Interest rate parity

The interest parity theory is a returning to John Maynard Keynes widespread national economic model. First, it provides an explanation for behavior of investors: investors invest where the greatest return can be earned. Based on the interest parity theory is secondly a product now used in foreign trade short-term model for explaining exchange rate movements. She explains exchange rate movements only with the return interest of investors. It can be the covered and uncovered distinguish the form of interest rate parity.

• 7.1 Example of the covered interest parity

Definition of the interest rate parity

Interest parity ( parity of Latin par 'equal' ) implies that the domestic rate of return is equal to the foreign rate of return. The domestic rate of return is defined by the nominal domestic interest rate i, the foreign return by the nominal, foreign interest rate i * plus expected exchange rate change ():.

"Interest rate parity is the relationship between national money market to the international money market, where the exchange rate adjusts so that the difference between domestic and foreign interest rate the difference between the actual and the expected rate of such ".

" The foreign exchange market is in equilibrium when deposits offer the same expected return in all currencies. This equality of expected returns on deposits in any two currencies, measured in the same currency, is called interest rate parity ".

"Interest rate parity relates the law of one price to fixed income and homogeneous financial stocks, which means that assets with similar risk regardless of the country in which they are traded, have the same expected return ."

Prerequisites for the achievement of the interest parity

This makes it (permanently) is to interest rate parity, it requires perfect capital mobility and perfect substitutability of securities. With perfect capital mobility, capital is at all times fully into the desired form of investment transferable, while the imperfect capital mobility delays the reaction of the capital markets.

Perfect substitutability of assets applies only to investors who are risk neutral, the financial assets are compared only on the basis of expected returns. Investors demand for the exchange rate risk an additional risk premium or an additional hedging transaction within the meaning of swaps so the facilities are not perfect substitutes.

Furthermore, the interest parity demands the existence of the foreign exchange market efficiency. This means that the exchange rate at any time reflects all relevant information available for the price formation. Here are no transaction costs, there are no barriers to trade, and all market participants need to have identical expectations about exchange rate developments.

With flexible exchange rates, an additional variable, the uncertainty of exchange rates of change needs to be incorporated into the calculation that influence over the investment period the income from investments abroad.

The condition of the interest parity

The condition of the interest rate parity exists when the difference between the domestic and foreign interest rate the difference between the actual and the expected exchange rate corresponds.

This leads to the following conclusion: The higher the rate of change of the exchange rate of a country, that is, the faster the country's currency depreciates, the higher must be the nominal rate of interest of this country to be.

The presence of the condition of interest rate parity has a yield equality of domestic and foreign investments as a result. Investors will therefore be indifferent with respect to an investment in the domestic and overseas investment.

The basic idea

Central assumption of the interest rate parity theory is that investors invest where they can generate the greatest return. Behavior of investors accordingly, then, in a two-country case always upgraded the currency of the attractive investment location. The interest parity theory in its basic structure considered rates of return only the interest rate and exchange rate expectations. If one distinguishes as a possible place of investment between home and abroad, the following applies:

Domestic return

The yield on the country conforms to the domestic interest rate, ie

Foreign yield

The return abroad is accordingly influenced by the foreign interest rate. In addition, however, it is for a domestic investor also important, as the exchange rate between domestic and foreign currency e evolved over the investment period; for the domestic investor an investment abroad would be useful in terms of return issues, if the foreign currency is revalued, as long as the investor has invested abroad. Conversely, the expectation of a future devaluation of the foreign currency will reduce the interest of the investor in a foreign investment.

The interest parity theory modeled this relationship on the introduction of an expected exchange rate ( ). This variable represents the expectations of the investor on the amount the exchange rate at the end of the investment period - that is, the price the investor expects the redemption price, before undertaking the investment. About an approximate formula, the model determines the income of an investor by expected exchange rate movements:

Note: The figure used here is based on the set notation of the exchange rate.

