new_GMV_portfolio_weights_BDPS19: Constructor of GMV portfolio object.

In HDShOP: High-Dimensional Shrinkage Optimal Portfolios

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. The weights of the target portfolio.
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 \insertCite@see Section 4.3 of @BDNT21HDShOP. weight_intervals is only computed when p<n.

References

\insertRef

BDPS2019HDShOP

\insertRef

BPS2018HDShOP

\insertRef

BDNT21HDShOP

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)

HDShOP documentation built on Nov. 10, 2022, 5:12 p.m.