Design of High-Order Portfolios Including Skewness and Kurtosis

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: R. Zhou and D. P. Palomar (2021). "Solving High-Order Portfolios via Successive Convex Approximation Algorithms." . X. Wang, R. Zhou, J. Ying, and D. P. Palomar (2022). "Efficient and Scalable High-Order Portfolios Design via Parametric Skew-t Distribution." .

highOrderPortfolios

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")