Design of High-Order Portfolios Including Skewness and Kurtosis.

highOrderPortfolios

The classical Markowitz's mean-variance portfolio formulation ignores heavy tails and skewness. High-order portfolios use higher order moments to better characterize the return distribution. Different formulations and fast algorithms are proposed for high-order portfolios based on the mean, variance, skewness, and kurtosis. The package is based on the papers Zhou and Palomar (2021) and Wang, Zhou, Ying, and Palomar (2022).

Installation

The package can be installed from CRAN or GitHub:

# install stable version from CRAN
install.packages("highOrderPortfolios")

# install development version from GitHub
devtools::install_github("dppalomar/highOrderPortfolios")

To get help:

library(highOrderPortfolios)
help(package = "highOrderPortfolios")
?design_MVSK_portfolio_via_sample_moments
?design_MVSK_portfolio_via_skew_t

To cite highOrderPortfolios in publications:

citation("highOrderPortfolios")

Usage

library(highOrderPortfolios)
data(X50)

# non-parametric case: estimate sample moments
X_moments <- estimate_sample_moments(X50)

# parametric case: estimate the multivariate skew t distribution
X_skew_t_params <- estimate_skew_t(X50)

# choose hyper-parameter moment weights for the MVSK formulation
xi <- 10
lmd <- c(1, xi/2, xi*(xi+1)/6, xi*(xi+1)*(xi+2)/24)

# design portfolio
sol_nonparam <- design_MVSK_portfolio_via_sample_moments(lmd, X_moments)
sol_param    <- design_MVSK_portfolio_via_skew_t(lmd, X_skew_t_params)

# plot
barplot(cbind("via sample moments" = sol_nonparam$w, "via skew t modeling" = sol_param$w), beside = TRUE, 
        col = c(rep("darkblue", 50), rep("darkred", 50)),
        main = "MSVK portfolio", xlab = "asset indexes", ylab = "portfolio weights")

Documentation

For more detailed information, please check the vignette: CRAN-vignette and GitHub-vignette.

Links

Package: CRAN and GitHub.

README file: CRAN-readme and GitHub-readme.

Vignette: CRAN-vignette and GitHub-vignette.