# 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: VALUE AT RISK MEASURES:
# normalVaR Returns normal VaR
# normalVaRRatio Returns normal VaR ratio
# normalRewardToVaR Returns annualised normal reward to VaR ratio
# conditionalVaR Returns unnualised conditional VaR
# conditionalSharpeRatio Returns conditional VaR Sharpe ratio
# modifiedVaR Returns annualised Cornish-Fishers modified VaR
# modSharpeRatio Returns annualised modified Sharpe ratio
################################################################################
normalVaR <-
function(periodPercentReturns, probability = 0.95)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns normal VaR
# Example:
# normalVaR(R)
# FUNCTION:
# Check Arguments:
stopifnot(isUnivariate(periodPercentReturns))
# Data:
R = periodPercentReturns
# Result:
ans = mean(R) - qnorm(probability) * nVariance(R)
names(ans) = paste(probability, "normal VaR")
# Return Value:
ans
}
# ------------------------------------------------------------------------------
normalVaRRatio <-
function(periodPercentReturns, probability = 0.95, nAssets = 1)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns normal VaR ratio
# Example:
# normalVaRRatio(R)
# FUNCTION:
# Check Arguments:
stopifnot(isUnivariate(periodPercentReturns))
# Data:
R = periodPercentReturns
normalVaR = normalVaR(R, probability)
# Result:
ans = normalVaR / nAssets
names(ans) = paste(probability, "normal VaR Ratio")
# Return Value:
ans
}
# ------------------------------------------------------------------------------
normalRewardToVaR <-
function(periodPercentReturns, targetReturn = 0, probability = 0.95,
method = c("geometric", "arithmetic"),
scale = c("quarterly", "monthly", "weekly", "daily"), nAssets = 1)
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns annualised normal reward to VaR ratio
# Example:
# normalRewardToVaR(R, 0, 0.95, "g", "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 = normalVaRRatio(R, probability)
# Result:
ans = Return / Risk
names(ans) = paste(probability, "Normal Reward to VaR")
# Return Value:
ans
}
# ------------------------------------------------------------------------------
conditionalVaRRatio <-
function(periodPercentReturns, targetReturn = 0, probability = 0.95,
method = c("geometric", "arithmetic"),
scale = c("quarterly", "monthly", "weekly", "daily"))
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns unnualised conditional VaR
# Example:
# conditionalVaRRatio(R, 0, "g", "m"); conditionalVaRRatio(R, 0, "a", "m")
# FUNCTION:
# Check Arguments:
stopifnot(isUnivariate(periodPercentReturns))
method = match.arg(method)
Scale = .scale(match.arg(scale))
# Data:
R = periodPercentReturns
Return = annualisedReturn(R, method, scale) - targetReturn * Scale
Risk =
# Result:
ans = Return / Risk
names(ans) = "Conditional VaR Ratio"
# Return Value:
ans
}
# ------------------------------------------------------------------------------
conditionalSharpeRatio <-
function(periodPercentReturns, targetReturn = 0, probability = 0.95,
method = c("geometric", "arithmetic"),
scale = c("quarterly", "monthly", "weekly", "daily"))
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns conditional VaR Sharpe Ratio
# Example:
# conditionalSharpeRatio(R, 0, "g", "m"); conditionalSharpeRatio(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 =
# (rp-rf) / conditionalVaR
# Result:
ans = Return / Risk
names(ans) = "Conditional Sharpe Ratio"
# Return Value:
ans
}
# ------------------------------------------------------------------------------
modifiedVaR <-
function(periodPercentReturns, targetReturn = 0, probability = 0.95,
method = c("geometric", "arithmetic"),
scale = c("quarterly", "monthly", "weekly", "daily"))
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns annualised Cornish-Fishers modified VaR
# Example:
# modifiedVaR(R, 0, 0.95, "g", "m"); modifiedVaR(R, 0, 0.95, "a", "m")
# FUNCTION:
# Check Arguments:
stopifnot(isUnivariate(periodPercentReturns))
method = match.arg(method)
Scale = .scale(match.arg(scale))
# Data:
R = periodPercentReturns
M = mean(R)
S = nSkewness(R)
KE = excessKurtosis(R)
V = nVariance(R)
zc = -qnorm(probability)
Return = annualisedReturn(R, method, scale) - targetReturn
Risk = M + V *
( zc + ((zc^2-1)/6)*S + ((zc^3-3*zc)/24)*KE - ((2*zc^3-5*zc)/36) * S^2 )
# Result:
ans = Return / Risk
names(ans) = "Cornish Fischer VaR"
# Return Value:
ans
}
# ------------------------------------------------------------------------------
modSharpeRatio <-
function(periodPercentReturns, targetReturn = 0, probability = 0.95,
method = c("geometric", "arithmetic"),
scale = c("quarterly", "monthly", "weekly", "daily"))
{
# A function implemented by Diethelm Wuertz
# Description:
# Returns annualised modified Sharpe ratio
# Example:
# modSharpeRatio(R, 0, 0.95, "g", "m"); modSharpeRatio(R, 0, 0.95, "a", "m")
# FUNCTION:
# Check Arguments:
stopifnot(isUnivariate(periodPercentReturns))
method = match.arg(method)
Scale = .scale(match.arg(scale))
# Data:
R = periodPercentReturns
Return = annualisedReturn(R, method, scale) - targetReturn * Scale
Risk = modifiedVaR(R, targetReturn, probability, method, scale)
# Result:
ans = Return / Risk
names(ans) = "Modified Sharpe Ratio"
# Return Value:
ans
}
################################################################################
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.