Interest rate parity is a no-
arbitrage
Arbitrage (, ) is the practice of taking advantage of a difference in prices in two or more marketsstriking a combination of matching deals to capitalize on the difference, the profit being the difference between the market prices at which th ...
condition representing an
equilibrium state under which investors compare
interest rate
An interest rate is the amount of interest due per period, as a proportion of the amount lent, deposited, or borrowed (called the principal sum). The total interest on an amount lent or borrowed depends on the principal sum, the interest rate, ...
s available on
bank deposits in two countries.
The fact that this condition does not always hold allows for potential opportunities to earn riskless profits from
covered interest arbitrage. Two assumptions central to interest rate parity are
capital mobility and
perfect substitutability of domestic and foreign
assets
In financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or intangible) that can be used to produce positive economic value. Assets represent value of ownership that can b ...
. Given
foreign exchange market
The foreign exchange market (forex, FX, or currency market) is a global decentralized or over-the-counter (OTC) market for the trading of currencies. This market determines foreign exchange rates for every currency. By trading volume, ...
equilibrium, the interest rate parity condition implies that the expected
return on domestic assets will equal the
exchange rate
In finance, an exchange rate is the rate at which one currency will be exchanged for another currency. Currencies are most commonly national currencies, but may be sub-national as in the case of Hong Kong or supra-national as in the case of ...
-adjusted expected return on foreign currency assets. Investors then cannot earn arbitrage profits by borrowing in a country with a lower interest rate, exchanging for foreign currency, and investing in a foreign country with a higher interest rate, due to gains or losses from exchanging back to their domestic currency at
maturity.
Interest rate parity takes on two distinctive forms: ''uncovered interest rate parity'' refers to the parity condition in which exposure to
foreign exchange risk (unanticipated changes in exchange rates) is uninhibited, whereas ''covered interest rate parity'' refers to the condition in which a
forward contract
In finance, a forward contract, or simply a forward, is a non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on in the contract, making it a type of derivative instrument.John C Hu ...
has been used to ''cover'' (eliminate exposure to) exchange rate risk. Each form of the parity condition demonstrates a unique relationship with implications for the forecasting of future exchange rates: the
forward exchange rate and the future
spot exchange rate.
Economists have found
empirical evidence
Empirical evidence is evidence obtained through sense experience or experimental procedure. It is of central importance to the sciences and plays a role in various other fields, like epistemology and law.
There is no general agreement on how the ...
that covered interest rate parity generally holds, though not with precision due to the effects of various risks, costs, taxation, and ultimate differences in liquidity. When both covered and uncovered interest rate parity hold, they expose a relationship suggesting that the forward rate is an unbiased predictor of the future spot rate. This relationship can be employed to test whether uncovered interest rate parity holds, for which economists have found mixed results. When uncovered interest rate parity and
purchasing power parity
Purchasing power parity (PPP) is a measure of the price of specific goods in different countries and is used to compare the absolute purchasing power of the countries' currency, currencies. PPP is effectively the ratio of the price of a market bask ...
hold together, they illuminate a relationship named ''real interest rate parity'', which suggests that expected
real interest rates represent expected adjustments in the
real exchange rate. This relationship generally holds strongly over longer terms and among
emerging market countries.
Assumptions
Interest rate parity rests on certain assumptions, the first being that capital is mobile - investors can readily exchange domestic assets for foreign assets. The second assumption is that assets have perfect substitutability, following from their similarities in
riskiness and
liquidity. Given capital mobility and perfect substitutability, investors would be expected to hold those assets offering greater returns, be they domestic or foreign assets. However, both domestic and foreign assets are held by investors. Therefore, it must be true that no difference can exist between the returns on domestic assets and the returns on foreign assets.
That is not to say that domestic investors and foreign investors will earn equivalent returns, but that a single investor on any given side would expect to earn equivalent returns from either investment decision.
Uncovered interest rate parity

When the no-arbitrage condition is satisfied ''without'' the use of a forward contract to hedge against exposure to exchange rate risk, interest rate parity is said to be ''uncovered''. Risk-neutral investors will be indifferent among the available interest rates in two countries because the exchange rate between those countries is expected to adjust such that the dollar return on dollar deposits is equal to the dollar return on euro deposits, thereby eliminating the potential for
uncovered interest arbitrage profits. Uncovered interest rate parity helps explain the
determination of the spot exchange rate. The following equation represents uncovered interest rate parity.
:
where
:
is the expected future spot exchange rate at time ''t + k''
:''k'' is the number of periods into the future from time ''t''
:''S
t'' is the current spot exchange rate at time ''t''
:''i
$'' is the interest rate in one country (for example, the
United States
The United States of America (USA), also known as the United States (U.S.) or America, is a country primarily located in North America. It is a federal republic of 50 U.S. state, states and a federal capital district, Washington, D.C. The 48 ...
