Interest Rates and Exchange Rates - Assignment Example

? INTEREST RATES AND EXCHANGE RATES Table of Content Covered Interest Rate Parity (CIRP) 3 2. Uncovered Interest Rate Parity (UIRP) – Investment in First Country 4 a) Expected Exchange Rate Three Months from Birthday 5 b) Expected Exchange Rate Six Months from Birthday 7 c) Difference between Expected Exchange Rates 7 d) Comparison of Expected Exchange Rates with Cover Interest Rate Parity 8 3) Uncovered Interest Rate Parity (UIRP) – Investment in Second Country 9 a) Gain or Loss from Investment 9 b) Significance of Spreads in FOREX – Arbitrage 10 4) Opportunity for CIRP on Six Month Data 10 References 11 Bibliography 12 1. Covered Interest Rate Parity (CIRP) According to covered interest rate parity when there exists no arbitrage opportunity due to equilibrium, the use of forward contracts to minimise exposure of exchange rate fluctuations then the interest rate parity is said to be covered (Madura, 2011, p.223). This is mainly because of the indifference of the investors. When the interest rate parity is covered, the interest rates and the forward exchange rate between two countries will be in equilibrium. This means that in such equilibrium, each unit return of home currency will be equal to the foreign currency. Thus, the covered interest rate parity states that the forward premium and the interest rate between two countries are equal and there will be no opportunity for arbitrage (Wang, 2009, pp.49-56). (Source: Dollery, University of Hull) The application of covered interest parity is that when it holds true, an investor will be indifferent of investment choice between two countries. For instance, if a French investor has the choice of either to invest or deposit in € or $ then under CIRP, the investor will get same return irrespective of choice of currency. This is because in equilibrium the future value of investment or deposit will be same for both the currencies (Johann, 2008, p.10). Additionally, there will not be any scope for making profit due to the condition of no-arbitrage in CIRP (Gandolfo, 2002, pp.43-45). The covered interest rate parity is represented by the following equation: (1 + r$) = Ft/St x (1 + r€) Where, Ft = forward exchange rate during time‘t’; & the left hand side of the equation shows that dollar deposits return is equal to euro deposits the returns (Ullrich, 2009, pp.19-22). 2. Uncovered Interest Rate Parity (UIRP) – Investment in First Country The interest rate parity assumes that investors are willing to exchange foreign assets with domestic assets and vice-versa when there is opportunity of making profit from transactions. The theory also assumes that the assets are identical and hence perfect substitutes (Clark, 2002, pp.72-75). On the basis of this assumption it can be said that the investors will be willing to hold assets that yields superior returns irrespective of the origin country. This means that any random investor’s choice of investment decision will not be influenced by forward rates since the investor will earn equal returns on either option. This is because of the interest rate parity theory discussed earlier which assumes that there is no opportunity for arbitrage and the returns of domestic assets will be equal to that of foreign asset (Baillie and McMahon, 1990, pp.150-159). When the investor do not use the forward contract to hedge exchange rate fluctuations and the interest rate parity holds true (no opportunity for arbitrage), then the IRP is said to be uncovered (Harvey, 2008, p.90). The significance of uncovered interest rate parity is that it helps to determine the spot exchange rate by using the concept that expected changes in spot rate of two countries is equal to their interest rate differential (Melvin and Norrbin, 2012, p.115-119). a) Expected Exchange Rate Three Months from Birthday For the purpose of the study, the interest rates based on three month treasury bonds and changes in the interest rates were collected on daily basis. The exchange rates were extracted are the daily close price of exchange rates taken on the same date as the interest rates. The forward exchange rates are three month forward from the start date. In this project the start date is chosen as per birthday 28/06/2011 (since birthday is 28/06/1993). Hence, the data is to be selected starting from 28/06/2011 and three months hence. The three month forward date 28/09/2011 from the chosen start date. The country selected for study is US and UK whose exchange rate between currencies is 1.6003 as on 28/06/2011. The three month forward rate as on 28/09/2011 is 1.56535, which is at discount. Hence, the three month difference in exchange rate between US$ to UK? will be equal -0.03495 (1.56535 – 1.6003). The negative sign indicates that the exchange rate between the currencies of the two countries is expected to fall in future. Similarly, the spot rate of US$ to UK? as on 29/06/2011 is 1.60245 and the three month forward rate as on 29/09/2011 is 1.56535. This means that the three month difference between forward rate and spot rate is -0.03455 (1.56535 - 1.60245). Similarly, the three month difference between the forward and spot rate will be calculated starting from the birthday till the next three months. The interest rate in UK is 0.7% as on 28/06/2011 and the same in US is 0.24575% and the spot $/? rate is 1.6003 which means that the expected forward rate after three month will be calculated as follows: E0 (S1) = S0 * (1 + rh)/ (1+rf) = 1.6003 * (1 + 0.0024575)/ (1+0.007) = 1.59308 (approx) Where, rh = interest rate in home = 0.24575% rf = interest rate in foreign country = 0.7% Hence, the three month forward rate is expected to