# Design MVSK portfolio without shorting based on the parameters of generalized hyperbolic skew-t distribution 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. ``` ```r 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. ## Returns 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. ## Examples ```r 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) ``` ## 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. . ## Author(s) Xiwen Wang, Rui Zhou and Daniel P. Palomar

design_MVSK_portfolio_via_skew_t function