FINANCIAL MODELING OF FOREIGN EXCHANGE RATES USING THE US DOLLAR AND THE EURO EXCHANGE RATES: A PEDAGOGICAL NOTE Carl B. McGowan, Jr., Norfolk State University, 700 Park Avenue, Norfolk, VA, cbmcgowan@yahoo.com, (757) 823-8806 Demir Yener, Johns Hopkins University, Ten International Drive, Baltimore, MD, 21202 Demiryener@aol.com, (410) 516-8000 ABSTRACT This paper shows how to download weekly exchange rates from the internet to determine if the rates are time dependent or serial correlated. We find that levels of the Dollar/Euro exchange rate exhibit spurious correlation and changes in the exchange rate do not follow a random walk. INTRODUCTION One of the fundamental factors determining FDI decisions for MNC is the foreign exchange rate effect. Although there are numerous ways to hedge foreign exchange rate effects, MNC are never able to totally eliminate foreign exchange rate gains and losses even with hedging, McGowan, Asabere, and Collier (1993). Consequently, it is necessary for the MNC decision maker to understand the impact that foreign exchange rate changes have on the value of a multinational subsidiary and the FDI process but also to understand the nature of foreign exchange rate changes. Most courses that teach multinational finance and multinational business spend a significant amount of time discussing foreign exchange rate parity conditions and the impact of foreign exchange rates on the FDI and the capital budgeting project decision. The purpose of this paper is to show how to collect data and use that data to demonstrate foreign exchange rate modeling. The need for forecasts of future exchange rates derives from the need to determine the value of foreign currency generated by the multinational subsidiary because the net cash flow generated by the multinational subsidiary foreign must eventually be converted to dollars. Foreign exchange rate parity conditions summarize the relationships between the current spot rate, the future spot rate, and forward rates and interest rates and inflation rates, McGowan and Collier (1993). However, one of the fundamental features of foreign exchange rate changes is that they theoretically follow a random walk. Thus, it is necessary to show students, who later become MNC decision makers, how to analyze the behavior of foreign exchange rates.\ DATA COLLECTION We use the weekly exchange rates for the US Dollar to the Euro foreign exchange rate for the five year period from March 18, 2007 to March 11, 2012. The data are downloaded to an Excel 671913-1
spreadsheet from OANDA following the steps outlined in Figure 1A, 1B, 2-4. The URL for OANDA and for each page is provided. The final step is to download the data to a spreadsheet. Log onto the internet and go to the OANDA website at http://www.oanda.com/. On the OANDA website, scroll down to FOREIGN EXCHANGE TOOLS and left click on Historical Exchange Rates. The window for historical exchange rates is at URL http://www.oanda.com/currency/historical-rates/ which provides a window that can be used to enter the two currencies to be analyzed, the dates under consideration, and the interval frequency, one week in this paper. For this demonstration, we will use the weekly Dollar/Euro exchange rate for the period from March 18, 2007 to March 11, 2012. After entering the input criteria, OANDA will return the weekly exchange rate between the Dollar and the Euro for the period from March 18, 2007 to March 11, 2012 and a graph. Left click on the download icon to download the data to an Excel spreadsheet. The entire data set will be downloaded to a spreadsheet which can be saved and used for analysis. Figure 5 shows the weekly Dollar/Euro exchange rate for the period from March 18, 2007 to March 11, 2012 and Figure 6 shows the changes in the foreign exchange rate. Figure 1A Web Site for OANDA http://www.oanda.com/ Log onto the internet and go to the OANDA website at http://www.oanda.com/. 671913-2
Figure 1B Web Site for OANDA http://www.oanda.com/ On the OANDA website, scroll down to FOREIGN EXCHANGE TOOLS and left click on Historical Exchange Rates. 671913-3
Figure 2 OANDA Historical Rates Page http://www.oanda.com/currency/historical-rates/ The window for historical exchange rates is at URL http://www.oanda.com/currency/historicalrates/ provides a window that can be used to enter the two currencies to be analyzed, the dates, and the frequency. For this demonstration we will use the weekly Dollar/Euro exchange rate for the period from March 18, 2007 to March 11, 2012. Figure 3 OANDA Dollar/Euro Page http://www.oanda.com/currency/historical-rates/ Table 3 has been left out for to meet space requirements but is available from the corresponding auther. An Excel chart of the same data is available in Figure 5. After entering the input criteria, OANDA will return the weekly exchange rate between the Dollar and the Euro for the period from March 18, 2007 to March 11, 2012 and a graph. Left click on the download icon to download the data to an Excel spreadsheet. 671913-4
