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
- You are given a series of crude oil futures prices, see the attached excel file. Calculate and plot the daily log returns.
- 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. )
- Calculate the 1-day, 1% VaR on each day in Jan. 2014 using Historical Simulation with a 250-day moving window.
- 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).
- 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.
- Plot the VaRs from above three methodologies.
- 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.)
