1. Chapter 5 International Parity Relationships and Forecasting FX Rates Management 3460 Institutions and Practices in International Finance Fall 2003 Greg Flanagan

2. Oct 9-14, 2003 2 Chapter Objectives The student will be able to: Define Interest Rate Parity State and apply the IRP equation Explain and calculate covered Interest Arbitrage Give reasons for Deviations from IRP Explain the adjustment process when IRP does not hold that brings it to equilibrium.

3. Oct 9-14, 2003 3 Chapter Objectives The student will be able to: Define Purchasing Power Parity (PPP) Explain why there are PPP Deviations and the Real Exchange Rate Discuss the Evidence for Purchasing Power Parity Explain the Fisher Effect

4. Oct 9-14, 2003 4 Chapter Objectives The student will be able to: Explain the different approaches to forecasting exchange rates: Efficient Market Fundamental Technical Discuss the performance of forecasters.

5. Oct 9-14, 2003 5 Interest Rate Parity (IRP) Definition: IRP is the situation where the forward FX premium (discount) of one currency just offsets the higher (lower) interest rate in another country. It is an arbitrage equilibrium condition. If IRP did not hold, then it would be possible for a trader to make a profit exploiting the arbitrage opportunity. persistent arbitrage conditions rarely exist suggesting that we can assume that IRP holds.

6. Oct 9-14, 2003 6 Interest Rate Parity (IRP) Return in country j = i j Covered interest return (1 + i k ) F(j/k) S(j/k) or: (1 + i k )(F/S) IRP equilibrium: (1 + i j ) = (F/S)(1 + i k )

7. Oct 9-14, 2003 7 Interest Rate Parity Example Suppose you have $100,000 to invest for one year. You can either 1.invest in the U.S. at i $. Future value = $100,000(1 + i $ ) or 2.trade your dollars for pounds at the spot rate, invest in UK at i £ and hedge your exchange rate risk by selling the future value of the British investment forward. The future value = $100,000(F/S)(1 + i £ ) Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage would exist, therefore (F/S)(1 + i £ ) = (1 + i $ ) j = US k =UK

8. Oct 9-14, 2003 8 Interest Rate Parity $100,000$100,000(1 + i $ ) $100,000(F/S)(1 + i £ ) 1.Trade $100,000 for £ at S 2.Invest £100,000 at i £ S 3.One year later, trade £ for $ at F

9. Oct 9-14, 2003 9 Interest Rate Parity (F/S)(1 + i k ) = (1 + i j ) IRP is sometimes approximated as 1 + i k 1 + i j = S F i j – i k = S F – S or

10. Oct 9-14, 2003 10 IRP and Covered Interest Arbitrage If IRP failed to hold, an arbitrage would exist. Example: Spot exchange rateS($/£)=$1.25/£ 360-day forward rateF 360 ($/£)=$1.20/£ U.S. discount ratei$i$ =7.10% British discount rate i £ =11.56%

11. Oct 9-14, 2003 11 IRP and Covered Interest Arbitrage trader with $1,000 to invest could invest in the U.S., 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, (note that £800 = $1,000÷$1.25/£) invest £800 at i £ = 11.56% for one year to achieve £892.48. Translate £892.48 back into dollars at F 360 ($/£) = $1.20/£, the £892.48 will be exactly $1,071.

12. Oct 9-14, 2003 12 IRP & 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:

13. Oct 9-14, 2003 13 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/£, £892.48 will be more than enough to repay your dollar obligation of $1,071.

14. Oct 9-14, 2003 14 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/£, $1,071 will be more than enough to repay your £ obligation of £892.48.

15. Oct 9-14, 2003 15 IRP adjustment process If the covered interest return was greater in another country, then (F/S)(1 + i k ) > (1 + i Cdn$ ) A trader will borrow locally and invest in the foreign country and pocket the difference without risk.

16. Oct 9-14, 2003 16 IRP adjustment process The interest rate in Canada i j  interest rate in the other country i k will  Sk Sk  Fk Fk  i.e. arbitrage will occur as interest rates approach and Forward and Spot markets differences decrease.

17. Oct 9-14, 2003 17 (F-S)/S(%) IRP line 1 2 3 4 -4 -3 -2 1 2345 -5 -4-3-2 (i j )- i k (%) The difference in interest rates falls The difference in forward and spot rates rises A combination of both changes occur

18. Oct 9-14, 2003 18 Uncovered IRP Expectations play a considerable role in Exchange rates The expected rate of change in the exchange rate is approximately equal to the difference in the interest rates between two countries. E(e) = i j - i k

19. Oct 9-14, 2003 19 Reasons for Deviations from IRP Transactions Costs The interest rate available to an arbitrageur for borrowing, i b, may exceed the rate he can lend at, i l. There may be bid-ask spreads to overcome, F b /S a < F/S Thus (F b /S a )(1 + i J l )  (1 + i J b )  0

