INTERNATIONAL FINANCIAL MANAGEMENT Fourth Edition EUN RESNICK 6

International Parity Relationships & Forecasting Chapter Six Foreign Exchange Rates INTERNATIONAL FINANCIAL Chapter Objective:

Chapter Outline Interest Rate Parity n Covered Interest Arbitrage l l Purchasing Power Parity

Interest Rate Parity l l Interest Rate Parity Defined Covered Interest Arbitrage Interest Rate

Interest Rate Parity Defined l l l IRP is an arbitrage condition. If IRP

Interest Rate Parity Carefully Defined Consider alternative one year investments for $100, 000: 1.

Alternative 2: Send your $ on a round trip to Britain $1, 000 S$/£

Interest Rate Parity Defined l The scale of the project is unimportant $1, 000

Interest Rate Parity Defined Formally, 1 + i$ F$/¥ = 1 + i¥ S$/¥

Forward Premium l l l It’s just the interest rate differential implied by forward

Interest Rate Parity Carefully Defined l Depending upon how you quote the exchange rate

IRP and Covered Interest Arbitrage If IRP failed to hold, an arbitrage would exist.

IRP and Covered Interest Arbitrage A trader with $1, 000 could invest in the

Alternative 2: Arbitrage I buy pounds £ 1 £ 800 = $1, 000× $1.

Interest Rate Parity & Exchange Rate Determination According to IRP only one 360 -day

Arbitrage Strategy I If F 360($/£) > $1. 20/£ i. Borrow $1, 000 at

Step 2: buy pounds £ 1 £ 800 = $1, 000× $1. 25 $1,

Arbitrage Strategy II If F 360($/£) < $1. 20/£ i. Borrow £ 800 at

Step 2: buy dollars $1. 25 $1, 000 = £ 800× £ 1 $1,

IRP and Hedging Currency Risk You are a U. S. importer of British woolens

IRP and a Forward Market Hedge To form a forward market hedge: Borrow $112.

Forward Market Hedge Where do the numbers come from? We owe our supplier £

Reasons for Deviations from IRP l Transactions Costs n n n l The interest

Transactions Costs Example l Will an arbitrageur facing the following prices be able to

l l l l Try borrowing $1. 000 at 5%: Trade for € at

Purchasing Power Parity l l l Purchasing Power Parity and Exchange Rate Determination PPP

Purchasing Power Parity and Exchange Rate Determination l The exchange rate between two currencies

Purchasing Power Parity and Exchange Rate Determination l l l Suppose the spot exchange

Purchasing Power Parity and Exchange Rate Determination l The euro will trade at a

Purchasing Power Parity and Interest Rate Parity l Notice that our two big equations

Expected Rate of Change in Exchange Rate as Inflation Differential l We could also

Expected Rate of Change in Exchange Rate as Interest Rate Differential E(e) = 6

Quick and Dirty Short Cut l Given the difficulty in measuring expected inflation, managers

Evidence on PPP l PPP probably doesn’t hold precisely in the real world for

Approximate Equilibrium Exchange Rate Relationships E(e) ≈ IFE (i$ – i¥) ≈ FEP ≈

The Exact Fisher Effects An increase (decrease) in the expected rate of inflation will

International Fisher Effect If the Fisher effect holds in the U. S. 1 +

International Fisher Effect If the International Fisher Effect holds, E(1 + ¥) 1 +

Exact Equilibrium Exchange Rate Relationships FEP IFE 1 + i¥ 1 + i$ PPP

Forecasting Exchange Rates l l Efficient Markets Approach Fundamental Approach Technical Approach Performance of

Efficient Markets Approach l l l Financial Markets are efficient if prices reflect all

Fundamental Approach l Involves econometrics to develop models that use a variety of explanatory

Technical Approach l l l Technical analysis looks for patterns in the past behavior

Performance of the Forecasters l l l Forecasting is difficult, especially with regard to

End Chapter Six 6 -44 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc.

