# purchasing power parity

See attached file for full problem description.

Directions: Type your answer to each question where indicated. Use more space if needed.

1. Two countries, the United States and England, produce only one good, wheat. Suppose the price of wheat is $3.25 in the United States and is 1.35 pounds in England.

a. According to the law of one price, what should the $:Pound spot exchange rate be?

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b. Suppose the price of wheat over the next year is expected to rise to $3.50 in the United States and 1.60 pounds in England. What should the one-year $:pound forward rate be?

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c. If the U.S. government imposes a tariff of $0.50 per bushel on wheat imported from England, what is the maximum possible change in the spot exchange rate that could occur?

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2. If expected inflation is 100% and the real required return is 5%, what will the nominal interest rate be according to the Fisher effect?

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3. Suppose that in Japan the interest rate is 8% and inflation is expected to be 3%. Meanwhile, the expected inflation rate in France is 12%, and the English interest rate is 14%. To the nearest whole number, what is the best estimate of the one-year forward exchange premium (discount) at which the pound will be selling relative to the French Franc.

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4. Suppose the spot rates for the euro, pound sterling, and Swiss franc are $0.92, $1.13 and $0.38, respectively. The associated 90-day interest rates (annualized) are 8%, 16%, and 4%; the U.S. 90 day rate (annualized is 12%. What is the 90-day forward rate on an ACU (ACU1=E1+Pound 1+ SFr1) if interest parity holds?

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5. Assume the interest rate is 16% on pounds sterling and 7% on euros. At the same time, inflation is running at an annual rate of 3% in Germany and 9% in England.

a. If the euro is selling at a one-year forward premium of 10% against the pound, is there an arbitrage opportunity? Explain

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b. What is the real interest rate in Germany? In England?

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Here is the course work

Interest Rate Parity (IRP)

Example: Covered Interest Arbitrage

Exchange rate between the U.S. dollar ($) and the British pound (£)

Spot $1.6865/£

1-month forward $1.6854/£

3-month forward $1.6828/£

Assume that the prime rate of interest is 8 percent in the United States and 6 percent in the United Kingdom. In this situation, an arbitrage opportunity exists as the dollar is at a premium in a forward market, and there is an interest rate differential of 2 percent. To take advantage of arbitrage an investor can do the following:

1) Borrow £1,000 in the United Kingdom at 6 percent for one month with the intent to repay after a month. The calculation is shown in the equation below.

2) Convert £1,000 to U.S. dollars ($) in a spot market at $1.6865/£. See the equation below.

3) Invest $1,686.50 in U.S. dollars ($) at 8 percent for one month. In this case, you will end up with the following equation:

4) Sell $1,697.74 in a 1-month forward market at £0.5933/$. The equation below shows what you will receive.

$1,697.74 × £0.5933/$ = £1007.27

5) Therefore, profit is the difference between forward transaction and repayment

£1,007.27 - £1,005 = £2.27 per £1,000 borrowed

Because of market forces, the following conditions are true:

? Demand for British pound (£ ) will increase, and as a result the interest rate in the United Kingdom will go up.

? Supply of dollars will increase in the United States, so the interest rate in the United States will come down.

? The dollar will appreciate in the spot market.

This will continue until equilibrium is reached, that is, no arbitrage opportunity exists.

With IRP, currency with a lower interest rate should be at forward premium in terms of the currency with a higher interest rate, or the interest rate differential should be equal to the forward differential.

where

? rh is the interest rate of home currency

? rf is the interest rate of foreign currency

? F1 is the forward rate

? e0 is the spot exchange rate

Purchasing Power Parity (PPP)

There are two versions of PPP: absolute and relative.

In the absolute version of PPP (also known as law of one price), exchange-adjusted price levels should be identical worldwide. Absolute version assumes that markets are perfect, that is, there are no transportation costs, no tariffs, and so on, which is not realistic. However, it provides a useful definition of exchange rate. For example, if a loaf of bread is $2 in the United States and £1.25 in the United Kingdom, then the exchange rate between the two currencies is shown in the equation below:

Therefore, the exchange rate between the U.S. dollar and the British pound is shown in the equation below, where

? P$ is the price level in U.S.

? P£ is the price level in U.K.

? e$/£ is the exchange rate

The relative form of PPP considers market imperfections and states that the exchange rate between home currency and any foreign currency will adjust to reflect changes in the price levels of two countries.

The derivation of PPP is shown below:

Let

be the current exchange rate between the U.S. dollar and the U.K. pound

and let

be the exchange rate between the U.S. dollar and the U.K. pound in the future.

This equation is known as the PPP condition.

Fisher Effect

The Fisher effect is a market condition versus an arbitrage. It states that nominal interest rate will be equal to the real rate of interest compounded by inflation. In other words, the real rate of interest is the difference between nominal rate of interest and inflation. See the equation below.

where

? rr is the real rate of interest

? rn is the nominal rate of interest

International Fisher Effect

The international Fisher effect states that the real rate of interest must be the same for assets of equal risk, even if they are in different countries. In other words, the real rate of interest should be equal all around the world. See the equations below.

The inflation term is the same as PPP, and the interest rate term is the same as an IRP, therefore,

Unbiased Forward Rate Hypothesis

The unbiased forward rate hypothesis states that forward rates should be unbiased predictors of future spot rates, that is,

#### Solution Preview

Please see the attached file.

Directions: Type your answer to each question where indicated. Use more space if needed.

1. Two countries, the United States and England, produce only one good, wheat. Suppose the price of wheat is $3.25 in the United States and is 1.35 pounds in England.

a. According to the law of one price, what should the $:Pound spot exchange rate be?

The ...

#### Solution Summary

The exchange rate between the U.S. dollar and the British pound is depicted.