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Variance analysis can be carried out for both costs and revenues. Variance analysis is usually associated with explaining the difference (or variance) between actual costs and the standard costs allowed for the good output. For example, the difference in materials costs can be divided into a materials price variance and a materials usage variance.
The variance is the square of differences of measurements from the mean divided by the number of samples. The standard deviation is the square root of the variance. The standard deviation of the continuously compounded returns of a financial instrument is called volatility.
This is because when calculating standard deviation (or variance), all differences are squared, so that negative and positive differences are combined into one quantity. Two instruments with different volatilities may have the same expected return, but the instrument with higher volatility will have larger swings in values over a given period ...
That is, it is the risk of the actual return being below the expected return, or the uncertainty about the magnitude of that difference. [ 1 ] [ 2 ] Risk measures typically quantify the downside risk, whereas the standard deviation (an example of a deviation risk measure ) measures both the upside and downside risk.
The variance of return (or its transformation, the standard deviation) is used as a measure of risk, because it is tractable when assets are combined into portfolios. [1] Often, the historical variance and covariance of returns is used as a proxy for the forward-looking versions of these quantities, [ 2 ] but other, more sophisticated methods ...
In financial mathematics, a deviation risk measure is a function to quantify financial risk (and not necessarily downside risk) in a different method than a general risk measure. Deviation risk measures generalize the concept of standard deviation .
By using the relationship between standard deviation and variance, and the definition of correlation, (,) (), market beta can also be written as =,, where , is the correlation of the two returns, and , are the respective volatilities.
The residual is the difference between the observed value and the estimated value of the quantity of interest (for example, a sample mean). The distinction is most important in regression analysis , where the concepts are sometimes called the regression errors and regression residuals and where they lead to the concept of studentized residuals .