R/CVaRMultiNTS.R
In aaron9011/temStaR-v0.814: Tempered Stable Distribution
Defines functions
setPortfolioParam
cvarGauss
mctCVaRnts
mctCVaRmnts
mctVaRnts
mctVaRmnts
dCVaR_numint
integrand_dCVaRstdNTS
psi_stdNTS
dinvCdf_stdNTS
dBeta
mctStdDev
portfolioCVaRmnts
portfolioVaRmnts
getPortNTSParam
Documented in
cvarGauss
dBeta
dCVaR_numint
dinvCdf_stdNTS
getPortNTSParam
mctCVaRmnts
mctCVaRnts
mctStdDev
mctVaRmnts
mctVaRnts
portfolioCVaRmnts
portfolioVaRmnts
setPortfolioParam
#' @export
#' @title getPortNTSParam
#' @description Portfolio return with capital allocation weight is \eqn{R_p=<w,r>},
#' which is a weighted sum of of elements in the N-dimensional NTS random vector.
#' \eqn{R_p} becomes an 1-dimensional NTS random variable.
#' \code{getPortNTSParam} find the parameters of \eqn{R_p}.
#'
#' @param strPMNTS Structure of parameters for the n-dimensional NTS distribution.
#'
#' \code{strPMNTS$ndim} : dimension
#'
#' \code{strPMNTS$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{strPMNTS$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{strPMNTS$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{strPMNTS$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{strPMNTS$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{res$Rho} : \eqn{\rho} matrix (Correlation) of the std NTS distribution (X).
#'
#' \code{res$Sigma} : Covariance \eqn{\Sigma} matrix of return data \eqn{r}.
#'
#' @param w Capital allocation weight vector.
#' @param stdform If \code{stdform} is \code{FALSE}, then the return parameter has the following representation
#'
#' \eqn{R_p = <w, r> = \mu + diag(\sigma) X},
#'
#' where
#'
#' \eqn{X} follows \eqn{stdNTS_1(\alpha, \theta, \beta, 1)}.
#'
#' If \code{stdform} is \code{TRUE}, then the return parameter has the following representation
#'
#' \eqn{R_p = <w, r>} follows \eqn{NTS_1(\alpha, \theta, \beta, \gamma, \mu, 1)}
#'
#' @usage
#' \code{res <- setPortfolioParam(strPMNTS,w)}
#' \code{res <- setPortfolioParam(strPMNTS,w, FALSE)}
#'
#' @return The weighted sum follows 1-dimensional NTS.
#'
#' \eqn{R_p = <w, r> = \mu + diag(\sigma) X},
#'
#' where
#'
#' \eqn{X} follows \eqn{stdNTS_1(\alpha, \theta, \beta, 1)}.
#'
#' Hence we obtain
#'
#' \code{res$mu} : \eqn{\mu} mean of \eqn{R_p}.
#'
#' \code{res$sigma} : \eqn{\sigma} standard deviation of \eqn{R_p}.
#'
#' \code{res$alpha} : \eqn{\alpha} of \eqn{X}.
#'
#' \code{res$theta} : \eqn{\theta} of \eqn{X}.
#'
#' \code{res$beta} : \eqn{\beta} of \eqn{X}.
#'
#' @references
#' Proposition 2.1 of
#' Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk
#' \url{https://arxiv.org/pdf/2007.13972.pdf}
#'
#' @examples
#' library("temStaR")
#' strPMNTS <- list(ndim = 2,
#' mu = c( 9.876552e-05, 4.747343e-04 ),
#' sigma = c( 0.01620588, 0.02309643 ),
#' alpha = 0.1888129 ,
#' theta = 0.523042,
#' beta = c( -0.04632938, 0.04063555 ),
#' Rho = matrix( data = c(1.0, 0.469883,
#' 0.469883, 1.0),
#' nrow = 2, ncol = 2)
#' CovMtx = matrix( data = c(0.0002626304, 0.0001740779,
#' 0.0001740779, 0.0005334452),
#' nrow = 2, ncol = 2)
#' )
#' w <- c(0.3, 0.7)
#' res <- getPortNTSParam(strPMNTS,w)
#'
getPortNTSParam <- function(strPMNTS, w, stdform = TRUE){
if(strPMNTS$ndim != length(w)){
print("The dimension of the weight vector must be the same as strPMNTS$ndim")
return(NULL)
}
w <- matrix(data = w, nrow = strPMNTS$ndim, ncol = 1)
sigmaBar <- as.numeric(sqrt(t(w)%*%strPMNTS$CovMtx%*%w))
mbar <- sum(w*strPMNTS$mu)
betbar <- sum(w*strPMNTS$sigma*strPMNTS$beta)/sigmaBar
stdntsparam <- c(as.numeric(strPMNTS$alpha), as.numeric(strPMNTS$theta), betbar)
names(stdntsparam) <- c("alpha", "theta", "beta")
param <- list(stdparam = stdntsparam, mu = mbar, sig = sigmaBar)
if (stdform == FALSE){
param <- change_stdntsparam2ntsparam(param$stdparam, mbar, sigmaBar)
param <- param[1:5]
}
return(param)
}
#' @export
#' @title portfolioVaRmnts
#' @description
#' Calculate portfolio value at risk on the NTS market model
#'
#' @param strPMNTS Structure of parameters for the n-dimensional NTS distribution.
#'
#' \code{strPMNTS$ndim} : dimension
#'
#' \code{strPMNTS$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{strPMNTS$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{strPMNTS$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{strPMNTS$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{strPMNTS$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{res$Rho} : \eqn{\rho} matrix (Correlation) of the std NTS distribution (X).
#'
#' \code{res$Sigma} : Covariance \eqn{\Sigma} matrix of return data \eqn{r}.
#'
#' @param w Capital allocation weight vector.
