1.) On a single chart, plot the value of $1 invested in each of the five indexes over time. I.e., for all ??, plot the cumulative return series for each index: ?????? = (1 + ?��1)(1 + ?��2)...(1 + ????) What patterns do you observe? (10 points) 2.) Plot a histogram of only the Global index returns. Does the distribution look normal? (5 points) 3.) Estimate the following for each of the indices. In calculating the statistics, “monthly” can be interpreted as “not annualized”. (30 points) a. Arithmetic average of monthly returns, and annualized arithmetic return using the APR method b. Geometric average of monthly returns, and annualized geometric return using the EAR method. Why does the geometric average differ from the arithmetic average? c. Standard deviation of monthly returns, and annualized standard deviation d. Sharpe Ratio of monthly returns, and annualized Sharpe Ratio e. Skewness of monthly returns f. Kurtosis of monthly returns g. 5% Value at Risk (VaR) of monthly returns h. 5% Expected Shortfall of monthly returns i. Only for the Global index: based on your answers for (e)-(h), what do each indicate about using just the standard deviation to estimate risk?
1.) On a single chart, plot the value of $1 invested in each of the five indexes over time. I.e., for all
??, plot the cumulative return series for each index:
?????? = (1 + ?��1)(1 + ?��2)...(1 + ????)
What patterns do you observe? (10 points)
2.) Plot a histogram of only the Global index returns. Does the distribution look normal? (5 points)
3.) Estimate the following for each of the indices. In calculating the statistics, “monthly” can be
interpreted as “not annualized”. (30 points)
a. Arithmetic average of monthly returns, and annualized arithmetic return using the APR
method
b. Geometric average of monthly returns, and annualized geometric return using the EAR
method. Why does the geometric average differ from the arithmetic average?
c. Standard deviation of monthly returns, and annualized standard deviation
d. Sharpe Ratio of monthly returns, and annualized Sharpe Ratio
e. Skewness of monthly returns
f. Kurtosis of monthly returns
g. 5% Value at Risk (VaR) of monthly returns
h. 5% Expected Shortfall of monthly returns
i. Only for the Global index: based on your answers for (e)-(h), what do each indicate
about using just the standard deviation to estimate risk?
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To plot the value of $1 invested in each of the five indexes over time, you will need historical data for each index. Once you have the data, you can calculate the cumulative return series for each index using the formula you provided: Cumulative Return = (1 + Return1) x (1 + Return2) x ... x (1 + ReturnN). Then, you can plot the cumulative return series for each index on the same chart to observe any patterns.
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