Foreign exchange rate distribution, and forecasting
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: I.

I. Rt=????+??????, Random Walk Model (RWM)

II. Rt=????+?p rt-1+???????, Autoregressive of order 1 (AR(1)) model
Note: Use last 100 trading days’ data. (10 marks)
i. Compute the forecast of S(USD/AUD) from the above models in the hold out period. (10 marks)
j. Calculate MAE, MSE, RMSE of the forecasts made in part i. above and report the best model for the forecast. (10 marks)

k. Compute composite forecast of the exchange rate from AR(1) and log(????????)=????+????????+????????, where ???????? is S(USD/AUD). Estimate weights from regression. (10 marks)
l. Highlight an international finance issue that you would like to do the research on in future if you get an opportunity whether in a research department of a major invest bank or in PhD studies. Please limit the write-up to two A4 pages with minimum font size of 11. (10 marks)
m. Using last 100 days USD/AUD data, calculate one day 1%VaR of USD1 million invested in AUD using historical and parametric approaches. (5 marks)