Foreign Exchange Risk
Sources of FX Risk
 On-balance-sheet: FI may have assets or liabilities denominated in foreign currency
 Buy financial assets (bonds, loans) denominated in foreign currencies to receive high
returns
 Issue financial liabilities (CDs, bonds) denominated in foreign currencies to raise
fund
 Trading activities:
 Purchase and sale of currencies to complete international transactions
 Facilitating positions in foreign real and financial investments
 Accommodating hedging activities
 Speculation
 Off-balance-sheet: Forward positions denominated in foreign currency
 Mismatches between foreign asset and liability portfolios
Net exposure = (FX assets - FX liab.) + (FX bought - FX sold)
FX Risk Exposure
 Exposure to a foreign currency can be measured by DEAR.
 Dollar loss/gain in currency i
= [Net exposure in foreign currency measured in U.S. $] × Volatility of the
foreign exchange rate
 Example:
An FI has $100,000 of net positions outstanding in EUR and -$30,000 in Swiss
Franc (SF). The standard deviation of the net positions as a result of exchange rate
changes is 1 percent for the EUR and 1.3 percent for the SF. The correlation
coefficient between the changes in exchange rates of the EUR and the SF is 0.80.
a. What is the risk exposure to the FI of fluctuations in the EUR/$ rate?
Since the FI has a positive EUR position, an appreciation of the EUR will increase
the value of its EUR-denominated assets more than its liabilities, providing a net
gain. The opposite will occur if the EUR depreciates.
b. What is the risk exposure to the FI of fluctuations in the SF/$ rate?
Since the FI has a negative net position in FFs, the value of its Frenchdenominated assets will increase in value but not as greatly as the value of its
liabilities. Hence, an appreciation of the FF will lead to a net loss. The opposite will
occur if the currency depreciates.
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 Return of foreign investments
 Returns are affected by:
 Spread between costs and revenues
 Changes in FX rates: Changes in FX rates are not under the control of the FI
 Example:
Sun Bank USA purchased a 10.5 million one-year euro loan that pays 10 percent
interest annually. The spot rate for euro is EUR1.05/$. Sun Bank has funded this
loan by accepting a British pound (BP)-denominated deposit for the equivalent
amount and maturity at an annual rate of 6 percent. The current spot rate of the
British pound is $1.50/£.
a. What is the total income earned in dollars on this one-year transaction if the
spot rates at the end of the year are EUR1.00/$ and $1.60/£?.
b. What should be the BP to US $ spot rate in order for the bank to earn a return
of 4 percent?

Risk and Hedging
 Hedge can be constructed on balance sheet or off balance sheet
 On - balance-sheet hedge will also require duration matching to control exposure
to foreign interest rate risk
 Off-balance-sheet hedge using forwards, futures, or options
 Example:
North Bank has been borrowing in the U.S. markets and lending abroad, thus
incurring foreign exchange risk. In a recent transaction, it issued a one-year $2
million CD at 2 percent and funded a loan in euro at 8 percent. The spot rate for
the euro was EUR1.05/$ at the time of the transaction.
a. Information received immediately after the transaction closing indicated that
the euro will depreciate to EUR1.10/$ by year-end. If the information is
correct, what will be the realized spread on the loan? What should have been
the bank interest rate on the loan to maintain the 2 percent spread? Assume
adjustments in principal value are included in the spread.
b. The bank had an opportunity to sell one-year forward euro at EUR1.08. What
would have been the spread on the loan if the bank had hedged forward its
foreign exchange exposure?
c. What would have been an appropriate change in loan rates to maintain the 2
percent spread if the bank intended to hedge its exposure using the forward
rates?
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
Interest rate parity condition
 Equilibrium condition is that there should be no arbitrage opportunities available
through lending and borrowing across currencies. This requires that
F £/$= S£/$ [1+r (£ or foreign)] /[1+r($ or domestic)]
 Difference in interest rates will be offset by the expected change in exchange rates
 Example:
Assume that annual interest rates are 6 percent in the United States and 2 percent in
Japan. An FI can borrow (by issuing CDs) or lend (by purchasing CDs) at these rates.
The spot rate is ¥100/ $.
a. If the forward rate is ¥102/ $, how could the bank arbitrage using a sum of $1million?
What is the expected spread?
Borrow ¥100,000,000 in Japan by issuing CDs
 Interest and principal at year-end = ¥100,000,000 x 1.02 = ¥102,000,000
Make a loan in US
 Interest and principal = $1,000,000*1.06 = $1,060,000
Purchase ¥ at the forward rate of $1,060,000x¥102/ $ = ¥108,120,000
Spread =¥108,120,000 - ¥102,000,000 = ¥6,120,000 (6.12%)
b. What forward rate will prevent an arbitrage opportunity?
The forward rate that will prevent any arbitrage is given by solving the following
equation:
Ft = [(1 + 0.02) * 100]/(1.06) = ¥96.23/ $

Classroom problem:
A money market mutual fund manager is looking for some profitable investment
opportunities and observes the following one-year interest rates on government securities
and exchange rates: rUS = 12%, rUK = 9%, S = $1.50/£, f = $1.6/£, where S is the spot
exchange rate and f is the forward exchange rate. Which of the two types of government
securities would constitute a better investment?
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