CoCalc -- test_qp

GitHub Repository: braverock/portfolioanalytics
Path: blob/master/inst/tests/test_qp_gmv.R
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library(PortfolioAnalytics)
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library(ROI)
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library(ROI.plugin.quadprog)
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library(quadprog)
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library(testthat)
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# Test that PortfolioAnalytics with ROI.plugin.quadprog solutions equal quadprog solutions
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context("GMV Portfolios: PortfolioAnalytics with ROI.plugin.quadprog and quadprog")
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##### Data #####
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data(edhec)
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R <- edhec[, 1:5]
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funds <- colnames(R)
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m <- ncol(R)
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##### Parameters #####
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portf <- portfolio.spec(funds)
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portf <- add.constraint(portf, type="full_investment")
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portf <- add.constraint(portf, type="box", min=-Inf, max=Inf)
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portf <- add.objective(portf, type="risk", name="var")
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# Quadratic part of objective function
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objQ <- 2 * cov(R)
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# Linear part of objective function
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objL <- rep(0, m)
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# Constraints matrix
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Amat <- matrix(1, nrow=1, ncol=m)
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# right hand side of constraints
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rhs <- 1
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##### Unconstrained #####
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# Solve optimization with quadprog
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opt.qp <- solve.QP(Dmat=objQ, dvec=objL, Amat=t(Amat), bvec=rhs, meq=1)
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# Solve optimization with PortfolioAnalytics
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opt.pa <- optimize.portfolio(R, portf, optimize_method="quadprog")
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weights <- as.numeric(extractWeights(opt.pa))
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test_that("Unconstrained: PortfolioAnalytics and quadprog solution weights are equal", {
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  expect_that(weights, equals(opt.qp$solution))
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})
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test_that("Unconstrained: PortfolioAnalytics and quadprog solution objective values are equal", {
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  expect_that(opt.pa$out, equals(opt.qp$value))
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})
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##### Long Only #####
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# Upper and lower bounds (i.e. box constraints)
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lb <- rep(0, m)
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ub <- rep(1, m)
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Amat <- rbind(1, diag(m), -diag(m))
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rhs <- c(1, lb, -ub)
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# Update box constraints in portfolio
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portf$constraints[[2]]$min <- lb
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portf$constraints[[2]]$max <- ub
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# Solve optimization with quadprog
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opt.qp <- solve.QP(Dmat=objQ, dvec=objL, Amat=t(Amat), bvec=rhs, meq=1)
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# Solve optimization with PortfolioAnalytics
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opt.pa <- optimize.portfolio(R, portf, optimize_method="quadprog")
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# some of the optimal weights are slightly negative (-7.602276e-18), but they
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# are essentially zero
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weights <- round(as.numeric(extractWeights(opt.pa)), 10)
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test_that("Long Only: PortfolioAnalytics and quadprog solution weights are equal", {
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  expect_that(weights, equals(opt.qp$solution))
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})
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test_that("Long Only: PortfolioAnalytics bounds are respected", {
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  expect_that(all(weights >= lb) & all(weights <= ub), is_true())
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})
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test_that("Long Only: quadprog bounds are respected", {
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  expect_that(all(round(opt.qp$solution, 10) >= lb) & all(round(opt.qp$solution, 10) <= ub), is_true())
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})
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test_that("Long Only: PortfolioAnalytics and quadprog solution objective values are equal", {
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  expect_that(opt.pa$out, equals(opt.qp$value))
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})
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##### Box #####
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# Upper and lower bounds (i.e. box constraints)
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lb <- rep(0.05, m)
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ub <- rep(0.55, m)
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Amat <- rbind(1, diag(m), -diag(m))
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rhs <- c(1, lb, -ub)
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# Update box constraints in portfolio
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portf$constraints[[2]]$min <- lb
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portf$constraints[[2]]$max <- ub
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# Solve optimization with quadprog
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opt.qp <- solve.QP(Dmat=objQ, dvec=objL, Amat=t(Amat), bvec=rhs, meq=1)
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# Solve optimization with PortfolioAnalytics
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opt.pa <- optimize.portfolio(R, portf, optimize_method="quadprog")
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weights <- as.numeric(extractWeights(opt.pa))
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test_that("Box: PortfolioAnalytics and quadprog solution weights are equal", {
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  expect_that(weights, equals(opt.qp$solution))
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})
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test_that("Box: PortfolioAnalytics bounds are respected", {
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  expect_that(all(weights >= lb) & all(weights <= ub), is_true())
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})
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test_that("Box: quadoprog bounds are respected", {
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  expect_that(all(opt.qp$solution >= lb) & all(opt.qp$solution <= ub), is_true())
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})
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test_that("Box: PortfolioAnalytics and quadprog solution objective values are equal", {
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  expect_that(opt.pa$out, equals(opt.qp$value))
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})
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##### Box with Shorting #####
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# Upper and lower bounds (i.e. box constraints)
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lb <- rep(-0.05, m)
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ub <- rep(0.55, m)
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Amat <- rbind(1, diag(m), -diag(m))
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rhs <- c(1, lb, -ub)
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# Update box constraints in portfolio
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portf$constraints[[2]]$min <- lb
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portf$constraints[[2]]$max <- ub
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# Solve optimization with quadprog
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opt.qp <- solve.QP(Dmat=objQ, dvec=objL, Amat=t(Amat), bvec=rhs, meq=1)
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# Solve optimization with PortfolioAnalytics
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opt.pa <- optimize.portfolio(R, portf, optimize_method="quadprog")
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weights <- as.numeric(extractWeights(opt.pa))
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test_that("Box with Shorting: PortfolioAnalytics and quadprog solution weights are equal", {
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  expect_that(weights, equals(opt.qp$solution))
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})
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test_that("Box with Shorting: PortfolioAnalytics bounds are respected", {
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  expect_that(all(weights >= lb) & all(weights <= ub), is_true())
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})
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test_that("Box with Shorting: quadprog bounds are respected", {
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  expect_that(all(opt.qp$solution >= lb) & all(opt.qp$solution <= ub), is_true())
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})
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test_that("Box with Shorting: PortfolioAnalytics and quadprog solution objective values are equal", {
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  expect_that(opt.pa$out, equals(opt.qp$value))
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})
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