CFA Study Guide

Quantitative Methods: Statistical Concepts

Regular variance telsl you the probability of both greater and lesser outcomes compared to the mean. Since most investors are more heavily influenced by downside risk of their investments than the possible upside gains, often times it will be imperative to show the variance only below the mean instead of around both sides of it. Obviously the mean is still an important factor. Although, since you will be using only some the variance data (the lower bounded), you'll have to work only with the subset of values that fall below the mean, and this is where it gets the designation "Semi", or part of.

Semivariance of a normal curve is essentially figured as equal to its regular variance. You can see in the illustration that the lower bounded subset (negative variance) is a mirror image of the upper bound. Semivariance becomes more complicated to compute when the distribution is skewed and those pieces are not mirror images. Even when the distribution is still normal, if the target at which the lower bound is set below the mean, you cannot rely on semivariance equaling the variance. For these two instances you'd have to measure the dispersion below the mean or target by squaring the differences of those observations below that point.

I've not seen any problems in the curriculuum asking for a computation of a skewed or target semivaiance. You should probably get by just knowing the effect of skewness and targets on the variance in relation to a normal instance.