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International Parity Relationships & Forecasting Chapter Six Foreign Exchange Rates INTERNATIONAL FINANCIAL Chapter Objective: MANAGEMENT 6 This chapter examines several key international parity relationships, such as interest rate parity and Fourth Edition purchasing power parity. EUN / RESNICK 6 -1 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Chapter Outline Interest Rate Parity n Covered Interest Arbitrage l l Purchasing Power Parity n n IRP and Exchange Rate Determination PPP Deviations and the Real Exchange Rate l l The Fisher Effects n n Reasons for Deviations from IRP Evidence on Purchasing Power Parity l l Forecasting Exchange Rates l l Purchasing Power Parity The Fisher Effects n Efficient Market Approach l l The Fisher Effects Forecasting Exchange Rates n Fundamental Approach l Forecasting Exchange Rates n Technical Approach l l n 6 -2 Performance of the Forecasters Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Interest Rate Parity l l Interest Rate Parity Defined Covered Interest Arbitrage Interest Rate Parity & Exchange Rate Determination Reasons for Deviations from Interest Rate Parity 6 -3 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Interest Rate Parity Defined l l l IRP is an arbitrage condition. If IRP did not hold, then it would be possible for an astute trader to make unlimited amounts of money exploiting the arbitrage opportunity. Since we don’t typically observe persistent arbitrage conditions, we can safely assume that IRP holds. 6 -4 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Interest Rate Parity Carefully Defined Consider alternative one year investments for $100, 000: 1. Invest in the U. S. at i$. Future value = $100, 000 × (1 + i$) Trade your $ for £ at the spot rate, invest $100, 000/S$/£ in Britain at i£ while eliminating any exchange rate risk by F$/£ selling the future value of the British investment forward. Future value = $100, 000(1 + i£)× 2. S$/£ Since these investments have the same risk, they must have the same future value (otherwise an arbitrage would exist) F$/£ (1 + i£) × = (1 + i$) S$/£ 6 -5 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Alternative 2: Send your $ on a round trip to Britain $1, 000 S$/£ $1, 000 Alternative 1: invest $1, 000 at i$ Step 3: repatriate future value to the U. S. A. IRP Step 2: Invest those pounds at i£ Future Value = $1, 000 (1+ i£) S$/£ IRP $1, 000 (1+ i£) × F$/£ $1, 000×(1 + i$) = S$/£ Since both of these investments have the same risk, they must Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved. 6 -6 have the same future value—otherwise an arbitrage would exist

Interest Rate Parity Defined l The scale of the project is unimportant $1, 000 (1+ i ) × F $1, 000×(1 + i$) = £ $/£ S$/£ F$/£ × (1+ i£) (1 + i$) = S$/£ 6 -7 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Forward Premium l l l It’s just the interest rate differential implied by forward premium or discount. For example, suppose the € is appreciating from S($/€) = 1. 25 to F 180($/€) = 1. 30 The forward premium is given by: f 180, €v$ 6 -9 F 180($/€) – S($/€) 360 $1. 30 – $1. 25 = × 180 = × 2 = 0. 08 S($/€) $1. 25 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Interest Rate Parity Carefully Defined l Depending upon how you quote the exchange rate ($ per ¥ or ¥ per $) we have: 1 + i¥ F¥/$ = 1 + i$ S¥/$ or 1 + i$ F$/¥ = 1 + i¥ S$/¥ …so be a bit careful about that 6 -10 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

IRP and Covered Interest Arbitrage If IRP failed to hold, an arbitrage would exist. It’s easiest to see this in the form of an example. Consider the following set of foreign and domestic interest rates and spot and forward exchange rates. Spot exchange rate 360 -day forward rate 6 -11 S($/£) = $1. 25/£ F 360($/£) = $1. 20/£ U. S. discount rate i$ = 7. 10% British discount rate i£ = 11. 56% Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

