Normal Distribution

Hi, everybody! Today I'm going to talk about the misuse of the normal distribution in the financial world. The normal distribution is a continuous distribution where the mean, the mode, and the median are all equal. Another defining characteristic of the normal distribution is that it has a skewness of 0, in other words it is symmetrical. The standard deviation helps tell us the cumulative probability of getting a certain x within the distribution. The distribution holds that 68.27% of all values fall within plus/minus one standard deviation, 95.45% are within plus/minus two standard deviations, and 99.73% are within plus/minus three standard deviations.
While the normal distribution is appropriate for many phenomena such as people's height, thermal noise, and IQ tests which are actually based on the normal distribution, among others, people tend to overuse it and ignore the long-tails that occur in some financial distributions. Although many financial measures can be approximated using the normal distribution, events such as worst case scenarios regarding cash flow can have some long-tails which don't fit under the normal curve. A distribution such as the pareto or the log-normal would account better for large losses since these distributions are skewed to the right allowing the possibility of large losses to be realized.