what is the accurate formula for semivariance? I see two versions up to now:
- this version which considers as N (denominator) all the numbers over/under the mean-or any other number. This is the same of a version of CFA (book: Quantitative Methods for Investment Analysis - 2004 page 136). This is the formula:
- Another version (stated in another CFA´s book) shows a different formula. This is the formula (taken for another source):
The first difference is in the numerator (which is Min between "a","b") and the second is in the denominator (where N is over the entire sample).
Which one is the correct one and why? I want to use this in the Sortino ratio
PD: In addition, I found this other comment which summarizes what I meant (link):
ShaktiRathore It was my understanding that the downside deviation (i.e., denominator in Sortino) does not include the zeros; i.e., when PMAR, these positive excess values are EXCLUDED, not treated as zero. Although I had understood this to be the GIPS-compliant method (at the time I sat for the CIPM but this was several years ago ....), it seems to be controversial...
Thank you very much!