FRBSF Economic Letter
2006-31; November 17, 2006
Interest Rates, Carry Trades, and Exchange Rate Movements
and Print PDF Version (134KB)
Pacific Basin Notes. This series appears
on an occasional basis. It is prepared under the auspices of
the Center for Pacific
Basin Studies within the FRBSF's Economic Research Department.
The U.S. dollar has seen some remarkable swings against major
currencies recently. For example, over most of 2005, it gained
nearly 18% against the yen and 13% against the euro, while between
March and May 2006, it depreciated sharply against these currencies,
losing almost 10% of its value. Many observers have related these
swings to what is known as the carry trade. This is a strategy
widely used by investors in international financial markets that
is based on exploiting the existence of interest rate differentials
The use of this strategy by investors is puzzling, as the
theory of interest parity conditions implies that it should not
predictable profits. This Economic Letter explores this puzzle
by first describing the structure of a carry trade transaction.
It then reviews research documenting the payoff properties
of carry trades and discusses how these strategies can be linked
to the swings in exchange rates observed over recent years.
it presents some evidence on the size of carry trade strategies.
What is the carry trade?
In the most common version of this strategy, an investor borrows
a given amount in a low-interest-rate currency (the "funding" currency),
converts the funds into a high-interest-rate currency (the "target" currency)
and lends the resulting amount in the target currency at
the higher interest rate.
Another version exploits the forward premium of one currency
relative to another. The forward premium is basically the
percent difference between the forward exchange rate and
the spot exchange
rate between two currencies. Specifically, the forward
exchange rate between two currencies indicates the amount of
to be delivered at a specific future date that can be bought
with a single unit of the other currency, while the spot
exchange rate refers to immediate delivery. This version
transactions. The first involves selling currencies that
are at a forward premium, that is, currencies for which
exchange rate is higher than the spot exchange rate. The
second involves buying currencies that are at a forward
discount, that is, currencies for which the forward exchange
the spot exchange rate. Thus, currencies that are at a
forward premium are like funding currencies and those that are
forward discount are like target currencies.
Why is this version equivalent to the one based on interest
rate differentials? According to an equilibrium condition
financial markets, called "covered interest parity," the
forward premium of one currency relative to another is
equal to the interest rate differential between them.
Traders in foreign
exchange markets, in fact, use this condition to set
forward exchange rates and, thereby, forward premiums.
This implies that
currencies with a low interest rate are typically at
a forward premium, whereas currencies with a high interest
rate are typically
at a forward discount. Therefore, borrowing in currencies
with low interest rates and lending in currencies with
rates is equivalent to selling currencies that are at
a forward premium and buying currencies that are at a
Not profitable in theory, but profitable in practice
According to economic theory, an investment strategy
based on exploiting differences in interest rates across
yield no predictable profits. Consider two countries,
one with a high interest rate, and the other with a
According to another equilibrium condition of international
financial markets called the "uncovered interest parity," the
difference in interest rates between the two countries
simply reflects the rate at which investors expect
currency to depreciate against the low-interest-rate
currency. When this depreciation occurs, investors
who borrowed a given
amount in the low-interest-rate currency and then lent
it in the high-interest-rate currency will find that
their return is
worth less. The uncovered interest parity condition
implies, indeed, that investors should expect to receive
no profits, as
they should expect the return from lending in the high-interest-rate
currency to be worth ultimately as much as the cost
of borrowing in the low-interest-rate currency.
In practice, however, investors in international financial
markets do seem able to make profits through such strategies.
market participants and commentators have often cited
the carry trade as the source of several recent exchange
Why can carry trades be profitable? If the exchange
rate between the funding and the target currencies
move, then the
profit from the carry trade is proportional to both
the interest rate differential and the forward premium
currencies. But, of course, exchange rates do move,
and, therefore, a carry
trade involves exchange rate risk, in particular, the
possibility that the target currency will depreciate
against the funding
currency. In that case, the value of the amount initially
borrowed in the funding currency will increase in terms
of the target
currency, effectively increasing the borrowing cost
of the strategy. By the same token, the higher interest
in the target currency will be worth less in terms
the funding currency, ultimately trimming its profitability.
If the carry trade is a risky strategy, why are investors
reported to use it extensively? The answer lies in
the "forward premium
puzzle." This is a well-known empirical anomaly
of foreign exchange markets, and it concerns the implications
of the forward
premium for the realized rate of change in the value
of one currency relative to another. Empirical evidence
shows that currencies
that are at a forward premium and that, correspondingly,
have a low interest rate, actually tend, on average,
not appreciate, as the theory of interest parity conditions
predicts. Similarly, currencies that are at a forward
discount and that,
correspondingly, have a high interest rate, tend, on
average, to appreciate, not depreciate. This anomaly,
then, implies that
an investor who enters a carry trade is quite likely
to make predictable profits from two sources: the interest
between two currencies and the appreciation of the
high-interest-rate currency that was originally bought
at a forward discount.
Carry trade profits and exchange rate swings
How large are the profits from carry trade strategies?
Work by Burnside et al. (2006) provides one answer
to this question.
