Forward Exchange Rates and Covered Interest Parity

Forward Exchange Rates and Covered
Interest Parity
This appendix explains how forward exchange rates are determined. Under the assumption
that the interest parity condition always holds, a forward exchange rate equals the spot
exchange rate expected to prevail on the forward contract’s value date.
As the first step in the discussion, we point out the close connection among the forward
exchange rate between two currencies, their spot exchange rate, and the interest rates on
deposits denominated in those currencies. The connection is described by the covered
interest parity condition, which is similar to the (noncovered) interest parity condition
defining foreign exchange market equilibrium but involves the forward exchange rate
rather than the expected future spot exchange rate.
To be concrete, we again consider dollar and euro deposits. Suppose you want to buy a
euro deposit with dollars but would like to be certain about the number of dollars it will be
worth at the end of a year. You can avoid exchange rate risk by buying a euro deposit and,
at the same time, selling the proceeds of your investment forward. When you buy a euro
deposit with dollars and at the same time sell the principal and interest forward for dollars,
we say you have “covered” yourself, that is, avoided the possibility of an unexpected
depreciation of the euro.
The covered interest parity condition states that the rates of return on dollar deposits
and “covered” foreign deposits must be the same. An example will clarify the meaning of
the condition and illustrate why it must always hold. Let stand for the one-year
forward price of euros in terms of dollars, and suppose per euro. Assume
that at the same time, the spot exchange rate per euro, , and
. The (dollar) rate of return on a dollar deposit is clearly 0.10, or 10 percent, per
year. What is the rate of return on a covered euro deposit?
We answer this question as we did in the chapter. A deposit costs today, and
it is worth after a year. If you sell forward today at the forward exchange
rate of per euro, the dollar value of your investment at the end of a year is
The rate of return on a covered purchase of a
euro deposit is therefore . This 10.3 percent per year rate of
return exceeds the 10 percent offered by dollar deposits, so covered interest parity does not
hold. In this situation, no one would be willing to hold dollar deposits; everyone would
prefer covered euro deposits.
More formally, we can express the covered return on euro deposits as
which is approximately equal to
R€ +
F$/€ - E$/€
E$/€
F$/€(1 + R€) - E$/€
E$/€
,
(1.158 - 1.05)/1.05 = 0.103
($1.113 per euro) * (€1.04) = $1.158.
$1.113
€1.04 €1.04
€1 $1.05
R€ = 0.04
E$/€ = $1.05 R$ = 0.10
F$/€ = $1.113
F$/€
when the product is a small number. The covered interest parity
condition can therefore be written
The quantity
is called the forward premium on euros against dollars. (It is also called the forward discount
on dollars against euros.) Using this terminology, we can state the covered interest
parity condition as follows: The interest rate on dollar deposits equals the interest rate on
euro deposits plus the forward premium on euros against dollars (the forward discount on
dollars against euros).
There is strong empirical evidence that the covered interest parity condition holds for
different foreign currency deposits issued within a single financial center. Indeed, currency
traders often set the forward exchange rates they quote by looking at current interest rates
and spot exchange rates and using the covered interest parity formula.12 Deviations from
covered interest parity can occur, however, if the deposits being compared are located in
different countries. These deviations occur when asset holders fear that governments may
impose regulations that will prevent the free movement of foreign funds across national
borders. Our derivation of the covered interest parity condition implicitly assumed there
was no political risk of this kind. Deviations can occur also because of fears that banks
will fail, making them unable to pay off large deposits.13
By comparing the (noncovered) interest parity condition,
with the covered interest parity condition, you will find that both conditions can be true at
the same time only if the one-year forward rate quoted today equals the spot exchange
rate people expect to materialize a year from today:
This makes intuitive sense. When two parties agree to trade foreign exchange on a date in
the future, the exchange rate they agree on is the spot rate they expect to prevail on that
date. The important difference between covered and noncovered transactions should be
kept in mind, however. Covered transactions do not involve exchange rate risk, whereas
noncovered transactions do.14
F$/€ = E$/€
e .
$/€
R$ = R€ + (E$/€
e - E$/€)/E$/€,
(F$/€ - E$/€)/E$/€
R$ = R€ + (F$/€ - E$/€)/E$/€.
R€ * (F$/€ - E$/€)/E$/€
352 PART THREE Exchange Rates and Open-Economy Macroeconomics
12Empirical evidence supporting the covered interest parity condition is provided by Frank McCormick in
“Covered Interest Arbitrage: Unexploited Profits? Comment,” Journal of Political Economy 87 (April 1979),
pp. 411–417, and by Kevin Clinton in “Transactions Costs and Covered Interest Arbitrage: Theory and
Evidence,” Journal of Political Economy 96 (April 1988), pp. 358–370.
13For a more detailed discussion of the role of political risk in the forward exchange market, see Robert Z. Aliber,
“The Interest Parity Theorem: A Reinterpretation,” Journal of Political Economy 81 (November/December 1973),
pp. 1451–1459. Of course, actual government restrictions on cross-border money movements can also cause
covered interest parity deviations. On the fear of bank failure as a cause for deviations from covered interest parity,
see Naohiko Baba and Frank Packer, “Interpreting Deviations from Covered Interest Parity During the Financial
Market Turmoil of 2007–2008,” Working Paper No. 267, Bank for International Settlements, December 2008. The
events underlying this last paper are discussed in Chapter 21.
14We indicated in the text that the (noncovered) interest parity condition, while a useful simplification, may not
always hold exactly if the riskiness of currencies influences demands in the foreign exchange market. Therefore,
the forward rate may differ from the expected future spot rate by a risk factor even if covered interest parity holds
true. As noted earlier, the role of risk in exchange rate determination is discussed more fully in Chapter 18.
CHAPTER 14 Exchange Rates and the Foreign Exchange Market: An Asset Approach 353
The theory of covered interest parity helps explain the close correlation between the
movements in spot and forward exchange rates shown in Figure 14-1, a correlation typical
of all major currencies. The unexpected economic events that affect expected asset returns
often have a relatively small effect on international interest rate differences between
deposits with short maturities (for example, three months). To maintain covered interest
parity, therefore, spot and forward rates for the corresponding maturities must change
roughly in proportion to each other.
We conclude this appendix with one further application of the covered interest parity
condition. To illustrate the role of forward exchange rates, the chapter used the example of
an American importer of Japanese radios anxious about the exchange rate it would
face in 30 days when the time came to pay the supplier. In the example, Radio Shack
solved the problem by selling forward for yen enough dollars to cover the cost of the
radios. But Radio Shack could have solved the problem in a different, more complicated
way. It could have (1) borrowed dollars from a bank; (2) sold those dollars immediately
for yen at the spot exchange rate and placed the yen in a 30-day yen bank deposit; (3) then,
after 30 days, used the proceeds of the maturing yen deposit to pay the Japanese supplier;
and (4) used the realized proceeds of the U.S. radio sales, less profits, to repay the original
dollar loan.
Which course of action—the forward purchase of yen or the sequence of four transactions
described in the preceding paragraph—is more profitable for the importer? We leave
it to you, as an exercise, to show that the two strategies yield the same profit when the
covered interest parity condition holds.