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FIN 645: International Financial Management Lecture 3

FIN 645: International Financial Management Lecture 3 International Parity Relationships & Forecasting Exchange Rates. Long and Short Forward Positions. One can buy (take a long position) or sell (take a short position) foreign exchange forward A speculative forward position

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FIN 645: International Financial Management Lecture 3

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  1. FIN 645: International Financial Management Lecture 3 International Parity Relationships & Forecasting Exchange Rates

  2. Long and Short Forward Positions • One can buy (take a long position) or sell (take a short position) foreign exchange forward • A speculative forward position • $ will likely appreciate in value against the Swiss Franc • The trader will short the three-month $/SF contract on January 4,2008 at F3 = $0.9077 • Assume (S)he sells SF 5,000,000 forward against dollars • On April 4, S($/SF) = $0.9007 • The trader can buy Swiss Franc spot at $0.9007 and deliver it under the forward contract at a price of $0.9077 • Speculative profit($0.9077- $0.9007) =$0.0070 • Total profit from the trade $35000 = (SF 5,000,000x$0.0070) • What if the $ depreciated and S3 = $0.9107? • Graph of long and short position

  3. Graph of Long and Short Forward Positions Profit(+) F3($/SF) Long position .0070 .9107 S3=($/SF) .9007 F3($/SF)= .9077 -.0030 Short position -F3($/SF) Loss

  4. Lecture Outline • Forces Driving Exchange Rate Changes • Interest Rate Parity (IRP) • Covered Interest Arbitrage • IRP and Exchange Rate Determination • Reasons for Deviations from IRP • The Law of One Price • The two things that are equal to each other must be selling for the same price • Forecasting Foreign Exchange Rates? • How are Foreign Exchange Rates Determined?

  5. Lecture Outline • Purchasing Power Parity (PPP) • PPP Deviations and the Real Exchange Rate • Evidence on PPP • The Fisher Effect • Forecasting Exchange Rates • Efficient Market Approach • Fundamental Approach • Technical Approach • Performance of the Forecasters

  6. Arbitrage Equilibrium • The term Arbitrage can be defined as the act of buying and selling the same or equivalent assets or commodities for the purpose of making certain guaranteed profit. • As long as there are profitable arbitrage opportunities, the market cannot be in equilibrium • The market is said to be in equilibrium when no profitable arbitrage opportunities exist • Parity relationships such as IRP and PPP, in fact, represent arbitrage equilibrium condition

  7. Interest Rate Parity Defined • IRP is an arbitrage condition that must hold when international financial markets are in equilibrium. • 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.

  8. Interest Rate Parity Defined Suppose you have $ 1 to invest for 1 yr. You can either • invest in the U.S. at i$, receive future maturity value = $1 (1 + i$); or • exchange your dollars for pound at the spot rate (S), get £(1/S), • invest in the U.K. at interest rate i£ ,with the maturity value of £(1/S) (1 + i£). • hedge your exchange rate risk by selling the future value of the U.K investment forward (for a predetermined dollar amount). The future value = $[(1/S)(1 + i£)] F, where F denotes the forward exchange rate.

  9. Interest Rate Parity Defined • Please note that when your British investment matures in one year, you will receive the full maturity value, £(1/S) (1 + i£). But you have to deliver exactly the same amount of pounds to the counterparty of the forward contract, your net pound position is reduced to zero. In other words, the exchange risk is completely hedged • You have effectively denominated the UK investment in dollar terms • Since both of these investments have the same risk, they must have the same future value—otherwise an arbitrage opportunity would exist. (F/S)(1 + i£) = (1 + i$)

  10. Interest Rate Parity Defined Formally, (F/S)(1 + i£) = (1 + i$) or if you prefer, IRP is sometimes approximated as IRP is a manifestation of the law of one price (LOP) to international money market instruments.

