# Variance

• A measure of dispersion of a set of data points around their mean value. The mathematical expectation of the squared deviations from the mean. The square root of the variance is the standard deviation.

• Is a measure of volatility, risk, or statistical dispersion. It is the square of the standard deviation. The variance is calculated by:

• computing the mean of the series
• then taking the deviation or subtracting the mean from each observation,
• square the differences or deviations for each observation,
• and divide the sum of the squared deviations by the

number of observations. This computation is the precursor to the standard deviation. The standard deviation is calculated by taking the square root of the variance.

Embedded terms in definition
Dispersion
Mean
Risk
Series
Standard deviation
Volatility

Referenced Terms
Black scholes option model: Is the seminal work about options pricing models. It was developed by Fisher Black and Myron Scholes. It initially focused on securities prices. Subsequently, it was refined by Fisher Black for the futures markets. Most options models depart from this seed. This important work was published by Fischer Black and Myron Scholes in the May-June 1973 edition of The Journal of Political Economy. It laid the foundation for the quantitative analysis and practical calculation of puts and calls. The model indicated that options would eliminate risk from stock portfolios subject to some assumptions. The lognormal model stated that option values could be determined by using the current stock price, time left to expiration, the strike or exercise price, the Variance of the stock's rate of return (standard deviation applied) and the risk-free rate of interest.

Country beta: CoVariance of a national economy's rate of return and the rate of return the world economy divided by the variance of the world economy.

Country risk analysis models: Country Risk Analysis Models incorporate variables such as Debt Service ratio, Import Ratio, Variance of Export Revenue. Domestic Money Supply Growth Rate and others to predict the probability of debt rescheduling problems.

Heteroskedasticity or heteroscedasticity: Is the condition where the residual Variance is nonconstant. This tends to happen in cross-sectional analyses. It also occurs in various consumer, income, risk, and size of firm studies. This compares to Homoskedasticity.

Homoskedasticity or homoscedasticity: Is the condition of constant residual Variance. This compares to Heteroskedasticity.

Related Terms
Mean variance analysis
Mean variance criterion
Mean variance efficient portfolio
Minimum variance frontier
Minimum variance portfolio
Portfolio variance
Variance minimization approach to tracking
Variance rule

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