Not sure if we need to know how to calculate, but if we do… When calculating downside dev we assign value of 0 to observations which are above MAR, and still use them in calculation (i.e. end up dividing by n-1). When calculating semivariance, do we do the same thing? Or do we ignore all observations above mean return and end up dividing by n/2?
downside deviation ignores anything over MAR semivariance ignores anything over average return in a distribution MAR isn’t necessarily the same thing as average return
hezagenius Wrote: ------------------------------------------------------- > downside deviation ignores anything over MAR > > semivariance ignores anything over average return > in a distribution > > MAR isn’t necessarily the same thing as average > return Not sure if i follow deviation is sqrt(var)
comp_sci_kid Wrote: ------------------------------------------------------- > Not sure if i follow deviation is sqrt(var) Yes, but semi-variance ignores the upper half of the distribution and downside deviation ignores returns above MAR The concept is the same for both. The cutoff is how they are different.
So we end up dividing by (n-1) in both cases? And if Mar = avg return, semivariance = downside deviation?
makes sense. So for Sortino we use downside deviation. Where would we use semivar?
Semi-variance isn’t used in any ratio. It is a concept that can be used in a similar way to downside duration to measure manager performance. If semivariance is low, that means most of the returns are positive (this sort of implies that the average return in the distribution is 0).
Yes, definitely use full (n-1) rather than just the subset of returns below avg or MAR. See CFAI Reading #34, Problem 12 The logic is as follows: Imagine that you are comparing downside deviation for two samples. In first sample, lets call it “good manager”, there are 4 below MAR and 100 above. In bad sample, let’s say that have same 4 below, but only 10 above. If you used just subset below, then these would look the same. That would be penalizing the “good” manager. You want to reward that manager by using full (n-1) in the comparison.
Yeah use N-1 for all, not just the # under MAR as Stalla ahs in its books. Not sure if they fixed this or not.
tanyusha, its usually n-1 its a sample that you are provided…most cases n-1 is the one to go with. If population then go with, n. Question for all: If returns are not symmetrical i.e non-normal, would it be appropriate to use downside deviation?
What is this n-1 stuff? Haven’t seen that anywhere and haven’t taken the time to learn or calculate downside deviation… In fact, don’t recall seeing a single question in CFAI or Schweser for that matter on this… did i miss it?
n-1 (# of obesrvations - 1) is denominator in variance equation, downside deviation calculation is nothing more than standard deviation where you assign 0 to all observations above MAR in the numerator
Here are calculations for the downside (reading 34, Q11) monthly hurdle rate=5/12=0.4167 (return - monthly hurdle rate). only #s below hurdle rate considered. march=2.41 april=2.41 may=1.41 july=1.41 nov=0.0167 dec=3.61 n=12 monthly downside deviation= sqrt (sum of squared deviations / n-1) sqrt (28.62/11)=1.613 annual deviation=1.618 * sqrt(12) = 5.58
downside dev is also called target semivariance …