library(PortfolioAnalytics)
library(Rcplex)
library(ROI)
library(ROI.plugin.cplex)
library(testthat)
# Test that ROI.plugin.cplex solutions equal Rcplex solutions
context("Maximum Mean Return Portfolios: PortfolioAnalytics with ROI.plugin.cplex and Rcplex")
# args(Rcplex)
# ?Rcplex
##### Data #####
data(edhec)
R <- edhec[, 1:5]
funds <- colnames(R)
m <- ncol(R)
##### Parameters #####
portf <- portfolio.spec(funds)
portf <- add.constraint(portf, type="full_investment")
portf <- add.constraint(portf, type="box", min=0, max=1)
portf <- add.objective(portf, type="return", name="mean")
# Quadratic part of objective function
objQ <- NULL
# Linear part of objective function
objL <- -colMeans(R)
# Constraints matrix
Amat <- matrix(1, nrow=1, ncol=m)
# right hand side of constraints
rhs <- 1
# direction of inequality of constraints
dir <- "E"
##### Long Only #####
# Upper and lower bounds (i.e. box constraints)
# Rcplex bounds
lb <- rep(0, m)
ub <- rep(1, m)
# Solve optimization with Rcplex
opt.rcplex <- Rcplex(cvec=objL, Amat=Amat, bvec=rhs, Qmat=objQ, lb=lb, ub=ub,
sense=dir, control=list(trace=0))
# Solve optimization with PortfolioAnalytics
opt.pa <- optimize.portfolio(R, portf, optimize_method="cplex")
weights <- as.numeric(extractWeights(opt.pa))
test_that("Long Only: PortfolioAnalytics and Rcplex solution weights are equal", {
expect_that(weights, equals(opt.rcplex$xopt))
})
test_that("Long Only: PortfolioAnalytics bounds are respected", {
expect_that(all(weights >= lb) & all(weights <= ub), is_true())
})
test_that("Long Only: Rcplex bounds are respected", {
expect_that(all(opt.rcplex$xopt >= lb) & all(opt.rcplex$xopt <= ub), is_true())
})
test_that("Long Only: PortfolioAnalytics and Rcplex solution objective values are equal", {
expect_that(opt.pa$out, equals(opt.rcplex$obj))
})
##### Box #####
# Upper and lower bounds (i.e. box constraints)
# Rcplex bounds
lb <- rep(0.05, m)
ub <- rep(0.55, m)
# Update box constraints in portfolio
portf$constraints[[2]]$min <- lb
portf$constraints[[2]]$max <- ub
# Solve optimization with Rcplex
opt.rcplex <- Rcplex(cvec=objL, Amat=Amat, bvec=rhs, Qmat=objQ, lb=lb, ub=ub,
sense=dir, control=list(trace=0))
# Solve optimization with PortfolioAnalytics
opt.pa <- optimize.portfolio(R, portf, optimize_method="cplex")
weights <- as.numeric(extractWeights(opt.pa))
test_that("Box: PortfolioAnalytics and Rcplex solution weights are equal", {
expect_that(weights, equals(opt.rcplex$xopt))
})
test_that("Box: PortfolioAnalytics bounds are respected", {
expect_that(all(weights >= lb) & all(weights <= ub), is_true())
})
test_that("Box: Rcplex bounds are respected", {
expect_that(all(opt.rcplex$xopt >= lb) & all(opt.rcplex$xopt <= ub), is_true())
})
test_that("Box: PortfolioAnalytics and Rcplex solution objective values are equal", {
expect_that(opt.pa$out, equals(opt.rcplex$obj))
})
##### Box with Shorting #####
# Upper and lower bounds (i.e. box constraints)
# Rcplex bounds
lb <- rep(-0.05, m)
ub <- rep(0.55, m)
# Update box constraints in portfolio
portf$constraints[[2]]$min <- lb
portf$constraints[[2]]$max <- ub
# Solve optimization with Rcplex
opt.rcplex <- Rcplex(cvec=objL, Amat=Amat, bvec=rhs, Qmat=objQ, lb=lb, ub=ub,
sense=dir, control=list(trace=0))
# Solve optimization with PortfolioAnalytics
opt.pa <- optimize.portfolio(R, portf, optimize_method="cplex")
weights <- as.numeric(extractWeights(opt.pa))
test_that("Box with Shorting: PortfolioAnalytics and Rcplex solution weights are equal", {
expect_that(weights, equals(opt.rcplex$xopt))
})
test_that("Box with Shorting: PortfolioAnalytics bounds are respected", {
expect_that(all(weights >= lb) & all(weights <= ub), is_true())
})
test_that("Box with Shorting: Rcplex bounds are respected", {
expect_that(all(opt.rcplex$xopt >= lb) & all(opt.rcplex$xopt <= ub), is_true())
})
test_that("Box with Shorting: PortfolioAnalytics and Rcplex solution objective values are equal", {
expect_that(opt.pa$out, equals(opt.rcplex$obj))
})
Rcplex.close()
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