Topic IIB: International Parity Relations

1.  Topic IIB: International Parity Relations

2. Outline Introduction Forward Contracts Interest Rate Parity Purchasing Power Parity International Fisher Relation

3. I. Introduction International parity conditions provide the relation between interest rates, exchange rates and inflation between two countries. They are the cornerstone of international finance, and the basis behind understanding international fixed income. Four main results: Covered and uncovered interest rate parity International Fisher relation Purchasing power parity

4. International Parity Conditions

5. Ft,T - the current forward rate for T periods hence exchange Example: the spot rate is S$/FF = $0.20/FF the 1year forward rate is F$/FF = $0.25/FF We can sell forward FF40,00 in 1yr, and guarantee the receipt of $10,000 II. Forward Contracts

6. Forward Premiums/Discounts Percentage forward premium/discount = (F1d/f - S0d/f ) / S0d/f Forward premium: nominal value in the forward exchange market is higher than in the spot exchange market Forward discount: nominal value in the forward exchange market is lower than in the spot exchange market

7. Suppose S$/FF = $0.20/FF and F$/FF = $0.25/FF Franc forward premium = ($.25/FF-$.20/FF)/($.20/FF) = +25% so the franc is selling at a 25% forward premium. Alternatively, S* = (1/S) = SFF/$ = FF5.00/$ F* =(1/F) = FFF/$ = FF4.00/$ Dollar forward premium = (FF4/$-FF5/$)/(FF5/$) = -20% so the dollar is selling at a 20% forward discount. Forward Premium/Discount: Example

8. III. Pricing Forwards:Interest Rate Parity Ftd/f/S0d/f = [(1+rd)/(1+rf)]t Forward premiums and discounts are entirely determined by interest rate differentials. This is a parity condition that you can trust. It holds by ARBITRAGE ...that is, if it didn�t, you could make an infinite profit

9. covered interest arbitrage =>Interest Rate Parity An Example: Given: r$ = 7% r� = 3% S0$/� = $1.20/� F1$/� = $1.25/� F1$/� / S0$/� = 1.041667 > (1+r$) / (1+r�) = 1.038835 The forward premium > The �synthetic� forward premium FX and Eurocurrency markets are not in equilibrium WHAT TO DO???

10. Interest Rate Parity:Arbitrage Opportunities If Ftd/f/S0d/f > [(1+rd)/(1+rf)]t then Ftd/f must fall, S0d/f must rise, rd must rise, rf must fall so Sell f at Ftd/f, Buy f at S0d/f, Borrow at rd , Lend at rf If Ftd/f/S0d/f < [(1+rd)/(1+rf)]t then Ftd/f must rise, S0d/f must fall, rd must fall, rf must rise so Buy f at Ftd/f, Sell f at S0d/f, Lend at rd, Borrow at rf

11. Covered Interest Arbitrage Example (cont�d) 1. Borrow $1,000,000 at 7% 2. Convert $s to �s at S0$/� = $1.20/� 3. Invest �s at 3% 4. Convert �s to $s at F1$/� = $1.25/� 5. Take your profit $1,072,920 - $1,070,000 = $2,920

12. Conclusion Covered Interest Rate Parity must hold by no arbitrage. There is a corresponding relation, uncovered interest rate parity, sometimes known as the expectations hypothesis for exchange rates: What about this relation?

13. Forwards as Predictors of Future Spot(or Uncovered Parity) �just like the expectations hypothesis in the context of interest rates, we have here: The �expectation hypothesis� for XRs Forward equals expected spot: Ft,1d/f = Et[St+1d/f] or Forward premium equals expected appr/depr: Ft,1d/f / Std/f = Et[St+1d/f] / Std/f If speculators think the spot rate will close above the forward rate, they can buy the forward contract and settle in the spot market at a positive expected profit. This type of speculative activity forces the forward price to rise and ensures that forward exchange rates are close to expected future spot rates. If speculators think the spot rate will close above the forward rate, they can buy the forward contract and settle in the spot market at a positive expected profit. This type of speculative activity forces the forward price to rise and ensures that forward exchange rates are close to expected future spot rates.

