Interest rate parity

# Interest rate parity

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Interest rate parity is a no-arbitrage
Arbitrage
In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...

condition representing an equilibrium state under which investors will be indifferent to interest rate
Interest rate
An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...

s available on bank deposits
Demand deposit
Demand deposits, bank money or scriptural money are funds held in demand deposit accounts in commercial banks. These account balances are usually considered money and form the greater part of the money supply of a country.-History:...

in two countries. Two assumptions central to interest rate parity are capital mobility and perfect substitutability
Substitute good
In economics, one way we classify goods is by examining the relationship of the demand schedules when the price of one good changes. This relationship between demand schedules leads economists to classify goods as either substitutes or complements. Substitute goods are goods which, as a result...

of domestic and foreign assets. The interest rate parity condition implies that the expected return
Rate of return
In finance, rate of return , also known as return on investment , rate of profit or sometimes just return, is the ratio of money gained or lost on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or...

on domestic assets will equal the expected return on foreign currency assets, due to an equilibrium in the foreign exchange market
Foreign exchange market
The foreign exchange market is a global, worldwide decentralized financial market for trading currencies. Financial centers around the world function as anchors of trading between a wide range of different types of buyers and sellers around the clock, with the exception of weekends...

resulting from changes in the exchange rate
Exchange rate
In finance, an exchange rate between two currencies is the rate at which one currency will be exchanged for another. It is also regarded as the value of one country’s currency in terms of another currency...

between two countries. Interest rate parity takes on two distinctive forms: uncovered interest rate parity refers to the parity condition in which exposure to exchange rate risk (unanticipated changes in exchange rates) is uninhibited, whereas covered interest rate parity refers to the condition in which a forward contract
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 today. This is in contrast to a spot contract, which is an agreement to buy or sell an asset today. It costs nothing to enter a...

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
Forward exchange rate
The forward exchange rate is the rate at which a bank is willing to exchange one currency for another at some specified future date. The forward exchange rate is a type of forward price...

and the future spot exchange rate.

## 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
Financial risk
Financial risk an umbrella term for multiple types of risk associated with financing, including financial transactions that include company loans in risk of default. Risk is a term often used to imply downside risk, meaning the uncertainty of a return and the potential for financial loss...

and liquidity
Market liquidity
In business, economics or investment, market liquidity is an asset's ability to be sold without causing a significant movement in the price and with minimum loss of value...

. 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. Investors are 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 foreign deposits, thereby eliminating the potential for uncovered interest arbitrage
Uncovered interest arbitrage
Uncovered interest arbitrage is a form of arbitrage where funds are transferred abroad to take advantage of higher interest in foreign monetary centers. It involves the conversion of the domestic currency to the foreign currency to make investment; and subsequent re-conversion of the fund from the...

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
St is the current spot exchange rate at time t
i\$ is the interest rate in the US
ic is the interest rate in a foreign country or currency area (for this example, following a US perspective, it is the interest rate available in the Eurozone
Eurozone
The eurozone , officially called the euro area, is an economic and monetary union of seventeen European Union member states that have adopted the euro as their common currency and sole legal tender...

)

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 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
Covered interest arbitrage
Covered interest arbitrage is the investment strategy where an investor buys a financial instrument denominated in a foreign currency, and hedges his foreign exchange risk by selling a forward contract in the amount of the proceeds of the investment back into his base currency...

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

Covered interest rate parity (CIRP) is found to hold when there is open capital mobility and limited capital control
Capital control
Capital controls are measures such as transaction taxes and other limits or outright prohibitions, which a nation's government can use to regulate the flows into and out of the country's capital account....

s, and this finding is confirmed for all currencies freely traded in the present-day. One such example is when the United Kingdom
United Kingdom
The United Kingdom of Great Britain and Northern IrelandIn the United Kingdom and Dependencies, other languages have been officially recognised as legitimate autochthonous languages under the European Charter for Regional or Minority Languages...

and Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

abolished capital controls between 1979 and 1981. Maurice Obstfeld
Maurice Obstfeld
Maurice Moses "Maury" Obstfeld is a professor of economics at the University of California, Berkeley.He is well known for his work in international economics. He is among the most influential economists in the world according to IDEAS/RePEc....

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 cost
Transaction cost
In economics and related disciplines, a transaction cost is a cost incurred in making an economic exchange . For example, most people, when buying or selling a stock, must pay a commission to their broker; that commission is a transaction cost of doing the stock deal...

s arising from fee
Fee
A fee is the price one pays as remuneration for services. Fees usually allow for overhead, wages, costs, and markup.Traditionally, professionals in Great Britain received a fee in contradistinction to a payment, salary, or wage, and would often use guineas rather than pounds as units of account...

s and other regulations
Financial regulation
Financial regulation is a form of regulation or supervision, which subjects financial institutions to certain requirements, restrictions and guidelines, aiming to maintain the integrity of the financial system...

, arbitrage opportunities are fleeting or nonexistent. While CIRP generally holds, it does not hold with precision due to the presence of transaction costs, political risk
Political risk
Political risk is a type of risk faced by investors, corporations, and governments. It is a risk that can be understood and managed with reasoned foresight and investment....

s, tax
Tax
To tax is to impose a financial charge or other levy upon a taxpayer by a state or the functional equivalent of a state such that failure to pay is punishable by law. Taxes are also imposed by many subnational entities...

implications for interest earnings versus gains from foreign exchange, and differences in the liquidity of domestic versus foreign assets.

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 expected 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 spot rate to be equal, both CIRP and UIRP conditions must hold). UIRP is found to have some empirical support in tests
Statistical hypothesis testing
A statistical hypothesis test is a method of making decisions using data, whether from a controlled experiment or an observational study . In statistics, a result is called statistically significant if it is unlikely to have occurred by chance alone, according to a pre-determined threshold...

for correlation
Correlation
In statistics, dependence refers to any statistical relationship between two random variables or two sets of data. Correlation refers to any of a broad class of statistical relationships involving dependence....

between expected rates of currency depreciation
Depreciation (currency)
Currency depreciation is the loss of value of a country's currency with respect to one or more foreign reference currencies, typically in a floating exchange rate system. It is most often used for the unofficial increase of the exchange rate due to market forces, though sometimes it appears...

and the forward premium or discount. Evidence for the validity and accuracy of the unbiasedness hypothesis, particularly evidence for cointegration
Cointegration
Cointegration is a statistical property of time series variables. Two or more time series are cointegrated if they share a common stochastic drift.-Introduction:...

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.

• Arbitrage
Arbitrage
In economics and finance, arbitrage is the practice of taking advantage of a price difference between two or more markets: striking a combination of matching deals that capitalize upon the imbalance, the profit being the difference between the market prices...

• Exchange rate
Exchange rate
In finance, an exchange rate between two currencies is the rate at which one currency will be exchanged for another. It is also regarded as the value of one country’s currency in terms of another currency...

• Forward exchange rate
Forward exchange rate
The forward exchange rate is the rate at which a bank is willing to exchange one currency for another at some specified future date. The forward exchange rate is a type of forward price...

• Interest rate
Interest rate
An interest rate is the rate at which interest is paid by a borrower for the use of money that they borrow from a lender. For example, a small company borrows capital from a bank to buy new assets for their business, and in return the lender receives interest at a predetermined interest rate for...

• International Fisher effect
International fisher effect
The International Fisher effect is a hypothesis in international finance that says that the difference in the nominal interest rates between two countries determines the movement of the nominal exchange rate between their currencies, with the value of the currency of the country with the lower...