Comparison of Exchange Rates of Australia and United Kingdom - Research Paper Example

Comparison of Exchange Rates of Australia and United Kingdom (AUD/USD and GBP/USD) HI 5008 Group Assignment Instructions Group Members 2. 3. 4. Total Word Count: Course: Statistics and Research Methods for Business Decision Making Date Executive Summary The exchange rate is a price that keeps one country balance with the rest of the world country. Many factors such as changes in terms of trade with other countries, relative productivity changes and the interest rate differential with other countries determine the exchange rate of currency. This paper will compare exchange rate of two countries, Australia and United Kingdom (UK) using descriptive and inferential statistical analysis. The statistical analysis suggests that the exchange rate of United Kingdom currency is higher as compared to Australian currency. Further, the exchange rates of Australian and United Kingdom currencies are associated and the exchange rate of the Australian currency can be predicted using the exchange rate of United Kingdom currency, vice-versa. The business implication of this statistical analysis is that it can be used for predicting the exchange rates of Australian or United Kingdom currency, if one of the exchange rates is known. In addition, one can use this analysis for an estimation of the exchange rates of Australian or United Kingdom currency. Table of Contents Introduction and Background 4 Sample Data 5 Research Questions 6 Summary of Analysis 7 Conclusion and Business Implications 9 Limitations of Analysis 10 References 11 Appendix 12 List of Figures 12 List of Tables 16 Introduction and Background The exchange rate is a price that keeps one country balance with the rest of the world country. Many factors determine the exchange rate of currency such as changes in terms of trade with other countries, relative productivity changes and the interest rate differential with other countries. Fall in terms of trade reduces export income and put downward pressure on exchange rate. An increase in relative productivity of country appreciate exchange rate over time and enables its citizen to buy imports more cheaply. Further, relative high interest rate attracts foreign capital that puts upward pressure on the exchange rate (Reserve Bank of Australia Bulletin, 1992). This paper will compare the exchange rate of two countries, Australia (AUD/USD)1 and the United Kingdom (GBP/USD)2 using statistical techniques, descriptive and inferential statistics and will present an analysis and recommendation based on it. The statistical analysis will include descriptive statistics, confidence interval and hypothesis testing, and correlation and regression. Sample Data For statistical analysis of the exchange rate of Australian and United Kingdom (UK) currencies a sample data is collected for the period January 2003 to December 2008 (GVI Forex Database: Free Forex Historical Data; Yahoo Finance). The sample data collected is on monthly basis and includes records of the exchange rates of 72 months from the period January 2003 to December 2008. Table 1 in appendix presents the sample data collected. The three variables in sample data are month, GBP/USD and AUD/USD. GBP/USD: Closing exchange rate of GBP/USD for the month AUD/USD: Closing exchange rate of AUD/USD for the month Research Questions The sample data collected for the exchanges rates of Australian and United Kingdom (UK) currencies can be used for answer different types of business problems. However, for this statistical analysis, the questions are restricted to six that will be answered using sample data. The six research questions are 1. How exchanges rates of Australian and United Kingdom (UK) currencies are distributed?  2. What are the average and range of exchange rates of the above-mentioned currencies? 3. What are the confidence intervals of exchange rates of Australian and UK currencies? 4. Is there any difference between the exchange rate of Australian currency and UK currency? 5. Is there any association or relation between the exchange rates of Australian and UK currencies? 