IRP and Covered Interest Arbitrage A trader with $1, 000 could invest in the U. S. at 7. 1%, in one year his investment will be worth $1, 071 = $1, 000 (1+ i$) = $1, 000 (1, 071) Alternatively, this trader could 1. Exchange $1, 000 for £ 800 at the prevailing spot rate, 2. Invest £ 800 for one year at i£ = 11, 56%; earn £ 892, 48. 3. Translate £ 892, 48 back into dollars at the forward rate F 360($/£) = $1, 20/£, the £ 892, 48 will be exactly $1, 071. 6 -12 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Alternative 2: Arbitrage I buy pounds £ 1 £ 800 = $1, 000× $1. 25 $1, 000 Alternative 1: invest $1, 000 at 7. 1% FV = $1, 071 6 -13 £ 800 Step 2: Invest £ 800 at i£ = 11. 56% £ 892. 48 In one year £ 800 will be worth Step 3: repatriate £ 892. 48 = to the U. S. A. at £ 800 (1+ i£) $1, 071 F 360($/£) = $1. 20/£ F£(360) $1, 071 = £ 892. 48 × £ 1 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Interest Rate Parity & Exchange Rate Determination According to IRP only one 360 -day forward rate, F 360($/£), can exist. It must be the case that F 360($/£) = $1. 20/£ Why? If F 360($/£) $1. 20/£, an astute trader could make money with one of the following strategies: 6 -14 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Arbitrage Strategy I If F 360($/£) > $1. 20/£ i. Borrow $1, 000 at t = 0 at i$ = 7. 1%. ii. Exchange $1, 000 for £ 800 at the prevailing spot rate, (note that £ 800 = $1, 000÷$1. 25/£) invest £ 800 at 11. 56% (i£) for one year to achieve £ 892. 48 iii. Translate £ 892. 48 back into dollars, if F 360($/£) > $1. 20/£, then £ 892. 48 will be more than enough to repay your debt of $1, 071. 6 -15 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Step 2: buy pounds £ 1 £ 800 = $1, 000× $1. 25 $1, 000 Arbitrage I £ 800 Step 3: Invest £ 800 at i£ = 11. 56% £ 892. 48 In one year £ 800 will be worth £ 892. 48 = £ 800 (1+ i£) Step 4: repatriate to the U. S. A. Step 1: borrow $1, 000 More than $1, 071 Step 5: Repay your dollar loan with $1, 071. F£(360) $1, 071 < £ 892. 48 × £ 1 If F£(360) > $1. 20/£ , £ 892. 48 will be more than enough to repay your dollar obligation of $1, 071. The excess is your profit. Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved. 6 -16

Arbitrage Strategy II If F 360($/£) < $1. 20/£ i. Borrow £ 800 at t = 0 at i£= 11. 56%. ii. Exchange £ 800 for $1, 000 at the prevailing spot rate, invest $1, 000 at 7. 1% for one year to achieve $1, 071. iii. Translate $1, 071 back into pounds, if F 360($/£) < $1. 20/£, then $1, 071 will be more than enough to repay your debt of £ 892. 48. 6 -17 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Step 2: buy dollars $1. 25 $1, 000 = £ 800× £ 1 $1, 000 £ 800 Arbitrage II Step 1: borrow £ 800 Step 5: Repay More Step 3: your pound loan than Invest $1, 000 with £ 892. 48 at i$ Step 4: repatriate to the U. K. In one year $1, 000 F£(360) will be worth $1, 071 > £ 892. 48 × $1, 071 £ 1 If F£(360) < $1. 20/£ , $1, 071 will be more than enough to repay your dollar obligation of £ 892. 48. Keep the rest as profit. Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved. 6 -18

