# Variability

## What is 'Variability'

Variability is the extent to which data points in a statistical distribution or data set diverge from the average, or mean, value as well as the extent to which these data points differ from each other. There are four commonly used measures of variability: range, mean, variance and standard deviation.

## BREAKING DOWN 'Variability'

The risk perception of an asset class is directly proportional to the variability of its returns. As a result, the risk premium that investors demand to invest in assets, such as stocks and commodities, is higher than the risk premium for assets such as Treasury bills, which have a much lower return variability. Variability refers to the difference being exhibited by data points within a dataset, as related to each other or as related to the mean. This can be expressed through the range, variance or standard deviation of a dataset.

## Largest and Smallest Value

The range refers to the difference between the largest and smallest value assigned to the variable being examined. In statistical analysis, the range is represented by a single number. The variance is the square of the standard deviation based on a list of data points, while the standard deviation is representative of the spread existing between data points.

## Variance With Regards to the Mean

The mean, or average, value of a dataset represents a midpoint of the values expressed within the data. This is separate from the median, which refers to the exact value of the data point that falls at the center of the data points should they be listed in ascending or descending order based on numerical value. While the median must be represented by the precise value of the midvalued data point, the mean may or may not be actually reflected as a figure within the dataset.

While the range only focuses on the most extreme data points, the variance considers the placement of each data point and is used as a source of information regarding overall data distribution.

## Variability in Investing

Variability is used to standardize the returns obtained on an investment and provides a point of comparison for additional analysis. One measure of reward-to-variability is the Sharpe ratio, which measures the excess return or risk premium per unit of risk for an asset. In essence, the Sharpe ratio provides a metric to compare the amount of compensation an investor receives with regard to the overall risk being assumed by holding said investment. The excess return is based on the amount of return experienced beyond investments that are considered free of risk. All else being equal, the asset with the higher Sharpe ratio delivers more return for the same amount of risk.