demo/demo_group_constraints.R

In PortfolioAnalytics: Portfolio Analysis, Including Numerical Methods for Optimization of Portfolios

#' ---
#' title: "Group Constraints Demo"
#' author: Ross Bennett
#' date: "7/17/2014"
#' ---

#' This script demonstrates how to solve a portfolio optimization problem with
#' group constraints.

#' Load the package and data
library(PortfolioAnalytics)

data(edhec)
R <- edhec[, 1:5]
colnames(R) <- c("CA", "CTAG", "DS", "EM", "EQM")
funds <- colnames(R)

#' Set up portfolio with objectives and constraints.
init.portf <- portfolio.spec(assets=funds)
init.portf <- add.constraint(portfolio=init.portf, type="full_investment")
init.portf <- add.constraint(portfolio=init.portf, type="long_only")

#' Add group constraints such that assets 1, 3, and 5 are in a group called
#' GroupA and assets 2 and 4 are in a group called Group B. The sum of the 
#' weights in GroupA must be between 0.05 and 0.7. The sum of the weights in
#' GroupB must be between 0.15 and 0.5.
init.portf <- add.constraint(portfolio=init.portf, type="group",
                             groups=list(groupA=c(1, 3, 5),
                                         groupB=c(2, 4)),
                             group_min=c(0.05, 0.15),
                             group_max=c(0.7, 0.5))
init.portf


#' Add an objective to minimize portfolio standard deviation.
init.portf <- add.objective(portfolio=init.portf, type="risk", name="StdDev")

#' The examples here use the obective to minimize standard deviation, but any
#' supported objective can also be used.

#' Minimizing standard deviation can be formulated as a quadratic programming 
#' problem and solved very quickly using optimize_method="ROI". Although "StdDev"
#' was specified as an objective, the quadratic programming problem uses the 
#' variance-covariance matrix in the objective function.
minStdDev.ROI <- optimize.portfolio(R=R, portfolio=init.portf, optimize_method="ROI")
minStdDev.ROI
extractGroups(minStdDev.ROI)

#' The leverage constraints should be relaxed slightly for random portfolios 
#' and DEoptim.
init.portf$constraints[[1]]$min_sum=0.99
init.portf$constraints[[1]]$max_sum=1.01

#' Run the optimization with random portfolios as the optimization backend.
#' By construction, the random portfolios will be generated to satisfy the
#' group constraint.
minStdDev.RP <- optimize.portfolio(R=R, portfolio=init.portf, 
                                   optimize_method="random", search_size=2000)
minStdDev.RP
extractGroups(minStdDev.RP)

#' Run the optimization with DEoptim as the optimization backend.
minStdDev.DE <- optimize.portfolio(R=R, portfolio=init.portf, 
                                   optimize_method="DEoptim", search_size=2000)
minStdDev.DE
extractGroups(minStdDev.DE)