20. Oct 9-14, 2003 20 (F-S)/S(%) IRP line 1 2 3 4 -4 -3 -2 1 2345 -5 -4-3-2 (i j )- i k (%) Transaction Costs

21. Oct 9-14, 2003 21 Reasons for Deviations from IRP Capital Controls Governments sometimes restrict import and export of money through taxes or outright bans. Political Risks

22. Oct 9-14, 2003 22 Purchasing Power Parity The exchange rate between two currencies should equal the ratio of the countries’ price levels: S(j/k) = PkPk PjPj i.e. Prices after exchange transactions should be the same—the absolute version of PPP

23. Oct 9-14, 2003 23 Purchasing Power Parity For example, if an ounce of gold costs $300 in the U.S. and £150 in the U.K., then the price of one pound in terms of dollars should be: S($/ £ ) = P£P£ P$P$ £150 $300 == $2/£

24. Oct 9-14, 2003 24 Purchasing Power Parity Relative PPP states that the rate of change in the exchange rate (e) is equal to the differences in the rates of inflation (  ): e = (1 +  £ ) (  $ –  £ ) ≈  $ –  £ If Cdn inflation is 5% and U.K. inflation is 8%, the pound should depreciate by 2.78% or around 3%.

25. Oct 9-14, 2003 25 PPP Deviations and the Real Exchange Rate The real exchange rate (q) is: q = (1 + e)(1+  £ ) (1 +  $ ) If PPP holds, (1 + e) = (1 +  £ ) (1 +  $ ) then q = 1. If q < 1 competitiveness of domestic country improves with currency depreciations. If q > 1 competitiveness of domestic country deteriorates with currency depreciations.

26. Oct 9-14, 2003 26 Evidence on PPP PPP doesn’t hold precisely in the real world for a variety of reasons: Labour: Haircuts cost 10 times as much in the developed world as in the developing world. Standards: Film, on the other hand, is a highly standardized commodity that is actively traded across borders. Shipping costs, tariffs, and quotas can lead to deviations from PPP. Capital investment differences. PPP-determined exchange rates still provide a valuable benchmark.

27. Oct 9-14, 2003 27

28. Oct 9-14, 2003 28 The Fisher Effects An increase (decrease) in the expected rate of inflation will cause a proportionate increase (decrease) in the interest rate in the country.  $ is the equilibrium expected “real” interest rate E[  $ ] is the expected rate of inflation i $ is the equilibrium expected nominal interest rate

29. Oct 9-14, 2003 29 Expected Inflation The Fisher effect implies that the expected inflation rate is approximated as the difference between the nominal and real interest rates in each country, i.e. E[  $ ] = (1 +  $ ) (i$ – $)(i$ – $) ≈ i $ –  $ i $ =  $ + (1 +  $ )E[  $ ] ≈  $ + E[  $ ]

30. Oct 9-14, 2003 30 International Fisher Effect If the Fisher effect holds in the U.S. i $ = (1+  $ )(1 + E[  $ ]) ≈  $ + E[  $ ] and the Fisher effect holds in Japan, i ¥ = (1+  ¥ )(1 + E[  ¥ ]) ≈  ¥ + E[  ¥ ] and if the real rates are the same in each country (i.e.  $ =  ¥ ), then we get the International Fisher Effect E(e) = (1 + i ¥ ) (i$ – i¥)(i$ – i¥) ≈ i $ – i ¥

31. Oct 9-14, 2003 31 International Fisher Effect If the International Fisher Effect holds: then forward parity holds. E(e) = (1 + i ¥ ) (i$ – i¥)(i$ – i¥) and if IRP also holds = (1 + i ¥ ) (i$ – i¥)(i$ – i¥) S F – SF – S S F – SF – S E(e) =

32. Oct 9-14, 2003 32 ≈ Forward PPP ≈ Fisher Effect ≈ Forward Expectations Parity ≈ International Fisher Effect Approximate Equilibrium Exchange Rate Relationships E(  $ –  ¥ ) ≈ IRP ≈ PPP S F – SF – S E(e)E(e) (i$ – i¥))(i$ – i¥))

33. Oct 9-14, 2003 33 Foreign Exchange Forecasting

34. Oct 9-14, 2003 34 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: S t = E[S t+1 ] and F t = E[S t+1 | I t ] Predicting exchange rates using the is affordable and is hard to beat.

35. Oct 9-14, 2003 35 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.

36. Oct 9-14, 2003 36 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 Efficient Markets

37. Oct 9-14, 2003 37 At A the short-term moving average exchange rate is rising above the long –term moving average  appreciation of the £ At D the short-term moving average exchange rate is falling below the long –term moving average  depreciation of the £

38. Oct 9-14, 2003 38 Levich Analysis MAE(S) Mean Average forecast Error of a forecasting Service. MAE(F) Mean Average forecast Error of the Forward exchange rate predictor. R = MAE(S)/MAE(F) If the forecast service is more accurate  R< 1.

39. Oct 9-14, 2003 39 Only 25 out of 104 are < 1!

40. Oct 9-14, 2003 40 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.”