INTEREST PARITY The interest rate parity explains the relationship between returns to bond

investments between two countries. Interest rate parity results from profit-seeking arbitrage activity, specifically covered interest rate arbitrage. Let us go through an example of how covered interest arbitrage works. For expositional purposes

i $ 5 interest rate in the United States

i d 5 interest rate in the United Kingdom

F 5 forward exchange rate (dollars per pound)

E 5 spot exchange rate (dollars per pound) where the interest rates and the forward rate are for assets with the same term to maturity (e.g., three months or one year), the investor in the United States can earn (1 1 i $ ) at home by investing $1 for 1 period (for instance, one year). Alternatively, the U.S. investor can invest in the United Kingdom by converting dollars to pounds and then investing the pounds. Here, $1 is equal to 1/E pounds (where E is the dollar price of pounds). Thus, by investing in the United Kingdom, the U.S. resident

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the uncertainty regarding the future dollar value of (1 1 i d )/E by covering the d currency investment with a forward contract. By selling (1 1 i d )/E pounds to be received in a future period in the forward market today, the investor has guaranteed a certain dollar value of the pound investment

opportunity. The covered return is equal to (1 1 i d )F/E dollars. The U.S. investor can earn either 1 1 i $ dollars by investing $1 at home or (1 1 i d ) F/E dollars by investing the dollar in the United Kingdom. Arbitrage between the two investment opportunities results in

11i $ 5 ð1 1 i d ÞF =E

which can be rewritten as:

ð6 :1Þ Equation (6.1) can be put in a more useful form by subtracting 1 from

ð1 1 i $ Þ =ð1 1 i d Þ 5 F=E

both sides, giving us the exact interest rate parity equation: ði $ 2i d Þ =ð1 1 i d Þ 5 ðF 2 EÞ=E

ð6 :2Þ This equation can be approximated by noting that the denominator on

the left side is almost one. Approximating by assuming that the denominator is equal to one results in the approximate covered interest rate parity equation:

ð6 :3Þ The smaller i d , the better the approximation of Equation (6.3) to

ði $ 2i d Þ 5 ðF 2 EÞ=E

(6.2) . Equation (6.3) indicates that the interest differential between a comparable U.S. and U.K. investment is equal to the forward premium or discount on the pound. (We must remember that, since interest rates are quoted at annual rates or percent per annum, the forward premiums or discounts must also be quoted at annual rates.) Now let’s consider an example. Ignoring bid-ask spreads, we observe the following Eurocurrency market interest rates:

Euro $: 15% Euro d: 10% The exchange rate is quoted as the dollar price of pounds and is

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which simplifies to

F 5 2:00ð0:15 2 0:10Þ 1 2:00 5 2:10 Thus, we would expect a 12-month forward rate of $2.10 to give a

12-month forward premium equal to the 0.05 interest differential. Suppose a bank sets the 12-month forward rate at $2.15, instead of $2.10. This would lead to arbitrage opportunities. How would the arbitragers profit? They could buy pounds at the spot rate and then invest and sell the pounds forward for dollars, because the future price of pounds is higher than that implied by the interest parity relation. These actions would tend to increase the spot rate and lower the forward rate, thereby bringing the forward premium back in line with the interest differential. The interest rates could also move, because the movement of funds into pound investments would tend to depress the pound interest rate, whereas the shift out of dollar investments would tend to raise the dollar rate.

The interest parity relationship can also be used to illustrate the con- cept of the effective return on a foreign investment. Equation (6.3) can be rewritten so that the dollar interest rate is equal to the pound rate plus the forward premium. Thus, the returns to investing in dollar assets and pound denominated assets are:

ð6 :4Þ Covered interest parity ensures that Equation (6.4) will hold. Note

i $ 5i d 1ðF 2 EÞ=E

that the interest rate on the bond i d is not the relevant return measure by itself, since this is the return in pounds. Instead the effective return to a U.K. investment is composed of an interest rate return and an exchange rate return. But suppose we do not use the forward market, yet we are U.S. residents who buy U.K. bonds. Even in this case the effective return would be composed of two parts. The first part would

be the interest rate return and the second would be the expected change in the exchange rate, as we now need to take into account the expected spot rate in the future. In other words, the return on a

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yield a forward premium equal to the interest differential, we may ask: How well does interest rate parity hold in the real world? Since deviations from interest rate parity would seem to present profitable arbitrage opportunities, we would expect profit-seeking arbitragers to eliminate any deviations. Still, careful studies of the data indicate that small deviations from interest rate parity do occur. There are several reasons why interest rate parity may not hold exactly, and yet we can earn no arbitrage profits from the situation. The most obvious reason is the transactions cost between markets. Because buying and selling foreign exchange and international securities involves a cost for each transaction, there may exist deviations from interest rate parity that are equal to, or smaller than, these transaction costs. In this case, speculators cannot profit from the deviations, since the price of buying and selling in the market would wipe out any apparent gain. Studies indicate that for comparable financial assets that differ only in terms of currency of denomination (for example, dollar- and pound- denominated Eurodeposits in a German bank), 100 percent of the deviations from interest rate parity can be accounted for by transaction costs.

Besides transaction costs, there are other reasons why interest rate parity may not hold perfectly. One other reason, for small deviations from interest rate parity, is the potential difference in taxation of interest earnings and foreign exchange rate earnings. If these are differently taxed in a country then the effective return equation (6.4) might not hold since one side involves only interest earnings and the other interest earnings and foreign exchange earnings. Thus, it may be misleading to simply consider pretax effective returns to decide if profitable arbitrage is possible.

Two more reasons for why interest rate parity might not hold perfectly are government controls and political risk. If government controls on financial capital flows exist, then an effective barrier between national markets is in place. If an individual cannot freely buy or sell the currency or securities of a country, then the free market forces that work in response to effective return differentials will not function. Indeed, even the threat of controls could affect the interest rate parity condition. Political risk is often mentioned in conjunction with government

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currency. For instance, the Eurodollar market provides a market for U.S. dollar loans and deposits in major financial centers outside the United States, thereby avoiding any risk associated with U.S. government actions.

INTEREST PARITY The interest rate parity explains the relationship between returns to bond