1. Chapter Objective: This chapter examines several key international parity relationships, such as interest rate parity and purchasing power parity. 6 Chapter Six International Parity Relationships and Forecasting Foreign Exchange Rates 6-0

2. Chapter Outline Interest Rate Parity Purchasing Power Parity The Fisher Effects Forecasting Exchange Rates 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 Covered Interest Rate Parity (CIRP) Purchasing Power Parity (PPP): absolute & relative The Fisher Effects : Domestic & International Forward Parity Forecasting Exchange Rates 6-1

3. …almost all of the time! CIRP Defined Idea: $1 (or any amount in $ or in any FC) invested in anywhere should yield the same $ return (or FC return) If the world investment market is perfect, we expect competitive returns! Why? CIRP is an “no arbitrage” condition. If CIRP 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 CIRP holds. 6-2

4. A Simple Covered Interest Rate Arbitrage Example when CIRP does not hold! BOA 4% vs Nations Bank 5% Identify L and H, Borrow Low & Invest (Deposit) High Borrow say $1 from BOA and Deposit at NB Cash Flow at 0: +$1 from BOA -$1 to NB => Net CF= $0 Cash Flow at1: +$1.05 from NB -$1.04 to BOA => $0.01 arbitrage gain. A few issues: 1) Bid-Asked? How about 3.99~4.01% vs 4.99~5.01% Use average rates (Bid+Asked)/2 to determine H & L, then figure out! 2) Can it be sustained? What is the equilibrium situation, then?

5. What about 4% in the US vs 5% in the UK? Well, we need more info to determine the arbitrage opportunity. Why? & What needed? US interest rate, i $, is a $ interest rate and the UK rate, i £, is a £ interest rate. It is like comparing apples and oranges. What do you need? Exchange rates!

6. . A Box Diagram to show (LHS & RHS) $1 invested in the US => $1.04, or $1+i $ (more generally) $1 => 0.5 BPs at So = $2/£, or (1/So) BPs PV=0.5 BPs =>FV=0.5*(1.05) =0.525 BPs, or (1/So)*(1+i £ ) BPs To convert BPs to $s, we need a future exchange rate. To have no risks, we can use a forward contract with the forward rate, say F=$2.01/£. Then $ amount is $1.055, or $ (1/So)*(1+i £ )*F $ interest rate investing in the UK is 5.5% > 4% Why 5.5% > 5.0%? Investing in UK involves two investments (buying & selling pounds and buying and selling the security)! Borrow from the US and Invest in UK! Arbitrage strategy: Arbitrage profit = $0.015 In equilibrium with no arbitrage opportunity, => 1+i $ = (1/So)*(1+i £ )*F, LHS=RHS, CIRP (why Covered?)

7. S $/£ × F $/£ = (1 + i £ ) (1 + i $ ) CIRP Defined Consider alternative one-year investments for $1: 1. Invest in the U.S. at i $. LHS Future value = $ (1 + i $ ) 2. Trade your $ for £ at the spot rate, invest (1/ So ) £s in Britain at i £ while eliminating any exchange rate risk by selling the future value of the British investment forward. So F RHS Future value = $(1 + i £ ) x So F (1 + i $ ) = x (1 + i £ ) Since these investments have the same risk, they must have the same future value (otherwise an arbitrage would exist) 6-6

8. CIRP Invest those pounds at i £ $1,000 So $1,000 Future Value = Step 3: repatriate future value to the U.S.A. Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage would exist Alternative 1: invest $1,000 at i $ $1,000×(1 + i $ ) Alternative 2: Send your $ on a round trip to Britain Step 2: $1,000 So  (1+ i £ ) × F $1,000 So  (1+ i £ ) = 6-7

9. CIRP Defined Formally, CIRP is sometimes approximated as i $ – i ¥ ≈ So F – So 1 + i $ 1 + i ¥ So F = 6-8

10. CIRP and Covered Interest Arbitrage If CIRP failed to hold, an arbitrage would exist. Consider the following set of foreign and domestic interest rates and spot and forward exchange rates. Spot exchange rateSo=$2.0000/£ 360-day forward rateF 360 =$2.0100/£ U.S. discount ratei$i$ =3.00% British discount rate i £ =2.49% 6-9