The formula of the income from exchange rate changes can as follows be interpreted: Meet up time of investment, the current exchange rate ( Hintauschkurs ) and the expected redemption price, the investor is expected to neither additional exchange rate gains or incurred from the change in exchange rates extra cost.

If the expected exchange rate, however, below the current exchange rate, this means nothing more than the expectation of a devaluation of the domestic currency (example: The current exchange rate between the dollar and euro amounts to, the expected future - then accruing to the investor from an investment in the U.S. exchange rate returns because he receives $ 1.20 for one euro exchanged executed. , he Swaps at the end of the investment period, this 1.20 U.S. dollars back into euros back, he receives more than the original euro, since now already 1.10 U.S. dollars a euro correspond ). With existence of an appreciation expectation with respect to the foreign currency, ie the investment is worth abroad.

The opposite is true if the expected exchange rate is larger than the current one. The then existing anticipation of devaluation leads to costs for the investor (Example: The current exchange rate amounts to U.S. dollars per euro, the expected future, the investor exchanges thus beginning a Euro in U.S. $ 1.20 but at the end of the investment period, he would need. . 1.30 U.S. dollars to recover the original euro again - so he makes loss).

The total return on a foreign investment is calculated in accordance with interest rate parity theory then from the interest income and the expected exchange rate and income is therefore

Investor behavior due to lack of interest parity

Where the return on domestic larger than those in other countries ( ), the Investor will invest its capital in Germany. Conversely, it is a foreign investment prefer if their return is greater than that of a domestic system (). If both yields equal to ( ), the investor is indifferent.

Changes in exchange rates due to lack of interest parity

As already mentioned, implies an unequal return at home and abroad a certain exchange rate developments. Where the return is higher abroad than at home, so the resulting investment abroad will lead to an appreciation of the foreign currency because the foreign currency must be sought in order to put money abroad. Conversely, a higher domestic rate of return lead to an appreciation of the domestic currency, as capital is deducted from abroad and invested domestically. According to the interest parity theory is thus possible to explain exchange rate movements due to the search for yield by investors.

Interest parity as an equilibrium solution

However, the exchange rate changes adopted as a result of investment decisions have again repercussions on the investment decision itself ( Example: An investor realizes that the return on an investment in the United States with respect to the U.S. dollar [ and ] higher due to an appreciation expectancy than those in Europe It is accordingly. . invest in the U.S., so the U.S. dollar appreciates This appreciation, however, reduced for subsequent investors later appreciation expectation, as the U.S. dollar has indeed been upgraded before their investment [and]) - the attractiveness of an investment location so reduces its future attractiveness. The process of return Angle ego only comes to an end when the yields of both systems are identical.

As long as one of the two plants is more profitable to invest where it leads to an appreciation of the local currency and thus a decline in yield. According to the interest parity theory must therefore be applied. Or in other words:

This so-called interest rate parity condition must be fulfilled according to the theory, at any time, since any deviation from the parity would have an immediate arbitrage behavior.

Interest parity using the example

First, some key model assumptions are made to understand explanation and illustration. The model is applied to two countries with two different monetary systems broken down ( Germany € / U.S. $). It is assumed that the financial markets of both countries are open and there are no restrictions. Furthermore, the investor can first act only securities with a term of one year. Let us now consider the calculation of a German investor who decides whether to invest in a German securities with one-year term or an American with the same maturity. It must be checked that system promises a higher return.

Is the nominal interest rate for German securities. The investor receives a return of euro for each euro. ( This is visualized in the following presentation by the upper right-pointing arrow).

