R/solve-Rquadprog.R

In fPortfolio: Rmetrics - Portfolio Selection and Optimization

# This library is free software; you can redistribute it and/or
# modify it under the terms of the GNU Library General Public
# License as published by the Free Software Foundation; either
# version 2 of the License, or (at your option) any later version.
#
# This library is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR Description. See the
# GNU Library General Public License for more details.
#
# You should have received a copy of the GNU Library General
# Public License along with this library; if not, write to the
# Free Foundation, Inc., 59 Temple Place, Suite 330, Boston,
# MA 02111-1307 USA


################################################################################
# FUNCTION:                     DESCRIPTION:
#  solveRquadprog                Portfolio interface to solver Rquadprog
#  .rquadprogArguments           Returns arguments for solver
#  .rquadprog                    Wrapper to solver function
################################################################################


solveRquadprog <-
    function(data, spec, constraints)
{
    # A function implemented by Diethelm Wuertz
    
    # Description:
    #   Portfolio interface to solver Rquadprog

    # FUNCTION:

    # Transform Data:
    Data <- portfolioData(data, spec)
    data <- getSeries(Data)
    nAssets <- getNAssets(Data)

    # Compile Arguments for Solver:
    args <- .rquadprogArguments(Data, spec, constraints)

    # Solve Multiassets Portfolio:
    ans <- .rquadprog(
        Dmat = args$Dmat,
        dvec = args$dvec,
        Amat = args$Amat,
        bvec = args$bvec,
        meq = args$meq)

    # Save Arguments:
    ans$optim$args <- args

    # class:
    class(ans) = c("solver", "list")

    # Return Value:
    ans
}


################################################################################


.rquadprogArguments <-
    function(data, spec, constraints)
{
    # A function implemented by Diethelm Wuertz
    
    # Description:
    #   Returns quadprog conform arguments for the solver

    # FUNCTION:

    # Data and Constraints as S4 Objects:
    Data <- portfolioData(data, spec)
    data <- getSeries(Data)
    Sigma <- getSigma(Data)
    nAssets <- getNAssets(Data)

    # Set up A_mat of Constraints:
    eqsumW <- eqsumWConstraints(Data, spec, constraints)
    minsumW <- minsumWConstraints(Data, spec, constraints)
    maxsumW <- maxsumWConstraints(Data, spec, constraints)
    Amat = rbind(eqsumW[, -1], diag(nAssets), -diag(nAssets))
    if(!is.null(minsumW)) Amat = rbind(Amat, minsumW[, -1])
    if(!is.null(maxsumW)) Amat = rbind(Amat, -maxsumW[, -1])

    # Set up Vector A_mat >= bvec of Constraints:
    minW <- minWConstraints(Data, spec, constraints)
    maxW <- maxWConstraints(Data, spec, constraints)
    bvec <- c(eqsumW[, 1], minW, -maxW)
    if(!is.null(minsumW)) bvec = c(bvec, minsumW[, 1])
    if(!is.null(maxsumW)) bvec = c(bvec, -maxsumW[, 1])

    # Part (meq=1) or Full (meq=2) Investment, the Default ?
    meq <- nrow(eqsumW)

    # Directions:
    dir <- c(
        rep("==", times = meq),
        rep(">=", times = length(bvec) - meq))

    # Return Value:
    list(
        Dmat = Sigma, 
        dvec = rep(0, nAssets),
        Amat = t(Amat), 
        bvec = bvec, 
        meq = meq, 
        dir = dir)
}


################################################################################


.rquadprog <-
    function(Dmat, dvec, Amat, bvec, meq)
{
    # A function implemented by Diethelm Wuertz
    
    # Description:
    #   Goldfarb and Idnani's quadprog solver function

    # Note:
    #   Requires to load contributed R package quadprog from which we use
    #   the Fortran subroutine of the quadratic solver.

    # Package: quadprog
    #   Title: Functions to solve Quadratic Programming Problems.
    #   Author: S original by Berwin A. Turlach <berwin.turlach@anu.edu.au>
    #       R port by Andreas Weingessel <Andreas.Weingessel@ci.tuwien.ac.at>
    #   Maintainer: Andreas Weingessel <Andreas.Weingessel@ci.tuwien.ac.at>
    #   Description: This package contains routines and documentation for
    #       solving quadratic programming problems.
    #   License: GPL-2

    # Value of slove.QP():
    #   solution - vector containing the solution of the quadratic
    #       programming problem.
    #   value - scalar, the value of the quadratic function at the
    #       solution
    #   unconstrained.solution - vector containing the unconstrained
    #       minimizer of the quadratic function.
    #   iterations - vector of length 2, the first component contains
    #       the number of iterations the algorithm needed, the second
    #       indicates how often constraints became inactive after
    #       becoming active first. vector with the indices of the
    #       active constraints at the solution.

    # FUNCTION:

    # Optimize:
    optim <- try(quadprog::solve.QP(Dmat, dvec, Amat, bvec, meq), silent = TRUE)
    if (inherits(optim, "try-error")) {
        weights <- rep(0, length(dvec))
        optim <- list()
        status <- 1
    } else {
        # Set Tiny Weights to Zero:
        weights <- .checkWeights(optim$solution)
        attr(weights, "invest") = sum(weights)
        status <- 0
    }

    # Compose Output List:
    ans <- list(
        type = "MV",
        solver = "solveRquadprog",
        optim = optim,
        weights = weights,
        targetReturn = bvec[1],
        targetRisk = sqrt(weights %*% Dmat %*% weights)[[1, 1]],
        objective = sqrt(weights %*% Dmat %*% weights)[[1, 1]],
        status = status, 
        message = NA)

    # Return Value:
    ans
}


################################################################################