Testing the Validity of International Fisher Effect Finance Essay

Foreign exchange trading refers to trading one country's money for that of another country. The need for such trade arises due to tourism, international trade, or investments across boundaries. The foreign-exchange market, as we usually think of it, refers to large commercial banks in financial centers, like New York or London, trading foreign-currency-dominated deposits among each other. Theories aiming to explore and understand interactions in international monetary variables became increasingly more important as deregulations and international integration of financial markets throughout the world continued to evolve and increase faster than it has ever been. One theory linked two important financial variables, exchange rates and interest rates, is the International Fisher Effect (IFE). IFE states that future spot exchange rates can be determined from nominal interest differentials. In turn, real interest rate will be equalized across the world through arbitrage. Differences in observed nominal interest rates will be stemming from differences in expected inflations. These differences in anticipated inflations are embedded in nominal interest rates as described by Fisher equation. The effect of these variables on exchange rates are more likely to occur under flexible exchange rates where currencies are allowed to fluctuates without government interventions but rather lift to free market forces to determine the appropriate exchange rates. In this project, some of the most important theories in international finance literature are going to be explored with an attempt to clarify the logic behind them as well as the basic mathematical formulas that describes these theories. After that, a statistical test will be employed using regression analysis on two currencies that are viewed to be the most traded and free of, or more realistically, exhibit minimal government interventions. The test aims to verify the validity of IFE theory and its explanatory power of fluctuations in exchange rates. However, an overview of the market is going to explore the history of foreign exchange market in addition to the major products and players in that particular market.

Gold Standard From 1876 to 1913 Each currency is convertible into gold at a specified rate Price of each currency relative to the other is determined by gold convertibility rate Suspended when World War I began in 1914 Some attempts were made in the 1920s to go back to the gold standard, but the Great Depression stood for them Bretton Woods Agreement Was signed in 1944 Called for fixed exchange rate between currencies Governments had to prevent their currencies from moving more than 1% By 1971 the dollar was overvalued as demand for dollar was less than supply Governments had difficulty in maintaining exchange rates at their pre-specified levels Smithsonian Agreement Signed in 1971 Devalued the dollar Allowed currencies to fluctuates in either direction by 2.25% Governments had difficulties in maintaining exchange rate despite the wider limits Floating exchange Started in 1973 after floatation of dollar Free market forces drive values of currencies

Spot market Immediate exchange of currencies The most common type of foreign exchange transactions Forward market Buying and selling currencies at a specified price today but future delivery Mostly used by multinational corporations and speculators Used to eliminate uncertainty Currency swaps Buying one currency today and selling another in the future in one transaction It is a spot and forward transaction in one deal Mostly used in interbank trading in order to avoid excessive transaction costs It serves as a borrowing and lending operations combined Options A contract that provides the right to buy or sell a given amount of currency at a specified price in the future The right holder pays a non-refundable premium to the option writer Like forward contracts except forwards are obligation on both parties while options are obligations only on the option writer Mainly used for risk hedging strategies

Foreign exchange markets involves hundreds of thousands participants at any given day; among those are hundreds of banks facilitating foreign exchange transactions, but the top 20 banks handle about 50% of the market. Deutsche Bank, Citibank and J.P. Morgan Chase are the largest traders in the market. (5) Commercial banks charge fees for conducting foreign exchange transactions. Banks bid (buy) foreign currencies at a price and ask (sell) them at a higher price. The bid/ask spread covers banks' costs plus a profit margin. Usually, bid/ask spreads are functions profit margins of banks and of the risk of the currency, liquidity risk for instance. At any given point in time, exchange rate between two currencies should be similar across the various banks otherwise an arbitrage opportunity arises immediately. If a bank experiences a shortage in a particular foreign currency, it can purchase that currency from another bank in what is called interbank market. Usually, the interbank market takes place through brokers (10 brokerage firms handle most of the transactions in this market). (5) Central banks play an integral role in the foreign exchange market. Exchange rates affect the competitive position of products of a country in the international market place through changes in the relative price of currencies. This is the main reason for government intervention in the exchange market. Central banks like the Federal Reserve in the U.S. buy and sell currencies to drive values of their currency to level the free market would not establish. For example, buying dollars and selling pounds would lower supply of dollar and increase the pound which will eventually drives the price of the dollar upward and pushes the pound downward (supply and demand game) (6). The course of normal operations of the government might require some foreign currencies which can be another reason for central banks to operate in the foreign exchange market.

In this section, the theoretical frame that describes factors affecting exchange rates are going to be described. The section begins with purchasing power parity (PPP) that relates changes in exchange rates to inflation differential between two countries. The intuition behind the theory and its versions (absolute and relative) are going to be explained in addition to the basic mathematical frame of the theory. After that, the analysis will head to the Fisher equation which states that nominal interest rate in a country is a function of real interest rate plus a premium for anticipated inflation. That theory is not directly related to exchange markets but it builds a necessary bridge to the International Fisher Effect. The section ends with linking the above-mentioned theories, namely PPP and Fisher equation, to form the International Fisher Effect (IFE). IFE relates exchange rate changes to interest rate differentials between two currencies. That theory, if valid, allows foreign exchange market participants to predict movements in exchange rates using widely available public information which is market interest rates. By the end of this section, we are going to be equipped by enough theory to start analyzing historical data to assess how closely markets move to what Fisher predicted in his theory.

Purchasing power parity (PPP) has two versions: absolute and relative. Absolute PPP states that exchange rate between any two currencies should be equal to the ratio of their price indexes (6). If we let E denotes exchange rate of the foreign currency and Ph and Pf be the price index of the home and foreign country, respectively, the relation can be described mathematically, (1) Equation 1 can be restated differently, (2) Equation 2 is called the Law of One Price (6). That means prices of domestically produced products equal prices of foreign country's products in the local currency. If that condition was violated, domestic consumers will shift consumption from foreign products to domestic products when prices of foreign products increase relative to domestic products and the vice versa if prices of foreign country's products decrease. When that happens, exchange rates will adjust to cancel out the price difference between the two countries to retain equilibrium. Relative PPP stresses the relative change in exchange rate as well as price indexes. It holds that the percentage change in foreign exchange rate equals the difference between percentage change in price indexes of home (domestic) and foreign country (5).

Since percentage change in price index is called inflation rate, relative PPP can be stated as "percentage change in foreign exchange rate equals inflation differential between the two countries". Mathematically, (3) Where: Percentage change in foreign currency's exchange rate Home country's inflation Foreign country's inflation Equation 3 is just an approximation of the mathematical formula of relation PPP. In order to arrive the precise definition of International Fisher Effect, later on, the exact relative PPP needs to be established. First, we assume that price index of home Ph and foreign country Pf are equal. Relative PPP suggests that foreign currency exchange rate will change if inflation differs between any home and foreign country. Now, if we let ef be the percentage change in foreign currency; then, domestic consumer will perceive prices of the foreign country's goods to be (4) And to maintain relative PPP, the following should be true (5) Solving fore ef (6) Since Ph=Pf, (as we assumed earlier) (7) Equation 7 states, in plain language, that the foreign currency price relative to home currency will appreciate if domestic inflation exceeds foreign inflation, and vice versa, proportionally to inflation differential. The chart bellows shows graphically how inflation differential and relative change in exchange rate should behave if relative PPP holds. The y-axis represents inflation differential while x-axis represents relative change in foreign exchange rate. Arguments of PPP, whether relative or absolute, makes economic sense under very simplified assumptions that does not capture the complexity if the real world. The table bellow shows these assumptions and their limitation. Table 3: Limitation of Purchasing Power Parity

 

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