A different sort of generalization of variance partitions.
The post “Generalizing risk fractions” described additional (to version 1.04 of Portfolio Probe) ways of dividing the variance among the assets. This post describes the other major addition in the new version.
Linear constraints on sectors, industries and countries are quite common. These constrain the weights within the categories, but their purpose is really to constrain risk rather than weight.
Version 1.04 of Portfolio Probe allows you to constrain the variance attributable to sectors, industries, countries, and so on. That is done simply by changing one argument:
lin.style = "weight"
performs the usual constraint, and
lin.style = "varfraction"
performs the constraint with the fraction of variance attributable to each category.
In the larger scheme these are not linear constraints at all — they are dynamic quadratic constraints. But you need not be concerned with that. Operationally they are just the same as constraining weights. The important difference is that they conform to the original intention of the constraints.
Sector constraints on weights exist not because they make sense, but because suitable technology hasn’t been available.
It is possible to provide multiple variances and to have constraints on each variance. For example you could have your usual optimization, but impose linear risk fraction constraints on one or more additional variance matrices that represent difficult times.