––––––––––—
Skew of data set 0.565
Skew test p-value 0.000
Kurt of data set 31.987
Kurt test p-value 0.000
Norm test p-value 0.000
Results for symbol MSFT
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Skew of data set 0.043
Skew test p-value 0.415
Kurt of data set 10.180
Kurt test p-value 0.000
Norm test p-value 0.000
Throughout, the p-values of the different tests are all zero, strongly rejecting the test
hypothesis that the different sample data sets are normally distributed. This shows that the
normal assumption for stock market returns — as, for example, embodied in the geometric
Brownian motion model — cannot be justified in general and that one might have to use
richer models generating fat tails (e.g., jump diffusion models or models with stochastic
volatility).
