new_MV_portfolio_weights_BDOPS21 {HDShOP}

Constructor of MV portfolio object

Description

Constructor of mean-variance shrinkage portfolios. new_MV_portfolio_weights_BDOPS21 is for the case p<n, while new_MV_portfolio_weights_BDOPS21_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_MV_portfolio_weights_BDOPS21(x, gamma, b, beta)

new_MV_portfolio_weights_BDOPS21_pgn(x, gamma, b, beta)

Arguments

x

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

gamma

a numeric variable. Coefficient of risk aversion.

b

a numeric variable. 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 MV_portfolio_weights_BDOPS21.

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 of the asset returns
W_mv_hat	sample estimator of the portfolio weights
weights	shrinkage estimator of the 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, value of the 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, Okhrin Y, Parolya N, Schmid W (2021). “Statistical Inference for the Expected Utility Portfolio in High Dimensions.” IEEE Transactions on Signal Processing, 69, 1-14.

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

# Assets with a diagonal covariance matrix

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

x <- matrix(data = rnorm(n*p), nrow = p, ncol = n)

test <- new_MV_portfolio_weights_BDOPS21(x=x, gamma=gamma, b=b, beta=0.05)
summary(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_MV_portfolio_weights_BDOPS21(x=x, gamma=gamma, b=b, beta=0.05)
str(test)


# c>1

n <-2e2 # number of realizations
p <-1.2*n # number of assets
b <-rep(1/p,p)
x <- matrix(data = rnorm(n*p), nrow = p, ncol = n)

test <- new_MV_portfolio_weights_BDOPS21_pgn(x=x, gamma=gamma,
                                             b=b, beta=0.05)
summary(test)

# Assets with a non-diagonal covariance matrix