International Financial Management P G Apte

1. CHAPTER - 11 Exchange Rate Determination and Forecasting • International Financial Management • P G Apte

2. Some Fundamental Relationships • Absolute Purchasing Power Parity (PPP) • Law of one price: Price of a specified bundle of goods and services, denominated in a given currency is same everywhere. Then • St = Pt/P*t • P and P* are domestic and foreign price levels • Relative Purchasing Power Parity and Exchange Rates • Proportionate change in exchange rate equals inflation • differential : • d(lnSt) = d(lnPt) – d(lnP*t) • This will be true if St = k(Pt/P*t) k : Some constant

3. Purchasing Power Parity (PPP)some history • The theory of PPP has been around as long as paper money. It is one of the oldest theories of exchange rate determination. Hence we present it first. • It was discussed in 16th Century Spain, for example. • It was last resurrected by Gustav Cassel in the period between WWI and WWII. He used it in discussions of how much European countries would have to either change their exchange rates or their domestic price levels, given that WWI had changed the relative prices in the countries (causing different inflation rates in the countries). • It is based on the Law Of One Price (LOOP).

4. International LOOP • Transportation costs can be significant. • Legal barriers and tariffs may exist. • Some goods are not traded internationally. These are goods for which inter-regional price differentials cannot be eliminated by arbitrage. Examples of nontradeable “goods” are: • Houses • Medical services • Goods that are not available in all countries • Goods that do not survive transportation

6. Big Mac Price Local Curr In USD COUNTRY ACTUAL EXCH RATE OVERVAL(+) UNDERVAL(-) IMPLIED PPP RATE

7. Big Mac Price Local Curr In USD OVERVAL(+) UNDERVAL(-) COUNTRY IMPLIED PPP RATE ACTUAL EXCH RATE + The Purchasing Power Parity (PPP) rate is the local Big Mac price divided by its price in the United States. Prices and their corresponding implied PPP rates are the latest figures available from The Economist.++ The Over/Under valuation against the dollar is calculated as follows using OANDA's latest rates: 100 x (PPP - Exchange Rate) / Exchange Rate

8. The Big Mac Index: An Imperfect MeasureThe Big Mac Index does have its shortcomings. A Big Mac's price reflects more than just the cost of bread and meat and vegetables. It also reflects non-tradable elements -- such as rent and labor. For that reason, the Big Mac Index probably is best when comparing countries at roughly the same stage of development. In any case, there is no theoretical reason why non-tradable goods and services should be equal in different countries. That explains why PPPs are different from market exchange rates over time.Furthermore, eating a Big Mac means different things in different countries. Indians eat fewer Big Macs than Americans. In some countries, eating at McDonald's is a relative luxury. Whereas low-income Americans may eat at McDonald's a few times a week, low-income Malaysians rarely eat Big Macs. Finally, local taxes, levels of competition, and import duties on Big Mac components may not be representative of the country's economy as a whole.

9. Big Mac prices build in the differences in local production costs between countries. For example, the price of beef is lower in Australia than in Japan, and Australian Big Mac prices reflect the lower input cost. Perhaps a standardized commodity that is free of variations in local costs would provide more accurate PPP exchange rate estimates.Consider individual song downloads on iTunes. Like Big Macs, their pricing is set by a single firm--in this case, Apple. Unlike Big Macs, we can expect that there are no local variations in costs. Apple negotiates with the same music company (Sony, BMG, etc.) for the rights to digital provision of a given song. Hence, any cross-country differences in download prices likely arise from differences in demand.

10. i-TUNE EXCHANGE RATES vs. BIG-MAC EXCHANGE RATES

11. Inflation and Exchange Rate vs US 1999-2006: Is PPP Valid?

12. 1 The CPIRATIO for each country is the ratio of its 2006 CPI to 1999 CPI 2 CPIR/CPIRUS is the ratio of CPIRATIO for each country to CPIRATIO for US. A value less than 1.0 indicates the country had slower inflation than US 3 The ERATERATIO is the ratio of the exchange rate of the country against USD in 2006 to the exchange rate in 1999. The exchange rate is stated as number of USD per unit of the currency. Thus a rise in ERATERATIO indicates depreciation of US dollar against the other currency.

