distributional characteristics of the returns

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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.

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