Mathematical Models in Calculations for Projection and Prediction in Financial Management - Coursework Example

THE FIVE KEY THEORETICAL RELATIONSHIPS AMONG SPOT EXCHANGE RATES, FORWARD EXCHANGE RATES, INFLATION RATES AND INTEREST RATES THAT RESULT FROM INTERNATIONAL ARBITRAGE ACTIVITIES Name Course Institution 24 March 2015 Introduction Arbitrage in competitive markets refers to a situation where buyers and sellers purchase and sell commodities or financial instruments for higher gains from unequal prices without the risk. It is characteristic of low-cost information access, adjusted exchange prices of similar tradable products and financial assets that are within the transaction costs of equality internationally. According to Clark (2002), when there are no market flaws, risk-adjusted projected returns on financial assets in various markets should be equal. Arbitrage takes advantage of price discrepancies in different markets buying when they are low and selling when prices are high to make riskless profits. The effect of arbitrage on demand and supply is to realign prices so that no further risk-free profits are made. In international monetary and foreign exchange markets, arbitrage takes three forms namely; locational, triangular and covered interest arbitrage. Locational arbitrage occurs when the bid price of a bank for the same currency is higher than another banks selling price. On the other hand, triangular arbitrage occurs when the exchange rate quote is different from the calculated rate from spot rate quotes. Similarly, covered interest rate capitalizes on interest rate differential between two countries while covering the risk of exchange rate. It exploits the relationship between forward rate premiums and interest rate differentials. The arbitrage activities result in five theoretical economic relationships that explain the connections among prices, interest rates, spot exchange rates and forward exchange rates. The relationships are; purchasing power parity, Fischer effect, international Fischer effect, interest rate parity and forward rates as unbiased predictors of future spot rates (Werner and Stoner, 2010). Purchasing Power Parity It is a theory that determines the adjustments required in the currency exchange rates of two countries, to make them in equilibrium when their purchasing powers at that exchange rate are equivalent (Lyhagen, Osterholm and Calrsson, 2007). In other words, the expenditure on a particular commodity ought to be the same in both currencies once exchange rate takes it into account. For instance, suppose one US Dollar is selling at 120 Japanese yens. In the United States, say a baseball bat is selling for $50, while in Japan the same bat goes at JPY 500. Then it means the bat will cost only $10 if bought in Japan. It is advantageous to purchase the bat in Japan and consumers will show preference to the low cost. In the event of this, American consumers will desire more Japanese Yens hence they will exchange their dollars to Yens, which in the long run, will gain more value over the dollar. Similarly, the price of American retailers for the bats will go down, while that of retailers in Japan will increase due increase in demand. Arbitrage causes the exchange rates and the prices of the two countries to change so that there is purchasing power parity. According to Ignatiuk, the price differentials between countries are not sustainable in eventuality, as market forces will put in equilibrium, prices and exchange rates from the countries (2009). It may sound expensive for a consumer to travel all the way to Japan for a little cost bat, but for companies that buy them in large scale, they will benefit from the low-cost manufacturers in Japan. Sustainability is not enhanced by the difference in prices between the two countries because an individual is likely to gain arbitrage profits by buying the goods cheaply in one market and selling them highly in another. Considering that the price of a good should be equal across markets, there is supposed to be a collective price. Theoretically, that is how the principle works, but that is not always the case in practice. Absolute purchasing power parity, however, ignores the effects on free trade of transport costs, product differentiation, quotas, tariffs and other international restrictions. Kim argues that the applicable version of purchasing power parity has it that the exchange rates between countries should adjust in reflection of price changes in these countries (2005). For instance, take inflation in United States at 5% and at 1% in Japan, then to match the dollar price of goods in the two countries the dollar value of the Yen should raise by 4%. It implies that changes in exchange rates should be equal to the inflation differential at the same period. Therefore, currencies with high inflation rates should degenerate in correspondence to currencies of lower rates of inflation. In essence, exchange rate changes indicate the difference in inflation rates between countries, therefore purchasing power parity will predict movements in exchange rates to offset changes in a foreign price relative to domestic prices (McDermott and Cashing, 2001). The offsetting movements do not affect competitive advantage between foreign and domestic firms, hence nominal exchange rate changes become insignificant in determining the actual effects of currency changes on a firm or country. According to Somanath, it should not be overly agreed that purchasing power parity of all goods and financial assets obey the law of one price, but eventually the theory works (2011). Purchasing power parity can fail at times since prices of goods are sticky, hence violation of the law of one price. The Fisher Effect Financial contracts are always stated in nominal terms hence real interest rate requires necessary adjustments to reflect expected inflation. Therefore, Fisher effect is the sum of real interest rate and expected inflation to give the nominal interest rate (Kallianiotis, 2013). According to Kim, nominal interest rate is made up of real required rate of return and the inflation premium equal to the expected inflation (2011). What this