Bell Curve - Explained
What is a Bell Curve?
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Table of ContentsWhat is a Bell Curve?How does a Bell Curve Work? Bell Curves in FinanceAcademic Research on Bell Curve Portfolio
What is a Bell Curve?
A bell curve is referred to as a normal distribution because it is the most common type of distribution for a variable. The term bell curve' is derived from the graph depicting a normal distribution because it consists of a bell-shaped line. The highest point in the curve represents the most probable events in a series of data. All the other possible occurrences are distributed equally around the most probable event and end up forming a downward sloping line on either side of the peak.
How does a Bell Curve Work?
A bell curve refers to the graphical representation of normal probability distribution. The underlying standard deviations of this distribution from the median or the highest point of the curve give it the shape of a curved bell. The standard deviation is a measurement that is utilized in the quantification of the variability of data dispersion in a given set of values, while the mean gives the average of the total data points in the data set. The calculation of standard deviation is done after that of the mean, and it represents a percentage of the total data. For example, if a series of 100 test scores are collected and used in a normal probability distribution, 68% of the entire test scores are expected to fall below the mean or within one standard deviation. When two standard deviations are moved away from the mean, 95% of the test scores are included. 99.7% of the test scores are represented when three standard deviations are moved away from the mean. Text scores which are extreme outliers are considered as long tail data points they lie outside the range of the three standard deviations. Such outliers include 100 or 0.
Bell Curves in Finance
When analyzing the returns of the overall market or a security sensitivity, financial analysts and investors usually use a normal probability distribution. In finance, volatility is used to refer to standard deviations that show the returns of security. For example, blue chip stocks are the ones usually depicting a bell curve, and they have predictable low volatility. By using the normal probability distribution of the past returns of stock, investors can make assumptions with regards to the expected future returns. In some cases though, stocks and other securities display distributions that are non-normal. Fatter tails than normal ones characterize these non-normal distributions. When the fatter tail is skewed negative, it signals to the investors that there is a higher probability of negative returns. The converse is also true.