#' @param eta significanlt level
#' @return portfolio value at risk on the NTS market model
#'
portfolioVaRmnts <- function(strPMNTS, w, eta){
if(strPMNTS$ndim != length(w)){
print("The dimension of the weight vector must be the same as strPMNTS$ndim")
return(NULL)
}
ntsparam <- getPortNTSParam(strPMNTS, w)
VaR <- (- ntsparam$mu - ntsparam$sig * qnts(eta, ntsparam$stdparam))
return(VaR)
}
#' @export
#' @title portfolioCVaRmnts
#' @description
#' Calculate portfolio conditional value at risk (expected shortfall) on the NTS market model
#'
#' @param strPMNTS Structure of parameters for the n-dimensional NTS distribution.
#'
#' \code{strPMNTS$ndim} : dimension
#'
#' \code{strPMNTS$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{strPMNTS$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{strPMNTS$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{strPMNTS$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{strPMNTS$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{res$Rho} : \eqn{\rho} matrix (Correlation) of the std NTS distribution (X).
#'
#' \code{res$Sigma} : Covariance \eqn{\Sigma} matrix of return data \eqn{r}.
#'
#' @param w Capital allocation weight vector.
#' @param eta significanlt level
#' @return portfolio value at risk on the NTS market model
#'
portfolioCVaRmnts <- function(strPMNTS, w, eta){
if(strPMNTS$ndim != length(w)){
print("The dimension of the weight vector must be the same as strPMNTS$ndim")
return(NULL)
}
ntsparam <- getPortNTSParam(strPMNTS, w)
CVaR <- (- ntsparam$mu + ntsparam$sig * cvarnts(eta, ntsparam$stdparam))
return(CVaR)
}
#' @export
#' @title mctStdDev
#' @description
#' Morginal contribution to Risk for Standard Deviation.
#'
#' @param n The targer stock to calculate the mctCVaR
#' @param w The capital allocation rate vector for the current portfolio
#' @param CovMtx Covariance matrix of return data.
#'
mctStdDev <- function(n, w, covMtx){
sig <- sqrt(w%*%covMtx%*%t(w))
return( w%*%covMtx[,n]/sig )
}
#' @export
#' @title dBeta
#' @description
#' The first derivative of the beta.
#' Developer's version.
#'
dBeta <- function(n, w, betaArray, covMtx){
barsig <- sqrt(w%*%covMtx%*%t(w))
barBeta <- sum(w*betaArray)
mctsd <- mctStdDev(n, w, covMtx)
sig <- sqrt(covMtx[n,n])
#db <- w[n]*sig*betaArray[n]/(barsig^2)-(barBeta/barsig)*mctsd
db <- sig*betaArray[n]/barsig-(barBeta/barsig)*mctsd
return( db )
}
#' @export
#' @title dinvCdf_stdNTS
#' @description
#' The first derivative of inverse CDF for the beta parameter of the stdNTS.
#' Developer's version.
#'
dinvCdf_stdNTS <- function(eta, alpha, theta, beta){
h <- abs(beta)*(0.0001)
Fu <- ipnts(eta, ntsparam = c(alpha, theta, beta+h))
Fd <- ipnts(eta, ntsparam = c(alpha, theta, beta-h))
return( (Fu-Fd)/(2*h) )
}
psi_stdNTS <- function( z, a, th, b ){
sz <- (2-a)/(2*th)
return(-1i*z+(1-1i*z*b/th+(1-b^2*sz)*z^2/(2*th))^(a/2-1)*(1i*z+b*sz*z^2))
}
integrand_dCVaRstdNTS <- function( u, eta, alpha, theta, beta, rho = 0.0001 ){
param <- c(alpha, theta, beta)
Finv <- ipnts(eta, param)
dFinv <- dinvCdf_stdNTS(eta, alpha, theta, beta)
res <- (exp((1i*u+rho)*Finv)*chf_stdNTS(-u+rho*1i, param)/(rho*1i-u)^2)
res <- res*((rho+1i*u)*dFinv+psi_stdNTS(-u+1i*rho, alpha, theta, beta))
return(res)
}
#' @export
#' @title dCVaR_numint
#' @description
#' The first derivative of CVaR for the beta parameter of the stdNTS.
#' Developer's version.
#'
dCVaR_numint <- function( eta, alpha, theta, beta, N = 200, rho = 0.1 ){
dFinv <- dinvCdf_stdNTS(eta, alpha, theta, beta)
f <- Re(pracma::integral(functional::Curry(integrand_dCVaRstdNTS,
eta = eta,
alpha = alpha,
theta = theta,
beta = beta,
rho = rho),
0, N))
dcvar <- -dFinv-f/(pi*eta)
return( dcvar )
}
#' @export
#' @title mctVaRmnts
#' @description Calculate the marginal contribution to VaR for the multivariate NTS market model:
#' the random vector \eqn{r} is
#'
#' \eqn{r = \mu + diag(\sigma) X}
#'
#' where
#'
#' \eqn{X} follows \eqn{stdNTS_N(\alpha, \theta, \beta, \Sigma)}
#'
#' @usage
#' \code{mctVaRmnts(eta, n, w, st)}
#'
#' @param eta Significant level of CVaR.
#' @param n The targer stock to calculate the mctCVaR
#' @param w The capital allocation rate vector for the current portfolio
#' @param st Structure of parameters for the N-dimensional NTS distribution.
#'
#' \code{st$ndim} : Dimension of the model. Here \code{st$ndim=N}.
#'
#' \code{st$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{st$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{st$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{st$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{st$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{st$Rho} : \eqn{\rho} matrix of the std NTS distribution (X),
#' which is correlation matrix of epsilon.
#'
#' \code{st$CovMtx} : Covariance matrix of return data \eqn{r}.