14. �Uncovered Interest Parity� Strategy 1: invest in US$ E[$ROR]=r d Strategy 2: invest in FX E[$ROR]=(1/St) * r f * E[S t+1] E[ROR]�s must be equal: r d =(1/St) * r f * E[S t+1] => E[St+1]= Ft,1

15. Uncovered Interest Parity This condition does not hold by no arbitrage; like the expectations hypothesis, it is a theory for how interest rates and exchange rates evolve. It, for example, assumes no risk premium. Independent of the risk premium, it also assumes rational expectations.

16. IV. The Law of One Price(purchasing power parity, or PPP) �Equivalent assets sell for the same price� Ptd = price of an asset in domestic currency Ptf = price of the same asset in foreign currency Ptd /Ptf = Std/f � Ptd = Ptf Std/f seldom holds for nontraded assets cannot be used to compare assets that vary in quality may not hold when there are market frictions

17. An Example of the Law of One Price:The World Price of Gold Suppose P$ = $500/oz in New York PDM = DM800/oz in Berlin The law of one price requires: Pt$ /PtDM = St$/DM ($500/oz)/(DM800/oz) = $.6250/DM If this relation does not hold, then there is an opportunity to lock in a riskless arbitrage profit

18. How Well Does the LOP Hold? For the LOP to hold, we need a number of conditions What are they? Example: �Big MacCurrencies� Country Price Implied PPP Actual XR %+/- USA $2.25 1 1 0 Japan Y380 169 135 -20 Ger DM4.30 1.91 1.67 -13

19. http://www.economist.com/editorial/freeforall/focus/focus_bigmac_tframeset.html P(BMindonesia)/P(BMusa) =rupiah3900/$ Actual rate: rupiah 14,100/$ ==> * We can buy 4MBs in Indonesia for the price of one in the US * The rupiah is 72% undervalued

20. Big Macs in Japan From a PPP point in 1990, a combination of weak $ and strong Yen resulted in 100% overvaluation in 1995, followed by a sharp reversal

21. The effect of devaluation in the far east

23. Extending the LOP to PPP The �Price Level� is: P = SwiPi a sum of prices of various consumption goods A natural extension of the LOP is hence Pt$ = St$/DM PtDM the US price level should be the same as in Ger, adjusting for the XR How sound is this theory?

24. The Cost of Living Location cost of living index Tokyo, Japan 162.36 Geneva, Switzerland 122.95 Frankfurt, Germany 108.82 Hong Kong 107.54 Paris, France 101.82 New York, United States.................. 100 London, United Kingdom 92.91 Los Angeles, United States 83.42 Montreal, Canada 80.01 Mexico City, Mexico 77.22 Prague, Czech Republic 65.93

25. Relative Purchasing Power Parity (RPPP) Let Pt = consumer price index level at time t. Then inflation pt = (Pt - Pt-1)/Pt-1. Suppose PPP were to hold well, then P0 = S0 P0* Pt = St Pt * The expected change in the spot exchange rate should reflect the difference in inflation between two currencies: E[Std/f] / S0d/f = (E[Ptd] / E[Ptf]) / (P0d / P0f) = (E[Ptd]/P0d) / (E[Ptf]/P0f) = (1+E[pd])t / (1+E[pf])t

26. Relative PPP E[Std/f] / S0d/f = (1+E[pd])t / (1+E[pf])t Example: pUS=5%, pUK=10% ==> (1+pUS)/(1+pUK)=-5% ==> E[StUSD/GBP] / S0USD/GBP =.95 What does it mean?

27. RPPP and RPPP Deviations Consider again: pUS=5%, pUK=10%, St=$1.800/L According to RPPP: E[St+1]=1.80(1.05/1.10)=$1.718/L Suppose that in fact St+1=$1.75/L ==>The $ has appreciated, but_______________

28. The Importance of RPPP Deviations Consider again: pUS=5%, pUK=10%, St=$1.800/L According to RPPP: E[St+1]=1.80(1.05/1.10)=$1.718/L Suppose that in fact St+1=$1.718/L ==> RPPP HOLDS!!!

