You are recently employed as financial analysts to advice on the trading strategy for investing in Aussie dollar in the major Investment bank in Australia. You have been trained the importance of foreign exchange rate forecasting stems from the fact that the outcome of the bank’s decision taken now is contingent upon the value of the exchange rate prevailing sometime in the future, which you aim to forecast with utmost accuracy. The bank’s decisions pertain to a variety of activities, including speculation, hedging, investment, financing, pricing and strategic planning. Your forecast also feeds in the Technical Analysis and Mechanical Trading Rules Department of the bank which reports buy and sell signals. Your first assignment is to perform a thorough analysis using the foreign exchange rate between Australian and the US, S(USD/AUD). You note that the exchange rate is expressed in indirect quotation from the Australian perspective. Using your skills, knowledge, training, and experience perform the following tasks:
a. Obtain continuously compounded daily returns of S(USD/AUD) exchange rate. Draw a histogram and comment on the graph. (6 marks)
b. Calculate the mean and the standard deviation of daily returns and obtain the percentage of the values that are within I. one standard deviation of the mean, II. two standard deviations of the mean, and III. three standard deviations of the mean. (10 marks)
c. Based on part b, do you think that the distribution of the daily returns have a thicker tail than the Normal distribution. (4 marks)
d. What are the probabilities of the following moves by S(USD/AUD) the next day?
I. AUD will appreciate
II. AUD will depreciate (5 marks)
e. Test whether the average return on S(USD/AUD) of the last 30 days is significantly
different from zero at the 5% level of significance. (5 marks)
f. Simulate returns using the sample size, mean, and standard deviation of S(USD/AUD).
Assume normality for the returns data. (5 marks)
g. Draw a histogram and compare it with the corresponding histogram in part a. above.
What differences do you observe? (5 marks)
h. Estimate the following models for USD/AUD returns leaving out the last one week data: