What Is Semi-Variance?

Semi-variance is the value you get by picking out only the values that fall below a reference point (usually the mean or a target return), squaring those deviations, and averaging them.

Unlike ordinary variance, which counts both upside and downside deviations, semi-variance treats months that rose above the reference as simply 0 and ignores them. It counts only the 'losses that fell short of the reference.'

This idea is actually not new. Harry Markowitz, who created modern portfolio theory, himself remarked in 1959 that "since investors care more about downside risk, semi-variance may be a better measure."

If you apply a square root to semi-variance, you get downside deviation. It's exactly the same relationship as standard deviation being the square root of variance.

And using this downside deviation as the risk measure is precisely the Sortino ratio. Where the Sharpe ratio uses standard deviation, the Sortino puts in downside deviation.

In other words, semi-variance → downside deviation → Sortino ratio form one family. They all come from the same philosophy: 'don't penalize upward surges; treat only downward collapses as risk.'

The strength is that it aligns well with intuition. Since it doesn't call surges risk, it doesn't unfairly penalize an asset that surges big only upward and rarely falls.

There are limits too. First, the value changes depending on what you set as the reference point (the mean? 0%? a target return?). Second, if the sample is small, using only 'the data that fell below' can make the calculation unstable. Third, it doesn't add up cleanly like variance, so the portfolio math becomes complicated.

So rather than completely replacing standard deviation, it's viewed alongside as a complement when you want to see 'downside risk.'