## Calculate the mean, standard deviation, skewness, and kurtosis of returns. Plot a histogram of the returns with the normal distribution imposed as well.

### finance

##### Description

1. You are given a series of crude oil futures prices, see the attached excel file. Calculate and plot the daily log returns.
2. Calculate the mean, standard deviation, skewness, and kurtosis of returns. Plot a histogram of the returns with the normal distribution imposed as well. (Excel Hint: you can use the functions AVERAGE, STDEV, SKEW, KURT, and the array function FREQUENCY, as well as the NORMDIST function. Note that KURT computes excess kurtosis. )
3. Calculate the 1-day, 1% VaR on each day in Jan. 2014 using Historical Simulation with a 250-day moving window.
4. Calculate the 1-day, 1% VaR on each day in Jan. 2014 using Weighted Historical Simulation with a 250-day moving window and a weighting parameter (use formula 8.9). (Excel hint: Sort the returns along with their weights by selecting both columns in Excel and sorting by returns).
5. Set (the variance of the first observation) equal to the variance of the entire sequence of returns (you may square the standard deviation found earlier). Then calculate the 1-day, 1% VaR on each day in Jan. 2014 using the RiskMetrics volatility model.
6. Plot the VaRs from above three methodologies.
7. Compare the commonality and differences of the above three VaRs and give a brief analysis (pros and cons of each measure, which is better to capture the market condition, etc.)