simply means is that an increase in inflation results to a rise in nominal interest rate proportionally. For example, if real interest rate is given by 10% and its held constant and inflation rate rises from 4% to 5%, then the fisher effect indicates that nominal interest rate will increase by a figure of 1%, that is from 14% (10%real rate + 4% inflation rate) to 15% (10% real rate +5% inflation rate). Nominal interest rate describes the return rate from an asset in terms of currency units, while real interest rate on the other hand is the return rate of an asset in unit terms of basket goods that can be purchased. Inflation changes the real value of the currency since it is the general and sustained increase in price levels of basket goods. In general, the Fisher effect asserts that real returns across countries are arbitrated to be equal. If for instance expected real returns in a given currency were higher than in another, then capital would move from second to the first currency. The arbitrage process continues without government intervention till expected real returns are equalized. Hence, in a situation where there is no government interference, nominal interest differential ought to be in equilibrium with the expected inflation rate differential. Superficially, the Fisher effect has it that currencies with high rates of inflation should have higher interest rates compared to those with lower inflation rates. There is consistency in empirical evidence on the hypothesis that the majority of variations in nominal interest rates in various countries are attributed to different inflationary expectations (Giovanis, 2010). The Fisher effect takes the assumptions of a macroeconomics hypothesis in analysing the economy in the long run. It is based on neutrality of money, that is, changes in supply of money will only affect the nominal variables and not the real variables. Therefore, the change will only affect the inflation rate and not the real interest rate hence inflation can only lead to a change in nominal interest rate in a balanced way. Although the concept works in the long run, it is also visible in the short run where expected inflation changes have monetary and real variable effects. International Fisher Effect To discern the impact of changes in nominal interest rates and foreign exchange value between countries internationally, then the implications of purchase power parity and Fisher effect should be well considered. Purchase power parity implies that exchanges rates change to offset inflation rate changes, hence the combination of the two conditions results in international Fisher effect. It relates real interest rates to nominal interest rates in foreign countries (Vyuptakesh, 2006). The principle builds on the law of one price for financial implications. For instance, an international investor will earn exact returns in a foreign country as his country after adjustments of their returns to a currencys exchange rate. Therefore, exchange rates indicate interest rate differences the investor is deemed to profit. Since countries with high-interest rates are expected to experience appreciating currency, it will woe investors who want to earn high-interest rates. However, countries with high-interest rates are likely to experience high inflation rates making it impossible for the central bank to sustain the high-interest rates (Bhole and Mahakud, 2009). The consequence is depreciation in the value of the currency in the long run as the central bank will look to increase its monetary supply. For instance, the recent Russian Ruble crisis saw the value of the Ruble depreciate the value of the dollar. The dollar continues to gain value as the Ruble continues to dip. According to Teall, what international Fisher effect says is that arbitrage between financial markets in the form of capital flow ensures that interest differential between countries is an unbiased predictor of future changes in the spot rate of exchange (2013). Once investors have exploited all arbitrage opportunities, they cease moving their capital to other countries thus the international Fisher effect holds with the expected cost and expected return on lending, becoming identical across currencies. Interest Rate Parity Interest rate parity shows the relationship between the spot rate and the corresponding future rate currencies. According to Vij, the difference between two currencies reflects in discount for forward exchange rate on foreign currency given no arbitrage (2003). It provides for balance in discount on foreign currency between countries. More so, in an efficient market that has no transaction costs, the differential interest should be in equilibrium with the forward differential. Under these conditions, the forward rate is thus said to be at interest parity and equilibrium reigns in money markets. Interest parity ensures that the return on a covered foreign investment will be equal to domestic interest rate on investments of similar risk, hence eliminating the probability of having a money machine. If the condition is met, then the difference between domestic interest rate and covered interest rate cancels out. In situations where the difference does not become zero, an arbitrage incentive factors in to move money from one market to the other (Wang, 2009). Interest rate parity will only hold if there are no covered interest arbitrage opportunities. For example, suppose Google Inc. plans to pay its European employees in a month’s time. Google being an American outfit can achieve this through covered interest rate parity. They will buy euro, forward 30 days and lock in the exchange rate. Google will invest the dollars in 30 days till it can convert them into Euros after 30 days. That way they will have covered the rate thus no exchange rate fluctuation risk. Alternatively, they can convert the dollars today into Euros at spot exchange rate and invest in euro bonds for 30 days, then pay its obligations in Euros at the end of the month. Under the model, the firm is assured of the interest rate that it will earn, and the covering eliminates the risk of fluctuating exchange rate. Interest rate parity has it that