mvskPortfolio: Higher Moment Efficient Portfolios

In cdries/mvskPortfolios: Higher Moment Efficient Portfolios

Description

function for determining risk-based portfolios that are mean-variance-skewness-kurtosis efficient.

Usage

mvskPortfolio(
  m1 = NULL,
  M2 = NULL,
  M3 = NULL,
  M4 = NULL,
  w0 = NULL,
  g = NULL,
  lb = NULL,
  ub = NULL,
  lin_eq = NULL,
  lin_eqC = NULL,
  nlin_eq = NULL,
  lin_ieq = NULL,
  lin_ieqC = NULL,
  nlin_ieq = NULL,
  href = NULL,
  kappa = NULL,
  relative = FALSE,
  param = NULL,
  options = list(),
  mompref = NULL
)

Arguments

m1	mean vector; not used if NULL
M2	covariance matrix
M3	coskewness matrix; not used if NULL
M4	cokurtosis matrix; not used if NULL
w0	weight of the benchmark portfolio / initial portfolio name, see details
g	vector with preferences for the moments, see details
lb	lower bound for the weights, default rep(0, p)
ub	upper bound for the weights, default rep(1, p)
lin_eq	equality constraints: eq w = eqC (should be matrix!), see details
lin_eqC	equality constraints: eq w = eqC, see details
nlin_eq	function with non-linear equality constraint (returns objective value and jacobian)
lin_ieq	inequality constraints: ieq w leq ieqC (should be matrix!)
lin_ieqC	inequality constraints: ieq w leq ieqC
nlin_ieq	function with non-linear inequality constraints (returns objective value and jacobian)
href	reference function to keep into account while tilting the portfolios (name or function)
kappa	vector of values indicating maximum deviation of the reference objective
relative	boolean indicating if kappa is absolute or relative
param	list with extra arguments for the href function
options	optimization options
mompref	direction of preference for the moments, defaults to higher mean and skewnes, lower variance and kurtosis

Details

All moments with NULL are ignored as tilting constraints. The default uses the most diversified portfolio of houeifaty & Coignard (2008) as initial portfolio. For unconstrained portfolio tilting, set kappa to 1, which allows 100 is g = (0, sigma_^2_w0, abs(phi_w0), psi_w0). Additional linearity and non-linearity constraints can be included in the optimization procedure with the arguments lin_eq, lin_eqC, nlin_eq, lin_ieq, lin_ieqC and nlin_ieq. The default includes a full investment constraint (sum of weights equal to 1), overriding lin_eq and lin_eqC removes the default constraint.

Author(s)

Dries Cornilly

References

Boudt, K., Cornilly, D., Van Holle, F., & Willems, J. (2020). Algorithmic portfolio tilting to harvest higher moment gains. Heliyon, 6(3).

Briec, W., Kerstens, K., & Jokung, O. (2007). Mean-variance-skewness portfolio performance gauging: a general shortage function and dual approach. Management science, 53(1), 135-149.

Choueifaty, Y., & Coignard, Y. (2008). Toward maximum diversification. Journal of Portfolio Management, 35(1), 40.

Examples

# load data
library(PerformanceAnalytics)
data(edhec)
x <- edhec[, 1:5]

# estimate moments
m1 <- colMeans(x)
M2 <- cov(x)
M3 <- PerformanceAnalytics:::M3.MM(x, as.mat = FALSE)
M4 <- PerformanceAnalytics:::M4.MM(x, as.mat = FALSE)

# MVSK tilting - starting from "DR", tilting with margin on "DR"
resMVSK <- mvskPortfolio(m1 = m1, M2 = M2, M3 = M3, M4 = M4, w0 = "DR",
                         g = "mvsk", ub = rep(0.3, 5), href = "DR",
                         kappa = c(0, 0.01, 0.025, 0.05))

# show weights
barplot(resMVSK$w, beside = TRUE)

# VSK tiltin - starting from "DR", tilting with maximum tracking error
# volatility
resVSK <- mvskPortfolio(M2 = M2, M3 = M3, M4 = M4, w0 = "DR",
                        g = "mvsk", ub = rep(0.3, 5), href = "TEvol",
                        kappa = c(0, 0.001, 0.025))

# show weights
barplot(resVSK$w, beside = TRUE)

cdries/mvskPortfolios documentation built on Feb. 10, 2021, 7:31 p.m.