11. CIRP and Covered Interest Arbitrage A trader with $1,000 could invest in the U.S. at 3.00%, in one year his investment will be worth LHS = $1,000  (1+ i $ ) = $1,000  (1.03) = $1,030 Alternatively, this trader could (RHS) 1. Exchange $1,000 for £500 at the prevailing spot rate, 2. Invest £500 for one year at i £ = 2.49%; earn £512.45 3. Translate £512.45 back into dollars at the forward rate F 360 ($/£) = $2.01/£, the £512.45 will be worth $1,030. 6-10

12. Arbitrage I Invest £500 at i £ = 2.49% $1,000 £500 $1,000× $2.00 £1 In one year £500 will be worth £512.45 = £500  (1+ i £ ) $1,030 =£512.45 × £1 F Step 3: repatriate to the U.S.A. at F 360 ($/£) = $2.01/£ Alternative 1: invest $1,000 at 3% FV = $1,030 Alternative 2: buy pounds Step 2: £512.45 $1,030 6-11

13. CIRP & Exchange Rate Determination There is only one 360-day forward rate which would satisfy CIRP, F 360 = $2.01/£ Implied Forward Rate: a “theoretical” forward rate which satisfies CIRP. If the actual F 360  $2.01/£, the implied forward rate, an astute trader could make money with one of the following strategies: 6-12

14. Arbitrage Strategy I If actual F 360 > $2.01/£ implied => then LHS<RHS => Borrow Low from the US and Invest High in UK i. Borrow $1,000 at t = 0 at i $ = 3%. ii. Exchange $1,000 for £500 at the prevailing spot rate, (note that £500 = $1,000 ÷ $2/£) invest £500 at 2.49% (i £ ) for one year to achieve £512.45 iii. Translate £512.45 back into dollars, if the actual F 360 > $2.01/£, then you can sell £512.45 for more than $1,030. If the actual F 360 = 2.08 for example, your arbitrage profit = $35.90 after repaying your debt of $1,030. 6-13

15. Arbitrage Strategy II If actual F 360 RHS => Borrow Low from UK and Invest High in the US i. Borrow £500 ($1,000 equivalent amount at $2/£) at t = 0 at i £ = 2.49%. FV of £500 is £512.45 (principal + interest) ii. Exchange £500 for $1,000 at the prevailing spot rate, invest $1,000 at 3% for one year in the US to achieve $1,030. iii. Since the actual F 360 arbitrage profit of $30.72. 6-14

16. Reasons for Deviations from CIRP Transactions Costs bid-ask spreads, fees, etc. Investing in or borrowing from a foreign country may incur additional costs. Capital Controls Governments sometimes restrict import and export of money through taxes or outright bans. Different risks So far, risks are not considered. However, CIRP is applicable with the same amount of risks in both countries. Investing in Libya or Afghanistan may look attractive in terms of higher $ (as well as LC) returns, but would you be interested? 6-15

17. Transactions Costs Example Will an arbitrageur facing the following prices be able to make money one year later? BorrowingLending $5.0%4.50% €5.5%5.0% BidAsk Spot$1.42 = €1.00$1.45 = €1,00 Forward$1.415 = €1.00$1.445 = €1.00 6-16

18. . Averages of (Bid+Asked)/2 => i $ = 4.75%, i £ = 5.25%, So = 1.435, F = 1.430 LHS = 1+i $ = 1.0475 RHS = (1/So)*(1+i £ )*F = (1/1.435)*(1.0525)*(1.430) = 1.0488 Since LHS < RHS, an arbitrage opportunity, if exists, can be exploited by Borrowing Low from the US and Investing High in Europe Borrow say $1 from the US => Buy euro at $1.45/€, (1/1.45) euro => Invest in Europe at 5%, will have (1/1.45)*(1.05) euro => knowing today this amount will be available, forward contract today to sell the euro for $s in the future, (1/1.45)*(1.05)*(1.415) = 1.0247 USDs. On the other hand, to be able to pay off the $1 debt, you need 1.05 $s. => No Arbitrage Opportunity!

