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INTERNATIONAL FINANCIAL MANAGEMENT

INTERNATIONAL FINANCIAL MANAGEMENT. Fourth Edition. EUN / RESNICK. International Parity Relationships & Forecasting Foreign Exchange Rates. 6. Chapter Six. Chapter Objective:

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INTERNATIONAL FINANCIAL MANAGEMENT

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  1. INTERNATIONAL FINANCIAL MANAGEMENT Fourth Edition EUN / RESNICK

  2. International Parity Relationships & Forecasting Foreign Exchange Rates 6 Chapter Six • Chapter Objective: • This chapter examines several key international parity relationships, such as interest rate parity and purchasing power parity. INTERNATIONAL FINANCIAL MANAGEMENT Fourth Edition EUN / RESNICK

  3. Chapter Outline • Interest Rate Parity • Covered Interest Arbitrage • IRP and Exchange Rate Determination • Reasons for Deviations from IRP • Purchasing Power Parity • The Fisher Effects • Forecasting Exchange Rates • Interest Rate Parity • Purchasing Power Parity • PPP Deviations and the Real Exchange Rate • Evidence on Purchasing Power Parity • The Fisher Effects • Forecasting Exchange Rates • Interest Rate Parity • Purchasing Power Parity • The Fisher Effects • Forecasting Exchange Rates • Interest Rate Parity • Purchasing Power Parity • The Fisher Effects • Forecasting Exchange Rates • Efficient Market Approach • Fundamental Approach • Technical Approach • Performance of the Forecasters • Interest Rate Parity • Purchasing Power Parity • The Fisher Effects • Forecasting Exchange Rates • Interest Rate Parity • Purchasing Power Parity • The Fisher Effects • Forecasting Exchange Rates

  4. Interest Rate Parity • Interest Rate Parity Defined • Covered Interest Arbitrage • Interest Rate Parity & Exchange Rate Determination • Reasons for Deviations from Interest Rate Parity

  5. Interest Rate Parity Defined • 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. F$/£ Future value = $100,000(1 + i£)× S$/£ F$/£ (1 + i£) × = (1 + i$) S$/£ Interest Rate Parity Carefully Defined Consider alternative one year investments for $100,000: • Invest in the U.S. at i$. 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 selling the future value of the British investment forward. Since these investments have the same risk, they must have the same future value (otherwise an arbitrage would exist)

  7. $1,000 S$/£ $1,000 $1,000  (1+ i£)  (1+ i£) × F$/£ S$/£ S$/£ IRP Alternative 2: Send your $ on a round trip to Britain IRP Step 2: Invest those pounds at i£ $1,000 Future Value = Step 3: repatriate future value to the U.S.A. Alternative 1: invest $1,000 at i$ $1,000×(1 + i$) = Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage would exist

  8. $1,000  (1+ i£) × F$/£ = $1,000×(1 + i$) S$/£ F$/£ × (1+ i£) = (1 + i$) S$/£ Interest Rate Parity Defined • The scale of the project is unimportant

  9. 1 + i$ F$/¥ = 1 + i¥ S$/¥ F – S i$ – i¥ ≈ S Interest Rate Parity Defined Formally, IRP is sometimes approximated as

  10. F180($/€) – S($/€) 360 $1.30 – $1.25 f180,€v$ = × = × 2 = 0.08 S($/€) 180 $1.25 Forward Premium • It’s just the interest rate differential implied by forward premium or discount. • For example, suppose the € is appreciating from S($/€) = 1.25 to F180($/€) = 1.30 • The forward premium is given by:

  11. 1 + i¥ F¥/$ = 1 + i$ S¥/$ 1 + i$ F$/¥ = 1 + i¥ S$/¥ Interest Rate Parity Carefully Defined • Depending upon how you quote the exchange rate ($ per ¥ or ¥ per $) we have: or …so be a bit careful about that

  12. 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.

  13. 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 • Exchange $1,000 for £800 at the prevailing spot rate, • Invest £800 for one year at i£ = 11,56%; earn £892,48. • Translate £892,48 back into dollars at the forward rate F360($/£) = $1,20/£, the £892,48 will be exactly $1,071.

  14. £800 £1 £800 = $1,000× $1.25 $1,000 F£(360) $1,071 = £892.48 × £1 Alternative 2: buy pounds Arbitrage I Step 2: Invest £800 at i£ = 11.56% In one year £800 will be worth £892.48 = £892.48 Step 3: repatriate to the U.S.A. at F360($/£) = $1.20/£ £800 (1+ i£) Alternative 1: invest $1,000 at 7.1% FV = $1,071 $1,071

  15. Interest Rate Parity & Exchange Rate Determination According to IRP only one 360-day forward rate, F360($/£), can exist. It must be the case that F360($/£) = $1.20/£ Why? If F360($/£)  $1.20/£, an astute trader could make money with one of the following strategies:

  16. Arbitrage Strategy I If F360($/£) > $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÷$1.25/£) invest £800 at 11.56% (i£) for one year to achieve £892.48 iii. Translate £892.48 back into dollars, if F360($/£) > $1.20/£, then £892.48 will be more than enough to repay your debt of $1,071.

  17. £800 £1 £800 = $1,000× $1.25 $1,000 F£(360) $1,071 < £892.48 × £1 Step 2: buy pounds Arbitrage I Step 3: Invest £800 at i£ = 11.56% In one year £800 will be worth £892.48 = £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. 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.

