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title: "Semi-variance and semi-standard deviation"
canonical: "https://modelassist.epixanalytics.com/space/EA/26575506/Semi-variance%20and%20semi-standard%20deviation"
format: markdown
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Variance and standard deviation are often used as measures of risk in the financial sector because they represent uncertainty. However, in a distribution of cashflow, a large positive tail (equivalent to the chance of a large income) is not really a "risk', although this tail will contribute to, and often dominate, the value of the calculated standard deviation and variance.


![image](media://b7df0457-5b21-41eb-9823-a11dac3a1c12)


The semi-standard deviation and semi-variance compensate for this problem by considering only those generated values below (or above, as required) a threshold: the threshold delineating these scenarios that represent a "risk' and therefore should be included from those that are not a risk and therefore should be excluded.


The semi-variance and semi-standard deviation are:

![image](media://8457e3fa-8d77-4a18-b0d0-c224273f1d02)


> Macro (mathblock)


where x0 is the specified threshold value and x<sub>1</sub>....x<sub>k</sub> are all of the data points that are either above or below x0 , as required.




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