design_MVSK_portfolio_via_skew_t: Design MVSK portfolio without shorting based on the...

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

Design MVSK portfolio without shorting based on the parameters of generalized hyperbolic skew-t distribution

Description

Design MVSK portfolio without shorting based on the parameters of generalized hyperbolic skew-t distribution:

  minimize     - lambda1*phi1(w) + lambda2*phi2(w)
               - lambda3*phi3(w) + lambda4*phi4(w)
  subject to   w>=0, sum(w) == 1.

Usage

design_MVSK_portfolio_via_skew_t(
  lambda,
  X_skew_t_params,
  w_init = rep(1/length(X_skew_t_params$mu), length(X_skew_t_params$mu)),
  method = c("L-MVSK", "DC", "Q-MVSK", "SQUAREM", "RFPA", "PGD"),
  gamma = 1,
  zeta = 1e-08,
  tau_w = 0,
  beta = 0.5,
  tau = 1e+05,
  initial_eta = 5,
  maxiter = 1000,
  ftol = 1e-06,
  wtol = 1e-06,
  stopval = -Inf
)

Arguments

lambda	Numerical vector of length 4 indicating the weights of first four moments.
X_skew_t_params	List of fitted parameters, including location vector, skewness vector, scatter matrix, and the degree of freedom, see estimate_skew_t().
w_init	Numerical vector indicating the initial value of portfolio weights.
method	String indicating the algorithm method, must be one of: "L-MVSK", "DC", "Q-MVSK", "SQUAREM", "RFPA", "PGD".
gamma	Number (0 < gamma <= 1) indicating the initial value of gamma for the Q-MVSK method.
zeta	Number (0 < zeta < 1) indicating the diminishing parameter of gamma for the Q-MVSK method.
tau_w	Number (>= 0) guaranteeing the strong convexity of approximating function.
beta	Number (0 < beta < 1) decreasing the step size of the projected gradient methods.
tau	Number (tau > 0) hyper-parameters for the fixed-point acceleration.
initial_eta	Initial eta for projected gradient methods
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)

Xiwen Wang, Rui Zhou and Daniel P. Palomar

References

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/2206.02412.pdf>.

Examples

library(highOrderPortfolios)
data(X50)

# estimate skew t distribution
X_skew_t_params <- estimate_skew_t(X50)

# decide moment weights
xi <- 10
lambda <- c(1, 4, 10, 20)

# portfolio optimization
sol <- design_MVSK_portfolio_via_skew_t(lambda, X_skew_t_params, method = "RFPA", tau = 10)

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