Now we compare the return of an American security. Before the German investor can invest in American securities, it first has to buy American dollars. If the nominal exchange rate between euro and dollar, one acquires for each Euro dollars. (This is shown in Figure 1 by the arrow visualized down)

Denotes the nominal interest rate for American securities. Thus obtained at the end of the term ( after one year) dollars. ( This can be seen in Figure 2.2.1 at the bottom right-pointing arrow)

At the end of the year, the investor must exchange his dollars back into euros. Investors expect at the end of the term of an exchange rate, which can be explained by the expected value of the exchange rate in the form of. This implies that the investor gets back at the end of the year for every euro that he has invested EUR. ( This is illustrated in Figure 2.2.1 by the right pointing upward arrow)

The essence of this idea is obvious - if you compare the investment returns of the two countries together, one comes to the conclusion that not only the yield differences are relevant to the decision, but also the exchange rate expectations, the investor has at the end of the investment term. Based on this consideration, it is assumed that the investor is only and only interested in the highest expected return. This investor will then hold the securities in its portfolio, which is the highest expected return promises. This would mean that German and American securities achieve exactly the same expected rate of return; no one would be willing to hold a paper with a lower yield. So it must fulfill the following arbitrage condition:

Rearranging the equation yields:

The arbitrage has effect in this particular case (Equation 2.2.2) means that the yields of both countries adjust to each other. One speaks in this case of interest rate parity ( parity of Latin par 'equal' ) or uncovered interest parity.

Where the return on domestic higher than those abroad, the Investor will invest its capital in Germany. Conversely, it is a foreign investment prefer if their return is greater than that of a domestic plant. If both returns the same, so the investor is indifferent.

As already mentioned, implies an unequal return in home and abroad a certain exchange rate developments. Where the return is higher abroad than at home, so the resulting investment abroad will lead to an appreciation of the foreign currency because the foreign currency must be sought in order to put money abroad. Conversely, a higher domestic rate of return lead to an appreciation of the domestic currency, as capital is deducted from abroad and invested domestically. According to the interest parity theory is thus possible to explain exchange rate movements due to the search for yield by investors. That would mean, for example, an investor who holds which American securities, invested in German securities if this system can deliver a higher return. Thus, this investor will exchange dollars for Euros, consequently the demand for euros and the supply of dollars increases. This has the consequence that the price rises ( exchange rate ) for EUR and the price ( exchange rate ) for dollar falls. The reason for this is the lack of interest rate parity. Taking the two adjacent figures, the return depending on the exchange rate dollars to euros described can detect a current example. The interest rates fall over time and at the same time the dollar is devalued against the euro.

Uncovered interest rate parity

Every profit-oriented investors is therefore interested in the securities, which bring the highest returns, and will hold them in its portfolio.

This in turn would mean that German and American securities would bring the same return in order to be attractive for investors.

If the equation just listed in Figure 1 to concerns approximately it:

This equation is also known as uncovered interest parity.

The ratio here indicates the percentage exchange rate change expectations. Market participants expect so for example, a two per cent devaluation of the domestic currency over the given investment period, they will only be willing to invest in the domestic system, if the domestic interest rate exactly two percentage points higher than the foreign interest rate.

In the uncovered interest parity is assumed that market participants for bearing the uncertainty of making the transfer in foreign investment itself. They thus accept the exchange rate risk, which is unfunded. Due to the exchange rate risk is a speculative transaction is based here.

Covered interest parity

Will investors take no exchange risk, it can simultaneously enter into a forward contract.

This forward transaction in the currency futures market, which in addition to the "actual" foreign exchange market ( forex spot market ) exists. Of commerce on these futures markets are financial derivatives. In such a forward contract is already at the beginning of the year the price at which passed the currency in one year or are to be converted again, fixed. This type of hedge transaction is also known as swaps.

If in the equation of the uncovered interest rate parity the expected exchange rate by the forward rate, we obtain the equation for the covered interest parity.

When covered interest parity exchange rate risk is avoided. Consequently, it provides a pure arbitrage equilibrium dar. Would covered interest parity does not apply, the economic agents would have the opportunity to currency arbitrage, that is, they could use international interest rate differences to their advantage for profit.