#'
#' @references
#' Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk
#' \url{https://arxiv.org/pdf/2007.13972.pdf}
#'
#' @examples
#' library(functional)
#' library(nloptr)
#' library(pracma)
#' library(spatstat)
#' library(Matrix)
#' library(quantmod)
#' library(mvtnorm)
#' library("temStaR")
#'
#' #Fix alpha and theta.
#' #Estimate alpha dna theta from DJIA and use those parameter for IBM, INTL parameter fit.
#' getSymbols("^DJI", src="yahoo", from = "2020-8-25", to = "2020-08-31")
#' prDJ <- as.numeric(DJI$DJI.Adjusted)
#' ret <- diff(log(prDJ))
#' ntsparam <- fitnts(ret)
#' getSymbols("IBM", src="yahoo", from = "2016-1-1", to = "2020-08-31")
#' pr1 <- as.numeric(IBM$IBM.Adjusted)
#' getSymbols("INTL", src="yahoo", from = "2016-1-1", to = "2020-08-31")
#' pr2 <- as.numeric(INTL$INTL.Adjusted)
#'
#' returndata <- matrix(data = c(diff(log(pr1)),diff(log(pr2))),
#' ncol = 2, nrow = (length(pr1)-1))
#' st <- fitmnts( returndata = returndata,
#' n = 2,
#' alphaNtheta = c(ntsparam["alpha"], ntsparam["theta"]) )
#' w <- c(0.3, 0.7)
#' eta <- 0.01
#'
#' mctVaRmnts(eta, 1, w, st) #MCT-VaR for IBM
#' mctVaRmnts(eta, 2, w, st) #MCT-VaR for INTL
#'
#' mctCVaRmnts(eta, 1, w, st) #MCT-CVaR for IBM
#' mctCVaRmnts(eta, 2, w, st) #MCT-CVaR for INTL
#'
mctVaRmnts <- function(eta, n, w, st, icdf = NULL, dicdf = NULL ){
return(as.numeric(
mctVaRnts(eta=eta,
n = n,
w = matrix(data = w, nrow = 1, ncol = st$ndim),
covMtx = st$CovMtx,
alpha = st$alpha,
theta = st$theta,
betaArray = matrix(data = st$beta, nrow = 1, ncol = st$ndim),
muArray = matrix(data = st$mu, nrow = 1, ncol = st$ndim),
icdf = icdf,
dicdf = dicdf)
)
)
}
#' @export
#' @title mctVaRnts
#' @description
#' Calculate the marginal contribution to VaR for the multivariate NTS market model.
#' Developer's version.
#'
mctVaRnts <- function(eta, n, w, covMtx, alpha, theta, betaArray, muArray, icdf = NULL, dicdf = NULL ){
barsig <- sqrt(w%*%covMtx%*%t(w))
mcts <- mctStdDev(n, w, covMtx)
db <- dBeta(n, w, betaArray, covMtx)
barBeta <- sum(w*betaArray)
if( is.null(icdf) ) icdf <- ipnts(eta, ntsparam = c(alpha, theta, barBeta))
if( is.null(dicdf) ) dicdf <- dinvCdf_stdNTS(eta, alpha, theta, barBeta)
return(-muArray[n] - icdf*mcts - barsig*db*dicdf )
}
#' @export
#' @title mctCVaRmnts
#' @description Calculate the marginal contribution to CVaR for the multivariate NTS market model:
#' the random vector \eqn{r} is
#'
#' \eqn{r = \mu + diag(\sigma) X}
#'
#' where
#'
#' \eqn{X} follows \eqn{stdNTS_N(\alpha, \theta, \beta, \Sigma)}
#'
#' @usage
#' \code{mctCVaRmnts(eta, n, w, st)}
#'
#' @param eta Significant level of CVaR.
#' @param n The targer stock to calculate the mctCVaR
#' @param w The capital allocation rate vector for the current portfolio
#' @param st Structure of parameters for the N-dimensional NTS distribution.
#'
#' \code{st$ndim} : Dimension of the model. Here \code{st$ndim=N}.
#'
#' \code{st$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{st$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{st$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{st$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{st$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{st$Rho} : \eqn{\rho} matrix of the std NTS distribution (X),
#' which is correlation matrix of epsilon.
#'
#' \code{st$CovMtx} : Covariance matrix of return data \eqn{r}.
#'
#' @references
#' Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk
#' \url{https://arxiv.org/pdf/2007.13972.pdf}
#'
#' @examples
#' library(functional)
#' library(nloptr)
#' library(pracma)
#' library(spatstat)
#' library(Matrix)
#' library(quantmod)
#' library(mvtnorm)
#' library("temStaR")
#'
#' #Fix alpha and theta.
#' #Estimate alpha dna theta from DJIA and use those parameter for IBM, INTL parameter fit.
#' getSymbols("^DJI", src="yahoo", from = "2020-8-25", to = "2020-08-31")
#' prDJ <- as.numeric(DJI$DJI.Adjusted)
#' ret <- diff(log(prDJ))
#' ntsparam <- fitnts(ret)
#' getSymbols("IBM", src="yahoo", from = "2016-1-1", to = "2020-08-31")
#' pr1 <- as.numeric(IBM$IBM.Adjusted)
#' getSymbols("INTL", src="yahoo", from = "2016-1-1", to = "2020-08-31")
#' pr2 <- as.numeric(INTL$INTL.Adjusted)
#'
#' returndata <- matrix(data = c(diff(log(pr1)),diff(log(pr2))),
#' ncol = 2, nrow = (length(pr1)-1))
#' st <- fitmnts( returndata = returndata,
#' n = 2,
#' alphaNtheta = c(ntsparam["alpha"], ntsparam["theta"]) )
#' w <- c(0.3, 0.7)
#' eta <- 0.01
#'
#' mctVaRmnts(eta, 1, w, st) #MCT-VaR for IBM
#' mctVaRmnts(eta, 2, w, st) #MCT-VaR for INTL
#'
#' mctCVaRmnts(eta, 1, w, st) #MCT-CVaR for IBM
#' mctCVaRmnts(eta, 2, w, st) #MCT-CVaR for INTL
#'
mctCVaRmnts <- function(eta, n, w, st, CVaR = NULL, dCVaR = NULL ){
return(as.numeric(
mctCVaRnts(eta=eta,
n = n,
w = matrix(data = w, ncol = st$ndim, nrow = 1),
covMtx = st$CovMtx,
alpha = st$alpha,
theta = st$theta,
betaArray = matrix(data = st$beta, ncol = st$ndim, nrow = 1),
muArray = matrix(data = st$mu, ncol = st$ndim, nrow = 1),
CVaR = CVaR,
dCVaR = dCVaR)
)
)
}
#' @export
#' @title mctCVaRnts
#' @description
#' Calculate the marginal contribution to CVaR for the multivariate NTS market model.
