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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 PURPOSE. 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:
# assetsLPM Computes asymmetric lower partial moments
# assetsSLPM Computes symmetric lower partial moments
################################################################################
assetsLPM <-
function(x, tau=colMeans(x), a=1.5, ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Computes LPM and CLPM from multivariate time series
# Arguments:
# x - a multivariate time series, a data frame, or any other
# rectangular object of assets which can be converted into
# a matrix by the function 'as.matrix'. Optional Dates are
# rownames, instrument names are column names.
# References:
# Nawrocki 1991, Optimal Algorithms and Lower Partial Moment:
# Ex-Post Results
# Lee 2006, The Strengths and Limitations of Risk Measures in
# Real Estate: A Review
# Note:
# The output of this function can be used for portfolio
# optimization. LPM stands for lower partial moments.
# Example:
# LPP <- as.timeSeries(data(LPP2005REC))[, 1:6]; assetsLPM(LPP)
# FUNCTION:
# Transform Input:
x.mat <- as.matrix(x)
nCol <- ncol(x)
nRow <- nrow(x)
Tau <- matrix(rep(tau, nRow), byrow = TRUE, ncol = nCol)
TauX <- Tau-x
X.max <- ((TauX) + abs(TauX))/2
# Compute Lower Partial Moments:
LPM <- colMeans(X.max^a)
# Compute co-LPMs:
CLPM <- diag(0, nCol)
if (a > 1) {
for (i in 1:nCol) {
for (j in 1:nCol) {
CLPM[i, j] <- mean( (X.max[, i])^(a-1) * TauX[, j] )
}
CLPM[i, i] <- LPM[i]
}
} else if (a == 1) {
for (i in 1:nCol) {
for (j in 1:nCol) {
CLPM[i, j] <- mean( sign( X.max[, i]) * TauX[, j] )
}
CLPM[i, i] <- LPM[i]
}
}
# Result:
ans <- list(mu = LPM, Sigma = CLPM)
attr(ans, "control") <- c(a = a, tau = tau)
# Return Value:
ans
}
################################################################################
assetsSLPM <-
function(x, tau=colMeans(x), a=1.5, ...)
{
# A function implemented by Diethelm Wuertz
# Description:
# Computes LPM and SLPM from multivariate time series
# Arguments:
# x - a multivariate time series, a data frame, or any other
# rectangular object of assets which can be converted into
# a matrix by the function 'as.matrix'. Optional Dates are
# rownames, instrument names are column names.
# References:
# Nawrocki 1991, Optimal Algorithms and Lower Partial Moment:
# Ex-Post Results
# Lee 2006, The Strengths and Limitations of Risk Measures in
# Real Estate: A Review
# Note:
# The output of this function can be used for portfolio
# optimization. SLPM stands for symmetric lower partial moments.
# Example:
# LPP = as.timeSeries(data(LPP2005REC))[, 1:6]; assetsSLPM(LPP)
# FUNCTION:
# Transform Input:
x.mat <- as.matrix(x)
nCol <- ncol(x)
nRow <- nrow(x)
Tau <- matrix(rep(tau, nRow), byrow = TRUE, ncol = nCol)
TauX <- Tau-x
X.max <- ((TauX) + abs(TauX))/2
# Compute Lower Partial Moments:
LPM <- colMeans(X.max^a)
# Compute co-SLPMs:
SLPM <- LPM^(1/a) %o% LPM^(1/a) * cor(x.mat)
# Result:
ans <- list(mu = LPM, Sigma = SLPM)
attr(ans, "control") <- c(a = a, tau = tau)
# Return Value:
ans
}
################################################################################
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