The file P$02\_18.$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.

$1.$ Create a histogram of the percentage changes and describe its shape.

$2.$ Check the percentage of these percentage changes that are more than k standard deviations from the mean for $=1,2,3,4,5.$ 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$=1,2,3,4,5,$ they indicate that only $0\mathrm{.}006\%$ and $0\mathrm{.}0001\%$ of the observations should be this distant from the mean.$)$

Question from: Business Analytics by Albright and Wilson, Problem $18$ of Chapter:$2$