6. Does exchange rate of UK currency has any influence on the exchange rate of Australian currency? Summary of Analysis The average exchange rate of Australian Currency (AUD/USD) for last 6 years is 0.7690. The range of the exchange rate of Australian Currency is 0.3712 with the peak exchange rate of 0.9587 and lowest exchange rate of 0.5875. The standard deviation and coefficient of variation of the exchange rate of Australian currency is equal to 0.0861 and 11.20%, respectively. The shape of the distribution of the exchange rate of Australian currency can be assumed normal (figure 1 in appendix). This is also supported by the value of Skewness coefficient that is equal to 0.362, which is close to zero. However, the distribution is slightly positively skewed with low and high outliers (figure 3 in appendix). (See table 2 in appendix) The average exchange rate of United Kingdom currency (AUD/USD) for last 6 years is 1.8340. The range of the exchange rate of United Kingdom Currency is 0.6207 with the peak exchange rate of 2.0792 and lowest exchange rate of 1.4585. The standard deviation and coefficient of variation of the exchange rate of United Kingdom currency is equal to 0.1423 and 7.76%, respectively. The shape of the distribution of the exchange rate of Australian currency can be assumed normal (figure 2 in appendix). This is also supported by the value of Skewness coefficient that is equal to -0.4735, which is close to zero. However, the distribution is slightly negatively skewed (figure 4 in appendix). (See table 3 in appendix) The statistical analysis suggested that there is 95 percent chance that the exchange rate of Australian currency will fall in-between 0.7487 to 0.7892 (see table 4 in appendix). Similarly, there is 95 percent chance that the exchange rate of United Kingdom currency will fall in-between 1.8006 to 1.8675 (see table 5 in appendix). There is significant difference between the exchange rate of Australian currency and United Kingdom currency, t(117) = 54.33, p < .001 (see table 6 in appendix). The exchange rate of United Kingdom currency is higher as compared to Australian currency. The exchange rate of Australian and United Kingdom currency are strongly correlated, r(70) = .852, p < .01 (see table 7 in appendix). Therefore, there is an association between exchanges rates of Australian and United Kingdom currencies (see figure 5 in appendix). The exchange rate of United Kingdom currency significantly predicts the exchange rate of Australian currency, β = 0.5157, t(70) = 13.611, p < .001. The exchange rate of United Kingdom currency also explains a significant proportion of variance in the exchange rate of Australian currency, R2 = .7258, F(1, 70) = 185.2643, p < .001 (see table 8 and figure 6-7 in appendix). Therefore, the exchange rate of UK currency has influence on the exchange rate of Australian currency. Conclusion and Business Implications The average exchange rate of Australian and United Kingdom currencies for last 6 years are 0.7690, and 1.8340, respectively. There is 95 percent chance that the exchange rate of Australian and United Kingdom currencies will fall in-between 0.7487 to 0.7892, and 1.8006 to 1.8675, respectively. The exchange rate of United Kingdom currency is higher as compared to Australian currency. The exchange rates of Australian and United Kingdom currencies are associated and the exchange rate of the Australian currency can be predicted using the exchange rate of United Kingdom currency. The business implication of this statistical analysis is that it can be used for predicting the exchange rates of Australian or United Kingdom currency, if one of the exchange rates is known. In addition, one can use this analysis for an estimation of the exchange rates of Australian or United Kingdom currency. Lastly, the higher exchange rate of United Kingdom currency indicates that their citizen can buy imports more cheaply as compared to Australian citizen. Limitations of Analysis As such, there is no limitation of this statistical analysis because the sample data is quite large and represents the entire population significantly. However, the exchange rates of two countries can be represented in terms of hour, day or week , but this will make entire population very large and a more tedious job will be required to collect entire population and than sample from this population. References Zikmund, W. (2003). Business Research Methods. Seventh