#' Developer's version.
#'
mctCVaRnts <- function(eta, n, w, covMtx, alpha, theta, betaArray, muArray, CVaR = NULL, dCVaR = NULL ){
barBeta <- sum(w*betaArray)
if( is.null(CVaR) ) CVaR <- cvarnts(eps = eta, ntsparam = c(alpha, theta, barBeta))
if( is.null(dCVaR) ) dCVaR <- dCVaR_numint(eta, alpha, theta, barBeta)
barsig <- sqrt(w%*%covMtx%*%t(w))
mcts <- mctStdDev(n, w, covMtx)
db <- dBeta(n, w, betaArray, covMtx)
return(-muArray[n] + CVaR*mcts + barsig*db*dCVaR )
}
#' @export
#' @title cvarGauss
#' @description
#' Calculate the CVaR for the normal distributed market model.
#' Developer's version.
#'
cvarGauss <- function( eta, mu = 0, sigma = 1){
#var = -qnorm(eta, mu, sigma)
stdK = qnorm(eta, 0, 1)
cvar = sigma/(eta*sqrt(2*pi))*exp(-stdK^2/2)-mu
return(cvar)
}
#' @title setPortfolioParam
#' @description Please use \code{getPortNTSParam} instead of \code{setPortfolioParam}.
#'
#' Portfolio return with capital allocation weight is \eqn{R_p=<w,r>},
#' which is a weighted sum of of elements in the N-dimensional NTS random vector.
#' \eqn{R_p} becomes an 1-dimensional NTS random variable.
#' \code{setPortfolioParam} find the parameters of \eqn{R_p}.
#'
#' @param strPMNTS Structure of parameters for the n-dimensional NTS distribution.
#'
#' \code{strPMNTS$ndim} : dimension
#'
#' \code{strPMNTS$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{strPMNTS$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{strPMNTS$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{strPMNTS$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{strPMNTS$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{strPMNTS$Rho} : \eqn{\Sigma} matrix of the std NTS distribution (X).
#'
#' @param w Capital allocation weight vector.
#'
#' @usage
#' \code{res <- setPortfolioParam(strPMNTS,w)}
#'
#' @return The weighted sum follows 1-dimensional NTS.
#'
#' \eqn{R_p = <w, r> = \mu + diag(\sigma) X},
#'
#' where
#'
#' \eqn{X} follows \eqn{stdNTS_1(\alpha, \theta, \beta, 1)}.
#'
#' Hence we obtain
#'
#' \code{res$mu} : \eqn{\mu} mean of \eqn{R_p}.
#'
#' \code{res$sigma} : \eqn{\sigma} standard deviation of \eqn{R_p}.
#'
#' \code{res$alpha} : \eqn{\alpha} of \eqn{X}.
#'
#' \code{res$theta} : \eqn{\theta} of \eqn{X}.
#'
#' \code{res$beta} : \eqn{\beta} \eqn{X}.
#'
#' @references
#' Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk
#' \url{https://arxiv.org/pdf/2007.13972.pdf}
#'
#' @examples
#' library("temStaR")
#' strPMNTS <- list(ndim = 2,
#' mu = c( 9.876552e-05, 4.747343e-04 ),
#' sigma = c( 0.01620588, 0.02309643 ),
#' alpha = 0.1888129 ,
#' theta = 0.523042,
#' beta = c( -0.04632938, 0.04063555 ),
#' Rho = matrix( data = c(1.0, 0.469883,
#' 0.469883, 1.0),
#' nrow = 2, ncol = 2)
#' CovMtx = matrix( data = c(0.0002626304, 0.0001740779,
#' 0.0001740779, 0.0005334452),
#' nrow = 2, ncol = 2)
#' )
#' w <- c(0.3, 0.7)
#' res <- setPortfolioParam(strPMNTS,w)
#'
setPortfolioParam <- function(strPMNTS, w){
if(strPMNTS$ndim != length(w)){
print("The dimension of the weight vector must be the same as strPMNTS$ndim")
return(NULL)
}
w <- matrix(data = w, nrow = strPMNTS$ndim, ncol = 1)
m <- sum(w*strPMNTS$mu)
b <- sum(w*strPMNTS$sigma*strPMNTS$beta)
gammaMtx <- diag(as.numeric(sqrt(1-strPMNTS$beta^2*(2-strPMNTS$alpha)/(2*strPMNTS$theta))))
sigMtx <- diag(as.numeric(strPMNTS$sigma))
g <- as.numeric(sqrt(t(w)%*%sigMtx%*%gammaMtx%*%strPMNTS$Rho%*%gammaMtx%*%sigMtx%*%w))
a <- as.numeric(strPMNTS$alpha)
th <- as.numeric(strPMNTS$theta)
param <- change_ntsparam2stdntsparam(c(a, th, b, g, m))
return(param)
}
aaron9011/temStaR-v0.814 documentation built on Dec. 24, 2021, 6:16 p.m.