be 1.59308. So, from the above formula it can be said that if the UK interest rate is expected to increase in next three months, then the expected spot will be more than 1.59308. b) Expected Exchange Rate Six Months from Birthday Using the same data used above, the spot rate of US$ to UK? as on 28/06/2011 is 1.6003 and the six month forward rate is 1.5469. By applying the same formula, the expected forward rate after six months from spot rate can be calculated as follows: rh = interest rate in home = 0.57925% rf = interest rate in foreign country = 0.95281% E0 (S1) = S0 * (1 + rh)/(1+rf) = 1.6003 * (1 + 0.0057925)/(1+0.0095281) = 1.59438 (approx) Similarly, the expected exchange rate six months from birthday may be calculated for the subsequent days. c) Difference between Expected Exchange Rates The expected rate calculated in section 2(b) was 1.59438 while the actual exchange rate three months later was found to be 1.5469. Hence, there is a difference between actual and expected exchange rates in three months. The reason for this difference can be explained from the Uncovered Interest Rate Parity (UIRP) equation discussed earlier. According to the expression, If the interest rate in UK is expected to fall in six months (as in this case), then the expected spot rate will be larger than $1.5469/? which was found to be true since $1.59438/?. Although, this particular exchange rate was not expected but the as explained from the concept of UIRP, such difference was expected. d) Comparison of Expected Exchange Rates with Cover Interest Rate Parity From the UIRP equation and the three month forward rate (which is at discount) it can be said that the difference is expected to be larger when covered interest rate parity will be used to examine the data. (Source: Dollery, University of Hull) From the above discussion the following conclusions can be drawn: Equilibrium – Yield from investment in home currency will be same as that of foreign currency If the expected depreciation of foreign currency is less than interest differential, then investor will invest in home currency to earn higher returns If the expected depreciation of home currency is more than the interest rate differential, investor will invest in foreign currency to earn higher returns 3) Uncovered Interest Rate Parity (UIRP) – Investment in Second Country According to the given scenario, it is required to select any country for investment starting on birthday (28/06/2011) and the same would be redeemed in three months using spot rate. For this purpose, investment in Japanese Yen was selected. a) Gain or Loss from Investment The spot rate of US$ to JP? as on 28/06/2011 is $80.785/?. The three month forward rate as on 28/09/2011 is $76.425/?. In this case also, the forward rate will be at discount and the 3-month difference will be equal to -4.36. The expected change in exchange rate can be calculated as follows, E0 (S1) = S0 * (1 + rh)/(1+rf) = 80.785 * (1 + 0.0024575)/(1+0.0019531) = 80.82567 (approx) Hence, it is expected that the spot rate after 3 month would be $80.82567/? where as actually the same was $76.425/?. In this case, it resulted in loss of transaction. b) Significance of Spreads in FOREX – Arbitrage Spreads in foreign exchange (FOREX) refers to the difference in the forward rates and the spot rates. As discussed earlier, a rational investor will always try to maximise profits by investing in that currency which will yield maximum returns in future. But according to the IRP theory, the rate of return will be adjusted by exchange rate so as the investor remains indifferent regarding investment opportunity and thus no arbitrage exists. When there are spread in forward and spot rates, there will be opportunity for the investor to make profits by investing in one currency at spot rate and converting it to home currency at forward rate in future. When the actual rate in future is less than expected forward rate, the investor will make profit in transaction and vice-versa. This spread is will gradually reduce and try to converge the spot rate and future rate so as to bring equilibrium. The spread will get narrower as the maturity of forward date approaches which will further reduce arbitrage opportunities. 4) Opportunity for CIRP on Six Month Data The uncovered interest rate parity will hold true only when the following condition is satisfied: The CIRP links interest rate differentials, spot rates and forward rates. On the basis of six months data provided for the study, starting from birthday (06/28/2011) till (12/28/2011), it was found that on no particular day during this period the condition was satisfied. Hence, CIRP was not found to hold true over this period. References Madura, J., 2011. International Financial Management. 11. United States: Cengage Learning. Gandolfo, G., 2002. International Finance and Open Economy Macroeconomics. Germany: Springer. Wang, P., 2009. The Economics of Foreign Exchange and Global Finance. Germany: Springer. Ullrich, C., 2009. Forecasting and Hedging in Foreign Exchange Markets. Germany: Springer. Harvey, J. T., 2008. Currencies, Capital Flows and Crises: A Post Keynesian Analysis of Exchange Rate Determination. New York: Routledge. Clark, E., 2002. International Finance. United Kingdom: Cengage Learning EMEA. Baillie, R. T. and McMahon, P. C., 1990. The Foreign Exchange Market: Theory and Econometric Evidence. United Kingdom: Cambridge University Press. Johann, R., 2008. Determinants of an Exchange Rate. Germany: GRIN Verlag. Norrbin, S. C., 2012. International Money and Finance. United States: Academic Press. Bibliography Isard, P., 1995. Exchange Rate Economics. United States: Cambridge University Press. Read More