Example of the covered interest parity

In the interest parity and uncovered interest rate parity is one of three factors underlying ( exchange rate, return on investment, expected value of the return ), which is crucial for deciding whether to invest domestically or abroad. Here, some important factors are neglected. For example, fall when investing in foreign securities transaction costs, ie it must be bought dollars to invest in American securities market, and after the expiration of the term, the dollar income must be converted into euros again. Another example is the foreign currency risk, as the exchange rate at the end of the term is an uncertain variable. In addition, market participants can also be influenced by liquidity factors. In order to provide the uncertainty of factors stop, the investor uses the services covered interest parity the safety of the forward contract. About the derivatives can be secure in future exchange rates. This provides investors the opportunity to be expected in future exchange rates not only uncertainty, but to be able to secure from derivatives market trades. This would mean that an investor who buys with euro dollar deposits, wants to know with certainty how many euros deposit those dollars is worth after one year. This uncertainty he excludes, by selling at the same time with the purchase of a dollar deposit the principal amount plus interest on the due date (one year) against Euro. Thus he has his purchase "covered", which means that he has hedged against unexpected devaluation of the euro. Such transactions are called swaps.

An example will illustrate the importance of this condition and the reasons for their inevitable validity. The twelve-month forward price of euro in dollars was $ = 1.113 per euro. Simultaneously, the spot exchange rate = $ 1.05 per euro = was =, 0.10 and 0.04. The dollar return on one U.S. dollars insert so is 0.10 or 10% annually. What is the return on a covered Euro deposit? A deposit over € 1 now costs $ 1.05 and is after a year worth € 1.04. If you sell today € 1.04 for forward exchange rate of $ 1.113 per euro, the dollar value of your investment after one year is ( $ 1.113 per euro ) x (1.04 € ) = 1.158. The return on the covered call a euro deposit is therefore ( 1.158-1.05 ) / 1.05 = 0.103. This return of 10.3 % per year exceeds the return on dollar deposits in the amount of 10%, so no covered interest parity is given. In this situation, no one would be willing to hold dollar deposits, everyone would prefer euro deposits. Consequently, the covered yield on euro deposit can be expressed in the following form:

This roughly corresponds to

If the product is a small value. Covered interest parity can be expressed in the following form:

The size

Is called the forward premium (report) of the euro against the dollar (or as a forward discount or discount of the dollar against the euro ). Because of this terminology, we can describe the covered interest parity as follows: " The interest rate on dollar deposits is equal to the interest rate on euro deposits plus the forward premium of the euro against the dollar (or the forward discount of the dollar against the euro ) ." It should be remembered that both uncovered and covered interest parity are only satisfied when the twelve-month forward rate is equal to the spot price. But the crucial difference between uncovered and covered interest parity is the exchange rate risk. When uncovered interest parity as opposed to covered interest parity is a currency risk.

Empirical relevance and applications of the interest parity

Has been found in empirical studies that the condition of the covered interest parity can be regarded as fulfilled. But the same is not entirely true for the condition of uncovered interest parity. Inefficiencies in the foreign exchange markets and not risk-neutral behavior of market participants are seen as reasons that the condition of uncovered interest parity is not met.

The interest parity condition is often used as a basis as an integral component of modern model exchange rate theories. Thus, based on both the monetarist exchange rate model and the Dornbusch model of excessive exchange rates on the assumption of uncovered interest parity. Furthermore, the interest parity can also be applied to empirical exchange rate issues.

In addition, the interest rate parity theory is the subject of extensive research. It was checked frequently empirically because of the simple data collection. Surprisingly, the theory is, however, mostly empirically refuted. Most often this is attributed to the fact that other factors as interest rates and exchange rate expectations affect the investment decision or that important prerequisites for the validity of the theory (eg the existence of perfect capital markets) do not apply.

Thus, the German Bundesbank has found in a study that a so-called currency carry trade ( the recording of a loan in a currency with low interest rates and the simultaneous investment in a currency with high interest rates ) is highly profitable; for validity of the interest rate parity would have the high-interest currency to depreciate over time, actually - and thus reduce the interest rate advantage.

Nevertheless, it is considered scientific consensus that a strong deviation from the interest parity due to the then incipient arbitrage is hardly possible.