Bell Curve

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What is the 'Bell Curve'

The bell curve is the most common type of distribution for a variable, and due to this fact, it is known as a normal distribution. The term "bell curve" comes from the fact that the graph used to depict a normal distribution consists of a bell-shaped line. The highest point on the curve, or the top of the bell, represents the most probable event in a series of data, while all other possible occurrences are equally distributed around the most probable event, creating a downward-sloping line on each side of the peak.

BREAKING DOWN 'Bell Curve'

Bell curve is a general term that's used to describe a graphical depiction of a normal probability distribution. The normal probability distribution's underlying standard deviations from the median, or from the highest point on the curve, is what gives it the shape of a curved bell. A standard deviation is a measurement used to quantify the variability of data dispersion in a set of values. The mean is the average of all data points in the data set or sequence.

Standard deviations are calculated after the mean is calculated and represent a percentage of the total data collected. For example, if a series of 100 test scores are collected and used in a normal probability distribution, 68% of the 100 test scores should fall within one standard deviation above or below the mean. Moving two standard deviations away from the mean should include 95% of the 100 test scores collected, and moving three standard deviations away from the mean should represent 99.7% of the 100 test scores. Any test scores that are extreme outliers, such as a score of 100 or 0, would be considered long-tail data points and lie outside of the three standard deviation range.

Using Data Distributions in Finance

Financial analysts and investors often use a normal probability distribution when analyzing the returns of a security or of overall market sensitivity. Standard deviations that depict the returns of a security are known in the finance world as volatility. For example, stocks that display a bell curve are normally blue chip stocks and have lower and predictable volatility. Investors use the normal probability distribution of a stock's past returns to make assumptions regarding its expected future returns.

However, stocks and other securities sometimes display non-normal distributions, meaning that they do not look like a bell curve. Non-normal distributions have fatter tails than a normal probability distribution. If the fatter tail is skewed negative, it's a signal to investors that there is a greater probability of negative returns and vice versa. Positively skewed fat tails can be a sign of abnormal future returns.

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