design_MVSK_portfolio_via_sample_moments: Design high-order portfolio based on weighted linear...

In highOrderPortfolios: Design of High-Order Portfolios Including Skewness and Kurtosis

Design high-order portfolio based on weighted linear combination of first four moments

Description

Design high-order portfolio based on weighted linear combination of first four moments (i.e., mean, variance, skewness, and kurtosis):

  minimize     - lmd1*(w'*mu) + lmd2*(w'*Sigma*w) 
               - lmd3*(w'*Phi*w*w) + lmd4*(w'*Psi*w*w*w)
  subject to   ||w||_1 <= leverage, sum(w) == 1.

Usage

design_MVSK_portfolio_via_sample_moments(
  lmd = rep(1, 4),
  X_moments,
  w_init = rep(1/length(X_moments$mu), length(X_moments$mu)),
  leverage = 1,
  method = c("Q-MVSK", "MM", "DC"),
  tau_w = 0,
  gamma = 1,
  zeta = 1e-08,
  maxiter = 100,
  ftol = 1e-05,
  wtol = 1e-04,
  stopval = -Inf
)

Arguments

lmd	Numerical vector of length 4 indicating the weights of first four moments.
X_moments	List of moment parameters, see estimate_sample_moments().
w_init	Numerical vector indicating the initial value of portfolio weights.
leverage	Number (>= 1) indicating the leverage of portfolio.
method	String indicating the algorithm method, must be one of: "Q-MVSK", "MM", "DC".
tau_w	Number (>= 0) guaranteeing the strong convexity of approximating function.
gamma	Number (0 < gamma <= 1) indicating the initial value of gamma.
zeta	Number (0 < zeta < 1) indicating the diminishing paramater of gamma.
maxiter	Positive integer setting the maximum iteration.
ftol	Positive number setting the convergence criterion of function objective.
wtol	Positive number setting the convergence criterion of portfolio weights.
stopval	Number setting the stop value of objective.

Value

A list containing the following elements:

w	Optimal portfolio vector.
cpu_time_vs_iterations	Time usage over iterations.
objfun_vs_iterations	Objective function over iterations.
iterations	Iterations index.
convergence	Boolean flag to indicate whether or not the optimization converged.
moments	Moments of portfolio return at optimal portfolio weights.

Author(s)

Rui Zhou and Daniel P. Palomar

References

R. Zhou and D. P. Palomar, "Solving High-Order Portfolios via Successive Convex Approximation Algorithms," in IEEE Transactions on Signal Processing, vol. 69, pp. 892-904, 2021. <doi:10.1109/TSP.2021.3051369>.

X. Wang, R. Zhou, J. Ying, and D. P. Palomar, "Efficient and Scalable High-Order Portfolios Design via Parametric Skew-t Distribution," Available in arXiv, 2022. <https://arxiv.org/pdf/2206.02412v1.pdf>.

Examples

library(highOrderPortfolios)
data(X50)

# estimate moments
X_moments <- estimate_sample_moments(X50[, 1:10])

# decide moment weights
xi <- 10
lmd <- c(1, xi/2, xi*(xi+1)/6, xi*(xi+1)*(xi+2)/24)

# portfolio optimization
sol <- design_MVSK_portfolio_via_sample_moments(lmd, X_moments)

highOrderPortfolios documentation built on Oct. 20, 2022, 5:06 p.m.