理解variability vs. volatility vs. variance

• variability

  In statistics, dispersion (also called variability, scatter, or spread) is the extent to which a distribution is stretched or squeezed.

  Common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range.

  1. Standard deviation

     The standard deviation is a measure of the amount of variation or dispersion of a set of values.

     The standard deviation is the squared root of its variance.

  2. Variance

     Variance is the expectation of the squared deviation of a random variable from its mean.

     expectation:

     The expected value( expectation, mathematical expectation, mean, average, or first moment) of a random variable X, denoted E(X) or E[X], is a generalization of the weighted average, and is intuitively the arithmetic mean(the sum of a collection of numbers divided by the count of numbers in the collection) of a large number of independent realizations of X.

     Deviation:

     Deviation is a measure of difference between the observed value of a variable and some other value, often that variable’s mean.

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  3. Interquartile range(IQR)

  4. Range

  5. Mean absolute difference(Gini mean absolute difference)

  6. Median absolute deviation(MAD)

  7. Average absolute deviation

  8. Distance standard deviation

• Variance vs. Variation

  Variance is a parameter of a distribution (standard deviation suqared) that helps us describe the distribution’s shape and the data spread.

  Variation is a more generic term used to describe the dispersion/spread of the data from the mean, without a single precise formula.

  Variance 是一个具体的统计学/概率论指标，中文翻译“方差”，计算公式是随机变量距离其均值的偏差的平方的均值。

  Variation是一个笼统的泛化的改变，just like variability, its the amount of variability，表示波动性，并非具体的指标，也没有具体的数学公式，variance、standard deviation…都可以称为variation。更多的是一个金融学概念。

  1.Variance vs. variation

  2.Is variation the same as variance?

  3.What are the differences of Standard Deviation, Variance, Co-variance, Coefficient of Variation when it comes to measures of dispersion or variation?

• volatility

  In finance, volatility (usually denoted by $\sigma$) is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithemic returns.

• Variability vs. Volatility in Finance

  In general English, “volatility” refers to how a thing changs over time, while “variance” refers to dispersion among many things at a point in time.

  Variability and volatility both help investors understand the risk associated with a particular investment.

  Variability, as a statistical concept, describes how much a population changes. In finance, variability measures how spread out an asset’s returns are likely to be. One key aspect of variability is that it’s not defined over a set period of time. variability is more of a descripation of an asset’s personality. Assets with high variability will have returns that are spread all over the place, otherwise low variability will have returns that are much closer to each other.

  Volatility measures how much returns deviate from average over a set period of time.

  Assets which have high levels of variance are probably going to experience volatility over most periods of time.

  From the example with house and nozzle, Variance is the different settings on the nozzle, Volatility describes how the water hits the ground.

  In finance, volatility is usually understood as standard deviation.

  1.Variability vs. Volatility in Finance

  2.What is the difference between volatility and variance?

  3.Is Volatility Standard Deviation? Are They the Same Thing?