Figure 4 Downloaded Dollar/Euro Exchange Rate March 18, 2007 to March 11, 2012 Average weekly BID rates @ +/- 0% www.oanda.com/currency/historical-rates/ End Date USD/EUR 3/11/2012 0.7588 3/4/2012 0.7483 2/26/2012 0.7526 2/19/2012 0.7604 2/12/2012 0.7578 2/5/2012 0.7600 1/29/2012 0.7660 1/22/2012 0.7810 1/15/2012 0.7850 1/8/2012 0.7754 1/1/2012 0.7688 12/25/2011 0.7661 12/18/2011 0.7615 12/11/2011 0.7467 12/4/2011 0.7479 11/27/2011 0.7459 11/20/2011 0.7364 11/13/2011 0.7289 11/6/2011 0.7217 10/30/2011 0.7146 The entire data set will be downloaded to a spreadsheet which can be saved and used for analysis. 671913-5
Figure 5 USD/EURO Exchange Rate March 18, 2007 to March 11, 2012 E x c h a n g e R a t e 0.9000 0.8000 0.7000 0.6000 0.5000 0.4000 0.3000 0.2000 0.1000 0.0000 10/10/2006 2/22/2008 7/6/2009 11/18/2010 4/1/2012 8/14/2013 Date 0.06 Figure 6 Change in the USD/EURO Exchange Rate March 18, 2007 to March 11, 2012 0.04 C h a n g e 0.02 0.00 10/10/06 2/22/08 7/6/09 11/18/10 4/1/12 8/14/13-0.02-0.04-0.06-0.08 Date 671913-6
RESEARCH DESIGN In this analysis of the Dollar/Euro exchange rate we test four models. Model 1 is a regression using time as the independent variable which tests the Dollar/Euro exchange rate for a time trend. Each of the 260 weeks under study is given a sequential value from one to 260. If the regression coefficient is statistically significant, then the Dollar/Euro exchange rate follows a trend. Model 2 is the regression between the Dollar/Euro exchange rate and the lagged value of the Dollar/Euro exchange rate. This regression will indicate if the Dollar/Euro exchange rate is serial correlated. If the regression coefficient is statistically significant, then the Dollar/Euro exchange rate does not follow a random walk. Model 3 is the regression between the change in the Dollar/Euro exchange rate and time. If the regression coefficient is statistically significant, then, the change in the Dollar/Euro exchange rate is a function of time. Model 4 is the regression between the change in the Dollar/Euro exchange rate and the lagged value of the change in the Dollar/Euro exchange rate. This regression will indicate if the change in the Dollar/Euro exchange rate is serial correlated Model 1 Dollar/Euro = Alpha 1 + beta 1 (time variable) + error 1 (1) Dollar/Euro is the exchange rate between the US dollar and the Euro in terms of the US dollar, that is, the direct exchange rate. Alpha 1 is the intercept term of the regression and beta 1 is the regression coefficient. The time variable is the independent variable and is the week number and error 1 is the residual term. Model 2 Dollar/Euro (t=0) = Alpha 2 + beta 2 (lagged Dollar/Euro (t=-1) ) + error 2 (2) Dollar/Euro is the exchange rate between the US dollar and the Euro in terms of the US dollar, that is, the direct exchange rate. The t subscript indicates that the independent variable is the exchange rate value for (t=-1) and the dependent variable is the exchange rate at time (t=0). Alpha 2 is the intercept term of the regression and beta 2 is the regression coefficient. The lagged value of the Dollar/Euro exchange rate is the independent variable and error 2 is the residual term. Model 3 Ln(Dollar/Euro) = Alpha 3 + beta 3 (time) + error 3 (3) Ln(Dollar/Euro) is the natural logarithm of the exchange rate at time (t=0) divided by the exchange rate at time (t=-1) between the US dollar and the Euro in terms of the US dollar, that is, the direct exchange rate. Ln(Dollar/Euro) measures the continuously compounded rate of change in the Dollar/euro exchange rate. Alpha 3 is the intercept term of the regression and beta 3 671913-7
is the regression coefficient. The time variable is the independent variable and error 3 is the residual term. Model 4 Ln(Dollar/Euro (t=0) ) = Alpha 4 + beta 4 (lagged Ln(Dollar/Euro (t=-1) ))+ error 4 (4) Ln(Dollar/Euro) is the natural logarithm of the exchange rate at time (t=0) divided by the exchange rate at time (t=-1) between the US dollar and the Euro in terms of the US dollar, that is, the direct exchange rate. Ln(Dollar/Euro) measures the continuously compounded rate of change in the Dollar/euro exchange rate. Alpha 4 is the intercept term of the regression and beta 4 is the regression coefficient. The lagged value of the Ln(Dollar/Euro) exchange rate is the independent variable and error is the residual term. EMPIRICAL RESULTS Table 1 shows the summary statistics for the weekly Dollar/Euro exchange rate for the period from March 18, 2007 to March 11, 2012. Rate is the Dollar/Euro rate on the date and change is the natural logarithm of the exchange