high-interest rates on currency will get offset by forward discounts and low-interest rates will get offset by forward premiums. Interest rate parity demonstrates the best relationship in international finance, for instance, in Euromarkets, the forward rate is determined from the difference between two currencies under no-arbitrage condition. Sometimes deviations from interest rate parity can occur between the national capital markets, owing to capital controls tax imposition on payments to foreigners and transaction costs. Economically, the interest rate parity has some implications in that it can only hold whenever there is no arbitrage (Brigham and Ehrhardt, 2008). This implies that whether an investor invests at home or abroad, the rate of return remains the same just like he would have invested at home. In situations where domestic interest rates are less compared to foreign rates, foreign currency trades at a forward discount to offset any probability of higher interest rates in a foreign country to avoid arbitrage. If foreign currency trades at a forward discount to offset interest rate advantage of foreign country arbitrage, opportunity exists for domestic investors. Forward Rates as Unbiased Predictors of Future Spot Rates The operations of the foreign exchange market without government intervention indicate that spot rate and forward rate are influenced heavily by expectations of future events. Both rates move in a cycle with the connection between them being interest differentials. New information like change in interest rate differential reflects immediately in the spot and forward rate (Derosa, 2011). Forward discount refers to the excess of the forward price of foreign currency in relation to domestic currency over the spot price, usually represented as a fraction of the spot price. A positive discount implies that one has to pay more domestic units to purchase a foreign currency than he would have paid for a unit of that spot currency. A negative forward discount signifies that the foreign currency can be bought at a far less price than it can be purchased spot on by the domestic currency. Equilibrium can only be achieved when the forward differential cancels out the expected difference in the exchange rate. At this point, the incentive to buy or sell the currency forward becomes impractical. Formally, the unbiased nature of the forward rate reflects the expected future spot rate from the date of settling the forward contract. Therefore, investors will tend to speculate the future spot price of the currency in terms of another, so that if the prices are above the price, they can be purchased forward and they will try to buy them forward. The current forward price gets bid up till expected gains are no longer feasible. Market dynamics will dictate that when future spot price of a currency in terms of another currency is going to fall on current forward price, everyone will sell that currency forward with expectations that they will afford to buy them at spot price below the agreed upon forward sale price (Mankiw, 2009). The current forward price of the currency continues to bid down till an expected for doing so is not possible. Any investor willing to defy risk can gain from foreign exchange market speculations any time future spot rates are expected to differ from the current forward rate. Provided with enough such risk-neutral investors, the forward exchange rate bids into equality with the expected future spot rate, hence the forward rate will then equal the estimate of the market’s spot rate, when contract matures. Before forward rates were considered unbiased predictors of future spot rates, but with advancements, more powerful economic techniques consider it as a biased predictor because of the risk premium (Machiraju, 2002). However, the premium keeps deviating with it being negative or positive at times and averages nearly at zero. Economically, it will be stretching to consider forward rate as unbiased predictor of the future spot rate. Conclusion Although mathematical models are employed when making calculations of these models for projection and prediction purposes, they will not always yield precise results. Whatever value one arrives at, it should be treated as an approximation to the real case. Similarly, the models are said to work in theoretical aspects but in practical life, they may turn out to be not that applicable because of a range of factors that can cause variations that can extend beyond predicted time. Different economic statuses of countries can make an arbitrage tricky, for instance, factors that cause currency risks and inflation risks may make interest rate to be inflated and hence cause discrepancies. References Bhole, L. M. and Mahakud, J., 2009. Financial Institutions and Markets: Structure, Growth and Innovations. New Delhi, Tata McGraw-Hill Education Private Limited. Brigham, E. F. and Ehrhardt, M. C., 2008. Financial Management: Theory & Practice. Mason, OH: Thomson Higher Education. Clark, E., 2002. International Finance. London: Thomson. DeRosa, D. F., 2011. Options on Foreign Exchange. Hoboken, NJ: John Wiley & Sons. Giovanis, E., 2010. A Research Examination of Covered-Uncovered Interest Rate Parity and the Purchase Power Parity (PPP) hypothesis: Applications in MATLAB, RATS and EVIEWS. München: GRIN Verlag GmbH. Ignatiuk, A., 2009. The Principle, Practise and Problems of Purchasing Power Parity Theory. München: GRIN Verlag. Kallianiotis, J. N., 2013. International Financial Transactions and Exchange Rates: Trade, Investment, and Parities. New York, NY: Palgrave Macmillan. Kim, K. A., 2011. Global Corporate Finance: A Focused Approach. Toh Tuck: World Scientific Publishing Co. Pte, Ltd. KIM, S., 2005. Global Corporate Finance. Oxford: Blackwell Publishing Limited. Lyhagen, J., ÖSterholm, P. and Carlsson, M., 2007. Testing for Purchasing Power Parity in Cointegrated Panels. Washington: International Monetary Fund. Machiraju, H. R., 2002. International Financial Markets and India. New Delhi: New Age International (P) Limited Publishers. Mankiw, N. G., 2009. Principles of Economics. 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