R 预期收益和收益时间序列的协方差
我试图模拟此处定义的MatlabR 预期收益和收益时间序列的协方差,r,matlab,portfolio,R,Matlab,Portfolio,我试图模拟此处定义的Matlabewstats函数: Matlab给出的结果如下: > ExpReturn = 1×2 0.1995 0.1002 > ExpCovariance = 2×2 0.0032 -0.0017 -0.0017 0.0010 我试图用Riskr包复制这个例子: 我使用的R代码是: library(RiskPortfolios) rets <- as.matrix(cbind(c(0.24, 0.15, 0.27, 0.14),
ewstats
函数:
Matlab给出的结果如下:
> ExpReturn = 1×2
0.1995 0.1002
> ExpCovariance = 2×2
0.0032 -0.0017
-0.0017 0.0010
我试图用Riskr包复制这个例子:
我使用的R代码是:
library(RiskPortfolios)
rets <- as.matrix(cbind(c(0.24, 0.15, 0.27, 0.14), c(0.08, 0.13, 0.06, 0.13)))
w <- 0.98
rets
w
meanEstimation(rets, control = list(type = 'ewma', lambda = w))
covEstimation(rets, control = list(type = 'ewma', lambda = w))
我错过什么了吗?
谢谢他们正在使用不同的算法。从RiskPortfolio手册:
ewma
。。。见RiskMetrics(1996年)
从Matlab hlp页面:
ewstats函数与RiskMetrics®方法之间没有关系,该方法用于确定收益时间序列的预期收益和协方差
不幸的是,Matlab没有告诉我们使用了哪种算法。如果使用
type=“lw”
,他们给出了相同的答案:
round(covEstimation(rets, control = list(type = 'lw')), 4)
## 0.0032 -0.0017
## -0.0017 0.0010
对于那些最终需要在R中使用等效的
ewstats
函数的人,这里是我编写的代码:
ewstats <- function(RetSeries, DecayFactor=NULL, WindowLength=NULL){
#EWSTATS Expected return and covariance from return time series.
# Optional exponential weighting emphasizes more recent data.
#
# [ExpReturn, ExpCovariance, NumEffObs] = ewstats(RetSeries, ...
# DecayFactor, WindowLength)
#
# Inputs:
# RetSeries : NUMOBS by NASSETS matrix of equally spaced incremental
# return observations. The first row is the oldest observation, and the
# last row is the most recent.
#
# DecayFactor : Controls how much less each observation is weighted than its
# successor. The k'th observation back in time has weight DecayFactor^k.
# DecayFactor must lie in the range: 0 < DecayFactor <= 1.
# The default is DecayFactor = 1, which is the equally weighted linear
# moving average Model (BIS).
#
# WindowLength: The number of recent observations used in
# the computation. The default is all NUMOBS observations.
#
# Outputs:
# ExpReturn : 1 by NASSETS estimated expected returns.
#
# ExpCovariance : NASSETS by NASSETS estimated covariance matrix.
#
# NumEffObs: The number of effective observations is given by the formula:
# NumEffObs = (1-DecayFactor^WindowLength)/(1-DecayFactor). Smaller
# DecayFactors or WindowLengths emphasize recent data more strongly, but
# use less of the available data set.
#
# The standard deviations of the asset return processes are given by:
# STDVec = sqrt(diag(ECov)). The correlation matrix is :
# CorrMat = VarMat./( STDVec*STDVec' )
#
# See also MEAN, COV, COV2CORR.
NumObs <- dim(RetSeries)[1]
NumSeries <- dim(RetSeries)[2]
# size the series and the window
if (is.null(WindowLength)) {
WindowLength <- NumObs
}
if (is.null(DecayFactor)) {
DecayFactor = 1
}
if (DecayFactor <= 0 | DecayFactor > 1) {
stop('Must have 0< decay factor <= 1.')
