Chapter 6 International Parity Relationships and Forecasting Exchange

Chapter 6 International Parity Relationships and Forecasting Exchange Rates Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 1

Introduction § It is important to have a firm understanding of the forces driving exchange rate changes. § This chapter examines several key international parity relationships, such as interest rate parity and purchasing power parity. § An understanding of these parity relationships provides insights into: 1. how foreign exchange rates are determined. 2. how to forecast foreign exchange rates. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 2

Arbitrage definition § Arbitrage : the act of simultaneously buying and selling equivalent assets for the purpose of making guaranteed profits. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 3

Interest rate parity (IRP) § IRP is an arbitrage condition that must hold when international financial markets are in equilibrium. § If IRP did not hold, then it would be possible for an trader to make unlimited amounts of money exploiting the arbitrage opportunity. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 4

Interest rate parity (IRP) § Suppose that you have $1 to invest over a 1 year period. Consider two alternative ways: 1. invest domestically at the U. S. interest rate. 2. invest in a foreign country (e. g. UK) at the foreign interest rate and use a forward contract to eliminate the exchange risk. ➡your U. K. investment coupled with forward hedging is a perfect substitute for the domestic U. S. investment ➡Both investments yield the same cash flow. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 5

Interest rate parity (IRP) § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 6

Interest rate parity (IRP) § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 7

Covered interest arbitrage § A situation that occurs when IRP does not hold, thereby allowing certain arbitrage profits to be made without the arbitrageur investing any money out of pocket or bearing any risk. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 8

Example of CIA § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 9

Example of CIA § The arbitrager can carry out the following transactions: 1. In the United States, borrow $1, 000. Repayment in one year will be $1, 050, 000 = $1, 000 × 1. 05. 2. Buy £ 555, 556 spot using $1, 000. 3. Invest £ 555, 556 in the U. K. ; the maturity value will be £ 600, 000 = £ 555, 556 × 1. 08. 4. Sell £ 600, 000 forward in exchange for $1, 068, 000 = (£ 600, 000)($1. 78/£). § In one year, the arbitrager will 1. Receive £ 600, 000 from UK investment. 2. Deliver £ 600, 000 to the counterparty of the forward contract and receive $1, 068, 000. 3. Repay $1, 050, 000 for his US loan. 4. Arbitrage profit= $1, 068, 000 − $1, 050, 000= $18, 000 Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 10

Market adjustment § How long will this arbitrage opportunity last? § Only for a short while. As soon as deviations from IRP are detected, informed traders will immediately carry out CIA transactions. § The following adjustments restore IRP: 1. The pound will appreciate in the spot market (S↑). 2. The pound will depreciate in the forward market (F↓). 3. The interest rate will rise in the United States (i$↑). 4. The interest rate will fall in the U. K. (i£↓). Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 11

CIA example 2: § Suppose that the market condition is summarized as follows: § § Three-month interest rate in the United States: 8. 0% per annum. Three-month interest rate in Germany: 5. 0% per annum. Current spot exchange rate: € 0. 800/$. Three-month forward exchange rate: € 0. 7994/$. § Does a CIA opportunity exists? If yes, calculate the arbitrage profit, assuming that the arbitrager can borrow up to $1, 000 or the equivalent € amount. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 12

Interest Rate Parity and Exchange Rate Determination § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 13

Foreign exchange expectations § Some forecasters believe that for the major floating currencies, foreign exchange markets are “efficient” and forward exchange rate are unbiased predictors of future exchange rates. § The forward expectations hypothesis states that the forward exchange rate Ft is equal to the expected value of the spot exchange rate at time t. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 14 © Jon Moulton

Foreign exchange expectations § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 15 © Jon Moulton

Uncovered interest arbitrage (carry trade) § Borrowing in “cheap” rate country, exchanging to desired country for investment, and investing in desired securities. § Without using forward contracts FX risk exists § Works when exchange rate is relatively stable and interest rate differential exists between countries. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 16

