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CASE STUDY ONE

In this Case Study, you will look at modelling the Australian dollar vis-á-vis the New Zealand dollar exchange rate, using a conventional monetary model.  The data you will use is in the file called “The Monetary Model.xls”.  This contains the following data: ‘S(AUD/NZD)’ , which is the Australian dollar per NZ dollar exchange rate; ‘Aust. MS’ , which is the level of the Australian money supply; ‘NZ MS’ , which is the level of the New Zealand money supply; ‘Aust. GDP’ , which is a measure of Australian gross domestic product (GDP); ‘NZ GDP’ , which is a measure of New Zealand gross domestic product (GDP); ‘Aust. IR’ , which is a measure of short-term Australian interest rates, and ‘NZ IR’ , which is a measure of short-term New Zealand interest rates.  Data on these variables were collected from the IMF’s International Financial Statistics database, and from the Reserve Bank of Australia’s website.

To begin the empirical analysis, make sure you take the natural logarithm of S(AUD/NZD), Aust. MS, NZ MS, Aust. GDP, and NZ GDP.  Leave the interest rate variables, Aust. IR and NZ IR, in their raw form.  Also, use a level of significance of a = 0.05 for all tests in this study.

• Calculate the correlation between the spot exchange rate and all the other variables. Which variable has the strongest correlation with the exchange rate?  I will call this variable “PREDICTOR” in the questions that follow.                                                 (4 marks)
• Calculate the mean, median and mode of the spot exchange rate. What is the difference between these types of “averages”? Compare the values of the mean and median. State what you think is the most appropriate average for this set of data, giving brief reasons for your answer.                                                       (4 marks)

• Draw a histogram of the spot exchange rate. Calculate the variance, measure of skewness and kurtosis.  Using the descriptive statistics that you have calculated, do they indicate that the data is symmetric, and is this confirmed by the value of the skewness?  Comment on the value of kurtosis.  Based on these results, say why you believe that the spot exchange rate does, or does not, have a normal distribution.                                          (6 marks)

• Write some brief notes, in point form, describing your results for Case Study One. Be sure to report any conclusions that you have made, and submit these.  You will use them in a later tutorial when you write your final report.                                                    (2 marks)

CASE STUDY TWO

In this Case Study, you will be looking at the effect of the Global Financial Crisis (GFC) and the Great Recession on Apple stock.  In the file called “Apple Inc.xls”, there is monthly data from June, 2001 to June, 2016, on the share price of Apple stock and the Dow Jones Industrials.  You will be looking at a number of important dates: December 2007, when the GFC and the Great Recession had officially begun, September, 2008, when the US Government allowed Lehman Brothers, an Investment Bank, to go bankrupt, and June, 2009, when the National Bureau of Economic Research (NBER) declared that the Great Recession had ended.

• Obtain line graphs for both the share price of Apple stock and the Dow Jones Industrial average, over the whole period and comment on any similarities or differences between them.                                                                   (2 marks)

• Calculate the continuous returns on both indices. Obtain histograms and descriptive statistics up to, and including the November 2007, and then from December 2007 onwards. Comment on any similarities or differences between them.                                   (2 marks)

• For the Apple stock, calculate the 95% confidence intervals for the mean return over the two periods given in part (b). Use the critical t-values from the following website:

https://www.easycalculation.com/statistics/t-distribution-critical-value-table.php      (4 marks)

• Assume that the returns on the Apple stock has a normal distribution. Using the means and standard deviations previously calculated for each of the two periods, find the probability of getting a negative return on a day selected at random. (4 marks)

• Write some brief notes, in point form, describing your results for Case Study Two. Be sure to report any conclusions that you have made, and submit these.  You will use them in a later tutorial when you write your final report.                                                    (2 marks)

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CASE STUDY ONE – continued

In this section, you will estimate a simple linear regression model to fit the exchange rate.  From Assignment One, choose the input variable that has the strongest correlation with the exchange rate that you believe will produce a good model (this is the variable that we called “PREDICTOR”).

Following on from Assignment One, use the same data set and a level of significance of a = 0.05 for all tests in this study.

• Draw the scatter diagram for these two variables. (2 marks)
• Estimate the model to predict the exchange rate. How much of the variation in the exchange rate is explained by your model?  Is this statistically significant?  Test to see whether the intercept is required in your model.                                                           (4 marks)

Obtain a graph of the residuals vis-á-vis the independent variable for part (b).  Is there any evidence of problems?                                                                                            (4 marks)