IRP and Hedging Currency Risk You are a U. S. importer of British woolens and have just ordered next year’s inventory. Payment of £ 100 M is due in one year. Spot exchange rate 360 -day forward rate S($/£) = $1. 25/£ F 360($/£) = $1. 20/£ U. S. discount rate i$ = 7. 10% British discount rate i£ = 11. 56% IRP implies that there are two ways that you fix the cash outflow to a certain U. S. dollar amount: a) Put yourself in a position that delivers £ 100 M in one year—a long forward contract on the pound. You will pay (£ 100 M)(1. 2/£) = $120 M in one year. b) Form a forward market hedge as shown below. 6 -19 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

IRP and a Forward Market Hedge To form a forward market hedge: Borrow $112. 05 million in the U. S. (in one year you will owe $120 million). Translate $112. 05 million into pounds at the spot rate S($/£) = $1. 25/£ to receive £ 89. 64 million. Invest £ 89. 64 million in the UK at i£ = 11. 56% for one year. In one year your investment will be worth £ 100 million—exactly enough to pay your supplier. 6 -20 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Forward Market Hedge Where do the numbers come from? We owe our supplier £ 100 million in one year—so we know that we need to have an investment with a future value of £ 100 million. Since i£ = 11. 56% we need to invest £ 89. 64 million at the start of the year. £ 100 £ 89. 64 = 1. 1156 How many dollars will it take to acquire £ 89. 64 million at the start of the year if S($/£) = $1. 25/£? $1. 00 $112. 05 = £ 89. 64 × £ 1. 25 6 -21 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Reasons for Deviations from IRP l Transactions Costs n n n l The interest rate available to an arbitrageur for borrowing, ib, may exceed the rate he can lend at, il. There may be bid-ask spreads to overcome, Fb/Sa < F/S Thus (Fb/Sa)(1 + i¥l) (1 + i¥ b) 0 Capital Controls n 6 -22 Governments sometimes restrict import and export of money through taxes or outright bans. Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Transactions Costs Example l Will an arbitrageur facing the following prices be able to make money? 1 + i$ F$/ € Borrowing Lending = 1 + i€ S$/ € $ 5% 4. 50% € 6 -23 6% 5. 50% Bid Ask Spot $1. 00=€ 1. 00 $1, 01=€ 1, 00 Forward $0. 99=€ 1. 00 $1. 00=€ 1. 00 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

l l l l Try borrowing $1. 000 at 5%: Trade for € at the ask spot rate $1. 01 = € 1. 00 Invest € 990. 10 at 5. 5% Hedge this with a forward contract on € 1, 044. 55 at $0. 99 = € 1. 00 Receive $1. 034. 11 Owe $1, 050 on your dollar-based borrowing Suffer loss of $15. 89 6 -24 Now try this backwards Transactions Costs Example Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Purchasing Power Parity l l l Purchasing Power Parity and Exchange Rate Determination PPP Deviations and the Real Exchange Rate Evidence on PPP 6 -25 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Purchasing Power Parity and Exchange Rate Determination l The exchange rate between two currencies should equal the ratio of the countries’ price levels: P$ S($/£) = P£ l For example, if an ounce of gold costs $300 in the U. S. and £ 150 in the U. K. , then the price of one pound in terms of dollars should be: P$ $300 S($/£) = = = $2/£ P£ £ 150 6 -26 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Purchasing Power Parity and Exchange Rate Determination l l l Suppose the spot exchange rate is $1. 25 = € 1. 00 If the inflation rate in the U. S. is expected to be 3% in the next year and 5% in the euro zone, Then the expected exchange rate in one year should be $1. 25×(1. 03) = € 1. 00×(1. 05) F($/€) = $1. 25×(1. 03) = $1. 23 € 1. 00×(1. 05) € 1. 00 6 -27 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Purchasing Power Parity and Exchange Rate Determination l The euro will trade at a 1. 90% discount in the forward market: F($/€) = S($/€) $1. 25×(1. 03) € 1. 00×(1. 05) $1. 25 € 1. 00 1. 03 1 + $ = = 1. 05 1 + € Relative PPP states that the rate of change in the exchange rate is equal to differences in the rates of inflation—roughly 2% 6 -28 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Purchasing Power Parity and Interest Rate Parity l Notice that our two big equations today equal each other: PPP IRP F($/€) 1 + $ = 1 + € S($/€) 1 + i$ F($/€) = 1 + i€ S($/€) 6 -29 = Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Expected Rate of Change in Exchange Rate as Inflation Differential l We could also reformulate our equations as inflation or interest rate differentials: F($/€) 1 + $ = 1 + € S($/€) F($/€) – S($/€) 1 + $ 1 + € = – 1 = – S($/€) 1 + € F($/€) – S($/€) $ – € E(e) = ≈ $ – € = S($/€) 1 + € 6 -30 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Expected Rate of Change in Exchange Rate as Interest Rate Differential E(e) = 6 -31 i$ – i€ F($/€) – S($/€) = S($/€) 1 + i€ ≈ i$ – i€ Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Evidence on PPP l PPP probably doesn’t hold precisely in the real world for a variety of reasons. n n n l Haircuts cost 10 times as much in the developed world as in the developing world. Film, on the other hand, is a highly standardized commodity that is actively traded across borders. Shipping costs, as well as tariffs and quotas can lead to deviations from PPP-determined exchange rates still provide a valuable benchmark. 6 -33 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Approximate Equilibrium Exchange Rate Relationships E(e) ≈ IFE (i$ – i¥) ≈ FEP ≈ PPP F – S ≈ IRP S ≈ FE ≈ FRPPP E( $ – £) 6 -34 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