Edition, Dryden, Orlando. Levine, D.M., Stephan, D.F., Krehbiel, T.C. & Brenson, M.L. (2008). Statistics for Managers Using Microsoft Excel: International Edition, Fifth Edition, Prentice Hall Doane, D.P. & Seward, L.E. (2007). Applied Statistics in Business and Economics. McGraw-Hill/Irwin: New York Yahoo Finance. http://finance.yahoo.com/q/cp?s=%5EGSPC accessed on January 29, 2009. Reserve Bank of Australia Bulletin, June 1992. Australia’s Recent Exchange Rate Experience, Retrieved on January30, 2009 from http://www.rba.gov.au/PublicationsAndResearch/Bulletin/bu_jun92/bu_0692_1.pdf GVI Forex Database: Free Forex Historical Data. Retrieved on January30, 2009 from http://www.global-view.com/forex-trading-tools/forex-history/index.html Appendix List of Figures Figure 1: Histogram of AUD/USD Figure 2: Histogram of GBP/USD Figure 3: BoxPlot of AUD/USD Figure 4: BoxPlot of GBP/USD Figure 5: ScatterPlot of AUD/USD vs. GBP/USD Figure 6: Normal Probability Plot Figure 7: GBP/USD Residual Plot List of Tables Table 1: Sample Data of Exchange Rates of AUD/USD and GBP/USD No. Month GBP/USD AUD/USD No. Month GBP/USD AUD/USD 1 Jan-03 1.647 0.5875 37 Jan-06 1.7804 0.7573 2 Feb-03 1.5739 0.6084 38 Feb-06 1.7541 0.7428 3 Mar-03 1.582 0.6038 39 Mar-06 1.7365 0.7159 4 Apr-03 1.599 0.6263 40 Apr-06 1.8218 0.76 5 May-03 1.6385 0.654 41 May-06 1.8701 0.7521 6 Jun-03 1.6555 0.6735 42 Jun-06 1.8475 0.743 7 Jul-03 1.61 0.648 43 Jul-06 1.8676 0.7662 8 Aug-03 1.577 0.6473 44 Aug-06 1.9047 0.7633 9 Sep-03 1.6625 0.68 45 Sep-06 1.8711 0.7456 10 Oct-03 1.6942 0.7073 46 Oct-06 1.9075 0.7745 11 Nov-03 1.7216 0.7246 47 Nov-06 1.966 0.7892 12 Dec-03 1.7855 0.752 48 Dec-06 1.9572 0.7879 13 Jan-04 1.8242 0.7639 49 Jan-07 1.9638 0.7758 14 Feb-04 1.8665 0.7737 50 Feb-07 1.9638 0.788 15 Mar-04 1.8438 0.7657 51 Mar-07 1.9672 0.8093 16 Apr-04 1.7782 0.722 52 Apr-07 1.9994 0.8308 17 May-04 1.8315 0.715 53 May-07 1.9797 0.8282 18 Jun-04 1.8174 0.6967 54 Jun-07 2.0075 0.8481 19 Jul-04 1.82 0.7012 55 Jul-07 2.0345 0.8568 20 Aug-04 1.8025 0.7045 56 Aug-07 2.0163 0.8154 21 Sep-04 1.8117 0.7274 57 Sep-07 2.0452 0.8882 22 Oct-04 1.8369 0.7479 58 Oct-07 2.0792 0.9314 23 Nov-04 1.911 0.7727 59 Nov-07 2.0567 0.882 24 Dec-04 1.9156 0.7829 60 Dec-07 1.9827 0.8777 25 Jan-05 1.8824 0.7753 61 Jan-08 1.9864 0.8977 26 Feb-05 1.923 0.7922 62 Feb-08 1.9881 0.9323 27 Mar-05 1.8905 0.7722 63 Mar-08 1.9832 0.9136 28 Apr-05 1.907 0.7805 64 Apr-08 1.9879 0.9463 29 May-05 1.8178 0.7559 65 May-08 1.9807 0.9566 30 Jun-05 1.7906 0.7598 66 Jun-08 1.9927 0.9587 31 Jul-05 1.758 0.7575 67 Jul-08 1.9825 0.942 32 Aug-05 1.804 0.7543 68 Aug-08 1.8194 0.8567 33 Sep-05 1.7622 0.7625 69 Sep-08 1.7767 0.7895 34 Oct-05 1.7703 0.748 70 Oct-08 1.6145 0.668 35 Nov-05 1.7286 0.7394 71 Nov-08 1.5415 0.6537 36 Dec-05 1.718 0.7332 72 Dec-08 1.4585 0.7052 Table 2: Descriptive Statistics of Exchange Rates of AUD/USD Mean 0.7690 Standard Error 0.0102 Median 0.7613 Mode #N/A Standard Deviation 0.0861 Sample Variance 0.0074 Kurtosis 0.0178 Skewness 0.3620 Coefficient of Variation (CV) 11.20% Range 0.3712 Minimum 0.5875 Maximum 0.9587 Sum 55.3669 Count 72 Confidence Level (95.0%) 0.0202 1st Quartile 0.7205 Median 0.7613 3rd Quartile 0.7965 Interquartile Range 0.0760 Low Extremes 0 Low Outliers 2 High Outliers 7 High Extremes 0 Table 3: Descriptive Statistics of Exchange Rates of GBP/USD Mean 1.8340 Standard Error 0.0168 Median 1.8342 Mode 1.9638 Standard Deviation 0.1423 Sample Variance 0.0202 Kurtosis -0.4204 Skewness -0.4735 Coefficient of variation (CV) 7.76% Range 0.6207 Minimum 1.4585 Maximum 2.0792 Sum 132.0510 Count 72 Confidence Level (95.0%) 0.0334 1st Quartile 1.757025 Median 1.834200 3rd Quartile 1.964350 Interquartile Range 0.207325 Low Extremes 0 Low Outliers 0 High Outliers 0 High Extremes 0 Table 4: 95% Confidence Interval of AUD/USD Standard Error of The Mean 0.0102 Confidence Interval 95.% Lower 0.7487 Confidence Interval 95.% Upper 0.7892 Half-Width 0.0202 Table 5: 95% Confidence Interval of GBP/USD Standard Error of The Mean 0.0168 Confidence Interval 95.% Lower 1.8006 Confidence Interval 95.% Upper 1.8675 Half-Width 0.0334 Table 6: t-Test: Two-Sample Assuming Unequal Variances   GBP/USD AUD/USD Mean 1.8340 0.7690 Variance 0.0202 0.0074 Observations 72 72 Hypothesized Mean Difference 0 df 117 t Stat 54.3305 P(T Read More