new_MV_portfolio_weights_BDOPS21: Constructor of MV portfolio object

In HDShOP: High-Dimensional Shrinkage Optimal Portfolios

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. 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 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, Dette, Parolya and Thorsén 2021). weight_intervals is only computed when p<n.

References

\insertRef

BDOPS2021HDShOP

\insertRef

BDNT21HDShOP

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

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