Symmetrical Distribution Definition

Symmetrical distribution occurs when the values of variables occur at regular frequencies and the mean, median and mode occur at the same point. In graph form, symmetrical distribution often appears as a bell curve. If a line were drawn dissecting the middle of the graph, it would show two sides that mirror each other. Symmetrical distribution is a core concept in technical trading as the price action of an asset is assumed to fit a symmetrical distribution curve over time.

Symmetrical distribution is used by traders to establish the value area for a stock, currency or commodity on a set time frame. This time frame is can be intraday, such as 30 minute intervals, or it can be longer-term using sessions or even weeks and months. A bell curve can be drawn around the price points hit during that time period and it is expected that most of the price action - approximately 68% of price points - will fall within one standard deviation of the centre of the curve. The curve is applied to the y-axis (price) as it is the variable whereas time throughout the period is simply linear. So the area within one standard deviation of the mean is the value area where price and the actual value of the asset are most closely matched.

If the price action takes the asset price out of the value area, then it suggests that price and value are out of alignment. If the breach is to the bottom of the curve, the asset is considered to be undervalued. If it is to the top of the curve, the asset is to be overvalued. The assumption is that the asset will revert to the mean over time.

Symmetrical distribution is most often used to put price action into context. The further the price action wanders from the value area one standard deviation on each side of the mean, the greater the probability that the underlying asset is being under or overvalued by the market. This observation will suggest potential trades to place based on how far the price action has wandered from the mean for the time period being used. On larger time scales, however, there is a much greater risk of missing the actual entry and exit points.

Opposite symmetrical distribution is asymmetrical distribution. A distribution is asymmetric if it is not symmetric with zero skewness; in other words, it does not skew. An asymmetric distribution is either left-skewed or right-skewed. A left-skewed distribution, what is known as a negative distribution, has a longer left tail. A right-skewed distribution, or a positively skewed distribution, has a longer right tail. Determining whether the mean is positive or negative is important when analyzing the skew of a data set because it affects data distribution analysis.

Skewness is often an important component of a trader’s analysis of a potential investment return. A symmetric distribution of returns is evenly distributed around the mean. An asymmetric distribution with a positive right skew indicates that historical returns that deviated from the mean were primarily concentrated on the bell curve’s left side. Conversely, a negative left skew shows historical returns deviating from the mean concentrated on the right side of the curve. 

A common investment refrain is that past performance does not guarantee future results; however, past performance can illustrate patterns and provide insight for traders looking to make a decision about a position. Symmetrical distribution is a general rule of thumb, but no matter the time period used, there will often be periods of asymmetrical distribution on that time scale. This means that, although the bell curve will generally return to symmetry, there can be periods of asymmetry that establish a new mean for the curve to center on. This means that trading based solely on the value area of a symmetrical distribution can be risky if the trades are not confirmed by other technical indicators.