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Foreign exchange rate distribution, and forecasting
You have recently been employed as a financial analyst to advise on the trading strategy for investing in the Australian dollar in a major Investment bank in Australia. You have been trained in the importance of foreign exchange rate forecasting stemming 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 into 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. Draw continuously compounded returns of S(USD/AUD) graphically which can extract information on the distributional characteristics of the returns. What kind of distribution features you find.
B. Using 68–95–99.7 normal rule of thumb, provide evidence that the distribution of S(USD/AUD) is different from the normal.
C. Compare artificially (normally) created returns data with that of the actual returns with a valid graphical presentation. What characteristics of the returns do you look for to gauge differences in the two returns?
D. What is your assessment for the directional move of S(USD/AUD) the next day based on your intuition and then based on a valid statistic.
E. How would you convince your team to advise the client on whether to invest or not to invest in S(USD/AUD) for the next 30 days. Your argument must be based on an acceptable hypothesis testing procedure.
F. What can you say about the efficiency of the FX market? Base your discussion on the following task: • Estimate the following models for USD/AUD returns leaving out the last week’s data:
i. 𝑟𝑟𝑡𝑡=𝜇𝜇+𝜀𝜀𝑡𝑡, Random Walk Model (RWM)
ii. 𝑟𝑟𝑡𝑡=𝜇𝜇+𝜌𝜌𝑟𝑟𝑡𝑡-1+𝜀𝜀𝑡𝑡, Autoregressive of order 1 (AR(1)) model
Note: Use last 100 trading days’ data: first 90 observations for estimation window and the last 10 observations for hold out period.
• Compute the individual forecasts and composite forecasts of S(USD/AUD) from the above models in the hold out period. Use regression method for weights in composite forecasts. Present the forecasting accuracy measures of MAE, MSE, and RMSE for forecasts. Report the best model for the forecast.
G. Perform a risk assessment analysis for the next 100 days for the USD1 million invested in AUD in terms of 1% VaR with historical, parametric, and simulated methods. What are the risk implications to your investments on a daily basis?
H. Video presentation. (Not more than 2 minutes)
• Explain the implications drawn about International Finance’s key variable exchange rate for its distributional characteristics and its market efficiency.
Data source: http://www.rba.gov.au/statistics/historical-data.html#exchange-rates. The sample period is beginning January 2003 to date.
Marking rule: Refer to the marking rubric for details on how this assessment will be marked
Hints: Continuously compounded returns are defined as the ratio of log(et/et-1)*100, where e is the exchange rate. In part b, you can use the “SUMPRODUCT( )” function in Excel to look for the observations that are within certain range.
Use Microsoft Excel for computations.
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