rate at time (t=0) divided by the exchange rate at time (t=-1) between the US dollar and the Euro in terms of the US dollar, that is, the direct exchange rate. The weekly Dollar/Euro exchange rate has an average value of 0.7212 dollars per Euro with a standard deviation of 0.0026. The maximum value is 0.8319 and the minimum value is 0.6294. The average value for the change in the weekly Dollar/Euro exchange rate is 0.00001066 and the range is from a minimum of -0.0628 to a maximum of 0.03854. The standard deviation of weekly Dollar/Euro exchange rate is 0.00079. Table 2 provides the regression statistics for the four regression models. Model 1 shows the regression between the Dollar/Euro exchange rate time and indicates a slight relationship between the exchange rate and time. Model 3 shows the relationship between the change in the Dollar/Euro exchange rate and time. The regression coefficient between time and the exchange rate in Model 1 has a statistically significant regression coefficient and time, and adjusted R 2 of 0.07 and an F value of 2204.This indicates a slight tendency to vary with time. However, the regression coefficient between the change in the exchange rate and time in Model 3 is not statistically significant, the adjusted R2 is -0.000986, and the F value is 0.74. These results indicate that the Dollar/Euro exchange rate is integrated in levels but not for changes. Model 2 is the regression between the foreign exchange rate and the lagged value of the exchange rate. The regression coefficient is statistically significant, the adjusted R 2 is 0.95, and the F value is 5184. However, this is spurious regression that would be expected when levels of variables are regressed. Model 4 is the regression between changes in the exchange rate and lagged values of the exchange rate. The regression coefficient is statistically significant, the adjusted R 2 is 0.14, and the F value is 43.95. These empirical results indicate that the Dollar/Euro foreign exchange rate does not follow a random walk. 671913-8
SUMMARY AND CONCLUSIONS The purpose of this paper is to demonstrate how to find foreign exchange rate data on the internet and how to analyze the foreign exchange rate data to determine if the data follow a random walk. We show how to download the weekly Dollar/Euro exchange rate for the period from March 18, 2007 to March 11, 2012 from OANDA. We test four models of the exchange rate to determine if the rates are time dependent or serial correlated. We find that the levels of the exchange rates do exhibit spurious correlation. We find that the changes in the exchange rate are serially correlated which indicates that the Dollar/Euro exchange rate does not follow a random walk. This paper demonstrates an exercise that can be used to demonstrate how to find and download data, how to process data, how to analyze data, and how to determine if the data follow a random walk, as predicted by theory. All of these skills are skills that are necessary for the proper analysis and management of foreign exchange rate risk for a multination corporation. McGowan (2008) provides an example showing the impact of foreign exchange rate risk on capital budgeting for a multination firm. Table 1 Summary Statistics Dollar/Euro Exchange Rate Weekly Rates 3/18/2007 to 3/11/2012 Statistic Rate Change Mean 0.7212 0.00001066 Standard Error 0.0026 0.00079346 Median 0.7227-0.00060646 Mode 0.7289 #N/A Standard Deviation 0.0427 0.01279408 Sample Variance 0.0018 0.00016369 Kurtosis -0.3927 2.12560103 Skewness -0.0820-0.10930515 Range 0.2025 0.10134617 Minimum 0.6294-0.06281056 Maximum 0.8319 0.03853561 Sum 188 0.00277137 Count 261 260 671913-9
Table 2 Regression Statistics Dollar/Euro Exchange Rate Weekly Rates 3/18/2007 to 3/11/2012 Statistic Model 1 Model 2 Model 3 Model 4 Intercept -0.1854757 0.0171918-0.0522466 0.0000569 T-Statistic -0.9602474 1.7556015-0.8628110 0.0772135 Beta 0.0000226 0.9761679 0.0000013 0.3827591 T-Statistic 4.6943468 72.0016502 0.8630612 6.6294721 Adj R 2 0.0748546 0.9524093-0.0009860 0.1427145 F 22.04 5184.24 0.74 43.95 Model Model 1 Model 2 Model 3 Model 4 Dependent Variable Rate Lagged Rate Change Lagged Change Independent Variable Time Rate Time Change REFERENCES McGowan, Carl B., Jr. and Henry W. Collier. (1993) "Foreign Exchange Rate Parity Conditions: A Pedagogical Note," Financial Practice and Education, Spring/Summer, 77-83 McGowan, Carl B., Jr., Paul Asabere, and Henry W. Collier. (1993) "Limitations on Using Foreign Exchange Rate Hedges to Hedge Stock Investments," Financial Practice and Education, Fall, 119-121. McGowan, Carl B., Jr. (2008) Evaluating the Impact of Foreign Exchange Rate Risk on the Capital Budgeting Process for Multinational Firms, International Business and Economics Research Journal, August, 7(8), 47-58. 671913-10