)
:''i
c'' is the interest rate in another country or currency area (for example, the
Eurozone
The euro area, commonly called the eurozone (EZ), is a Monetary union, currency union of 20 Member state of the European Union, member states of the European Union (EU) that have adopted the euro (Euro sign, €) as their primary currency ...
)
The dollar return on dollar deposits,
, is shown to be equal to the dollar return on euro deposits,
.
Approximation
Uncovered interest rate parity asserts that an investor with dollar deposits will earn the interest rate available on dollar deposits, while an investor holding euro deposits will earn the interest rate available in the eurozone, but also a potential gain or loss on euros depending on the rate of appreciation or depreciation of the euro against the dollar. Economists have extrapolated a useful approximation of uncovered interest rate parity that follows intuitively from these assumptions. If uncovered interest rate parity holds, such that an investor is indifferent between dollar versus euro deposits, then any excess return on euro deposits must be offset by some expected loss from depreciation of the euro against the dollar. Conversely, some shortfall in return on euro deposits must be offset by some expected gain from appreciation of the euro against the dollar. The following equation represents the uncovered interest rate parity approximation.
:
where
:
is the change in the expected future spot exchange rate
:
is the expected rate of depreciation (or appreciation) of the dollar
A more universal way of stating the approximation is "the home interest rate equals the foreign interest rate plus the expected rate of depreciation of the home currency."
Covered interest rate parity

When the no-arbitrage condition is satisfied ''with'' the use of a forward contract to hedge against exposure to exchange rate risk, interest rate parity is said to be ''covered''. Investors will still be indifferent among the available interest rates in two countries because the forward exchange rate sustains equilibrium such that the dollar return on dollar deposits is equal to the dollar return on foreign deposit, thereby eliminating the potential for
covered interest arbitrage profits. Furthermore, covered interest rate parity helps explain the
determination of the forward exchange rate. The following equation represents covered interest rate parity.
:
where
:
is the forward exchange rate at time ''t''
The dollar return on dollar deposits,
, is shown to be equal to the dollar return on euro deposits,
.
Empirical evidence
Traditionally, covered interest rate parity (CIRP) was found to hold when there is open capital mobility and limited
capital control
Capital controls are residency-based measures such as transaction taxes, other limits, or outright prohibitions that a nation's government can use to regulate flows from capital markets into and out of the country's capital account. These meas ...
s, and this finding is confirmed for all currencies freely traded in the present day. One such example is when the
United Kingdom
The United Kingdom of Great Britain and Northern Ireland, commonly known as the United Kingdom (UK) or Britain, is a country in Northwestern Europe, off the coast of European mainland, the continental mainland. It comprises England, Scotlan ...
and
Germany
Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...
abolished capital controls between 1979 and 1981.
Maurice Obstfeld and Alan Taylor calculated hypothetical profits as implied by the expression of a potential inequality in the CIRP equation (meaning a difference in returns on domestic versus foreign assets) during the 1960s and 1970s, which would have constituted arbitrage opportunities if not for the prevalence of capital controls. However, given financial liberalization and resulting capital mobility, arbitrage temporarily became possible until equilibrium was restored. Since the abolition of capital controls in the United Kingdom and Germany, potential arbitrage profits have been near zero. Factoring in
transaction costs arising from
fees and other
regulations, arbitrage opportunities are fleeting or nonexistent when such costs exceed deviations from parity.
While CIRP generally holds, it does not hold with precision due to the presence of transaction costs,
political risks,
tax
A tax is a mandatory financial charge or levy imposed on an individual or legal entity by a governmental organization to support government spending and public expenditures collectively or to regulate and reduce negative externalities. Tax co ...
implications for interest earnings versus gains from foreign exchange, and differences in the liquidity of domestic versus foreign assets.
Researchers found evidence that significant deviations from CIRP during the onset of the
2008 financial crisis
The 2008 financial crisis, also known as the global financial crisis (GFC), was a major worldwide financial crisis centered in the United States. The causes of the 2008 crisis included excessive speculation on housing values by both homeowners ...
were driven by concerns over risk posed by counter parties to banks and financial institutions in Europe and the US in the
foreign exchange swap market. The
European Central Bank
The European Central Bank (ECB) is the central component of the Eurosystem and the European System of Central Banks (ESCB) as well as one of seven institutions of the European Union. It is one of the world's Big Four (banking)#International ...
's efforts to provide US dollar liquidity in the foreign exchange swap market, along with similar efforts by the
Federal Reserve
The Federal Reserve System (often shortened to the Federal Reserve, or simply the Fed) is the central banking system of the United States. It was created on December 23, 1913, with the enactment of the Federal Reserve Act, after a series of ...