14. Tests of relative purchasing power parity are often carried out by estimating an equation like : Here the LHS captures the % change in exchange rate from t-1 to t while the RHS measures the difference in inflation rates between the two countries. PPP is tested by testing the hypotheses that a=0 and b=1. The test can be carried out using time series data for pairs of currencies or using a cross section sample of currencies.

15. Obstfeld has carried out a test using a cross section sample. He has estimated the following equation : Here Ei is the exchange rate of currency i vs. the US dollar defined as units of i per dollar, Pi is the consumer price index for country i and PUS is the CPI for US. Over the sample period of 1973-1993 the estimated value of the coefficient b is 1.15 and the coefficient of determination, R2 is 0.82.

16. Exchange Rates in the Long Run: PPP Purchasing Power Parity, United States/United Kingdom, 1973–2004 (Index: March 1973 = 100)

17. CROSS SECTIONAL REGRESSION RESULTS FOR RELATIVEPURCHASING POWER PARITY • Consider a regression of the (logarithmic) change in spot on relative inflation differentials with the US • Changes are measured over the period 1978.01 to 2005.12 • There are 11 observations inthis regression (AUD, CAD, JPY, NZD, SEK, NOK, CHF, GBP, SGD, DKK and synthetic EUR vs. USD) • Adjusted R-square = 60% Slope coefficient = 0.67; t-ratio = 4.00 Intercept = 0.046; t-ratio =0.61 • Direction of currency change is consistent with the inflation differential for 9 of11 currencies • A similar result holds for a more sophisticated versionof PPP, such as a FEER/BEER model

18. EFFECTIVE EXCHANGE RATES Can we assess how a currency is moving against a basket of currencies? One such measure is : NOMINAL EFFECTIVE EXCHANGE RATE (NEER) Suppose we state exchange rate of the rupee against the currency of country i as number of rupees per unit of currency i and denote it as Si. We choose a basket of n currencies 1,2…n. We define NEER as: n (S1)w1(S2)w2…(Si)wi…(Sn)wn = Π(Si)wi i=1 Here wi denotes share of country i in India’s foreign trade.

19. EFFECTIVE EXCHANGE RATES… • Two basic decisions: • How many and which countries’ currencies should be selected in the basket? • Countries which together account for 80/85/90/95 % of India’s trade? • (2) The weight assigned to country i viz. wi should reflect its share in India’s exports/imports/total trade? • Construct three separate indices? • NEER is stated as an index with reference to a base year. • Is it possible to combine exchange rate movements and inflation differences?

20. REAL EFFECTIVE EXCHANGE RATE (REER) • This is a measure which combines nominal exchange rate movements and inflation rates. Also stated as an index. • Bilateral version of REER: • Rt(B/A) = St(B/A)(PtB/PtA) • Multilateral version or REER: • i=n • (Sti Pti)wi/PtH • i=1 • Sti is the exchange rate of currency i against home currency at time t, Pti is the price level in country i and PtH is the price level in home country. Price levels are measured w.r.t. a common base year.

21. Some Fundamental Relationships How do we interpret movements in NEER and REER? An increase in NEER obviously implies depreciation of the home currency against the basket. An increase in bilateral REER implies that the exchange rate S(B/A) has increased more than the price ratio (PtB/PtA). Thus suppose between January 2005 and and August 2009 the rupee-dollar exchange rate has risen 20%, price level in US has gone up 12% while price level in India has gone up by 30%. REER would have increased between January 2005 and August 2009. Rupee has depreciated more than what is required to counter the gap in inflation rate. Rupee is said to have depreciated in real terms. Same logic would hold for multilateral REER. Thus an increase REER would indicate a real depreciation while a decrease would indicate real appreciation of the home currency against the basket.

23. Some Fundamental Relationships • Covered Interest Parity • Covered interest parity relation in the absence of transaction costs • iA and iB are annualized euromarket interest rates on n-year deposits, Fn(B/A) is the n-year forward rate and S(B/A) is the spot rate both expressed as units of A per unit of B. • Approximate Version : iA – iB = {[Fn(B/A) – S(B/A)]/S}(1/n) (1 + niA)/(1 + niB) = Fn(B/A)/S(B/A)

24. iA – iB 450 Line {[Fn(B/A) – S(B/A)]/S(B/A)}(1/n)

25. Why the Covered Interest Parity relationship may be violated in practice: 1. Transaction costs – Bid/Offer Spreads in currency and money markets. 2. Political/Country Risks perceived by investors. 3. Inelastic supply of arbitrage funds; Tying up credit lines. 4. Differential tax treatment of interest income and exchange gains/losses.

