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# 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:
# .solveRtwoAssets Two Assets LongOnly MV Portfolio
# .cvarSolveTwoAssets Two Assets LongOnly CVaR Portfolio
# .madSolveTwoAssets Two Assets LongOnly MAD Portfolio
################################################################################
.solveRtwoAssets <-
function(data, spec, constraints)
{
# Description:
# Two Assets LongOnly MV Portfolio
# Details:
# ... this is only thohgt for 'unlimited' LongOnly
# box and group constraints are discarded here.
# FUNCTION:
# Solver:
# print(".mvSolveTwoAssets")
# Convert Data and Constraints to S4 Objects:
Data = portfolioData(data, spec)
data <- getSeries(Data)
Constraints = portfolioConstraints(Data, spec, constraints)
# Stop if the Target Return is not Defined!
targetReturn = getTargetReturn(spec)
stopifnot(is.numeric(targetReturn))
# Optimize Portfolio:
nAssets = getNAssets(Data)
# Solve the two Assets Case Analytically:
mu <- getMu(Data)
Sigma <- getSigma(Data)
stopifnot(targetReturn >= min(mu))
stopifnot(targetReturn <= max(mu))
weights <- (targetReturn-mu[2]) / (mu[1]-mu[2])
weights <- c(weights, 1 - weights)
# Output List:
ans = list(
solver = "MVTwoAssets",
optim = NA,
weights = weights,
targetReturn = targetReturn,
targetRisk = NA,
objective = sqrt(weights %*% Sigma %*% weights),
status = 0,
message = NA)
# Return Value:
ans
}
# ------------------------------------------------------------------------------
.cvarSolveTwoAssets <-
function(data, spec, constraints)
{
# Description:
# Two Assets LongOnly CVaR Portfolio
# Details:
# ... this is only thohgt for 'unlimited' LongOnly
# box and group constraints are discarded here.
# FUNCTION:
# Solver:
# print(".cvarSolveTwoAssets")
# Convert Data and Constraints to S4 Objects:
Data <- portfolioData(data, spec)
data <- getSeries(Data)
Constraints = portfolioConstraints(Data, spec, constraints)
# Stop if the Target Return is not Defined!
targetReturn = getTargetReturn(spec)
stopifnot(is.numeric(targetReturn))
targetAlpha = getAlpha(spec)
# Optimize Portfolio:
nAssets <- getNAssets(Data)
# Solve the two Assets Case Analytically:
mu <- getMu(Data)
stopifnot(targetReturn >= min(mu))
stopifnot(targetReturn <= max(mu))
weights <- (targetReturn-mu[2]) / (mu[1]-mu[2])
weights <- c(weights, 1 - weights)
optim <- list(
VaR = .varRisk(data, weights, targetAlpha),
CVaR = -.cvarRisk(data, weights, targetAlpha),
targetAlpha = targetAlpha)
ans <- list(
solver = "CVaRTwoAssets",
optim = optim,
weights = weights,
targetReturn = targetReturn,
targetRisk = NA,
objective = optim$CVaR,
status = 0,
message = NA)
# Return Value:
ans
}
# ------------------------------------------------------------------------------
.madSolveTwoAssets <-
function(data, spec, constraints)
{
# Description:
# Two Assets LongOnly MAD Portfolio
# Details:
# ... this is only thohgt for 'unlimited' LongOnly
# box and group constraints are discarded here.
# FUNCTION:
# Convert Data and Constraints to S4 Objects:
Data = portfolioData(data, spec)
data <- getSeries(Data)
Constraints <- portfolioConstraints(Data, spec, constraints)
# Stop if the Target Return is not Defined!
targetReturn <- getTargetReturn(spec)
stopifnot(is.numeric(targetReturn))
# Optimize Portfolio:
nAssets <- getNAssets(Data)
# Solve the two Assets Case Analytically:
mu = getMu(Data)
stopifnot(targetReturn >= min(mu))
stopifnot(targetReturn <= max(mu))
weights = (targetReturn-mu[2]) / (mu[1]-mu[2])
weights = c(weights, 1 - weights)
targetRisk = mean( abs( (data - colMeans(data)) %*% weights ) )
# Output List:
ans = list(
solver = "MADTwoAssets",
optim = NA,
weights = weights,
targetReturn = targetReturn,
targetRisk = targetRisk,
objective = targetRisk,
status = 0,
message = NA)
# Return Value:
ans
}
################################################################################
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