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Defines functions setPortfolioParam cvarGauss mctCVaRnts mctCVaRmnts mctVaRnts mctVaRmnts dCVaR_numint integrand_dCVaRstdNTS psi_stdNTS dinvCdf_stdNTS dBeta mctStdDev portfolioCVaRmnts portfolioVaRmnts getPortNTSParam
Documented in cvarGauss dBeta dCVaR_numint dinvCdf_stdNTS getPortNTSParam mctCVaRmnts mctCVaRnts mctStdDev mctVaRmnts mctVaRnts portfolioCVaRmnts portfolioVaRmnts setPortfolioParam
#' @export
#' @title getPortNTSParam
#' @description Portfolio return with capital allocation weight is \eqn{R_p=<w,r>},
#' which is a weighted sum of of elements in the N-dimensional NTS random vector.
#' \eqn{R_p} becomes an 1-dimensional NTS random variable.
#' \code{getPortNTSParam} find the parameters of \eqn{R_p}.
#'
#' @param strPMNTS Structure of parameters for the n-dimensional NTS distribution.
#'
#' \code{strPMNTS$ndim} : dimension
#'
#' \code{strPMNTS$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{strPMNTS$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{strPMNTS$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{strPMNTS$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{strPMNTS$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{res$Rho} : \eqn{\rho} matrix (Correlation) of the std NTS distribution (X).
#'
#' \code{res$Sigma} : Covariance \eqn{\Sigma} matrix of return data \eqn{r}.
#'
#' @param w Capital allocation weight vector.
#' @param stdform If \code{stdform} is \code{FALSE}, then the return parameter has the following representation
#'
#' \eqn{R_p = <w, r> = \mu + diag(\sigma) X},
#'
#' where
#'
#' \eqn{X} follows \eqn{stdNTS_1(\alpha, \theta, \beta, 1)}.
#'
#' If \code{stdform} is \code{TRUE}, then the return parameter has the following representation
#'
#' \eqn{R_p = <w, r>} follows \eqn{NTS_1(\alpha, \theta, \beta, \gamma, \mu, 1)}
#'
#' @usage
#' \code{res <- setPortfolioParam(strPMNTS,w)}
#' \code{res <- setPortfolioParam(strPMNTS,w, FALSE)}
#'
#' @return The weighted sum follows 1-dimensional NTS.
#'
#' \eqn{R_p = <w, r> = \mu + diag(\sigma) X},
#'
#' where
#'
#' \eqn{X} follows \eqn{stdNTS_1(\alpha, \theta, \beta, 1)}.
#'
#' Hence we obtain
#'
#' \code{res$mu} : \eqn{\mu} mean of \eqn{R_p}.
#'
#' \code{res$sigma} : \eqn{\sigma} standard deviation of \eqn{R_p}.
#'
#' \code{res$alpha} : \eqn{\alpha} of \eqn{X}.
#'
#' \code{res$theta} : \eqn{\theta} of \eqn{X}.
#'
#' \code{res$beta} : \eqn{\beta} of \eqn{X}.
#'
#' @references
#' Proposition 2.1 of
#' Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk
#' \url{https://arxiv.org/pdf/2007.13972.pdf}
#'
#' @examples
#' library("temStaR")
#' strPMNTS <- list(ndim = 2,
#' mu = c( 9.876552e-05, 4.747343e-04 ),
#' sigma = c( 0.01620588, 0.02309643 ),
#' alpha = 0.1888129 ,
#' theta = 0.523042,
#' beta = c( -0.04632938, 0.04063555 ),
#' Rho = matrix( data = c(1.0, 0.469883,
#' 0.469883, 1.0),
#' nrow = 2, ncol = 2)
#' CovMtx = matrix( data = c(0.0002626304, 0.0001740779,
#' 0.0001740779, 0.0005334452),
#' nrow = 2, ncol = 2)
#' )
#' w <- c(0.3, 0.7)
#' res <- getPortNTSParam(strPMNTS,w)
#'
getPortNTSParam <- function(strPMNTS, w, stdform = TRUE){
if(strPMNTS$ndim != length(w)){
print("The dimension of the weight vector must be the same as strPMNTS$ndim")
return(NULL)
}
w <- matrix(data = w, nrow = strPMNTS$ndim, ncol = 1)
sigmaBar <- as.numeric(sqrt(t(w)%*%strPMNTS$CovMtx%*%w))
mbar <- sum(w*strPMNTS$mu)
betbar <- sum(w*strPMNTS$sigma*strPMNTS$beta)/sigmaBar
stdntsparam <- c(as.numeric(strPMNTS$alpha), as.numeric(strPMNTS$theta), betbar)
names(stdntsparam) <- c("alpha", "theta", "beta")
param <- list(stdparam = stdntsparam, mu = mbar, sig = sigmaBar)
if (stdform == FALSE){
param <- change_stdntsparam2ntsparam(param$stdparam, mbar, sigmaBar)
param <- param[1:5]
}
return(param)
}
#' @export
#' @title portfolioVaRmnts
#' @description
#' Calculate portfolio value at risk on the NTS market model
#'
#' @param strPMNTS Structure of parameters for the n-dimensional NTS distribution.
#'
#' \code{strPMNTS$ndim} : dimension
#'
#' \code{strPMNTS$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{strPMNTS$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{strPMNTS$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{strPMNTS$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{strPMNTS$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{res$Rho} : \eqn{\rho} matrix (Correlation) of the std NTS distribution (X).
#'
#' \code{res$Sigma} : Covariance \eqn{\Sigma} matrix of return data \eqn{r}.
#'
#' @param w Capital allocation weight vector.
