4/$-DKr5/$)/(DKr5/$)
= -20%
What goes up must come down
(and vice versa)
(1+sd/f) = 1 / (1+sf/d)
Example
100
100
80
125
+25%
+25%
-20%
-20%
An example of fx exposure
A . firm expects to receive 40,000 Polish zlotys (Z) in one year
The spot rate expected to prevail in one year is E[S1$/Z] = $
What effect will an actual spot rate of S1$/Z = $ have on the firm?
An example of fx exposure
Expected receipt
at E[S1$/Z] = $
Actual exchange
at S1$/Z = $
Net loss from
original position
Risk (or payoff) profile
of underlying exposure
DV$/Z
DS$/Z
-$
-$
+ slope
-$2,000
+Z40,000 +$8,000 at $
+Z40,000 +$10,000 at $
Currency hedging with forwards
Buy $10,000 forward
at F1$/Z = $
Sell Z40,000 forward
Market exchange of Z
for $ at S1$/Z = $
Net gain on forward
Risk profile of a
forward contract
DV$/Z
DS$/Z
-$
+$
- slope
+$10,000
-Z40,000
-Z40,000
+$8,000
+$2,000
Net currency exposure
Underlying position
(long zlotys)
Sell zlotys forward
(short zlotys and long dollars)
Net position
Net exposure
DV$/Z
long zlotys
DS$/Z
short zlotys
+Z40,000
+$10,000
-Z40,000
+$10,000
Types of exposure to currency risk
Economic exposure
Change in the value of all future cash flows from unexpected changes in exchange rates
Transaction exposure
Change in the value of contractual cash flows from unexpected changes in exchange rates
Operating exposure
Change in the value of noncontractual cash flows from unexpected changes in exchange rates
Types of exposure to currency risk
Translation (accounting) exposure
Change in financial statements from unexpected changes in exchange rates
Economic exposure
Real
assets
Monetary
assets
Common
equity
Monetary
Liabilities
A survey of corporate treasurers
Transaction exposure
Operating exposure
Translation exposure
Mean score
Key: 1 = strongly agree ... 3 = neutral
… 5 = strongly disagree
“Managing ______ is important.”
A survey of corporate treasurers
Transaction exposure is viewed by corporate treasurers as the most important currency risk exposure
Source: Jesswein, Kwok and Folks, “Adoption of Innovative Products in Currency Risk Management: Effects of Management Orientations and Product Characteristics,” Journal of Applied Corporate Finance (1995).
The empirical behavior
of exchange rates
Statistical thinking will one day be as necessary for efficient citizenship as the ability to read and write.
. Wells
Behavior of nominal exchange rates
Instantaneous exchange rate changes are approximately normally distributed
At each point in time, exchange rate variance is autoregressive (that is, it depends on previous variances and changes in exchange rates)
Autoregressive conditional heteroscedasticity
A complicated term for a simple idea…
Variance
depends on is conditional on
previous autoregressive
variance heteroscedasticity
Modeling variances with GARCH
st2 = a0 + Si ai st-i2 + Sj bj st-j2
The conditional estimate of variance st2 depends on previous variances (st-i2) and squared spot rate changes (st-j2)
Persistence: The st-i2 smooth the process so that it is not overly sensitive to recent changes in the spot rate
Sensitivity: The st-j2 force variance to respond to recent changes in the spot rate
This chapter describes the foreign exchange and Eurocurrency markets, and introduces the topics of fx risk and fx risk management.
Students can download an Adobe Acrobat .pdf file with a foreign exchange trading game (“The foreign exchange market game”) from my website at This exercise has been a big hit in my classes. It is both fun and useful.
It allows students to practice trading foreign exchange, particularly in following Rule #1 (Keep track of the currency being bought or sold) and dealing with bid and ask prices.
It helps develop intuition regarding market forces, including arbitrage.
Instructors can receive the same Powerpoint slideshow with suggestions for running the game (hidden in the Notespages) by contacting me directly at butler@.