  11. Alternative Derivation IRP • IRP can also be derived by constructing an arbitrage portfolio, which involves (i) no net investment; (ii) no risk, and then requiring that such a portfolio should not generate any net cash flow in equilibrium • Consider an arbitrage portfolio consisting of three separate positions: • Borrow $S in the US, which is just enough to buy £1 at the prevailing spot exchange rate (S). • Lending £1 in the UK at the UK interest rate • Selling the maturity value of the UK investment forward

  12. Dollar Cash Flows to An Arbitrage Portfolio • Selling the £ receivable “forward” will not result in any cash flow at the present time, that is, CF0=0. But at the maturity, the seller will receive $(F-S1) for each pound sold forward. S1 denotes the future spot exchange rate.

  13. Dollar Cash Flows to An Arbitrage Portfolio • Note that: • The Net cash flow at the time of investment is zero; i.e. the arbitrage portfolio is self financing; it does not cost any money to hold this portfolio; • The net cash flow on the maturity date is known with certainty, because S,F, i£, and i$ are all known. • Since no one should be able to make certain profits by holding this arbitrage portfolio, market equilibrium requires that the net cash flow on the maturity date be zero for this portfolio: (1+i£)F-(1+i$)S=0 By rearrangement, we have: (F/S)(1 + i£) = (1 + i$)

  14. IRP and Interest Rates • The IRP relationship is often approximated by: (i$-i£) = (F-S)/S • From the above relationship, it can be seen that IRP provides a relationship between interest rate of two countries. • Interest rate will be higher in the US than in the UK when the dollar is at a forward discount, i.e. F>S • Interest rate will be higher in the UK than in the US when the dollar is at a forward premium, i.e. F<S • Forward exchange rate will deviate from the spot rate as long as the interest rates of the two countries are not the same.

  15. Covered Interest Arbitrage • When IRP holds, you will be indifferent between investing your money in the US and investing in the UK with forward hedging. • If IRP is violated, you will be better off by investing in the US(U.K) if (1 + i$) is greater (less) than (F/S)(1 + i£). • On the other hand, if you need to borrow, you will choose to borrow where the dollar interest rate is lower. • When IRP does not hold, the situation gives rise to covered interest arbitrage opportunities

  16. Covered Interest Arbitrage: Cash Flow Analysis

  17. Interest Rate Parity Diagram (F-S)/S (%) IRP line 4 3 2 B 1 -1 -4 -3 -2 4 2 3 (i$-i£)(%) 1 -1 A -2 -3 -4

  18. Another CIA Example • Three month interest rate in the US: 8.0% per annum • Three month interest rate in Germany: 5.0% per annum • Current spot exchange rate: € 1.0114/$ • Three-month forward exchange rate: € 1.0101/$ • Again, we assume that the arbitrager can borrow $1,000,000 or the equivalent € amount, € 1,011,400 • Calculate arbitrage profit, if any.

  19. Covered Interest Arbitrage: Cash Flow Analysis 2

  20. Covered Interest Arbitrage (CIP) • Covered Interest Arbitrage is a situation which occurs when IRP does not hold, thereby allowing certain arbitrage profits to be made without the arbitrageur investing any money out of pocket or bearing any risk. • To see if any CIP opportunities exist?, Verify

  21. Deviations from IRP and Market Adjustments • How long will the arbitrage opportunity will last? • As soon as deviations from IRP are detected, informed traders will carry out CIA transactions • Borrow in the US, interest rate in the US will rise (i$ ↑) • Lend in the UK, interest rate will fall in the UK(i£↓) • Buy the pound spot, the pound will appreciate in the spot market (S↑) • Sell the pound forward, the pound will depreciate in the forward market (F↓) • These adjustments will raise LHS of IRP equation and lower the RHS until both sides are equalized, restoring IRP

  22. IRP and Exchange Rate Determination • IRP relationship can be written as • S = [(1 + i£)/(1 + i$)]*F, i.e.given the forward exchange rate, the spot exchange rate depends on the relative interest rates. • All else equal, in this example, an increase in the US interest rate will attract capital to the US, increasing demand for dollars and will lead to a lower spot exchange rate -higher foreign exchange value of the dollar. • A decrease in the US interest rate will lower foreign exchange value of the dollar.