#' @param eta significanlt level
#' @return portfolio value at risk on the NTS market model
#'
portfolioVaRmnts <- function(strPMNTS, w, eta){
if(strPMNTS$ndim != length(w)){
print("The dimension of the weight vector must be the same as strPMNTS$ndim")
return(NULL)
}
ntsparam <- getPortNTSParam(strPMNTS, w)
VaR <- (- ntsparam$mu - ntsparam$sig * qnts(eta, ntsparam$stdparam))
return(VaR)
}
#' @export
#' @title portfolioCVaRmnts
#' @description
#' Calculate portfolio conditional value at risk (expected shortfall) on the NTS market model
#'
#' @param strPMNTS Structure of parameters for the n-dimensional NTS distribution.
#'
#' \code{strPMNTS$ndim} : dimension
#'
#' \code{strPMNTS$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{strPMNTS$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{strPMNTS$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{strPMNTS$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{strPMNTS$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{res$Rho} : \eqn{\rho} matrix (Correlation) of the std NTS distribution (X).
#'
#' \code{res$Sigma} : Covariance \eqn{\Sigma} matrix of return data \eqn{r}.
#'
#' @param w Capital allocation weight vector.
#' @param eta significanlt level
#' @return portfolio value at risk on the NTS market model
#'
portfolioCVaRmnts <- function(strPMNTS, w, eta){
if(strPMNTS$ndim != length(w)){
print("The dimension of the weight vector must be the same as strPMNTS$ndim")
return(NULL)
}
ntsparam <- getPortNTSParam(strPMNTS, w)
CVaR <- (- ntsparam$mu + ntsparam$sig * cvarnts(eta, ntsparam$stdparam))
return(CVaR)
}
#' @export
#' @title mctStdDev
#' @description
#' Morginal contribution to Risk for Standard Deviation.
#'
#' @param n The targer stock to calculate the mctCVaR
#' @param w The capital allocation rate vector for the current portfolio
#' @param CovMtx Covariance matrix of return data.
#'
mctStdDev <- function(n, w, covMtx){
sig <- sqrt(w%*%covMtx%*%t(w))
return( w%*%covMtx[,n]/sig )
}
#' @export
#' @title dBeta
#' @description
#' The first derivative of the beta.
#' Developer's version.
#'
dBeta <- function(n, w, betaArray, covMtx){
barsig <- sqrt(w%*%covMtx%*%t(w))
barBeta <- sum(w*betaArray)
mctsd <- mctStdDev(n, w, covMtx)
sig <- sqrt(covMtx[n,n])
#db <- w[n]*sig*betaArray[n]/(barsig^2)-(barBeta/barsig)*mctsd
db <- sig*betaArray[n]/barsig-(barBeta/barsig)*mctsd
return( db )
}
#' @export
#' @title dinvCdf_stdNTS
#' @description
#' The first derivative of inverse CDF for the beta parameter of the stdNTS.
#' Developer's version.
#'
dinvCdf_stdNTS <- function(eta, alpha, theta, beta){
h <- abs(beta)*(0.0001)
Fu <- ipnts(eta, ntsparam = c(alpha, theta, beta+h))
Fd <- ipnts(eta, ntsparam = c(alpha, theta, beta-h))
return( (Fu-Fd)/(2*h) )
}
psi_stdNTS <- function( z, a, th, b ){
sz <- (2-a)/(2*th)
return(-1i*z+(1-1i*z*b/th+(1-b^2*sz)*z^2/(2*th))^(a/2-1)*(1i*z+b*sz*z^2))
}
integrand_dCVaRstdNTS <- function( u, eta, alpha, theta, beta, rho = 0.0001 ){
param <- c(alpha, theta, beta)
Finv <- ipnts(eta, param)
dFinv <- dinvCdf_stdNTS(eta, alpha, theta, beta)
res <- (exp((1i*u+rho)*Finv)*chf_stdNTS(-u+rho*1i, param)/(rho*1i-u)^2)
res <- res*((rho+1i*u)*dFinv+psi_stdNTS(-u+1i*rho, alpha, theta, beta))
return(res)
}
#' @export
#' @title dCVaR_numint
#' @description
#' The first derivative of CVaR for the beta parameter of the stdNTS.
#' Developer's version.
#'
dCVaR_numint <- function( eta, alpha, theta, beta, N = 200, rho = 0.1 ){
dFinv <- dinvCdf_stdNTS(eta, alpha, theta, beta)
f <- Re(pracma::integral(functional::Curry(integrand_dCVaRstdNTS,
eta = eta,
alpha = alpha,
theta = theta,
beta = beta,
rho = rho),
0, N))
dcvar <- -dFinv-f/(pi*eta)
return( dcvar )
}
#' @export
#' @title mctVaRmnts
#' @description Calculate the marginal contribution to VaR for the multivariate NTS market model:
#' the random vector \eqn{r} is
#'
#' \eqn{r = \mu + diag(\sigma) X}
#'
#' where
#'
#' \eqn{X} follows \eqn{stdNTS_N(\alpha, \theta, \beta, \Sigma)}
#'
#' @usage
#' \code{mctVaRmnts(eta, n, w, st)}
#'
#' @param eta Significant level of CVaR.
#' @param n The targer stock to calculate the mctCVaR
#' @param w The capital allocation rate vector for the current portfolio
#' @param st Structure of parameters for the N-dimensional NTS distribution.
#'
#' \code{st$ndim} : Dimension of the model. Here \code{st$ndim=N}.
#'
#' \code{st$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{st$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{st$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{st$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{st$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{st$Rho} : \eqn{\rho} matrix of the std NTS distribution (X),
#' which is correlation matrix of epsilon.
#'
#' \code{st$CovMtx} : Covariance matrix of return data \eqn{r}.
#'
#' @references
#' Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk
#' \url{https://arxiv.org/pdf/2007.13972.pdf}
#'
#' @examples
#' library(functional)
#' library(nloptr)
#' library(pracma)
#' library(spatstat)
#' library(Matrix)
#' library(quantmod)
#' library(mvtnorm)
#' library("temStaR")
#'
#' #Fix alpha and theta.