In international finance, it is imperative to keep track of your currencies. For this reason, these symbols explicitly list the relevant currencies.
Begin this chapter by defining these symbols. A few additional symbols are introduced in later chapters.
The symbol ι representing a real interest rate is pronounced “iota.”
In Chapter 6 on currency futures, we’ll also need the change in a forward (or futures) price during period t, ftd/f.
Example: The nominal euro rate on a 1-year deposit is 6%. Expected inflation is 4%. What is the expected real return?
Solution: The approximate expected real return is 6%-4% = 2%. More precisely, from the Fisher Equation,
= (1+) => = ( = , or %.
When interest rates are low, the approximation provides a answer that is close to the exact answer.
Example: The nominal peso interest rate on a one-year deposit is 60%. Expected inflation is 50%. What’s the expected real return?
Solution: The approximate expected real return is 60%-50% = 10%. More precisely, from the Fisher Equation,
= (1+) => = ( = , or %.
The Fisher equation is most useful when interest rates are high.
Markets: About 60% of the volume in the foreign exchange market is conducted in the forward market (which includes currency swap transactions).
The next slide displays spot, forward, and swap (forward) transaction volume over time.
Volume: Average daily volume was $ trillion in the April 2001 Bank for International Settlements (BIS) survey of central banks. For comparison, . gross national product was $ trillion in 2001.
Transactions in the interbank market comprise about 75% of all foreign exchange transactions.
The major banks’ remaining business is with retail customers including governments, business, and smaller financial institutions.
This is Figure from the text.
Global forex volume fell from $ trillion per day in the 1998 BIS survey to $ trillion in 2001.
Much of this decrease was attributable to the introduction of the euro, which replaced the national currencies of Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal, and Spain.
With the elimination of cross-currency trading within these countries, average daily volume fell from $332 billion in 1998 to $234 billion in 2001 within the euro-zone countries.
This is Figure from the text.
Because two currencies are involved in each foreign exchange transaction, the sum of these percentages sum to 200 percent rather 100 percent.
Percentages are capped at 100%, so the . dollar was involved in 90 percent of all interbank fx transactions.
This is Figure from the text.
The major trading centers within each area are located in
London
New York
Frankfurt and Paris
Tokyo
Active foreign exchange markets are also conducted in
Singapore
Hong Kong
Zurich
and other regional money centers
Foreign Exchange Dealers and Brokers
The interbank market makes up about 75% of all fx transactions.
Retail customers include governments, companies, domestic banks, investment funds, and individuals.
Spot trades are conventionally settled within 2 business days. Forward transactions are settled on the pre-arranged contract date plus two days.
Most customers prefer to settle only the gain or loss on a forward contract. Others settle the full amount. This is negotiated with the bank.
Dealers earn their profit on the bid-ask spread. Bid-ask spreads depend on 1) the size of the transaction, 2) the volatility of the exchange rate, and 3) liquidity in the market.
Just for fun (not in the text)
The text says that bid-ask spreads can be as low as 10 basis points (%) for large interbank transactions. In fact, spreads have fallen in the last ten years as major banks have adopted electronic trading platforms. Spreads are now as low as 2 basis points (%) for a benchmark $1 million transaction. (The median retail transaction is about $1 million in value.)
This is Figure from the text.
Source: Bank for International Settlements () Triennial Central Bank Survey, March 2002.
This is from Section .
These are the most useful rules-of-thumb in the entire book.
These rules seem obvious.
Nevertheless, they are students’ most reliable weapon in the fight against calculation errors in this and in later chapters.
The currency that is being referred to in a foreign exchange bid or offer quote is called the currency of reference or referent currency.
This is an example of what can go wrong when Rule #1 is not followed.
This calculation is simple when you follow Rules #1 and #2.
The next slide shows what can go wrong.
All the usual rules and intuition are reversed when you inadvertently think of the currency in the numerator as the asset being bought or sold.