  23. IRP and Exchange Rate Determination • In addition to the relative interest rates, the forward exchange rate is an important determinant of the spot exchange rate. • Under certain conditions, the forward exchange rate can be viewed as the expected future spot exchange rate conditional on all relevant information being available now. F = E(St+1|It)

  24. IRP and Exchange Rate Determination • S = [(1 + i£)/(1 + i$)]* E(St+1|It) • “Expectation” plays a key role in exchange rate determination, i.e. the expected future exchange rate is the major determinant of the current exchange rate. • Exchange rate behavior will be driven by news events(It)

  25. Uncovered Interest Parity • When the forward exchange rate F is replaced by the expected exchange rate, E(St+1), we get the uncovered interest rate parity relationship shown below: (i$-i£) = E(e), where E(e) is the expected rate of change in the exchange rate, i.e. [E(St+1)-St]/St • Interest rate differential between a pair of countries is(approximately ) equal to the expected rate of change in the exchange rate.

  26. Reasons for Deviations from IRP • Transactions Costs • The interest rate available to an arbitrager 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.

  27. Interest Rate Parity With Transaction Costs (F-S)/S (%) IRP line 4 3 2 D 1 -4 -3 -2 4 2 3 (i$-i£)(%) -1 1 -1 C -2 -3 -4 Unprofitable arbitrage

  28. Deviations from Interest Rate Parity • Empirical evidence • Japan imposed capital controls off and on until December 1980 • Otani and Tiwari investigated the effect of capital controls on IRP deviations during 1978-81. They compute deviations from IRP DIRP = [(1+i¥)S/(1+i$)F] -1 • If IRP strictly holds deviations from it would be randomly distributed, with the expected value of zero. They found that deviations from IRP hardly hover around zero. Highest during 1978(Japan discouraged capital inflows to keep the yen from appreciating). As these were removed deviations decreased in 1979. Increased again in 1980, as Japanese financial institutions were asked to reduce FC deposits. In December 1940, Japan liberalized FE transactions, deviations close to zero • Deviations from IRP, especially in 1978 and 1980, do not represent unexploited profit opportunities, rather barriers to cross border arbitrage.

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

  30. Purchasing Power Parity and Exchange Rate Determination • Absolute PPP • The exchange rate between two currencies should equal the ratio of the countries’ price levels. S(h/f) = Ph Pf h (home currency) and f (foreign currency); Ph (home price level) Pf (foreign price level) • Standard commodity basket in the US is $225, in the UK £150, the exchange rate should be $1.50 per pound. • PPP requires that the price of the standard commodity basket be the same across countries when measured in a common currency.

  31. “A Feast of Burgernomics”

  32. “A Feast of Burgernomics”

  33. Purchasing Power Parity and Exchange Rate Determination • Derivation of Relative PPP: • Assume that price of the home country Ph and the foreign country Pf are equal. • Home and foreign country experiences inflation rate of πh and πf respectively. • Home and foreign country price indices become Ph (1+ πh) and Pf (1+ πf) respectively. • If πh > πf or πf > πh, PPP does not hold. • Exchange rate will change to maintain the parity in purchasing power

  34. Purchasing Power Parity and Exchange Rate Determination Pf(1+f)(1+ef)=Ph(1+h), where ef represents the changein the value of the foreign currency Solving for ef we have (1+ef) = Ph(1+h)/ Pf(1+f); or ef= [(1+h)/ (1+f)]-1 -since we assumed that Ph and Pf were initially equal in both countries. The formula reflects the relationship between relative inflation rate and the exchange rate. The formula can also be expressed as e=(h- f)/(1+f) which can be approximated by e= h- f

  35. Purchasing Power Parity and Exchange Rate Determination • If h> f , ef should be positive • foreign currency will appreciate when home country’s inflation exceeds the foreign country’s inflation. • If f> h, ef should be negative • foreign currency will depreciate when foreign country’s inflation exceeds the home country’s inflation. • Relative PPP states that the rate of change in an exchange rate is equal to the differences in the rates of inflation. e = h- f • If U.S. inflation is 5% and U.K. inflation is 8%, the pound should depreciate by 3%.

