18. The file P02_18.xlsx contains daily values of the Standard & Poor's 500 Index from 1970 to mid-2015. It also contains percentage changes in the index from each day to the next. a. Create a histogram of the percentage changes and describe its shape. b. Check the percentage of these percentage changes that are more than k standard deviations from the mean for k = 1, 2, 3, 4, and 5. Are these approximately what the empirical rules indicate or are there fat tails? Do you think this has any real implications for the financial markets? (Note that we have discussed the empirical rules only for k= 1, 2, and 3. For k = 4 and 5, they indicate that only 0.006% and 0.0001% of the observations should be this distant from the mean.) 18. The file P02_18.xlsx contains daily values of the Standard & Poor's 500 Index from 1970 to mid-2015. It also contains percentage changes in the index from each day to the next. a. Create a histogram of the percentage changes and describe its shape. b. Check the percentage of these percentage changes that are more than k standard deviations from the mean for k = 1, 2, 3, 4, and 5. Are these approximately what the empirical rules indicate or are there fat tails? Do you think this has any real implications for the financial markets? (Note that we have discussed the empirical rules only for k= 1, 2, and 3. For k = 4 and 5, they indicate that only 0.006% and 0.0001% of the observations should be this distant from the mean.)