#' #Estimate alpha dna theta from DJIA and use those parameter for IBM, INTL parameter fit.
#' getSymbols("^DJI", src="yahoo", from = "2020-8-25", to = "2020-08-31")
#' prDJ <- as.numeric(DJI$DJI.Adjusted)
#' ret <- diff(log(prDJ))
#' ntsparam <- fitnts(ret)
#' getSymbols("IBM", src="yahoo", from = "2016-1-1", to = "2020-08-31")
#' pr1 <- as.numeric(IBM$IBM.Adjusted)
#' getSymbols("INTL", src="yahoo", from = "2016-1-1", to = "2020-08-31")
#' pr2 <- as.numeric(INTL$INTL.Adjusted)
#'
#' returndata <- matrix(data = c(diff(log(pr1)),diff(log(pr2))),
#' ncol = 2, nrow = (length(pr1)-1))
#' st <- fitmnts( returndata = returndata,
#' n = 2,
#' alphaNtheta = c(ntsparam["alpha"], ntsparam["theta"]) )
#' w <- c(0.3, 0.7)
#' eta <- 0.01
#'
#' mctVaRmnts(eta, 1, w, st) #MCT-VaR for IBM
#' mctVaRmnts(eta, 2, w, st) #MCT-VaR for INTL
#'
#' mctCVaRmnts(eta, 1, w, st) #MCT-CVaR for IBM
#' mctCVaRmnts(eta, 2, w, st) #MCT-CVaR for INTL
#'
mctVaRmnts <- function(eta, n, w, st, icdf = NULL, dicdf = NULL ){
return(as.numeric(
mctVaRnts(eta=eta,
n = n,
w = matrix(data = w, nrow = 1, ncol = st$ndim),
covMtx = st$CovMtx,
alpha = st$alpha,
theta = st$theta,
betaArray = matrix(data = st$beta, nrow = 1, ncol = st$ndim),
muArray = matrix(data = st$mu, nrow = 1, ncol = st$ndim),
icdf = icdf,
dicdf = dicdf)
)
)
}
#' @export
#' @title mctVaRnts
#' @description
#' Calculate the marginal contribution to VaR for the multivariate NTS market model.
#' Developer's version.
#'
mctVaRnts <- function(eta, n, w, covMtx, alpha, theta, betaArray, muArray, icdf = NULL, dicdf = NULL ){
barsig <- sqrt(w%*%covMtx%*%t(w))
mcts <- mctStdDev(n, w, covMtx)
db <- dBeta(n, w, betaArray, covMtx)
barBeta <- sum(w*betaArray)
if( is.null(icdf) ) icdf <- ipnts(eta, ntsparam = c(alpha, theta, barBeta))
if( is.null(dicdf) ) dicdf <- dinvCdf_stdNTS(eta, alpha, theta, barBeta)
return(-muArray[n] - icdf*mcts - barsig*db*dicdf )
}
#' @export
#' @title mctCVaRmnts
#' @description Calculate the marginal contribution to CVaR for the multivariate NTS market model:
#' the random vector \eqn{r} is
#'
#' \eqn{r = \mu + diag(\sigma) X}
#'
#' where
#'
#' \eqn{X} follows \eqn{stdNTS_N(\alpha, \theta, \beta, \Sigma)}
#'
#' @usage
#' \code{mctCVaRmnts(eta, n, w, st)}
#'
#' @param eta Significant level of CVaR.
#' @param n The targer stock to calculate the mctCVaR
#' @param w The capital allocation rate vector for the current portfolio
#' @param st Structure of parameters for the N-dimensional NTS distribution.
#'
#' \code{st$ndim} : Dimension of the model. Here \code{st$ndim=N}.
#'
#' \code{st$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{st$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{st$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{st$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{st$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{st$Rho} : \eqn{\rho} matrix of the std NTS distribution (X),
#' which is correlation matrix of epsilon.
#'
#' \code{st$CovMtx} : Covariance matrix of return data \eqn{r}.
#'
#' @references
#' Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk
#' \url{https://arxiv.org/pdf/2007.13972.pdf}
#'
#' @examples
#' library(functional)
#' library(nloptr)
#' library(pracma)
#' library(spatstat)
#' library(Matrix)
#' library(quantmod)
#' library(mvtnorm)
#' library("temStaR")
#'
#' #Fix alpha and theta.
#' #Estimate alpha dna theta from DJIA and use those parameter for IBM, INTL parameter fit.
#' getSymbols("^DJI", src="yahoo", from = "2020-8-25", to = "2020-08-31")
#' prDJ <- as.numeric(DJI$DJI.Adjusted)
#' ret <- diff(log(prDJ))
#' ntsparam <- fitnts(ret)
#' getSymbols("IBM", src="yahoo", from = "2016-1-1", to = "2020-08-31")
#' pr1 <- as.numeric(IBM$IBM.Adjusted)
#' getSymbols("INTL", src="yahoo", from = "2016-1-1", to = "2020-08-31")
#' pr2 <- as.numeric(INTL$INTL.Adjusted)
#'
#' returndata <- matrix(data = c(diff(log(pr1)),diff(log(pr2))),
#' ncol = 2, nrow = (length(pr1)-1))
#' st <- fitmnts( returndata = returndata,
#' n = 2,
#' alphaNtheta = c(ntsparam["alpha"], ntsparam["theta"]) )
#' w <- c(0.3, 0.7)
#' eta <- 0.01
#'
#' mctVaRmnts(eta, 1, w, st) #MCT-VaR for IBM
#' mctVaRmnts(eta, 2, w, st) #MCT-VaR for INTL
#'
#' mctCVaRmnts(eta, 1, w, st) #MCT-CVaR for IBM
#' mctCVaRmnts(eta, 2, w, st) #MCT-CVaR for INTL
#'
mctCVaRmnts <- function(eta, n, w, st, CVaR = NULL, dCVaR = NULL ){
return(as.numeric(
mctCVaRnts(eta=eta,
n = n,
w = matrix(data = w, ncol = st$ndim, nrow = 1),
covMtx = st$CovMtx,
alpha = st$alpha,
theta = st$theta,
betaArray = matrix(data = st$beta, ncol = st$ndim, nrow = 1),
muArray = matrix(data = st$mu, ncol = st$ndim, nrow = 1),
CVaR = CVaR,
dCVaR = dCVaR)
)
)
}
#' @export
#' @title mctCVaRnts
#' @description
#' Calculate the marginal contribution to CVaR for the multivariate NTS market model.
