Sequentially Tuned Moment Correction

Tunes \(\kappa\) on inner-validation RAFE and \(\tau\) on inner-validation C-RAFE independently — the bound's two channels are separable, so each parameter is chosen against its own channel.

Usage

sep_tune(
  R_train,
  kappa_grid = seq(0, 1, length.out = 101),
  tau_grid = seq(0, 0.5, length.out = 101),
  inner_split = c(40, 20),
  target = c("grandmean", "zero")
)

Arguments

R_train: Numeric matrix of training returns, observations in rows and assets in columns.
kappa_grid: Grid of shrinkage intensities to search. The default matches the working paper's grid, 101 points on [0, 1].
tau_grid: Grid of relative eigenvalue floors to search. The default matches the working paper's grid, 101 points on [0, 0.5]. Floors above 0.5 flatten the spectrum so aggressively that the cleaned covariance carries little information about the original, and are not admitted.
inner_split: Length-2 vector: rows used for inner training and for inner validation.
target: Shrinkage target passed to mu_rafe_stein().

Value

A list with components mu_tilde, Sigma_tilde, kappa, tau_rel, and the inner-validation loss profiles losses_kappa and losses_tau.

Details

The training window is split into an inner-training block and an inner-validation block (40 + 20 months by default). Moments are estimated on the inner-training block, the realised moments of the inner-validation block play the role of \((\mu, \Sigma)\) in the metrics, and the selected \((\kappa, \tau)\) are then applied to the moments of the full training window.

References

Stöckl, S., Salcher, L., & Hanke, M. Post-Optimal Moment Correction for Mean-Variance Portfolios. Working paper.

Examples

set.seed(1)
R <- matrix(rnorm(80 * 6, mean = 0.008, sd = 0.05), 80, 6)
fit <- sep_tune(R)
fit$kappa
#> [1] 0
fit$tau_rel
#> [1] 0.5