These authors document the return properties of a
version of the carry trade that they call an "optimally weighted" carry
trade portfolio. Like the earlier example, it involves selling
currencies that are at a forward premium and buying currencies
that are at a forward discount. It also entails choosing the
weights of the portfolio in order to maximize its Sharpe ratio,
which evaluates the risk-adjusted performance of a portfolio
by correcting a measure of its average return with the volatility
of its returns. Burnside et al. find that, for the period from
1977 to 2005, the realized cumulative return to their strategy
is very similar to that of investing in the S&P500 index.
The relative attractiveness of their strategy, however, lies
in the lower volatility of its returns: the Sharpe ratio of their
strategy is about one and a half times larger than the Sharpe
ratio of the S&P500 index, implying that the volatility of
the returns of their carry trade strategy is only two-thirds
of the volatility of the returns of the S&P500
Even though the Sharpe ratio of the optimally
carry trade portfolio is relatively high, transaction
as bid-ask spreads, lower its average payoff significantly,
are of the same order of magnitude as the portfolio
returns. This implies that, in order to generate
investors need to roll over the carry trade strategy
for prolonged periods.
Changes in supply and demand for currencies prompted
by the opportunity to exploit interest rate differentials
in sizeable and persistent exchange rate movements.
Specifically, carry trades based on interest
rate differentials and
premiums affect the balance of supply and demand
for funding and target currencies in foreign
as these strategies involve selling short funding
currencies and, at the same time, buying target
induce excess supply of the funding currencies
and excess demand
for target currencies. In turn, this leads to
the depreciation of low-interest-rate funding currencies
and to the
appreciation of high- interest-rate target currencies.
of high-interest-rate target currencies can encourage
number of investors to enter this strategy and,
ultimately, amplify the appreciation of target
well as the persistence
of exchange rate movements of the currencies
involved in these strategies.
The appreciation of the dollar against the yen
and the euro that occurred over most of 2005,
increasing interest rate differentials. As
interest rates rose in the U.S. while remaining at near-zero
in Japan and
at 2% in the euro area, the dollar looked like
an increasingly attractive target currency.
in early 2006,
the decline in the dollar has been related
to expectations of
rate differentials: As investors started to
expect rising interest rates in Japan and the euro area,
the dollar as a target currency decreased.
How big is the carry trade?
The effect of carry trades on exchange rates
most likely depends on the magnitude of the
transactions and investment positions associated
with them. Unfortunately,
evidence on these magnitudes is fairly limited,
in part because these strategies are generally
such as currency swaps, that are reported
items and, therefore, hard to monitor through
Two studies from the Bank for International
Settlements (BIS), however, provide some
evidence of the
size of carry trade
activity and thereby their significance
in exchange rate movements.
One study concerns foreign exchange market
turnover, which measures
the gross value in U.S. dollar equivalents
of all transactions involving the exchange
Melvin (2004) argue that the remarkable
increase in foreign exchange
turnover between 2001 and 2004 was likely
due to a rise in carry trade activities.
particularly strong for the Australian
and the New Zealand dollars, two currencies with
rates that simultaneously
had extended periods of appreciation against
low-interest-rate currencies, such as the
U.S. dollar and the yen.
The authors also illustrated graphically
that, between 2001 and 2004,
as the interest rate differential with
the U.S. widened, the Australian
dollar appreciated against the U.S. dollar
and foreign exchange turnover increased
based on survey
data from 1992 to 2004, they found that,
for major trading currencies,
increases in foreign exchange market turnover
were strongly related to interest rate
differentials with the U.S.
The second study concerns the stock of
outstanding BIS reporting banks' cross-border
denominated in yen,
that has been popular as a funding currency,
given the long period
of very low interest rates in Japan.
McGuire and Tarashev (2006) report that the stock
in the fourth quarter of 2005, continuing
a trend evident since 2004. They argue
of the increased
relevance of yen carry trade positions,
as a large share of the increase in yen-denominated
has been driven
in yen borrowing by investors in financial
Market participants and commentators
have often linked the swings in exchange
the use of
that is, investors' strategies that
exploit interest rate differentials across countries.
puzzling from a
however, is that investors should
even engage in carry trades, because the
implies that these strategies should
yield no predictable profits.
As this Economic Letter has explained,
the key to the puzzle is
yet another puzzle—the forward
premium puzzle—wherein currencies
or rising interest rates
tend to appreciate, and
currencies with low or declining
interest rates tend to depreciate, as investors
are lured into buying currencies
with positive interest rate differentials
short currencies with
negative interest rate differentials.
The evidence on the quantitative
of carry trades is fairly limited,
but to date it suggests that these strategies
factor in recent
exchange rate swings.
[URLs accessed November 2006.]
Burnside, C., M. Eichenbaum, I. Kleshchelski, and S. Rebelo.
2006. "The Returns to Currency Speculation." NBER
Working Paper 12489.
Galati, G., and M. Melvin. 2004. "Why Has FX Trading Surged?
Explaining the 2004 Triennial Survey." BIS Quarterly
Review (December), pp. 67-98.
McGuire, P., and N. Tarashev. 2006. "The International Banking
Market." BIS Quarterly Review (June), pp. 11-25.
Opinions expressed in this newsletter
do not necessarily reflect the views of the management
of the Federal Reserve Bank of San Francisco or of the
Board of Governors of the Federal Reserve System. Comments?
us via e-mail or write us at:
Federal Reserve Bank of San Francisco
P.O. Box 7702
San Francisco, CA 94120