Uncovered interest arbitrage (carry trade) § Suppose Japan’s 1 -year rate is 0. 4% per annum, S(Yen/$)=80, F 1(Yen/$)=79. 8013, and US rate is 0. 65%. § Is it possible to do CIA? § No § But if you can borrow more cheaply in Japan , and the spot rate does not vary within the year, then uncovered reexchange investment would be profitable. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 17 © Jon Moulton

Reasons for Deviations from Interest Rate Parity § IRP tends to hold well, but it may not hold precisely all the time for two reasons: transaction costs and capital controls. § The interest rate at which the arbitrager borrows, ia, tends to be higher than the rate at which he lends, ib, reflecting the bid-ask spread. § Governments sometimes restrict capital flows, inbound and/or outbound. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 18

Capital restrictions were removed in 1979 Dr. Yaqoub Alabdullah New capital controls introduced Kuwait University - College of Business Administration Japan adopted the new Foreign Exchange and Foreign Trade Control Law, which generally liberalized foreign exchange transactions 19

Purchasing Power Parity (PPP) § The PPP theory states that the exchange rate between currencies of two countries should be equal to the ratio of the countries' price levels. § It is an application of the law of one price internationally to a standard consumption basket. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 20

What is the law of one price? § The law of one price states that two identical assets should sell for the same price regardless of where they are sold (assuming no market frictions). Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 21

What is a consumption basket? § It is a list of the most common consumption items bought by people all around the world. § Provides an insight on the cost of living and is used to calculate inflation. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 22

Absolute PPP § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 23

Big Mac PPP § The Economist each year compiles local prices of Big Macs around the world and computes the so-called “Big Mac PPP. ” § They calculate the exchange rate that would equalize the hamburger prices between America and elsewhere. § It is a proxy for under/over-valuation of currencies. § http: //www. economist. com/content/big-mac-index Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 24

Example § A Big Mac costs $4. 33 in America and 15. 65 ¥ in China. Thus, the Big Mac PPP would imply the exchange rate would be § SPPP($/¥)=$4. 33 / ¥ 15. 65 = $0. 2767/¥ § The actual exchange rate, however, is $0. 1565/¥ , implying that the yuan is substantially undervalued. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 25

Example 2 § The price of Big Mac is Switzerland is CHF 6. 5 and $4. 33 in the USA. Calculate the Big Mac PPP implied CHF/$ exchange rate. If S(CHF/$)=0. 99, would you the say the CHF is over or undervalued? Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 26

S(FRN/$) Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 27

Testing Big Mac PPP § Pakko and Pollard (2003) conclude that Big Mac PPP holds in the long run, but currencies can deviate from it for lengthy periods. § The absolute version of PPP assumes no barriers to trade. High tariffs and transportation costs on beef and lettuce. § Prices are affected by taxes and competition. § Prices of non-tradeable goods (real estate, utilities, labor) are also inputs that affect production costs. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 28 © Jon Moulton

Relative form of PPP § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 29

Relative form of PPP § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 30

Relative PPP § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 31 © Jon Moulton

Evidence on Purchasing Power Parity § Even if PPP may not hold in reality, it can still play a useful role in economic analysis. 1. PPP-determined exchange rate can be used as a benchmark in deciding if a country's currency is undervalued or overvalued against other currencies. 2. PPP may hold over the very long term but not in the short term. 3. More meaningful international comparisons of economic data can be made using PPP-determined rather than market -determined exchange rates. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 33

Evidence on Purchasing Power Parity § Reasons for failure of PPP: § Baskets of goods might be different between countries. § Substantial barriers to international commodity arbitrage exist. § Deviations from PPP can result from transportation costs or tariffs and quotas imposed on international trade. § As long as there are nontradables in the consumption basket, PPP will not hold in its absolute version. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 34

International Fisher Effect § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 35 © Jon Moulton

International Fisher Effect § =1 Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 36 © Jon Moulton

International Fisher Effect § Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 37 © Jon Moulton

International Fisher Effect § Thus, actual results says: § Currencies with high interest rates tend to depreciate and currencies with low interest rates tend to appreciate. § Evidence indicates this also holds in the long-run but , but with significant deviations in the short-run. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 38 © Jon Moulton

