new_GMV_portfolio_weights_BDPS19 {HDShOP}

Constructor of GMV portfolio object.

Description

Constructor of global minimum variance portfolio. new_GMV_portfolio_weights_BDPS19 is for the case p<n, while new_GMV_portfolio_weights_BDPS19_pgn is for p>n, where p is the number of assets and n is the number of observations. For more details of the method, see MVShrinkPortfolio.

Usage

new_GMV_portfolio_weights_BDPS19(x, b, beta)

new_GMV_portfolio_weights_BDPS19_pgn(x, b, beta)

Arguments

x

a p by n matrix or a data frame of asset returns. Rows represent different assets, columns – observations.

b

a numeric vector. 1-beta is the confidence level of the symmetric confidence interval, constructed for each weight.

beta

a numeric variable. The confidence level for weight intervals.

Value

an object of class MeanVar_portfolio with subclass GMV_portfolio_weights_BDPS19.

Element	Description
call	the function call with which it was created
cov_mtrx	the sample covariance matrix of the asset returns
inv_cov_mtrx	the inverse of the sample covariance matrix
means	sample mean vector estimate of the asset returns
w_GMVP	sample estimator of portfolio weights
weights	shrinkage estimator of portfolio weights
alpha	shrinkage intensity for the weights
Port_Var	portfolio variance
Port_mean_return	expected portfolio return
Sharpe	portfolio Sharpe ratio
weight_intervals	A data frame, see details

weight_intervals contains a shrinkage estimator of portfolio weights, asymptotic confidence intervals for the true portfolio weights, the value of test statistic and the p-value of the test on the equality of the weight of each individual asset to zero (see Section 4.3 of Bodnar et al. 2023). weight_intervals is only computed when p<n.

References

Bodnar T, Dmytriv S, Parolya N, Schmid W (2019). “Tests for the weights of the global minimum variance portfolio in a high-dimensional setting.” IEEE Transactions on Signal Processing, 67(17), 4479–4493.

Bodnar T, Parolya N, Schmid W (2018). “Estimation of the global minimum variance portfolio in high dimensions.” European Journal of Operational Research, 266(1), 371–390.

Bodnar T, Dette H, Parolya N, Thorsén E (2023). “Corrigendum to "Sampling Distributions of Optimal Portfolio Weights and Characteristics in Low and Large Dimensions.".” Random Matrices: Theory and Applications, 12, 2392001. doi:10.1142/S2010326323920016.

Examples

# c<1

n <- 3e2 # number of realizations
p <- .5*n # number of assets
b <- rep(1/p,p)

# Assets with a diagonal covariance matrix
x <- matrix(data = rnorm(n*p), nrow = p, ncol = n)

test <- new_GMV_portfolio_weights_BDPS19(x=x, b=b, beta=0.05)
str(test)

# Assets with a non-diagonal covariance matrix
Mtrx <- RandCovMtrx(p=p)
x <- t(MASS::mvrnorm(n=n , mu=rep(0,p), Sigma=Mtrx))

test <- new_GMV_portfolio_weights_BDPS19(x=x, b=b, beta=0.05)
summary(test)

# c>1

p <- 1.3*n # number of assets
b <- rep(1/p,p)

# Assets with a diagonal covariance matrix
x <- matrix(data = rnorm(n*p), nrow = p, ncol = n)

test <- new_GMV_portfolio_weights_BDPS19_pgn(x=x, b=b, beta=0.05)
str(test)