  36. Purchasing Power Parity and Exchange Rate Determination • PPP and monetary approach, associated with Chicago School • Based on two basic tenets: PPP and quantity theory of money From quantity theory of money the following identity must hold for each country Ph=MhVh/yh, and Pf=MfVf/yf where M denotes money supply, V the velocity of money, y the national aggregate output, P is the general price level • Substituting the above two equations are substituted for the price levels in the PPP equation, we have: S = Ph / Pf = (Mh/Mf)(Vh/Vf)(yh/yf

  37. Purchasing Power Parity and Exchange Rate Determination • According to the monetary approach, what matters in exchange rate determination are: • The relative money supplies • The relative velocity of money • The relative national outputs • All else equal an increase in home money supply will • result in proportionate depreciation of the home currency • so will an increase in velocity of home currency, which is the same as increase in supply of home currency; • But increase in home output will cause appreciation of home currency • The monetary approach can be viewed as a long-run theory • It assumes prices adjusts fully and completely • In the short run there are price rigidities such as wage rate set by labor contract

  38. PPP Deviations and the Real Exchange Rate • If PPP holds and thus differential inflation rates between countries are exactly offset by exchange rate changes, countries’ competitive positions in world export market will not be systematically affected by exchange rate changes. • If there are deviations, changes in the nominal exchange rate cause changes in the real exchange rates, affecting international competitiveness and thus trade balances.

  39. PPP Deviations and the Real Exchange Rate The real exchange rate is: q= (1 + h)/[(1 + e)(1 + f)] If PPP holds, (1 + e) = (1 + h)/(1 + f), then q = 1. If q < 1 competitiveness of domestic country improves with currency depreciations. If q = 1 competitiveness of domestic country unaltered with currency depreciations If q > 1 competitiveness of domestic country deteriorates with currency depreciations.

  40. Evidence on PPP • PPP probably doesn’t hold precisely in the real world for a variety of reasons. • Substantial barriers to international commodity arbitrage exists • Haircuts cost 10 times as much in the developed world as in the developing world: non-tradeables. • Shipping costs, as well as tariffs and quotas can lead to deviations from PPP. • PPP-determined exchange rates still provide a valuable benchmark • In deciding if if a country’s currency is overvalued or undervalued. • Can often be used to make more meaningful international comparisons of economic data using PPP-determined rather than market determined exchange rates. • Size of the economy

  41. Comparison of GNP Per Capita

  42. 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. • For the home country, the Fisher effect is written as: ih = h + E(h) Where h is the equilibrium expected “real” home country’s interest rate E(h) is the expected rate of home country’s inflation ih is the equilibrium expected nominal home interest rate

  43. International Fisher Effect If the Fisher effect holds in the home country ih = h + E(h) and the Fisher effect holds in the foreign country if = f + E(f) and if the real rates are the same in each country h = f then we get the International Fisher Effect E(e) = ih - if .

  44. International Fisher Effect If the International Fisher Effect holds, E(e) = ih - if and if IRP also holds ih – if =(F-S)/S then forward expectation parity holds.

  45. Equilibrium Exchange Rate Relationships IFE FEP PPP IRP FE FPPP $- £

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

  47. 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, which is unpredictable. So, the exchange rate will change randomly over time. Thus, according to the random walk hypothesis, today’s exchange rate is the best predictor of tomorrow’s exchange rate: St = E[St+1] • While researchers found it difficult to reject the random walk hypothesis on empirical grounds, there is no theoretical base of this either.

  48. Efficient Markets Approach • The parity relationships indicate that the current forward exchange rate can be viewed as the market’s consensus forecast of the future exchange rate based on the available information (It) if the foreign exchange markets are efficient, that is, Ft = E[St+1| It] • To the extent that interest rates are different between two countries, the forward exchange rates will be different from the current spot exchange rate.

  49. Efficient Markets Approach • The efficient market hypothesis subscriber may predict the future exchange rate using either the current spot exchange rate or the current forward exchange rate. But which one is better? • The empirical findings indicate that these two models registered comparable performances. • Predicting exchange rates using the efficient markets approach is affordable and is hard to beat. • Advantages of efficient market hypothesis: • Since both the current spot and forward exchange rates are public information, generating forecasts using EMH is costless and freely accessible. • It is difficult to outperform the market-based forecasts unless the forecaster has access to private information that is not yet reflected in the current exchange rate.

  50. Fundamental Approach • The fundamental approach to exchange rate forecasting uses various models that involve econometrics using 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.

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