  18. Arbitrage Strategy II If F360($/£) < $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 $1,071 back into pounds, if F360($/£) < $1.20/£, then $1,071 will be more than enough to repay your debt of £892.48.

  19. Step 2: buy dollars $1.25 $1,000 = £800× £1 Step 3: Invest $1,000 at i$ Step 4: repatriate to the U.K. F£(360) $1,071 > £892.48 × £1 Arbitrage II £800 Step 1: borrow £800 $1,000 Step 5: Repay your pound loan with £892.48 . More than £892.48 In one year $1,000 will be worth $1,071 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.

  20. IRP and Hedging Currency Risk You are a U.S. importer of British woolens and have just ordered next year’s inventory. Payment of £100M is due in one year. 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 £100M in one year—a long forward contract on the pound. You will pay (£100M)(1.2/£) = $120M in one year. b) Form a forward market hedge as shown below.

  21. 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.

  22. £100 £89.64 = 1.1156 $1.00 $112.05 = £89.64 × £1.25 Forward Market Hedge Where do the numbers come from? We owe our supplier £100 million in one year—so we know that we need to have an investment with a future value of £100 million. Since i£ = 11.56% we need to invest £89.64 million at the start of the year. How many dollars will it take to acquire £89.64 million at the start of the year if S($/£) = $1.25/£?

  23. Reasons for Deviations from IRP • Transactions Costs • 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 • Governments sometimes restrict import and export of money through taxes or outright bans.

  24. 1 + i$ F$/ € = 1 + i€ S$/ € Transactions Costs Example • Will an arbitrageur facing the following prices be able to make money?

  25. Now try this backwards Transactions Costs Example • 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

  26. Purchasing Power Parity • Purchasing Power Parity and Exchange Rate Determination • PPP Deviations and the Real Exchange Rate • Evidence on PPP

  27. For example, if an ounce of gold costs $300 in the U.S. and £150 in the U.K., then the price of one pound in terms of dollars should be: P$ P$ $300 S($/£) = P£ S($/£) = = = $2/£ P£ £150 Purchasing Power Parity and Exchange Rate Determination • The exchange rate between two currencies should equal the ratio of the countries’ price levels:

  28. $1.25×(1.03) $1.23 F($/€) = = €1.00×(1.05) €1.00 Purchasing Power Parity and Exchange Rate Determination • 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)

  29. F($/€) = S($/€) $1.25×(1.03) €1.00×(1.05) Purchasing Power Parity and Exchange Rate Determination • The euro will trade at a 1.90% discount in the forward market: 1.03 1 + $ = = 1.05 1 + € $1.25 €1.00 Relative PPP states that the rate of change in the exchange rate is equal to differences in the rates of inflation—roughly 2%

  30. F($/€) PPP IRP = S($/€) 1 + $ 1 + i$ F($/€) = 1 + i€ 1 + € S($/€) Purchasing Power Parity and Interest Rate Parity • Notice that our two big equations today equal each other: =

  31. F($/€) = S($/€) F($/€) – S($/€) F($/€) – S($/€) 1 + $ 1 + $ 1 + € = = – 1 – S($/€) S($/€) 1 + € 1 + € 1 + € Expected Rate of Change in Exchange Rate as Inflation Differential • We could also reformulate our equations as inflation or interest rate differentials: 1 + $ 1 + € = $– € E(e) = ≈ $– € 1 + €

  32. F($/€) – S($/€) = S($/€) Expected Rate of Change in Exchange Rate as Interest Rate Differential i$– i€ ≈ i$ –i€ E(e) = 1 + i€

  33. $– € ≈ i$ –i€ Quick and Dirty Short Cut • Given the difficulty in measuring expected inflation, managers often use

  34. Evidence on PPP • PPP probably doesn’t hold precisely in the real world for a variety of reasons. • 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. • PPP-determined exchange rates still provide a valuable benchmark.

  35. F–S S Approximate Equilibrium Exchange Rate Relationships E(e) ≈ IFE ≈ FEP ≈ PPP (i$–i¥) ≈ IRP ≈ FE ≈ FRPPP E($– £)

  36. 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. • 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

  37. E(1 + ¥) 1 + i¥ 1 + i$ E(1 + $) International Fisher Effect If the Fisher effect holds in the U.S. 1 + i$ = (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 International Fisher Effect: =

  38. E(1 + ¥) 1 + i¥ = 1 + i$ E(1 + $) 1 + i¥ F¥/$ = 1 + i$ S¥/$ F¥/$ E(1 + ¥) = S¥/$ E(1 + $) International Fisher Effect If the International Fisher Effect holds, and if IRP also holds then forward rate PPP holds:

  39. IFE PPP 1 + i¥ IRP 1 + i$ FE FRPPP E(1 + ¥) E(1 + $) Exact Equilibrium Exchange Rate Relationships FEP

  40. Forecasting Exchange Rates • Efficient Markets Approach • Fundamental Approach • Technical Approach • Performance of the Forecasters

  41. Efficient Markets Approach • 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.

  42. Fundamental Approach • Involves econometrics to develop models that use a variety of explanatory variables. This involves three steps: • 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.

  43. Technical Approach • 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

  44. Performance of the Forecasters • 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.”

  45. End Chapter Six

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