For example, the phrase “buy high and sell low” (?!) is counter-intuitive, but is the correct way to go for the currency in the numerator.
It is easy to remember the two most common fx quotation conventions if students follow Rule #2 (place the currency of reference in the denominator).
European versus American quotes for the US $
A European quote is convenient for a European because it places the foreign currency (the . dollar) in the denominator; . €
An American quote is convenient for an American because it places the foreign currency (. the euro) in the denominator; . $
Direct v indirect quotes for foreign currency f
This convention relies on domestic-v-foreign, rather than on the . dollar.
A direct quote is convenient (d/f) for a domestic resident because it places the foreign currency in the denominator;
. ¥ for a resident of Japan
Indirect quotes are inconvenient (f/d) for a domestic resident because it places the foreign currency in the numerator;
. ¥ for a European resident
Neither quotation convention applies for cross-exchange-rate quotes of two foreign currencies, neither of which is the dollar.
Remind the students of Rule #2: This equation only holds for the foreign currency in the denominator of the foreign exchange quote.
When one currency is at a premium, the other must be at a discount.
(See next slide.)
After putting up this slide, challenge the students’ understanding with the following problem:
S0Ruble/$ = Ruble 5/$ Û S0$/Ruble = $
F1Ruble/$ = Ruble 6/$ Û F1$/Ruble = $
Is the ruble selling at a forward premium or discount?
To answer this correctly, follow Rule #2: “Always think of the currency in the denominator of a foreign exchange quote.”
The dollar (in the denominator) is selling at a forward premium.
Dollar’s forward premium = (R6/$-R5/$) / (R5/$) = +20%.
The ruble (in the numerator) must be selling at a forward discount.
Ruble’s forward premium = ($ / ($ = ,
or percent.
Risk exists whenever actual outcomes can differ from expectations.
Chapter 1 introduced the distinction between risk and exposure to risk.
Chapter 1 also introduced two related types of country risk.
Political Risk. The risk that the business environment in a host country will change unexpectedly due to political events.
Financial Risk. The risk of unexpected change in the financial or economic environment of a host country.
Currency risk is one of the most important financial risks of multinational operations.
Again, remind the students of Rule #2: This equation only holds for the currency in the denominator of the quote.
This is easy, because the currency of reference (the kroner) is already in the denominator of the fx quotes.
Challenge the students’ understanding with the following:
Given S0DKr/$ = DKr5/$ and S1DKr/$ = DKr8/$, what is the percentage change in the nominal value of the franc?
This requires that students translate exchange rates into direct terms so that the franc is in the denominator:
S0DKr/$ = DKr5/$ Û S0$/DKr = $
S1DKr/$ = DKr8/$ Û S1$/DKr = $
The percentage change in the kroner (in the denominator) is then ($ / $ = %, or percent.
Conversely, the dollar has appreciated by (DKr8/$-DKr5/$) / DKr5/$ = +, or +60 percent.
This visual device is sometimes easier than remembering Equation : (1+s$/¥) = 1/(1+s¥/$)
Suppose the yen-per-dollar rate starts out at ¥100/$ and rises to ¥125/$.
On the way up the hill, the dollar gains 25 percent.
On the other side of the hill, the drop from 125 to 100 corresponds to a change of (100-125)/125 = , or -20 percent in the value of the yen.
Consequently, if the dollar in the denominator has appreciated by 25 percent, then the yen must have depreciated by 20 percent.
This can be verified with Equation : (1+s$/¥) = 1/(1+s¥/$)
s$/¥ = 1/()-1 = , or -20 percent.
The . firm is receiving Polish zlotys, so what is good for the zloty is good for the . firm. That is, the . firm is positively exposed to the zloty.
In the underlying exposure, the foreign currency is being received.
Foreign currency cash inflows are positively exposed to foreign currency values.
Hence, the slope of the risk profile is positively sloped.
This relationship holds for direct, $/Z exchange rates.
