Skip to contents

Jointly T-RAFE-Tuned Moment Correction

Source: R/estimators.R
joint_trafe_tune.Rd

Tunes \((\kappa, \tau)\) jointly on the full grid to minimise inner-validation T-RAFE. Empirically close to indistinguishable from the sequential search of sep_tune(), which is the practical evidence that the bound's two channels are separable.

Usage

joint_trafe_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 full inner-validation loss surface loss_grid (kappa in rows, tau in columns).

References

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

See also

sep_tune() for the sequential search.

Examples

set.seed(1)
R <- matrix(rnorm(80 * 6, mean = 0.008, sd = 0.05), 80, 6)
fit <- joint_trafe_tune(R, kappa_grid = seq(0, 1, by = 0.1),
                           tau_grid = seq(0, 1, by = 0.2))
fit$kappa
#> [1] 0
fit$tau_rel
#> [1] 1