}
if (WindowLength > NumObs){
stop(sprintf('Window Length #d must be <= number of observations #d',
WindowLength, NumObs))
}
# ------------------------------------------------------------------------
# size the data to the window
RetSeries <- RetSeries[NumObs-WindowLength+1:NumObs, ]
# Calculate decay coefficients
DecayPowers <- seq(WindowLength-1, 0, by = -1)
VarWts <- sqrt(DecayFactor)^DecayPowers
RetWts <- (DecayFactor)^DecayPowers
NEff = sum(RetWts) # number of equivalent values in computation
# Compute the exponentially weighted mean return
WtSeries <- matrix(rep(RetWts, times = NumSeries),
nrow = length(RetWts), ncol = NumSeries) * RetSeries
ERet <- colSums(WtSeries)/NEff;
# Subtract the weighted mean from the original Series
CenteredSeries <- RetSeries - matrix(rep(ERet, each = WindowLength),
nrow = WindowLength, ncol = length(ERet))
# Compute the weighted variance
WtSeries <- matrix(rep(VarWts, times = NumSeries),
nrow = length(VarWts), ncol = NumSeries) * CenteredSeries
ECov <- t(WtSeries) %*% WtSeries / NEff
list(ExpReturn = ERet, ExpCovariance = ECov, NumEffObs = NEff)
}
ewstats我担心是这样的。我试着问这里使用的算法是什么:。但还是什么都没有。我想知道人们如何在不知道底层算法的情况下使用函数。奇怪的是“lw”方法不需要权重参数。ewstats函数使用它。这太奇怪了!
ewstats <- function(RetSeries, DecayFactor=NULL, WindowLength=NULL){
#EWSTATS Expected return and covariance from return time series.
# Optional exponential weighting emphasizes more recent data.
#
# [ExpReturn, ExpCovariance, NumEffObs] = ewstats(RetSeries, ...
# DecayFactor, WindowLength)
#
# Inputs:
# RetSeries : NUMOBS by NASSETS matrix of equally spaced incremental
# return observations. The first row is the oldest observation, and the
# last row is the most recent.
#
# DecayFactor : Controls how much less each observation is weighted than its
# successor. The k'th observation back in time has weight DecayFactor^k.
# DecayFactor must lie in the range: 0 < DecayFactor <= 1.
# The default is DecayFactor = 1, which is the equally weighted linear
# moving average Model (BIS).
#
# WindowLength: The number of recent observations used in
# the computation. The default is all NUMOBS observations.
#
# Outputs:
# ExpReturn : 1 by NASSETS estimated expected returns.
#
# ExpCovariance : NASSETS by NASSETS estimated covariance matrix.
#
# NumEffObs: The number of effective observations is given by the formula:
# NumEffObs = (1-DecayFactor^WindowLength)/(1-DecayFactor). Smaller
# DecayFactors or WindowLengths emphasize recent data more strongly, but
# use less of the available data set.
#
# The standard deviations of the asset return processes are given by:
# STDVec = sqrt(diag(ECov)). The correlation matrix is :
# CorrMat = VarMat./( STDVec*STDVec' )
#
# See also MEAN, COV, COV2CORR.
NumObs <- dim(RetSeries)[1]
NumSeries <- dim(RetSeries)[2]
# size the series and the window
if (is.null(WindowLength)) {
WindowLength <- NumObs
}
if (is.null(DecayFactor)) {
DecayFactor = 1
}
if (DecayFactor <= 0 | DecayFactor > 1) {
stop('Must have 0< decay factor <= 1.')
}
if (WindowLength > NumObs){
stop(sprintf('Window Length #d must be <= number of observations #d',
WindowLength, NumObs))
}
# ------------------------------------------------------------------------
# size the data to the window
RetSeries <- RetSeries[NumObs-WindowLength+1:NumObs, ]
# Calculate decay coefficients
DecayPowers <- seq(WindowLength-1, 0, by = -1)
VarWts <- sqrt(DecayFactor)^DecayPowers
RetWts <- (DecayFactor)^DecayPowers
NEff = sum(RetWts) # number of equivalent values in computation
# Compute the exponentially weighted mean return
WtSeries <- matrix(rep(RetWts, times = NumSeries),
nrow = length(RetWts), ncol = NumSeries) * RetSeries
ERet <- colSums(WtSeries)/NEff;
# Subtract the weighted mean from the original Series
CenteredSeries <- RetSeries - matrix(rep(ERet, each = WindowLength),
nrow = WindowLength, ncol = length(ERet))
# Compute the weighted variance
WtSeries <- matrix(rep(VarWts, times = NumSeries),
nrow = length(VarWts), ncol = NumSeries) * CenteredSeries
ECov <- t(WtSeries) %*% WtSeries / NEff
list(ExpReturn = ERet, ExpCovariance = ECov, NumEffObs = NEff)
}