, had a moderating impact on CIRP deviations between the dollar and the euro. Such a scenario was found to be reminiscent of deviations from CIRP during the 1990s driven by struggling Japanese banks which looked toward foreign exchange swap markets to try and acquire dollars to bolster their
creditworthiness.
A second period of deviations from CIRP after 2012, at a time of relatively calm markets, led to renewed debate about the extent and origin of deviations from CIRP. Explanations include intermediary constraints that can lead to
limits to arbitrage, such as balance sheet costs of arbitrage, raised by a team of researchers at the
Bank for International Settlements.
Other explanations question common assumptions underlying the CIRP condition, such as the choice of discount factors. Deviations from CIRP remain subject to ongoing debate.
When both covered and uncovered interest rate parity (UIRP) hold, such a condition sheds light on a noteworthy relationship between the forward and expected future spot exchange rates, as demonstrated below.
:
:
Dividing the equation for UIRP by the equation for CIRP yields the following equation:
:
which can be rewritten as:
:
This equation represents the
unbiasedness hypothesis, which states that the forward exchange rate is an unbiased predictor of the future spot exchange rate.
Given strong evidence that CIRP holds, the forward rate unbiasedness hypothesis can serve as a test to determine whether UIRP holds (in order for the forward rate and expected spot rate to be equal, both CIRP and UIRP conditions must hold). Evidence for the validity and accuracy of the unbiasedness hypothesis, particularly evidence for
cointegration between the forward rate and future spot rate, is mixed as researchers have published numerous papers demonstrating both empirical support and empirical failure of the hypothesis.
UIRP is found to have some empirical support in
tests for
correlation between expected rates of
currency depreciation and the
forward premium or discount.
Evidence suggests that whether UIRP holds depends on the currency examined, and deviations from UIRP have been found to be less substantial when examining longer time horizons.
Some studies of monetary policy have offered explanations for why UIRP fails empirically. Researchers demonstrated that if a central bank manages interest rate spreads in strong response to the previous period's spreads, that interest rate spreads had negative coefficients in regression tests of UIRP. Another study which set up a model wherein the central bank's monetary policy responds to
exogenous shocks, that the central bank's smoothing of interest rates can explain empirical failures of UIRP.
A study of central bank interventions on the US dollar and
Deutsche mark
The Deutsche Mark (; "German mark (currency), mark"), abbreviated "DM" or "D-Mark" (), was the official currency of West Germany from 1948 until 1990 and later of unified Germany from 1990 until the adoption of the euro in 2002. In English, it ...
found only limited evidence of any substantial effect on deviations from UIRP.
UIRP has been found to hold over very small spans of time (covering only a number of hours) with a high frequency of bilateral exchange rate data.
Tests of UIRP for economies experiencing institutional
regime changes, using monthly exchange rate data for the US dollar versus the Deutsche mark and the
Spanish peseta versus the
British pound, have found some evidence that UIRP held when US and German regime changes were volatile, and held between Spain and the United Kingdom particularly after Spain joined the
European Union
The European Union (EU) is a supranational union, supranational political union, political and economic union of Member state of the European Union, member states that are Geography of the European Union, located primarily in Europe. The u ...
in 1986 and began liberalizing capital mobility.
Real interest rate parity
When both UIRP (particularly in its approximation form) and purchasing power parity (PPP) hold, the two parity conditions together reveal a relationship among expected real interest rates, wherein changes in expected real interest rates reflect expected changes in the real exchange rate. This condition is known as ''real interest rate parity'' (RIRP) and is related to the
international Fisher effect.
The following equations demonstrate how to derive the RIRP equation.
:
:
where
:
represents inflation
If the above conditions hold, then they can be combined and rearranged as the following:
:
RIRP rests on several assumptions, including
efficient markets, no country risk premia, and zero change in the expected real exchange rate. The parity condition suggests that real interest rates will equalize between countries and that capital mobility will result in capital flows that eliminate opportunities for arbitrage. There exists strong evidence that RIRP holds tightly among emerging markets in Asia and also Japan. The half-life period of deviations from RIRP have been examined by researchers and found to be roughly six or seven months, but between two and three months for certain countries. Such variation in the half-lives of deviations may be reflective of differences in the degree of financial integration among the country groups analyzed.
RIRP does not hold over short time horizons, but empirical evidence has demonstrated that it generally holds well across long time horizons of five to ten years.
See also
*
Carry trade
*
Covered interest arbitrage
*
Financial crisis
A financial crisis is any of a broad variety of situations in which some financial assets suddenly lose a large part of their nominal value. In the 19th and early 20th centuries, many financial crises were associated with Bank run#Systemic banki ...
*
Foreign exchange derivative
*
Uncovered interest arbitrage
References
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Financial economics
Interest rates
Foreign exchange market
International finance