26. Taxes and CIP Consider a UK investor. Each GBP invested for a year at home brings, post tax : GBP[1+(1-I)iUK] Here I is the tax rate on ordinary income and iUK is the UK interest rate. A covered investment in dollars yields, pre-tax [F($/£)/S($/£)][1+iUS] = [(F-S)/S](1+iUS) + (1+iUS) The first term on the RHS is the exchange gain and the second term is principal plus interest.  

27. Taxes and CIP Post tax, the return is 1+(1-I)iUS + (1-C)[(F-S)/S](1+iUS) Here C is the capital gains tax rate. The investor would be indifferent if the two returns are equal i.e. if iUK-iUS = [(1-C)/(1-I)][(F-S)/S](1+iUS) If C < I, the UK interest rate will have to be higher for investor indifference than in the case when the two tax rates are equal.

28. iA – iB Band of Variation [Fn(B/A) – S(B/A)]/n

29. Some Fundamental Relationships • Uncovered Interest Rate Parity • In a world of perfect capital mobility the following condition, known asUncovered Interest Parity(UIP) must hold • UIP condition with n=1, can be re-written as

30. Some Fundamental Relationships • UIP condition is not a causal relationship • Combine UIP with relative PPP • Invoke definition of real interest rate • Implication? • What does UIP assume about (1) Cross-border capital flows and (2) Investors’ risk attitudes? Empirically not found to be very successful. Still an ingredient of many exchange rate models

31. Some Fundamental Relationships Barriers to UIP • Investors are risk averse and therefore would not be guided only by expected returns • Even if all investors are risk neutral, they could have differing views about future exchange rate movements • Transaction costs and liquidity needs would force people to hold some of their wealth in the currency of their operating habitat even though the expected return on a foreign currency is higher • Exchange controls may prohibit portfolio shifts between currencies and interfere with realization of UIP

32. Structural Models of Exchange Rate Determination • Models based on Trade Flows • Mundell-Fleming Model – Simple and Higher • Versions • Flex-price Monetary Model • Dornbusch Overshooting Model • Sticky-price Monetary Model • Portfolio Balance Models • Expectations, News and Exchange Rates

33. Flow Models of Exchange Rate Determination A simple model of exchange rate determination views exchange rate as a price – e.g. price of dollars in terms of rupees. Like any other price, it is determined by the interaction of demand and supply. With freely floating rates equilibrium exchange rate equates demand to supply. Consider the rupee-dollar exchange rate. The demand for dollars arises from imports of goods and services from US into India. The supply curve arises from India’s exports to the US. Will the supply curve of dollars be always up-ward sloping?

34. D Exchange S Rate USD/INR E SD Quantity of Dollars Exchange rate stated as No. of Rupees per Dollar

35. Is it possible that as dollar rises against rupee, Americans spend a smaller amount of dollars on Indian goods and services? The importance of demand elasticity can be understood by examining what happens to the number of dollars Americans would spend on India goods and services as the Rupee-$ exchange rate changes. Assume that Rupee prices of India goods remain fixed and the Rupee depreciates. Dollar prices of Indian goods in the US decrease. From elementary microeconomic theory we know that if the elasticity of Americans' demand for Indian goods is less (more) than one, the number of dollars spent by Americans on European goods will decrease (increase).

