DOSPortfolio {DOSPortfolio}

The Dynamic Optimal Shrinkage Portfolio interface.

Description

This is the main function to compute the weights of the global minimum variance portfolio by using the dynamic optimal shrinkage estimators presented in Eq. (2.11) and Eq. (2.23) of Bodnar et al. (2021). It implements two different estimators for the shrinkage coefficients, one using overlapping samples (see, Eq. (2.23) of Bodnar et al. (2021)) and one using non-overlapping samples (see, Eq. (2.11) of Bodnar et al. (2021)).

Usage

DOSPortfolio(
  data,
  reallocation_points,
  relative_loss = NULL,
  target_portfolio = rep(1, ncol(data))/ncol(data),
  shrinkage_type = "non-overlapping"
)

Arguments

data

an n by p matrix of asset returns. Columns represent different assets rows are observations, where n>p, containing, for instance, log-returns.

reallocation_points

a vector of reallocation points. The reallocation points determine when the holding portfolio should be reconstructed and its weights should be recomputed.

relative_loss

possibly a numeric or NULL. The initial value of the relative loss in the variance of the target portfolio. If its NULL, then it will be initialized with the first subsample and the function r0Strategy.

target_portfolio

a vector which determines the weights of the target portfolio used when the shrinkage estimator of the global minimum variance portfolio is constructed for the first time.

shrinkage_type

the type of shrinkage estimator to use. The two implemented approaches are "non-overlapping" and "overlapping".

Value

An S3 class which contains the matrix of the constructed weights of the dynamic shrinkage estimator of the global minimum variance portfolio and the type of the shrinkage estimator (i.e., "overlapping" or "non-overlapping") that was used in its construction. Each row of the weight matrix corresponds to the reallocation point and the column corresponds to the asset.

References

Bodnar T, Parolya N, Thorsén E (2021). “Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio.” arXiv preprint arXiv:2106.02131. https://arxiv.org/abs/2106.02131.

See Also

Section 2.1 and 2.2 of (Bodnar et al. 2021)

Examples

n <- 250*2
p <- 80
c <- p/n
reallocation_points <- c(120, 240)
data <- sqrt(5/3) * matrix(rt(n*p, df=5) , ncol=p, nrow=n)
weights <- DOSPortfolio(data, reallocation_points, 1)