The Exact Fisher Effects An increase (decrease) in the expected rate of inflation will cause a proportionate increase (decrease) in the interest rate in the country. l For the U. S. , the Fisher effect is written as: 1 + i$ = (1 + $ ) × E(1 + $) Where $ is the equilibrium expected “real” U. S. interest rate E( $) is the expected rate of U. S. inflation i$ is the equilibrium expected nominal U. S. interest rate l 6 -35 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

International Fisher Effect If the Fisher effect holds in the U. S. 1 + i$ = (1 + $ ) × E(1 + $) and the Fisher effect holds in Japan, 1 + i¥ = (1 + ¥ ) × E(1 + ¥) and if the real rates are the same in each country $ = ¥ then we get the E(1 + ¥) 1 + i¥ International Fisher Effect: 1 + i = E(1 + ) $ 6 -36 $ Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

International Fisher Effect If the International Fisher Effect holds, E(1 + ¥) 1 + i¥ = 1 + i$ E(1 + $) and if IRP also holds 1 + i¥ F¥/$ = 1 + i$ S¥/$ F¥/$ E(1 + ¥) then forward rate PPP holds: = S¥/$ E(1 + $) 6 -37 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Forecasting Exchange Rates l l Efficient Markets Approach Fundamental Approach Technical Approach Performance of the Forecasters 6 -39 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Efficient Markets Approach l l l Financial Markets are efficient if prices reflect all available and relevant information. If this is so, exchange rates will only change when new information arrives, thus: St = E[St+1] and Ft = E[St+1| It] Predicting exchange rates using the efficient markets approach is affordable and is hard to beat. 6 -40 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Fundamental Approach l Involves econometrics to develop models that use a variety of explanatory variables. This involves three steps: n n n l step 1: Estimate the structural model. step 2: Estimate future parameter values. step 3: Use the model to develop forecasts. The downside is that fundamental models do not work any better than the forward rate model or the random walk model. 6 -41 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Technical Approach l l l Technical analysis looks for patterns in the past behavior of exchange rates. Clearly it is based upon the premise that history repeats itself. Thus it is at odds with the EMH 6 -42 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.

Performance of the Forecasters l l l Forecasting is difficult, especially with regard to the future. As a whole, forecasters cannot do a better job of forecasting future exchange rates than the forward rate. The founder of Forbes Magazine once said: “You can make more money selling financial advice than following it. ” 6 -43 Copyright © 2007 by The Mc. Graw-Hill Companies, Inc. All rights reserved.