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because some foreign exchange transactions are relatively rare, making it more difficult
to exchange currency directly. When a third currency is used in these types of
5 Arbitrage and Interest Rates
Recall that most foreign currency operations involve bank deposits. A bank deposit is an
asset that generates interest for the depositor. The decision of where to maintain deposits
is largely a matter of convenience for most. However, for investors, this decision is
driven by the desire to generate a profit, or arbitrage.
The key difference between bank deposits at home and abroad is exchange rate risk.
To hedge against exchange rate risk, investors can use derivatives such as forwards.
In this way, the arbitrager eliminates exchange rate risk, that is, he or she is “covered.”
Riskless Arbitrage: Covered Interest Parity
This presentation mirrors the one in the text, but makes use of different exchange rates.
Riskless arbitrage refers to arbitrage that does not involve exchange rate risk. To
eliminate this risk, investors will make use of a forward contract. This allows the investor
to exchange foreign deposits at a predetermined rate (forward exchange rate) at a
specified date in the future.
The return on the U.S. deposits is equal to one plus the U.S. interest rate (1 + i$). This
is the gross dollar return Katya receives from her investment at the end of one year. For
the purposes of our example, suppose i$ is 0.252%.
The return on the British deposits includes two components. Katya receives one plus
the British interest rate (1 + i£) as gross pound return after one year. Suppose i£ is
0.490%. But pounds are not money in the United States. Katya must convert her British
pounds back into U.S. dollars. Therefore, any gain or loss she earns when she converts
her pounds back into U.S. dollars affects her rate of return.
This gain or loss is determined by the forward exchange rate, F$/£ (1.6090), and the
current spot rate, E$/£ (1.6114). Converting one U.S. dollar into British pounds would cost
At equilibrium, these two returns must be the same. If British deposits paid a higher
return than U.S. deposits, investors would sell U.S. dollars in exchange for British
pounds, causing the dollar to depreciate. For a given forward rate, this would lead to an
increase in the exchange rate E$/£, reducing the gain from converting British pounds into
U.S. dollars. Similarly, if American deposits paid a higher return than British deposits,
Summary CIP provides a theory of how forward contracts are formed. Rewriting the CIP
condition yields
APPLICATION
Evidence on Covered Interest Parity
To test whether covered interest parity holds, we can determine whether foreign
exchange traders could, in fact, earn a profit through establishing forward and spot
contracts. This application considers the German Deutsch Mark (GER) relative to the
The data illustrate that arbitrage led to zero profits in the absence of capital controls.
When capital controls are removed, arbitrage profits decrease.
As financial systems become more liberalized, arbitrage opportunities disappear
quickly. When governments imposed capital controls in the foreign exchange market,
Risky Arbitrage: Uncovered Interest Parity
Risky arbitrage does not “cover” investors with a forward contract. Instead, investors
must make their decisions based on what they think the exchange rate will be in the
future. The expected future exchange rate replaces the forward exchange rate in the CIP
Suppose that an American investor Katya is considering whether to put her $800 savings
into a U.S. bank account or in a British bank account for the next year. She must evaluate
the expected rate of return from these two investment strategies. (The numbers used in
The return on the U.S. deposits is equal to one plus the U.S. interest rate (1 + i$). This
The return on the British deposits includes two components. Katya receives one plus
the British interest rate (1 + i£) as gross pound return after one year. Suppose i£ is
0.490%. But pounds are not money in the United States. Katya must convert her British
pounds back into U.S. dollars. Therefore, any gain or loss she earns when she converts
her pounds back into U.S. dollars affects her rate of return.
This gain or loss will be determined by the spot exchange rate one year from now.
We call this the expected exchange rate, Ee$/£. Given the current spot rate, E$/£ (1.6114)
and the interest rates on the two accounts, we can calculate the market’s forecast of the
But, unlike covered interest parity, the forward exchange rate is not known. The
unknown variable in the uncovered interest parity equation is the expected exchange rate
one year from now, Ee$/£. As seen earlier, for our example, the expected exchange rate
one year from now is 1.6076$/£.
APPLICATION
Evidence on Uncovered Interest Parity
If the UIP and CIP hold, this implies the forward exchange rate is equal to the expected
future exchange rate. If we divide the CIP condition by the UIP condition, we get
Canceling terms yields
This implies F$/£ = Ee$/£.
The earlier empirical evidence on CIP was favorable, so we will assume CIP holds.
We can test whether UIP holds by comparing the forward premium ([F$/€/E$/€] – 1) with
the expected rate of depreciation over the next year or ([Ee$/€/E$/€] − 1), or
Uncovered Interest Parity: A Useful Approximation
It will be convenient to use the following approximation:
The left side of the equation is simply the interest earned from U.S. dollar deposits. This
approximately equals the interest earned from British pound deposits, plus the expected
depreciation of the dollar vis-à-vis the British pound during the next year.
UIP provides a theory of how expectations are linked to the current spot exchange
For example, suppose that the current spot rate is E$/£ = $1.50, the interest rate on U.S.
dollar deposits is 5%, and the interest rate on English deposits is 4%. Using the data, we
6 Conclusions
This chapter provides an overview of exchange rates, the forex market, and the
conditions defining equilibrium in the market, and discusses the ways in which private
actors and the government participate in the forex market. Although there are mainly two
types of exchange rate regimes, fixed and floating, some countries have adopted other
S I D E B A R
Assets and Their Attributes
Investors have many options in holding their wealth. There are many available assets:
cash, stocks, bonds, bank deposits, real estate, and so on. Investors make choices about
how to hold their wealth based on three criteria:
• Rate of return: the net increase in wealth generated from holding the asset.
Teaching Tips
Teaching Tip 1: Uncovered interest parity says the difference between the U.S. interest
rate and the foreign interest rate should equal the expected rate of depreciation of the U.S.
dollar. The Excel workbook for this chapter includes a worksheet that shows comparable
Teaching Tip 2: In this chapter, we assumed frictionless trading in the forex market.
This assumption is relaxed in the last chapter of the textbook. For now, explore the bid-
ask spread with your students. The bid price is the price at which a dealer is willing to
IN-CLASS PROBLEMS
1. Use Table 13-1 in the textbook to answer the following questions:
Exchange Rates on June 30, 2010
Exchange Rates on June 30, 2009
(one year previous)
