setPortfolioParam: setPortfolioParam

In aaron9011/temStaR-v0.90: Tempered Stable Distribution

setPortfolioParam

Description

Please use getPortNTSParam instead of setPortfolioParam.

Portfolio return with capital allocation weight is R_p=<w,r>, which is a weighted sum of of elements in the N-dimensional NTS random vector. R_p becomes an 1-dimensional NTS random variable. setPortfolioParam find the parameters of R_p.

Usage

res <- setPortfolioParam(strPMNTS,w)

Arguments

strPMNTS

Structure of parameters for the n-dimensional NTS distribution. strPMNTS$ndim : dimension strPMNTS$mu : \mu mean vector (column vector) of the input data. strPMNTS$sigma : \sigma standard deviation vector (column vector) of the input data. strPMNTS$alpha : \alpha of the std NTS distribution (X). strPMNTS$theta : \theta of the std NTS distribution (X). strPMNTS$beta : \beta vector (column vector) of the std NTS distribution (X). strPMNTS$Rho : \Sigma matrix of the std NTS distribution (X).

w

Capital allocation weight vector.

Value

The weighted sum follows 1-dimensional NTS.

R_p = <w, r> = \mu + diag(\sigma) X,

where

X follows stdNTS_1(\alpha, \theta, \beta, 1).

Hence we obtain

res$mu : \mu mean of R_p.

res$sigma : \sigma standard deviation of R_p.

res$alpha : \alpha of X.

res$theta : \theta of X.

res$beta : \beta X.

References

Kim, Y. S. (2020) Portfolio Optimization on the Dispersion Risk and the Asymmetric Tail Risk 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)

aaron9011/temStaR-v0.90 documentation built on June 1, 2025, 4:15 p.m.