29. RPPP Deviations:Real Vs. Nominal Rate Changes RPPP deviations have great economic importance affecting economic competitiveness, inflationary pressures, etc.... REAL EXCHANGE RATES measure RPPP deviations In the first example, the US$ appreciated in NOMINAL TERMS (from 1.80 to 1.75) BUT depreciated in REAL TERMS In the second example, the US$ appreciated in NOMINAL TERMS (from 1.80 to 1.718) BUT did not change in REAL TERMS

30. Deviations from RPPP RPPP states that: DSt+1d/f = (1+pd) / (1+pf) Note that this is an exchange rate determination model (the first one we see) What is the model�s empirical record? Var(DSt+1d/f) >> Var[ (1+pd) / (1+pf) ] This phenomenon is often described as �excess volatility�, that is, XRs change by more than is warranted by fundamentals. �excess� is normally interpreted as evidence of irrationality, with the exception of the �overshooting XRs model�. DSt+1d/f is highly unpredictable, (1+pd) / (1+pf) is highly predictable

31. Evidence on RPPP Deviations

32. The empirical Record of RPPP in the long run

33. Change in the Nominal Exchange Rate EXAMPLE S0�/$ = �100/$, E[p�] = 0%, E[p$] = 10% RPPP � E[S1�/$] = S0�/$ (1+ p�)/(1+ p$) = �90.91/$ �130/$ �120/$ �110/$ �100/$ �90/$ �80/$ t=0 t=1 In real (purchasing power) terms, the dollar has appreciated by (�110/$)/(�90.91/$)-1 = 21% more than expected.

34. The Real Exchange Rate The real exchange rate (RXR) adjusts the nominal exchange rate for differential inflation since an arbitrarily defined base period: 1+xtd/f = (Std/f / St-1d/f) [(1+ptf)/(1+ptd)] where Std/f = the nominal spot rate at time t ptc = inflation in currency c during period t What should the RXR be under RPPP?

35. Percentage Change in the RXR Xtd/f = level of the real exchange rate xtd/f +1 = (Std/f / St-1d/f) [(1+ptf)/(1+ptd)] = [(�110/$)/(�100/$)][(1.10)/(1.00)] = 1.21, or a 21% increase The real value of the dollar has appreciated by 21%.

36. Another Example Let�s go back to the previous example pUS=5%, pUK=10%, St=$1.800/L According to RPPP: E[St+1]=1.80(1.05/1.10)=$1.718/L Suppose that in fact: St+1=$1.75/L 1+xtd/f = (Std/f / St-1d/f) [(1+ptf)/(1+ptd)] = (1.75/1.80)(1.10/1.05)=�R$�1.018/ �RL� �the $ has depreciated in real terms� ... and in the second example = (1.718/1.80)(1.10/1.05)=�R$�1.00/ �RL�

37. Real Value of the Dollar (1970-1995)

38. PPP: an Exchange Rate Determination Theory Causality is Goods market ==> Currency Market The adjustment mechanism: real$ is weak and domestic prices are low => export will rise & import will fall => a trade surplus will generate a real and nominal $ appreciation We completely ignore the role of financial transaction the forward-looking nature of exchange rates the stickiness of prices

39. V. International Fisher Relation  The Fisher relation: (1+r) = (1+RR)(1+p) nominal returns are inflation times real return (denote RR) If real rates are equal across countries (RRd=RRf), then interest rate differentials reflect inflation differentials: (1+rd)/(1+rf) = [(1+RRd)(1+pd)] / [(1+RR)(1+pf)] = (1+pd)/(1+pf) This relation may not hold at any particular point in time, but does hold in the long run. WHY? At any point in time, there can be large differences in real exchange rates. Nominal interest rates, inflation rates, and implied real rates of interest can be drawn from a financial newspaper and compared in class. At any point in time, there can be large differences in real exchange rates. Nominal interest rates, inflation rates, and implied real rates of interest can be drawn from a financial newspaper and compared in class.

40. International Fisher Relation

41. Summary: International Parity Conditions