# 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: RETURN ADJUSTED DOWNSIDE RISK MEASURES:
# MS2Sortino Returns the M2 Sortino ratio
# omegaExcessReturn Returns the annualised M2 Omega excess return
# hurstIndex Returns the Hurst Index
################################################################################
MS2Sortino <-
function(periodPercentReturns, targetReturn = 0,
method = c("geometric", "arithmetic"),
scale = c("quarterly", "monthly", "weekly", "daily"))
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns the M2 Sortino ratio
# Example:
# MS2Sortino(R, 0, "g", "m"); MS2Sortino(R, 0, "a", "m")
# FUNCTION:
# Check Arguments:
stopifnot(isUnivariate(periodPercentReturns))
method = match.arg(method)
Scale = .scale(match.arg(scale))
# Data:
R = periodPercentReturns
targetReturn = targetReturn * Scale
Return = annualisedReturn(R, method, scale) - targetReturn
Risk = NA
# M2 for Sortino
# MS2 = rp + SortinoRatio * (SigmaDM - SigmaD)
# Result:
ans = Return / Risk
names(ans) = "M2 Sortino Ratio"
# Return Value:
ans
}
# ------------------------------------------------------------------------------
omegaExcessReturn <-
function(periodPercentReturns, targetReturn = 0,
method = c("geometric", "arithmetic"),
scale = c("quarterly", "monthly", "weekly", "daily"))
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns the annualised M2 Omega excess return
# Example:
# omegaExcessReturn(R, 0, "g", "m")
# omegaExcessReturn(R, 0, "a", "m")
# FUNCTION:
# Check Arguments:
stopifnot(isUnivariate(periodPercentReturns))
method = match.arg(method)
Scale = .scale(match.arg(scale))
# Data:
R = periodPercentReturns
targetReturn = targetReturn * Scale
Return = annualisedReturn(R, method, scale) - targetReturn
Risk = NA
# StyleBeta = SigmaD / SigmaMD
# DownsideRiskAdjustedStyleBemchmark = 3 * StyleBeta * sigmaMD^2
# OmegaExcessReturn = rp - DownsideRiskAdjustedStyleBemchmark
# Result:
ans = Return / Risk
names(ans) = "Omega Excess Return"
# Return Value:
ans
}
# ------------------------------------------------------------------------------
.hurstIndex <-
function(periodPercentReturns, targetReturn = 0,
method = c("geometric", "arithmetic"),
scale = c("quarterly", "monthly", "weekly", "daily"))
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns the Hurst Index
# Example:
# .hurstIndex(R, 0, "g", "m")
# .hurstIndex(R, 0, "a", "m")
# FUNCTION:
# Check Arguments:
stopifnot(isUnivariate(periodPercentReturns))
method = match.arg(method)
Scale = .scale(match.arg(scale))
# Data:
R = periodPercentReturns
targetReturn = targetReturn * Scale
Return = annualisedReturn(R, method, scale) - targetReturn
Risk = NA
# Result:
ans = Return / Risk
names(ans) = "Hurst Index"
# Return Value:
ans
}
################################################################################
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