If indirect terms are used, the risk profile looks like this.
What’s good for the zloty is good for the firm.
Conversely, what’s good for the dollar (and bad for the zloty) is bad for the dollar-per-zloty value of the firm (and good for the zloty-per-dollar value of the firm.
vZ/$
sZ/$
Exposure of a zloty cash inflow in indirect terms
In this forward contract, the foreign currency is being sold.
Foreign currency cash outflows are negatively exposed to foreign currency values.
Hence, the slope of the risk profile is negatively sloped.
Again, this is only true when exchange rates are stated in direct terms.
The forward contract provides a perfect hedge because the values of both the underlying exposure and the forward contract are derived from the same underlying asset price - the dollar value of the Polish zloty.
Monetary assets and liabilities are contractual and thus primarily affected by changes in nominal exchange rates.
Real assets are noncontractual and are thus primarily affected by changes in real (or inflation-adjusted) exchange rates; that is, changes in currencies’ relative purchasing power.
Each of these currency risk exposures is discussed in depth in later chapters of the text.
Chapter 9 The rationale for hedging currency risk
Chapter 11 Transaction exposure
Chapter 12 Operating exposure
Chapter 13 Translation exposure
Accounting (translation) exposure refers to changes in financial accounting statements as a result of changes in currency values.
Accounting exposure arises as the parent translates financial accounting statements of foreign subsidiaries back into its domestic currency.
Accounting exposure may or may not be related to cash flows and value.
Although accounting exposure may not be of direct concern to debt and equity stakeholders, it is vitally important to the managers of the firm.
Performance evaluation and compensation are often tied to accounting performance, so managers have a strong incentive to minimize their accounting exposure.
Debt and equity investors should be concerned with accounting exposure to the extent that managers change their actions based on own accounting exposures
Two related measures of exposure are relevant:
Net monetary assets are monetary assets less monetary liabilities
The exposure of common equity is a combination of the transaction exposure of monetary assets and liabilities and the operating exposure of real assets.
Translation exposure is considered to be of lesser importance, at least in the United States.
We’ll return to this topic in the chapter on Translation Exposure to Currency Risk.
Operating exposure is a more pervasive risk than transaction exposure in that it affects the firm’s operations and not just a few transactions.
Transaction exposure is important to managers because it is easily more apparent. This reminds one of the following story:
A drunk loses his car keys in a field one evening.
The drunk staggers over to a nearby street lamp
and begins looking for his keys under the light.
When his companion asks why he isn’t looking
for his keys in the field, the drunk responds
“I can’t see over there.”
This quote leads into the slides on the behavior of exchange rates, which require a bit of statistics.
Just for fun (not in the text)
In fact, changes in fx rates are leptokurtic or fat-tailed relative to the normal distribution. This is true of most financial prices.
Leptokurtosis is discussed in Chapter 20 in the context of continuously compounded returns to international stock market returns.
Although the normal distribution is not a perfect fit to exchange rate changes, it is a close approximation after adjusting for the conditional nature of exchange rate variances.
Exchange rate variances are commonly modeled as an ARCH process, which stands for “Autoregressive Conditional Heteroscedasticity.”
A general form of the ARCH model is the GARCH (generalized autoregressive conditional heteroscedasticity) model on the next slide.
GARCH models assume that conditional variance is a function of previous variances and previous squared spot rate changes.
(See the next slide.)
GARCH(p,q) general form:
At each point in time, this GARCH process is normally distributed with variance st2.
Variance depends on the recent history of variances st-i2 and squared spot rate changes st-j2.
The variables p and q identify the maximum number of lags that influence the variance through previous variances and squared spot rate changes.
The summation with the squared spot rate changes forces the variance at time t to respond to recent changes in the spot rate.
The summation with the lagged variances i=1,...,p ‘smoothes’ the process so that it is not overly sensitive to the most recent squared spot rate changes.
GARCH is usually applied with a single lag in a GARCH(1,1) model:
