design_MVSKtilting_portfolio_via_sample_moments: Design high-order portfolio by tilting a given portfolio to...

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

Design high-order portfolio by tilting a given portfolio to the MVSK efficient frontier

Description

Design high-order portfolio by tilting a given portfolio to the MVSK efficient frontier (i.e., mean, variance, skewness, and kurtosis):

  minimize     - delta
               m1(w) >= m1(w0) + delta*d1
               m2(w) <= m2(w0) - delta*d2
               m3(w) >= m3(w0) + delta*d3
               m4(w) <= m4(w0) - delta*d4
               (w-w0)'Sigma(w-w0) <= kappa^2
  subject to   ||w||_1 <= leverage, sum(w) == 1.

Usage

design_MVSKtilting_portfolio_via_sample_moments(
  d = rep(1, 4),
  X_moments,
  w_init = rep(1/length(X_moments$mu), length(X_moments$mu)),
  w0 = w_init,
  w0_moments = NULL,
  leverage = 1,
  kappa = 0,
  method = c("Q-MVSKT", "L-MVSKT"),
  tau_w = 1e-05,
  tau_delta = 1e-05,
  gamma = 1,
  zeta = 1e-08,
  maxiter = 100,
  ftol = 1e-05,
  wtol = 1e-05,
  theta = 0.5,
  stopval = -Inf
)

Arguments

d	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.
w0	Numerical vector indicating the reference portfolio vector.
w0_moments	Numerical vector indicating the reference moments.
leverage	Number (>= 1) indicating the leverage of portfolio.
kappa	Number indicating the maximum tracking error volatility.
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.
tau_delta	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.
theta	Number (0 < theta < 1) setting the combination coefficient when enlarge feasible set.
stopval	Number setting the stop value of objective.

Value

A list containing the following elements:

w	Optimal portfolio vector.
delta	Maximum tilting distance of the optimal portfolio.
cpu_time_vs_iterations	Time usage over iterations.
objfun_vs_iterations	Objective function over iterations.
iterations	Iterations index.
moments	Moments of portfolio return at optimal portfolio weights.
improvement	The relative improvement of moments of designed portfolio w.r.t. the reference portfolio.

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>.

Examples

library(highOrderPortfolios)
data(X50)

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

# decide problem setting
w0 <- rep(1/10, 10)
w0_moments <- eval_portfolio_moments(w0, X_moments)
d <- abs(w0_moments) 
kappa <- 0.3 * sqrt(w0 %*% X_moments$Sgm %*% w0)

# portfolio optimization
sol <- design_MVSKtilting_portfolio_via_sample_moments(d, X_moments, w_init = w0, w0 = w0, 
                                                       w0_moments = w0_moments, kappa = kappa)

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