Semi-variance
Dispersion computed only over periods that came in below a chosen threshold: how badly a portfolio fell, with no credit for how strongly it rose.
Formula
\sigma_d^2 = \frac{1}{n}\sum_{r_i < \tau}\left(r_i - \tau\right)^2The threshold is set in advance — zero or the risk-free rate. Only periods below it enter the sum, while the divisor stays the total number of observations.
How to read the number
It underpins the Sortino ratio and sits closer to what people actually mean by risk: nobody is frightened by an upside surprise, yet symmetric measures count it as one.
When the metric lies
There are always fewer observations below the threshold than above it, so the estimate rests on a short slice of the sample and moves visibly after a couple of new weak months.
Also known as: downside semi-variance