36. S D USD/INR RATE E D S NO. OF DOLLARS

37. D S USD/INR RATE E S D NO. OF DOLLARS

38. Will currency depreciation always improve trade balance? Marshall-Lerner condition: Simplest form : EX + EM > 1 EX : Price elasticity of demand for exports (Foreigners’ demand for home country’s exports) EM : Price elasticity of demand for imports (Domestic resident’s demand for imported goods and services) This version is valid when the starting point is a balanced trade account and supply elasticities of exports and imports are infinite. If the starting point is a trade deficit/surplus, the condition is : EX + (VM/VX) EM > 1 VM ,VX are starting values of imports and exports More complex versions allow for finite supply elasticities

39. Mundell-Fleming Model: Simplest Version • Constant domestic price level (Unemployed resources at home). • “Small country” assumption – Foreign income, interest rate, price level given • Capital flows proportional to interest rate difference • Monetary policy partly directed to a target exchange rate. Exogenous fiscal policy. • Other standard assumptions about private consumption, investment • Exports depend on exchange rate, foreign income; imports on exchange rate, home income

40. Mundell-Fleming Model Variables Endogenous: Y : Domestic GDP; S : Exchange Rate No.of units of HC per unit of FC r : Domestic interest rate; Md : Demand for money Ms : Supply of money; X : Exports; IM : Imports CAPF : Net capital inflows Exogenous Foreign GNP; Foreign interest rate; Target exchange rate

41. Mundell-Fleming Model: Simplest Version (1) Y = B0 + B1S – B2r (2) Md = B3Y – B4r (3) Ms = M#s – B5 (S – S˜) (4) Md = Ms (5) X = B6 + B7S (6) IM = B8 – B9S + B10Y (7) CAPF = B11(r – r*) (8) X - IM + CAPF = 0 8 equations, 8 unknowns : Y, S, r, Md, Ms, X, IM, CAPF Reduce to 2 equations in two unknowns – Y and S

42. Mundell-Fleming Model: Simplest Version L S S E I M Y

43. FISCAL EXPANSION IN MUNDELL-FLEMING MODEL S L S S' S0 S1 I I' M Y0 Y1 Y

44. Monetary Expansion in the Mundell-Fleming Model L' S S L S1 S0 M' I M Y0 Y1 Y

45. Flex-Price Monetary Model • Stable demand-for-money function • Relative PPP holds • UIP holds • Prices move instantaneously • Residents hold only home money; foreigners hold only foreign money. Money is the only asset. • Monetary authority has full control over money supply. There is no exchange rate target.

46. Flex-Price Monetary Model mA = pA + b1yA – b2rA (1) mB = pB + b3yB – b4rB (2) s = k + pA – pB (3) (1) and (2) are money demand functions in countries A and B; (3) is the relative PPP equation Use (1) and (2) to replace pA and pB in (3) to get s = k + (mA – mB) - b1yA + b3yB + b2rA - b4rB (4) Assume b1 = b3 and b2 = b4 s = k + (mA – mB) – b1(yA -yB) + b2(rA – rB) (5) If mA s -currency depreciates; If yA s -currency appreciates If rA s - currency depreciates (counterintuitive?)

47. The Dornbusch Overshooting and Sticky Price Monetary Model: (1) Purchasing Power Parity holds only in the long run. In the short run, goods prices are "sticky". (2) There is a stable demand for money function which relates real balances to real income and interest rate. (3) Uncovered interest parity holds and the foreign interest rate is fixed. (4) Real output is fixed at its full employment level. (5) Exchange rate expectations are rationally formed. This means that given a change in money supply, people know what the final equilibrium value of the exchange rate is going to be; short run changes in exchange rate are in the nature of adjustment to the gap between the final equilibrium value and the current value. (6) Prices adjust gradually to the gap between the current level of demand for output and the full employment output.

48. The implications of these assumptions are as follows: • In equilibrium, real output is fixed. Since UIP holds and foreign interest rate is constant, domestic interest rate is also fixed. • Hence, in the long run, price level must change in proportion to changes in money supply. • Also, since PPP holds in the long run and foreign price level is fixed, exchange rate must depreciate (appreciate) in proportion to the increase (decrease) in domestic price level in the long run. • In this context, rational expectations really means perfect foresight - people know what the long-run value of the exchange rate is going to be.

49. Notation of the Dornbusch model : yd : Demand for output y* : Full employment output pd : Domestic price level rd : Domestic interest rate s : Exchange rate (units of home currency per unit of foreign currency) s* : Long run "equilibrium" exchange rate. m : Nominal money stock rf : Foreign interest rate. Assumed to be constant Foreign price level assumed to be fixed – “Small country assumption. Superscript “e” denotes expected value.

50. Overshooting Model Equations