Semi-variance (Vs) and semi-standard deviation (ss)

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.

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:

where x0 is the specified threshold value and x1....xk are all of the data points that are either above or below x0 , as required.