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

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<ul><li> Slide 1 </li> <li> FIN 645: International Financial Management Lecture 3 International Parity Relationships &amp; Forecasting Exchange Rates </li> <li> Slide 2 </li> <li> 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 F 3 = $0.9077 Assume (S)he sells SF 5,000,000 forward against dollars On April 4, S($/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 S 3 = $0.9107? Graph of long and short position </li> <li> Slide 3 </li> <li> Graph of Long and Short Forward Positions Long position Short position F 3 ($/SF)=.9077 Loss Profit(+).9107.9007.0070 -.0030 F 3 ($/SF) -F 3 ($/SF) S 3 =($/SF) </li> <li> Slide 4 </li> <li> 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? </li> <li> Slide 5 </li> <li> 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 </li> <li> Slide 6 </li> <li> 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 </li> <li> Slide 7 </li> <li> 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 dont typically observe persistent arbitrage conditions, we can safely assume that IRP holds. </li> <li> Slide 8 </li> <li> Interest Rate Parity Defined Suppose you have $ 1 to invest for 1 yr. You can either 1.invest in the U.S. at i $, receive future maturity value = $1 (1 + i $ ); or your dollars for pound at the spot rate (S), get (1/S), 3.invest in the U.K. at interest rate i , with the maturity value of (1/S) (1 + i ). 4.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. </li> <li> Slide 9 </li> <li> 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 $ ) </li> <li> Slide 10 </li> <li> 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. </li> <li> Slide 11 </li> <li> 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 $S in the US, which is just enough to buy 1 at the prevailing spot exchange rate (S). Lending 1 in the UK at the UK interest rate Selling the maturity value of the UK investment forward </li> <li> Slide 12 </li> <li> Dollar Cash Flows to An Arbitrage Portfolio TransactionsCF 0 CF 1 1. Borrow in the U.S.$S-S(1+i $ ) 2. Lend in the U.K.-$SS 1 (1+i ) 3. Sell the receivable forward* 0(1+i )(F-S 1 ) Net cash flow0(1+i )F-(1+i $ )S Selling the receivable forward will not result in any cash flow at the present time, that is, CF 0 =0. But at the maturity, the seller will receive $(F-S 1 ) for each pound sold forward. S 1 denotes the future spot exchange rate. </li> <li> Slide 13 </li> <li> 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 $ ) </li> <li> Slide 14 </li> <li> 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&gt;S Interest rate will be higher in the UK than in the US when the dollar is at a forward premium, i.e. F </li> <li> Purchasing Power Parity and Exchange Rate Determination Derivation of Relative PPP: Assume that price of the home country P h and the foreign country P f are equal. Home and foreign country experiences inflation rate of h and f respectively. Home and foreign country price indices become P h (1+ h ) and P f (1+ f ) respectively. If h &gt; f or f &gt; h, PPP does not hold. Exchange rate will change to maintain the parity in purchasing power </li> <li> Slide 34 </li> <li> Purchasing Power Parity and Exchange Rate Determination P f (1+ f )(1+e f )=P h (1+ h ), where e f represents the change in the value of the foreign currency Solving for e f we have (1+e f ) = P h (1+ h )/ P f (1+ f ); or e f = [(1+ h )/ (1+ f )]-1 -since we assumed that P h and P f 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 </li> <li> Slide 35 </li> <li> Purchasing Power Parity and Exchange Rate Determination If h &gt; f, e f should be positive foreign currency will appreciate when home countrys inflation exceeds the foreign countrys inflation. If f &gt; h, e f should be negative foreign currency will depreciate when foreign countrys inflation exceeds the home countrys 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%. </li> <li> Slide 36 </li> <li> 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 P h =M h V h /y h, and P f =M f V f /y f 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 = P h / Pf = (M h /M f )(V h /V f )(y h /y f </li> <li> Slide 37 </li> <li> Purchasing Power Parity and Exchange Rate Determination According to the monetary approach, what matters in exchange rate determination are: 1.The relative money supplies 2.The relative velocity of money 3.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 </li> <li> Slide 38 </li> <li> 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. </li> <li> Slide 39 </li> <li> 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 &lt; 1 competitiveness of domestic country improves with currency depreciations. If q = 1 competitiveness of domestic country unaltered with currency depreciations If q &gt; 1 competitiveness of domestic country deteriorates with currency depreciations. </li> <li> Slide 40 </li> <li> Evidence on PPP PPP probably doesnt 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 countrys 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 </li> <li> Slide 41 </li> <li> Comparison of GNP Per Capita Country GNP per Capita US$ GNP per Capita PPP Remarks Bangladesh3501,407 Higher PPP GNP per Capita India4402,060 Higher PPP GNP per Capita Nepal2101,181 Higher PPP GNP per Capita Pakistan4701,652 Higher PPP GNP per Capita Singapore30,17025,295 Lower PPP GNP per Capita Japan32,35023,592 Lower PPP GNP per Capita Malaysia3,6707,699 Higher PPP GNP per Capita Thailand2,1605,524 Higher PPP GNP per Capita China7503051 Higher PPP GNP per Capita </li> <li> Slide 42 </li> <li> 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: i h = h + E( h ) Where h is the equilibrium expected real home countrys interest rate E( h ) is the expected rate of home countrys inflation i h is the equilibrium expected nominal home interest rate </li> <li> Slide 43 </li> <li> International Fisher Effect If the Fisher effect holds in the home country i h = h + E( h ) and the Fisher effect holds in the foreign country i f = 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) = i h - i f. </li> <li> Slide 44 </li> <li> International Fisher Effect If the International Fisher Effect holds, E(e) = i h - i f and if IRP also holds i h i f =(F-S)/S then forward expectation parity holds. </li> <li> Slide 45 </li> <li> Equilibrium Exchange Rate Relationships $ - IRP PPP FEFPPP IFEFEP </li> <li> Slide 46 </li> <li> Forecasting Exchange Rates Efficient Markets Approach Fundamental Approach Technical Approach Performance of the Forecasters </li> <li> Slide 47 </li> <li> 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, todays exchange rate is the best predictor of tomorrows exchange rate: S t = E[S t+1 ] While researchers found it difficult to reject the random walk hypothesis on empirical grounds, there is no theoretical base of this either. </li> <li> Slide 48 </li> <li> Efficient Markets Approach The parity relationships indicate that the current forward exchange rate can be viewed as the markets consensus forecast of the future exchange rate based on the available information (I t ) if the foreign exchange markets are efficient, that is, F t = E[S t+1 | I t ] To the extent that interest rates are different between two countries, the forward exchange rates will be different from the current spot exchange rate. </li> <li> Slide 49 </li> <li> 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. Efficient Markets Approach </li> <li> Slide 50 </li> <li> 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. </li> <li> Slide 51 </li> <li> Fundamental Approach Difficulties of fundamental approach: Forecasting a set of independent variables to forecast the exchange rates Forecasting the former will certainly be subject to errors and may not be necessarily easier than forecasting the latter The parameter values (, s) that are estimated using historical data may change over time because of changes in government poli...</li></ul>


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