What is a Normal Distribution?

Normal distribution, which is also referred to as the Gaussian distribution, denotes a probability distribution which shows symmetry regarding the mean. It signifies that the data that is closer to the average or mean occurs more frequently as compared to the data that is at a distance from the mean. When represented in a graph, normal distribution can be created as a bell curve.

Key points to remember

1. Normal distribution refers to a probability bell curve.
2. Normal distribution involves symmetrical distribution, but it is not necessary for all symmetrical distributions to be normal.
3. In real, majority of the pricing distributions dont show perfect normality.

How is a Normal Distribution Used? 

Analysts use normal distribution for analyzing technical movements in the stock market, and in different forms of statistical observations. The standard normal distribution usually consists of two factors including the average/mean and the standard deviation. Considering a normal distribution, 68% of the observations fall in the range of +/- one standard deviation of the average, while 95% fall in the range of +/- two standard deviations and 99.7% of the observations fall within +/- three standard deviations of the average. The Central Limit Theorem has influenced the normal distribution approach. The theorem says that the mean values ascertained from independent yet similarly allocated random variables have nearly normal distributions, irrespective of the nature of distribution from which the samples are taken. Some people mistakenly consider normal distribution and symmetrical distribution as same. In the symmetrical distribution, two mirror images may appear because of a dividing line. However, the real data can be in the form of two different humps or an array of hills including the bell curve that represents a normal distribution. 

Skewness and Kurtosis

It is not usual to see a perfect normal distribution in real life. The coefficients of skewness and kurtosis determine the difference between a specified distribution and a normal distribution. The skewness determines how symmetric the data in a distribution is. There is a sense of symmetry in normal distribution followed by zero skewness. If the skewness of a distribution data set is negative or below zero, then the length of left tail of the distribution is more than the right tail, and in case, the skewness is positive, or above zero, it states that the length of the left tail is less than the right tail. The kurtosis statistics determines how thick the distributions tail ends are in reference to the normal distributions tails. Distributions that have huge kurtosis show tail data going beyond the normal distributions tails. On the other side, distributions with less kurtosis show that the tail data tends to be less extreme as compared to normal distributions tails. Having a kurtosis of 3, the normal distribution doesnt show either thin or fat tails. Hence, if the kurtosis of an observed distribution is more than 3, this signifies that it has heavier tails than the normal distribution. In case, it is less than 3, the distribution would have thinner tails than the normal distribution.

How normal distribution is used in finance

Analysts consider using normal distribution on price movement as well as asset prices. For including current price movement in a normal distribution, traders can mark points of prices over a given period of time. When the price action or movement is far from the average or mean, there would be chances of the asset being undervalued or overvalued. Traders may also prefer using standard deviations for giving ideas about prospective trades. As it gets difficult to choose entry and exit points in the long-run, thats why, such trading is carried on a short-term basis. Also, there exists several theories that try to model asset prices on the belief that they use a normal distribution. However, in the real world, price distributions, having a kurtosis of more than 3, exhibit fat tails. These assets had experienced price fluctuations more than 3 standard deviations outside the mean more frequently than estimated as per the normal distributions assumption. In case, an asset gets included in a normal distribution in the long-run, it wont guarantee its previous performance exactly conveying the prospective possibilities ahead.