#' Developer's version.
#'
mctCVaRnts <- function(eta, n, w, covMtx, alpha, theta, betaArray, muArray, CVaR = NULL, dCVaR = NULL ){
barBeta <- sum(w*betaArray)
if( is.null(CVaR) ) CVaR <- cvarnts(eps = eta, ntsparam = c(alpha, theta, barBeta))
if( is.null(dCVaR) ) dCVaR <- dCVaR_numint(eta, alpha, theta, barBeta)
barsig <- sqrt(w%*%covMtx%*%t(w))
mcts <- mctStdDev(n, w, covMtx)
db <- dBeta(n, w, betaArray, covMtx)
return(-muArray[n] + CVaR*mcts + barsig*db*dCVaR )
}
#' @export
#' @title cvarGauss
#' @description
#' Calculate the CVaR for the normal distributed market model.
#' Developer's version.
#'
cvarGauss <- function( eta, mu = 0, sigma = 1){
#var = -qnorm(eta, mu, sigma)
stdK = qnorm(eta, 0, 1)
cvar = sigma/(eta*sqrt(2*pi))*exp(-stdK^2/2)-mu
return(cvar)
}
#' @title setPortfolioParam
#' @description Please use \code{getPortNTSParam} instead of \code{setPortfolioParam}.
#'
#' Portfolio return with capital allocation weight is \eqn{R_p=<w,r>},
#' which is a weighted sum of of elements in the N-dimensional NTS random vector.
#' \eqn{R_p} becomes an 1-dimensional NTS random variable.
#' \code{setPortfolioParam} find the parameters of \eqn{R_p}.
#'
#' @param strPMNTS Structure of parameters for the n-dimensional NTS distribution.
#'
#' \code{strPMNTS$ndim} : dimension
#'
#' \code{strPMNTS$mu} : \eqn{\mu} mean vector (column vector) of the input data.
#'
#' \code{strPMNTS$sigma} : \eqn{\sigma} standard deviation vector (column vector) of the input data.
#'
#' \code{strPMNTS$alpha} : \eqn{\alpha} of the std NTS distribution (X).
#'
#' \code{strPMNTS$theta} : \eqn{\theta} of the std NTS distribution (X).
#'
#' \code{strPMNTS$beta} : \eqn{\beta} vector (column vector) of the std NTS distribution (X).
#'
#' \code{strPMNTS$Rho} : \eqn{\Sigma} matrix of the std NTS distribution (X).
#'
#' @param w Capital allocation weight vector.
#'
#' @usage
#' \code{res <- setPortfolioParam(strPMNTS,w)}
#'
#' @return The weighted sum follows 1-dimensional NTS.
#'
#' \eqn{R_p = <w, r> = \mu + diag(\sigma) X},
#'
#' where
#'
#' \eqn{X} follows \eqn{stdNTS_1(\alpha, \theta, \beta, 1)}.
#'
#' Hence we obtain
#'
#' \code{res$mu} : \eqn{\mu} mean of \eqn{R_p}.
#'
#' \code{res$sigma} : \eqn{\sigma} standard deviation of \eqn{R_p}.
#'
#' \code{res$alpha} : \eqn{\alpha} of \eqn{X}.
#'
#' \code{res$theta} : \eqn{\theta} of \eqn{X}.
#'
#' \code{res$beta} : \eqn{\beta} \eqn{X}.
#'
#' @references
#' Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk
#' \url{https://arxiv.org/pdf/2007.13972.pdf}
#'
#' @examples
#' library("temStaR")
#' strPMNTS <- list(ndim = 2,
#' mu = c( 9.876552e-05, 4.747343e-04 ),
#' sigma = c( 0.01620588, 0.02309643 ),
#' alpha = 0.1888129 ,
#' theta = 0.523042,
#' beta = c( -0.04632938, 0.04063555 ),
#' Rho = matrix( data = c(1.0, 0.469883,
#' 0.469883, 1.0),
#' nrow = 2, ncol = 2)
#' CovMtx = matrix( data = c(0.0002626304, 0.0001740779,
#' 0.0001740779, 0.0005334452),
#' nrow = 2, ncol = 2)
#' )
#' w <- c(0.3, 0.7)
#' res <- setPortfolioParam(strPMNTS,w)
#'
setPortfolioParam <- function(strPMNTS, w){
if(strPMNTS$ndim != length(w)){
print("The dimension of the weight vector must be the same as strPMNTS$ndim")
return(NULL)
}
w <- matrix(data = w, nrow = strPMNTS$ndim, ncol = 1)
m <- sum(w*strPMNTS$mu)
b <- sum(w*strPMNTS$sigma*strPMNTS$beta)
gammaMtx <- diag(as.numeric(sqrt(1-strPMNTS$beta^2*(2-strPMNTS$alpha)/(2*strPMNTS$theta))))
sigMtx <- diag(as.numeric(strPMNTS$sigma))
g <- as.numeric(sqrt(t(w)%*%sigMtx%*%gammaMtx%*%strPMNTS$Rho%*%gammaMtx%*%sigMtx%*%w))
a <- as.numeric(strPMNTS$alpha)
th <- as.numeric(strPMNTS$theta)
param <- change_ntsparam2stdntsparam(c(a, th, b, g, m))
return(param)
}
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