A symmetrical distribution occurs when the values of variables appear at regular frequencies, and the mean, median, and mode all occur at the same point. If a line were drawn down the center of the graph, it would reveal two sides that mirror each other.
In graphical form, symmetrical distributions often appear as a normal distribution (i.e., bell curve). 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 distributions can be contrasted with asymmetrical distributions, which exhibit skewness or other irregularities in their shape.
Key Features of Symmetrical Distribution
- Symmetrical distributions divide the data into two mirror-image halves when split down the center.
- Bell curves are a commonly-cited example within symmetrical distributions.
- Statistical techniques rely on symmetrical distributions for analyzing data and making inferences.
- In finance, symmetrical distributions can aid trading decisions by assuming data-generating processes mirror the mean.
- Real-world price data, however, tend to exhibit asymmetrical qualities such as right-skewness.
Insights from Symmetrical Distribution
Symmetrical distributions help traders establish the value area for a stock, currency, or commodity over various time frames. These vary from intraday periods (like 30-minute intervals) to longer-term sessions encompassing weeks or months. The assumption is that approximately 68% of price points will fall within one standard deviation of the curve’s center. This area encapsulates the value area, where prices closely align with the asset’s actual value.
If the current price action takes the asset out of the value area, it signals a misalignment of price and value. A dip below the curve suggests undervaluation, while a rise above indicates overvaluation. Ultimately, it is expected that over time, the market will revert to the mean.
Example: Contextualizing Price Action through Symmetrical Distribution
Symmetrical distribution is often utilized to contextualize price action. The further price action deviates from one standard deviation of the mean, on either side, the higher the chances the asset is under or overvalued. This understanding suggests potential trades based on how far the price deviates from the mean, although larger time frames introduce the risk of missing optimal entry and exit points.
Image by Julie Bang
Symmetrical vs. Asymmetrical Distributions
The opposed concept to symmetrical distribution is asymmetrical distribution. An asymmetric distribution lacks zero skewness, manifesting either left-skewness (negative) or right-skewness (positive). For instance, a left-skewed distribution has a longer left tail, while a right-skewed one has a longer right tail.
Skewness plays a vital role in a trader’s analysis, depicting how historical returns spread in relation to mean. Positive right skew indicates returns deviating mainly to the left, while negative left skew shows deviation towards the right.
Normal vs. Skewed. Image by Sabrina Jiang
Understanding the Symmetrical Distribution’s Limitations
While past performance offers insight into patterns, it doesn’t guarantee future results. Symmetrical distribution, though reliable, is not infallible. Periods of asymmetry may occur, establishing a new mean and potential risks absent confirmation from other technical indicators. Thus, risk management is crucial when trading based on symmetrical distribution.
Relationship Between Mean, Median, and Mode in Symmetrical Distribution
In symmetrical distributions like the normal distribution (bell curve), mean, median, and mode converge. This holds true for other symmetric distributions as well, like the uniform distribution and binomial distribution.
Occasionally, a symmetrical distribution might have two distinct modes, presenting as two equidistant peaks.
Exploring Symmetric versus Asymmetric Data
Symmetric data reflects regularly occurring variable values around the mean. Conversely, asymmetric data embodies skewness or noise, appearing irregularly. Visualizing the shape helps quickly distinguish the symmetry or asymmetry in data.
Related Terms: mean, median, mode, central limit theorem, mean reversion.
