# Annualize downside deviation

A question gave monthly hedge fund returns, so downside deviation = [min(return – threshold),0)^2/ (n-1)] ^0.5 = √ [28.78/(12 – 1)]. For annualised downside deviation, we multiply by √12, so: annual downside deviation = √[28.78/(12 – 1)] x √12 Can someone please explain why we multiply by √12 and not just 12?

the way i remember - return is much plainer - multiply by 12. However risk needs to take the correlation effect so use square root. In this case i would multiply by sqrt(12)

(Statistically independent) variances add; so the annual lower semivariance will be 12 times the monthly lower semivariance. As lower semideviation is the square root of lower semivariance, the annual lower semideviation will be √12 times the monthly lower semideviation.

Okay but how does √12 fit with the below, i’m getting confused on the math? And i know there is a difference between one being weekly (√52) and one being monthly (√12) so (if given annual returns) weekly variance = (Variance / 52 ) weekly standard deviation = √ (Variance / 52 ) = √Variance / √52 = standard deviation / √52

annual variance = monthly variance * 12

so annual std dev = monthly std dev * sqrt(12)

how did we get the 28.78 in the CFAi example ?

find all the places where the return is lower than 0. square and add the variance…

and use 5% (rate at the bottom of the problem, in fine print) as the monthly benchmark return.