19. Real life examples My sister-in-law in New Zealand Yen carry trade HW Assignment Covered Interest Rates Parity (CIRP) - the investment horizon is 3 months (1) Collect S 0, F, i $, i FC for your country selected (choose one from the two countries assigned. (2) Determine the implied forward rate (3) Check if CIRP holds (4) If the CIRP does not hold, show how you can make an arbitrage profit using $1M or $1M equivalent amount in FC (show your steps)

20. Purchasing Power Parity Purchasing Power Parity and Exchange Rate Determination PPP Deviations and the Real Exchange Rate Evidence on PPP 6-19

21. PPP and Exchange Rate Determination The exchange rate between two currencies should equal the ratio of the countries’ price levels (Absolute PPP): So = P $ /P £ Alternatively, P $ = So*P £, Price level in each country determined in the same currency ($) should be the same in both countries. What you can buy with $100 should be the same anywhere in the world. => Living costs are the same!

22. Relative PPP If Absolute PPP holds at each point in time, say at t=0 and t=1, then We can show that %chg in the exchange rate (e ≡ (S 1 - So)/So, FC appreciation rate relative to $) is equal to the difference between the %chg in the US price level (=US inflation rate) and the %chg in the UK price level (=UK inflation rate), E(e) = E(π $ ) – E(π £ ) If the inflation rate in the U.S. is expected to be 5% in the next year and 3% in the euro zone, Then the expected change in the exchange rate in one year should be 5 - 3=2%, euro is expected to be 2% stronger against $ Make sense?

23. Evidence on PPP PPP probably doesn’t hold precisely in the real world for a variety of reasons. Non-tradable goods like services, perishable products Transactions & Transportation costs including trucking costs, tariffs, etc. Different consumption baskets However, PPP-determined exchange rates can still provide a valuable benchmark. So = P $ /P £ 6-22

24. Fisher Equations Domestic (Closed) i $ = ρ $ + E(π $ ), 1+i $ = (1+  $ )*(1+E(  $ )) to be exact International (Open) Assuming that ρ $ = ρ £, Then, i $ - i £ = E(π $ ) – E(π £ ) Relative PPP + International Fisher E(e) = E(π $ ) – E(π £ ) = i $ - i £ HW: Based on the collected information for CIRP, find out expected percentage change of the exchange rate Hint: use E(e) = i $ - i FC

25. Forward Parity F = E(S 1 ) (F – So)/So = (E(S 1 ) – So)/So = E(e)

26. Approximate Equilibrium Exchange Rate Relationships E(  $ –  £ ) ≈ CIRP ≈ Rel PPP ≈ Int Fisher ≈ Fwd Parity S F – SF – S E(e)E(e) (i$ – i¥)(i$ – i¥) 6-25

27. Forecasting Exchange Rates Efficient Markets Approach Fundamental Approach Technical Approach Performance of the Forecasters 6-26

28. 1) 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 | I t ] and/or F t = E[S t+1 | I t ] Predicting exchange rates using the efficient markets approach is affordable and is hard to beat if financial markets are efficient. 6-27

29. 2) Fundamental (Theoretical )Approach Develop models that use a variety of macro- economic variables. Logical explanations! The downside is that fundamental models do not work any better than the forward rate model or the random walk model. 6-28

30. 3) Technical Approach Technical/statistical analysis looks for patterns/trend in the past behavior of exchange rates. Clearly it is based upon the premise that history repeats itself. Pretty good forecasting performance, but little logical explanations. At odds with the EMH 6-29

31. 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 current spot rate or the forward rate. The founder of Forbes Magazine once said: “You can make more money selling financial advice than following it.” 6-30