Forecasting foreign exchange § Three approaches to exchange rate forecasting : 1. Efficient market approach: uses such market-determined prices as the current exchange rate or the forward exchange rate to forecast the future exchange rate. 2. Fundamental approach: uses various formal models of exchange rate determination forecasting purposes. 3. Technical approach: identifies patterns from the past history of the exchange rate and projects it into the future. § The existing empirical evidence indicates that neither the fundamental nor the technical approach outperforms the efficient market approach. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 39 © Mc. Graw-Hill Inc.

Practice problem 1 § Suppose that the treasurer of IBM has an extra cash reserve of $100, 000 to invest for six months. The six-month interest rate is 8 percent per annum in the United States and 7 percent per annum in Germany. Currently, the spot exchange rate is € 1. 01 per dollar and the six-month forward exchange rate is € 0. 99 per dollar. The treasurer of IBM does not wish to bear any exchange risk. Where should he/she invest to maximize the return? Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 40 © Mc. Graw-Hill Inc.

Practice problem 2 While you were visiting London, you purchased a Jaguar for £ 35, 000, payable in three months. You have enough cash at your bank in New York City, which pays 0. 35% interest per month, compounding monthly, to pay for the car. Currently, the spot exchange rate is $1. 45/£ and the threemonth forward exchange rate is $1. 40/£. In London, the money market interest rate is 2. 0% for a three-month investment. There are two alternative ways of paying for your Jaguar. (a) Keep the funds at your bank in the U. S. and buy £ 35, 000 forward. (b) Buy a certain pound amount spot today and invest the amount in the U. K. for three months so that the maturity value becomes equal to £ 35, 000. Evaluate each payment method. Which method would you prefer? Why? Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 41 © Mc. Graw-Hill Inc.

Practice problem 3 Currently, the spot exchange rate is $1. 50/£ and the three-month forward exchange rate is $1. 52/£. The three-month interest rate is 8. 0% per annum in the U. S. and 5. 8% per annum in the U. K. Assume that you can borrow as much as $1, 500, 000 or £ 1, 000. a. Determine whether the interest rate parity is currently holding. b. If the IRP is not holding, how would you carry out covered interest arbitrage? Show all the steps and determine the arbitrage profit. c. Explain how the IRP will be restored as a result of covered arbitrage activities. Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 42 © Mc. Graw-Hill Inc.

Practice problem 5 § In the issue of October 23, 1999, the Economist reports that the interest rate per annum is 5. 93% in the United States and 70. 0% in Turkey. Why do you think the interest rate is so high in Turkey? Based on the reported interest rates, how would you predict the change of the exchange rate between the U. S. dollar and the Turkish lira? Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 43 © Mc. Graw-Hill Inc.

Practice problem 6 § As of November 1, 1999, the exchange rate between the Brazilian real and U. S. dollar is R$1. 95/$. The consensus forecast for the U. S. and Brazil inflation rates for the next 1 year period is 2. 6% and 20. 0%, respectively. What would you forecast the exchange rate to be at around November 1, 2000? Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 44 © Mc. Graw-Hill Inc.

Practice problem 8 § Suppose that the current spot exchange rate is € 1. 50/₤ and the oneyear forward exchange rate is € 1. 60/₤. The one-year interest rate is 5. 4% in euros and 5. 2% in pounds. You can borrow at most € 1, 000 or the equivalent pound amount, i. e. , ₤ 666, 667, at the current spot exchange rate. a. Show you can realize a guaranteed profit from covered interest arbitrage. Assume that you are a euro-based investor. Also determine the size of the arbitrage profit. b. Discuss how the interest rate parity may be restored as a result of the above transactions. c. Suppose you are a pound-based investor. Show the covered arbitrage process and determine the pound profit amount. answers: a)profit=€ 68, 134 c) profit= £ 42. 584 Dr. Yaqoub Alabdullah Kuwait University - College of Business Administration 45 © Mc. Graw-Hill Inc.