I am wondering if it is possible to set a relative constraint for a specific asset within a group of assets. I feel like this is a rather common situation in portfolio optimization constraining. Box and group constraints are pretty straight forward, but not a relative constraint for a single asset within a group. I am open to other packages but I seem to run into the same issue with PortfolioAnalytics in R too.
Below is what I have so far. Basic box constraints and one group constraint.
Constraints <- c("minW[1]=0.00","maxW[1]=.25",# Asset1
"minW[2]=0.00","maxW[2]=.5",# Asset2
"minW[3]=0.00","maxW[3]=.25",# Asset3
"minW[4]=0.00","maxW[4]=.05",# Asset4
"minW[5]=0.00","maxW[5]=.1",# Asset5
"minW[6]=0.00","maxW[6]=.05",# Asset6
"minW[7]=0.00","maxW[7]=.25",# Asset7
"minW[8]=0.00","maxW[8]=.05",# Asset8
"minW[9]=0.00","maxW[9]=.05",# Asset9
"minW[10]=0.00","maxW[10]=.1",# Asset10
"minW[11]=0.00","maxW[11]=.15",# Asset11
"minW[12]=0.00","maxW[12]=.05",# Asset12
"minW[13]=0.00","maxW[13]=.05",# Asset13
"minsumW[c(7,8)]=.01","maxsumW[c(7,8)]=.10")
What if I want to constrain asset 7 to be max of 50% of the sum of assets 7 & 8?
So: Asset 7 / (Asset 7 + Asset 8) <= 50%